Daily Papers

Protein design, a grand challenge of the day, involves optimization on a fitness landscape, and leading methods adopt a model-based approach where a model is trained on a training set (protein sequences and fitness) and proposes candidates to explore next. These methods are challenged by sparsity of high-fitness samples in the training set, a problem that has been in the literature. A less recognized but equally important problem stems from the distribution of training samples in the design space: leading methods are not designed for scenarios where the desired optimum is in a region that is not only poorly represented in training data, but also relatively far from the highly represented low-fitness regions. We show that this problem of "separation" in the design space is a significant bottleneck in existing model-based optimization tools and propose a new approach that uses a novel VAE as its search model to overcome the problem. We demonstrate its advantage over prior methods in robustly finding improved samples, regardless of the imbalance and separation between low- and high-fitness training samples. Our comprehensive benchmark on real and semi-synthetic protein datasets as well as solution design for physics-informed neural networks, showcases the generality of our approach in discrete and continuous design spaces. Our implementation is available at https://github.com/sabagh1994/PGVAE.

The ability to engineer novel proteins with higher fitness for a desired property would be revolutionary for biotechnology and medicine. Modeling the combinatorially large space of sequences is infeasible; prior methods often constrain optimization to a small mutational radius, but this drastically limits the design space. Instead of heuristics, we propose smoothing the fitness landscape to facilitate protein optimization. First, we formulate protein fitness as a graph signal then use Tikunov regularization to smooth the fitness landscape. We find optimizing in this smoothed landscape leads to improved performance across multiple methods in the GFP and AAV benchmarks. Second, we achieve state-of-the-art results utilizing discrete energy-based models and MCMC in the smoothed landscape. Our method, called Gibbs sampling with Graph-based Smoothing (GGS), demonstrates a unique ability to achieve 2.5 fold fitness improvement (with in-silico evaluation) over its training set. GGS demonstrates potential to optimize proteins in the limited data regime. Code: https://github.com/kirjner/GGS

The study of hardest and easiest fitness landscapes is an active area of research. Recently, Kaufmann, Larcher, Lengler and Zou conjectured that for the self-adjusting (1,lambda)-EA, Adversarial Dynamic BinVal (ADBV) is the hardest dynamic monotone function to optimize. We introduce the function Switching Dynamic BinVal (SDBV) which coincides with ADBV whenever the number of remaining zeros in the search point is strictly less than n/2, where n denotes the dimension of the search space. We show, using a combinatorial argument, that for the (1+1)-EA with any mutation rate p in [0,1], SDBV is drift-minimizing among the class of dynamic monotone functions. Our construction provides the first explicit example of an instance of the partially-ordered evolutionary algorithm (PO-EA) model with parameterized pessimism introduced by Colin, Doerr and F\'erey, building on work of Jansen. We further show that the (1+1)-EA optimizes SDBV in Theta(n^{3/2}) generations. Our simulations demonstrate matching runtimes for both static and self-adjusting (1,lambda) and (1+lambda)-EA. We further show, using an example of fixed dimension, that drift-minimization does not equal maximal runtime.

Generative molecular design is shaped by simple proxy benchmarks for drug-like properties and models pretrained on large pharmaceutical datasets. This combination yields strong benchmark metrics but limits transferability to domains structurally distinct from drug discovery. To overcome this limitation and drive discovery toward real, scientifically grounded targets, we introduce the Nanotechnology Molecular Optimization (NMO) Benchmark, which bridges machine learning (ML) and quantum materials science. NMO acts simultaneously as a rigorous testbed for the ML community and a discovery engine for nanotechnology research. The suite replaces proxy oracles with quantum simulations and introduces strict protocols that prioritize scientific utility over leaderboard-oriented overfitting. The physics-based NMO tasks impose hard structural constraints and rugged fitness landscapes, posing fundamentally new requirements on generative models. Notably, advanced molecular optimization methods underperform much simpler approaches on the NMO tasks. We develop a new baseline method identifying the critical components to solve the NMO tasks, including a novel representation for modeling structural constraints and a domain-agnostic pretraining strategy to eliminate pharmaceutical dataset bias. Our results surpass state-of-the-art physical properties and reveal previously unknown structural motifs, offering new insights for the nanotechnology community and demonstrating that ML can drive genuine scientific discovery.

Ribosomally synthesized and post-translationally modified peptide (RiPP) biosynthetic enzymes often exhibit promiscuous substrate preferences that cannot be reduced to simple rules. Large language models are promising tools for predicting such peptide fitness landscapes. However, state-of-the-art protein language models are trained on relatively few peptide sequences. A previous study comprehensively profiled the peptide substrate preferences of LazBF (a two-component serine dehydratase) and LazDEF (a three-component azole synthetase) from the lactazole biosynthetic pathway. We demonstrated that masked language modeling of LazBF substrate preferences produced language model embeddings that improved downstream classification models of both LazBF and LazDEF substrates. Similarly, masked language modeling of LazDEF substrate preferences produced embeddings that improved the performance of classification models of both LazBF and LazDEF substrates. Our results suggest that the models learned functional forms that are transferable between distinct enzymatic transformations that act within the same biosynthetic pathway. Our transfer learning method improved performance and data efficiency in data-scarce scenarios. We then fine-tuned models on each data set and showed that the fine-tuned models provided interpretable insight that we anticipate will facilitate the design of substrate libraries that are compatible with desired RiPP biosynthetic pathways.

Recently, there has been great interest in learning how to best represent proteins, specifically with fixed-length embeddings. Deep learning has become a popular tool for protein representation learning as a model's hidden layers produce potentially useful vector embeddings. TAPE introduced a number of benchmark tasks and showed that semi-supervised learning, via pretraining language models on a large protein corpus, improved performance on downstream tasks. Two of the tasks (fluorescence prediction and stability prediction) involve learning fitness landscapes. In this paper, we show that CNN models trained solely using supervised learning both compete with and sometimes outperform the best models from TAPE that leverage expensive pretraining on large protein datasets. These CNN models are sufficiently simple and small that they can be trained using a Google Colab notebook. We also find for the fluorescence task that linear regression outperforms our models and the TAPE models. The benchmarking tasks proposed by TAPE are excellent measures of a model's ability to predict protein function and should be used going forward. However, we believe it is important to add baselines from simple models to put the performance of the semi-supervised models that have been reported so far into perspective.

A longstanding goal of biology is to identify the key genes and species that critically impact evolution, ecology, and health. Network analysis has revealed keystone species that regulate ecosystems and master regulators that regulate cellular genetic networks. Yet these studies have focused on pairwise biological interactions, which can be affected by the context of genetic background and other species present generating higher-order interactions. The important regulators of higher-order interactions are unstudied. To address this, we applied a new high-dimensional geometry approach that quantifies epistasis in a fitness landscape to ask how individual genes and species influence the interactions in the rest of the biological network. We then generated and also reanalyzed 5-dimensional datasets (two genetic, two microbiome). We identified key genes (e.g. the rbs locus and pykF) and species (e.g. Lactobacilli) that control the interactions of many other genes and species. These higher-order master regulators can induce or suppress evolutionary and ecological diversification by controlling the topography of the fitness landscape. Thus, we provide mathematical intuition and justification for exploration of biological networks in higher dimensions.

Computational RNA design tasks are often posed as inverse problems, where sequences are designed based on adopting a single desired secondary structure without considering 3D geometry and conformational diversity. We introduce gRNAde, a geometric RNA design pipeline operating on 3D RNA backbones to design sequences that explicitly account for structure and dynamics. Under the hood, gRNAde is a multi-state Graph Neural Network that generates candidate RNA sequences conditioned on one or more 3D backbone structures where the identities of the bases are unknown. On a single-state fixed backbone re-design benchmark of 14 RNA structures from the PDB identified by Das et al. [2010], gRNAde obtains higher native sequence recovery rates (56% on average) compared to Rosetta (45% on average), taking under a second to produce designs compared to the reported hours for Rosetta. We further demonstrate the utility of gRNAde on a new benchmark of multi-state design for structurally flexible RNAs, as well as zero-shot ranking of mutational fitness landscapes in a retrospective analysis of a recent ribozyme. Open source code: https://github.com/chaitjo/geometric-rna-design

We derive an expression for the variation between parallel trajectories in phenotypic evolution, extending the well known result that predicts the mean evolutionary path in adaptive dynamics or quantitative genetics. We show how this expression gives rise to the notion of fluctuation domains - parts of the fitness landscape where the rate of evolution is very predictable (due to fluctuation dissipation) and parts where it is highly variable (due to fluctuation enhancement). These fluctuation domains are determined by the curvature of the fitness landscape. Regions of the fitness landscape with positive curvature, such as adaptive valleys or branching points, experience enhancement. Regions with negative curvature, such as adaptive peaks, experience dissipation. We explore these dynamics in the ecological scenarios of implicit and explicit competition for a limiting resource.

The ability to accurately model the fitness landscape of protein sequences is critical to a wide range of applications, from quantifying the effects of human variants on disease likelihood, to predicting immune-escape mutations in viruses and designing novel biotherapeutic proteins. Deep generative models of protein sequences trained on multiple sequence alignments have been the most successful approaches so far to address these tasks. The performance of these methods is however contingent on the availability of sufficiently deep and diverse alignments for reliable training. Their potential scope is thus limited by the fact many protein families are hard, if not impossible, to align. Large language models trained on massive quantities of non-aligned protein sequences from diverse families address these problems and show potential to eventually bridge the performance gap. We introduce Tranception, a novel transformer architecture leveraging autoregressive predictions and retrieval of homologous sequences at inference to achieve state-of-the-art fitness prediction performance. Given its markedly higher performance on multiple mutants, robustness to shallow alignments and ability to score indels, our approach offers significant gain of scope over existing approaches. To enable more rigorous model testing across a broader range of protein families, we develop ProteinGym -- an extensive set of multiplexed assays of variant effects, substantially increasing both the number and diversity of assays compared to existing benchmarks.

We test whether artificial intelligence architectural evolution obeys the same statistical laws as biological evolution. Compiling 935 ablation experiments from 161 publications, we show that the distribution of fitness effects (DFE) of architectural modifications follows a heavy-tailed Student's t-distribution with proportions (68% deleterious, 19% neutral, 13% beneficial for major ablations, n=568) that place AI between compact viral genomes and simple eukaryotes. The DFE shape matches D. melanogaster (normalized KS=0.07) and S. cerevisiae (KS=0.09); the elevated beneficial fraction (13% vs. 1-6% in biology) quantifies the advantage of directed over blind search while preserving the distributional form. Architectural origination follows logistic dynamics (R^2=0.994) with punctuated equilibria and adaptive radiation into domain niches. Fourteen architectural traits were independently invented 3-5 times, paralleling biological convergences. These results demonstrate that the statistical structure of evolution is substrate-independent, determined by fitness landscape topology rather than the mechanism of selection.

The development of powerful natural language models have increased the ability to learn meaningful representations of protein sequences. In addition, advances in high-throughput mutagenesis, directed evolution, and next-generation sequencing have allowed for the accumulation of large amounts of labeled fitness data. Leveraging these two trends, we introduce Regularized Latent Space Optimization (ReLSO), a deep transformer-based autoencoder which features a highly structured latent space that is trained to jointly generate sequences as well as predict fitness. Through regularized prediction heads, ReLSO introduces a powerful protein sequence encoder and novel approach for efficient fitness landscape traversal. Using ReLSO, we explicitly model the sequence-function landscape of large labeled datasets and generate new molecules by optimizing within the latent space using gradient-based methods. We evaluate this approach on several publicly-available protein datasets, including variant sets of anti-ranibizumab and GFP. We observe a greater sequence optimization efficiency (increase in fitness per optimization step) by ReLSO compared to other approaches, where ReLSO more robustly generates high-fitness sequences. Furthermore, the attention-based relationships learned by the jointly-trained ReLSO models provides a potential avenue towards sequence-level fitness attribution information.

The fields of Origin of Life and Artificial Life both question what life is and how it emerges from a distinct set of "pre-life" dynamics. One common feature of most substrates where life emerges is a marked shift in dynamics when self-replication appears. While there are some hypotheses regarding how self-replicators arose in nature, we know very little about the general dynamics, computational principles, and necessary conditions for self-replicators to emerge. This is especially true on "computational substrates" where interactions involve logical, mathematical, or programming rules. In this paper we take a step towards understanding how self-replicators arise by studying several computational substrates based on various simple programming languages and machine instruction sets. We show that when random, non self-replicating programs are placed in an environment lacking any explicit fitness landscape, self-replicators tend to arise. We demonstrate how this occurs due to random interactions and self-modification, and can happen with and without background random mutations. We also show how increasingly complex dynamics continue to emerge following the rise of self-replicators. Finally, we show a counterexample of a minimalistic programming language where self-replicators are possible, but so far have not been observed to arise.

Despite being self-supervised, protein language models have shown remarkable performance in fundamental biological tasks such as predicting impact of genetic variation on protein structure and function. The effectiveness of these models on diverse set of tasks suggests that they learn meaningful representations of fitness landscape that can be useful for downstream clinical applications. Here, we interrogate the use of these language models in characterizing known pathogenic mutations in curated, medically actionable genes through an exhaustive search of putative compensatory mutations on each variant's genetic background. Systematic analysis of the predicted effects of these compensatory mutations reveal unappreciated structural features of proteins that are missed by other structure predictors like AlphaFold. While deep mutational scan experiments provide an unbiased estimate of the mutational landscape, we encourage the community to generate and curate rescue mutation experiments to inform the design of more sophisticated co-masking strategies and leverage large language models more effectively for downstream clinical prediction tasks.

Bayesian optimisation is a popular approach for optimising expensive black-box functions. The next location to be evaluated is selected via maximising an acquisition function that balances exploitation and exploration. Gaussian processes, the surrogate models of choice in Bayesian optimisation, are often used with a constant prior mean function equal to the arithmetic mean of the observed function values. We show that the rate of convergence can depend sensitively on the choice of mean function. We empirically investigate 8 mean functions (constant functions equal to the arithmetic mean, minimum, median and maximum of the observed function evaluations, linear, quadratic polynomials, random forests and RBF networks), using 10 synthetic test problems and two real-world problems, and using the Expected Improvement and Upper Confidence Bound acquisition functions. We find that for design dimensions ge5 using a constant mean function equal to the worst observed quality value is consistently the best choice on the synthetic problems considered. We argue that this worst-observed-quality function promotes exploitation leading to more rapid convergence. However, for the real-world tasks the more complex mean functions capable of modelling the fitness landscape may be effective, although there is no clearly optimum choice.

Common deep learning approaches for antibody engineering focus on modeling the marginal distribution of sequences. By treating sequences as independent samples, however, these methods overlook affinity maturation as a rich and largely untapped source of information about the evolutionary process by which antibodies explore the underlying fitness landscape. In contrast, classical phylogenetic models explicitly represent evolutionary dynamics but lack the expressivity to capture complex epistatic interactions. We bridge this gap with CoSiNE, a continuous-time Markov chain parameterized by a deep neural network. Mathematically, we prove that CoSiNE provides a first-order approximation to the intractable sequential point mutation process, capturing epistatic effects with an error bound that is quadratic in branch length. Empirically, CoSiNE outperforms state-of-the-art language models in zero-shot variant effect prediction by explicitly disentangling selection from context-dependent somatic hypermutation. Finally, we introduce Guided Gillespie, a classifier-guided sampling scheme that steers CoSiNE at inference time, enabling efficient optimization of antibody binding affinity toward specific antigens.

In here presented in silico study we suggest a way how to implement the evolutionary principles into anti-cancer therapy design. We hypothesize that instead of its ongoing supervised adaptation, the therapy may be constructed as a self-sustaining evolutionary process in a dynamic fitness landscape established implicitly by evolving cancer cells, microenvironment and the therapy itself. For these purposes, we replace a unified therapy with the `therapy species', which is a population of heterogeneous elementary therapies, and propose a way how to turn the toxicity of the elementary therapy into its fitness in a way conforming to evolutionary causation. As a result, not only the therapies govern the evolution of different cell phenotypes, but the cells' resistances govern the evolution of the therapies as well. We illustrate the approach by the minimalistic ad hoc evolutionary model. Its results indicate that the resistant cells could bias the evolution towards more toxic elementary therapies by inhibiting the less toxic ones. As the evolutionary causation of cancer drug resistance has been intensively studied for a few decades, we refer to cancer as a special case to illustrate purely theoretical analysis.

Protein fitness optimization involves finding a protein sequence that maximizes desired quantitative properties in a combinatorially large design space of possible sequences. Recent developments in steering protein generative models (e.g diffusion models, language models) offer a promising approach. However, by and large, past studies have optimized surrogate rewards and/or utilized large amounts of labeled data for steering, making it unclear how well existing methods perform and compare to each other in real-world optimization campaigns where fitness is measured by low-throughput wet-lab assays. In this study, we explore fitness optimization using small amounts (hundreds) of labeled sequence-fitness pairs and comprehensively evaluate strategies such as classifier guidance and posterior sampling for guiding generation from different discrete diffusion models of protein sequences. We also demonstrate how guidance can be integrated into adaptive sequence selection akin to Thompson sampling in Bayesian optimization, showing that plug-and-play guidance strategies offer advantages compared to alternatives such as reinforcement learning with protein language models.

Recent work such as AlphaEvolve has shown that combining LLM-driven optimization with evolutionary search can effectively improve programs, prompts, and algorithms across domains. In this paradigm, previously evaluated solutions are reused to guide the model toward new candidate solutions. Crucially, the effectiveness of this evolution process depends on the search strategy: how prior solutions are selected and varied to generate new candidates. However, most existing methods rely on fixed search strategies with predefined knobs (e.g., explore-exploit ratios) that remain static throughout execution. While effective in some settings, these approaches often fail to adapt across tasks, or even within the same task as the search space changes over time. We introduce EvoX, an adaptive evolution method that optimizes its own evolution process. EvoX jointly evolves candidate solutions and the search strategies used to generate them, continuously updating how prior solutions are selected and varied based on progress. This enables the system to dynamically shift between different search strategies during the optimization process. Across nearly 200 real-world optimization tasks, EvoX outperforms existing AI-driven evolutionary methods including AlphaEvolve, OpenEvolve, GEPA, and ShinkaEvolve on the majority of tasks.

The Unmanned Aerial Vehicle (UAV) path planning problem is a complex optimization problem in the field of robotics. In this paper, we investigate the possible utilization of this problem in benchmarking global optimization methods. We devise a problem instance generator and pick 56 representative instances, which we compare to established benchmarking suits through Exploratory Landscape Analysis to show their uniqueness. For the computational comparison, we select twelve well-performing global optimization techniques from both subfields of stochastic algorithms (evolutionary computation methods) and deterministic algorithms (Dividing RECTangles, or DIRECT-type methods). The experiments were conducted in settings with varying dimensionality and computational budgets. The results were analyzed through several criteria (number of best-found solutions, mean relative error, Friedman ranks) and utilized established statistical tests. The best-ranking methods for the UAV problems were almost universally the top-performing evolutionary techniques from recent competitions on numerical optimization at the Institute of Electrical and Electronics Engineers Congress on Evolutionary Computation. Lastly, we discussed the variable dimension characteristics of the studied UAV problems that remain still largely under-investigated.

We present a Spatially Embedded Evolutionary Algorithm where robot individuals exist in a physically simulated 2D environment, must navigate to encounter potential mates, and compete for survival under various spatially-aware selection pressures. Using HyperNEAT evolved neural controllers for ARIEL gecko-inspired quadrupeds in MuJoCo, we investigate how spatial structure fundamentally alters evolutionary dynamics. Our experiments show a modest 4.9% difference in peak fitness between proximity-based and random pairing possibly within stochastic variation while combining spatial parent selection with stochastic death selection produces unstable population dynamics. We discover a continuous phase transition in energy-based selection experiments, with critical zone count separating extinction-dominated and explosion-dominated regimes. Our density-dependent death selection mechanism achieves 97% completion rates but causes fitness decline, revealing a fundamental dilemma where decoupled mechanisms produce bistable dynamics, positively coupled mechanisms create counter-selection pressures, and only deterministic fitness-based selection maintains stability. These findings provide important constraints for future spatial EA design.

How areas of land are allocated for different uses, such as forests, urban areas, and agriculture, has a large effect on the terrestrial carbon balance, and therefore climate change. Based on available historical data on land-use changes and a simulation of the associated carbon emissions and removals, a surrogate model can be learned that makes it possible to evaluate the different options available to decision-makers efficiently. An evolutionary search process can then be used to discover effective land-use policies for specific locations. Such a system was built on the Project Resilience platform and evaluated with the Land-Use Harmonization dataset LUH2 and the bookkeeping model BLUE. It generates Pareto fronts that trade off carbon impact and amount of land-use change customized to different locations, thus providing a proof-of-concept tool that is potentially useful for land-use planning.

Large-scale land enclosure for speculative mega-development constitutes a non-equilibrium spatial process whose velocity, topology, and irreversibility remain poorly quantified. We study the Pantai Indah Kapuk 2 (PIK2) coastal mega-development north of Jakarta, Indonesia, using eight years (2017--2024) of Sentinel-2 land-use/land-cover (LULC) data at 10-meter resolution. The landscape is projected onto a Marxian probability simplex partitioning terrestrial pixels into Commons, Agrarian, and Capital fractions. Fisher-Rao (FR) geodesic distances on this simplex identify a transformation pulse of 0.405~rad/yr during 2019--2020, coinciding with major construction activity. Absorbing Markov chain analysis yields expected absorption times into the built environment of 46.0~years for cropland and 38.1~years for tree cover, with a pooled built-area self-retention rate of 96.4%. Percolation analysis reveals that a giant connected component containing 89--95% of all built pixels persists at occupation probabilities p in [0.096, 0.162], far below the random percolation threshold p_c approx 0.593, indicating planned rather than stochastic spatial growth. The box-counting fractal dimension of the urban boundary increases from d_f = 1.316 to 1.397, consistent with increasingly irregular frontier expansion. These results suggest that information-geometric and statistical-mechanical tools can characterize the kinematic and topological signatures of capitalist spatial accumulation with quantitative precision.

While the field of Quality-Diversity (QD) has grown into a distinct branch of stochastic optimization, a few problems, in particular locomotion and navigation tasks, have become de facto standards. Are such benchmarks sufficient? Are they representative of the key challenges faced by QD algorithms? Do they provide the ability to focus on one particular challenge by properly disentangling it from others? Do they have much predictive power in terms of scalability and generalization? Existing benchmarks are not standardized, and there is currently no MNIST equivalent for QD. Inspired by recent works on Reinforcement Learning benchmarks, we argue that the identification of challenges faced by QD methods and the development of targeted, challenging, scalable but affordable benchmarks is an important step. As an initial effort, we identify three problems that are challenging in sparse reward settings, and propose associated benchmarks: (1) Behavior metric bias, which can result from the use of metrics that do not match the structure of the behavior space. (2) Behavioral Plateaus, with varying characteristics, such that escaping them would require adaptive QD algorithms and (3) Evolvability Traps, where small variations in genotype result in large behavioral changes. The environments that we propose satisfy the properties listed above.

Building world models that accurately and comprehensively represent the real world is the utmost aspiration for conditional image generative models as it would enable their use as world simulators. For these models to be successful world models, they should not only excel at image quality and prompt-image consistency but also ensure high representation diversity. However, current research in generative models mostly focuses on creative applications that are predominantly concerned with human preferences of image quality and aesthetics. We note that generative models have inference time mechanisms - or knobs - that allow the control of generation consistency, quality, and diversity. In this paper, we use state-of-the-art text-to-image and image-and-text-to-image models and their knobs to draw consistency-diversity-realism Pareto fronts that provide a holistic view on consistency-diversity-realism multi-objective. Our experiments suggest that realism and consistency can both be improved simultaneously; however there exists a clear tradeoff between realism/consistency and diversity. By looking at Pareto optimal points, we note that earlier models are better at representation diversity and worse in consistency/realism, and more recent models excel in consistency/realism while decreasing significantly the representation diversity. By computing Pareto fronts on a geodiverse dataset, we find that the first version of latent diffusion models tends to perform better than more recent models in all axes of evaluation, and there exist pronounced consistency-diversity-realism disparities between geographical regions. Overall, our analysis clearly shows that there is no best model and the choice of model should be determined by the downstream application. With this analysis, we invite the research community to consider Pareto fronts as an analytical tool to measure progress towards world models.

Evolvability is an important feature that impacts the ability of evolutionary processes to find interesting novel solutions and to deal with changing conditions of the problem to solve. The estimation of evolvability is not straightforward and is generally too expensive to be directly used as selective pressure in the evolutionary process. Indirectly promoting evolvability as a side effect of other easier and faster to compute selection pressures would thus be advantageous. In an unbounded behavior space, it has already been shown that evolvable individuals naturally appear and tend to be selected as they are more likely to invade empty behavior niches. Evolvability is thus a natural byproduct of the search in this context. However, practical agents and environments often impose limits on the reach-able behavior space. How do these boundaries impact evolvability? In this context, can evolvability still be promoted without explicitly rewarding it? We show that Novelty Search implicitly creates a pressure for high evolvability even in bounded behavior spaces, and explore the reasons for such a behavior. More precisely we show that, throughout the search, the dynamic evaluation of novelty rewards individuals which are very mobile in the behavior space, which in turn promotes evolvability.

Many have observed that the development and deployment of generative machine learning (ML) and artificial intelligence (AI) models follow a distinctive pattern in which pre-trained models are adapted and fine-tuned for specific downstream tasks. However, there is limited empirical work that examines the structure of these interactions. This paper analyzes 1.86 million models on Hugging Face, a leading peer production platform for model development. Our study of model family trees -- networks that connect fine-tuned models to their base or parent -- reveals sprawling fine-tuning lineages that vary widely in size and structure. Using an evolutionary biology lens to study ML models, we use model metadata and model cards to measure the genetic similarity and mutation of traits over model families. We find that models tend to exhibit a family resemblance, meaning their genetic markers and traits exhibit more overlap when they belong to the same model family. However, these similarities depart in certain ways from standard models of asexual reproduction, because mutations are fast and directed, such that two `sibling' models tend to exhibit more similarity than parent/child pairs. Further analysis of the directional drifts of these mutations reveals qualitative insights about the open machine learning ecosystem: Licenses counter-intuitively drift from restrictive, commercial licenses towards permissive or copyleft licenses, often in violation of upstream license's terms; models evolve from multi-lingual compatibility towards english-only compatibility; and model cards reduce in length and standardize by turning, more often, to templates and automatically generated text. Overall, this work takes a step toward an empirically grounded understanding of model fine-tuning and suggests that ecological models and methods can yield novel scientific insights.

Weight-perturbation evolution strategies (ES) can fine-tune billion-parameter language models with surprisingly small populations (e.g., N!approx!30), contradicting classical zeroth-order curse-of-dimensionality intuition. We also observe a second seemingly separate phenomenon: under fixed hyperparameters, the stochastic fine-tuning reward often rises, peaks, and then degrades in both ES and GRPO. We argue that both effects reflect a shared geometric property of fine-tuning landscapes: they are low-dimensional in curvature. A small set of high-curvature dimensions dominates improvement, producing (i) heterogeneous time scales that yield rise-then-decay under fixed stochasticity, as captured by a minimal quadratic stochastic-ascent model, and (ii) degenerate improving updates, where many random perturbations share similar components along these directions. Using ES as a geometric probe on fine-tuning reward landscapes of GSM8K, ARC-C, and WinoGrande across Qwen2.5-Instruct models (0.5B--7B), we show that reward-improving perturbations remain empirically accessible with small populations across scales. Together, these results reconcile ES scalability with non-monotonic training dynamics and suggest that high-dimensional fine-tuning may admit a broader class of viable optimization methods than worst-case theory implies.

Evolutionary program synthesis systems such as AlphaEvolve, OpenEvolve, and ShinkaEvolve offer a new approach to AI-assisted mathematical discovery. These systems utilize teams of large language models (LLMs) to generate candidate solutions to a problem as human readable code. These candidate solutions are then 'evolved' with the goal of improving them beyond what an LLM can produce in a single shot. While existing mathematical applications have mostly focused on problems of establishing bounds (e.g., sphere packing), the program synthesis approach is well suited to any problem where the solution takes the form of an explicit construction. With this in mind, in this paper we explore the use of OpenEvolve for combinatorial bijection discovery. We describe the results of applying OpenEvolve to three bijection construction problems involving Dyck paths, two of which are known and one of which is open. We find that while systems like OpenEvolve show promise as a valuable tool for combinatorialists, the problem of finding novel, research-level bijections remains a challenging task for current frontier systems, reinforcing the need for human mathematicians in the loop. We describe some lessons learned for others in the field interested in exploring the use of these systems.

Maintaining genetic diversity as a means to avoid premature convergence is critical in Genetic Programming. Several approaches have been proposed to achieve this, with some focusing on the mating phase from coupling dissimilar solutions to some form of self-adaptive selection mechanism. In nature, genetic diversity can be the consequence of many different factors, but when considering reproduction Sexual Selection can have an impact on promoting variety within a species. Specifically, Mate Choice often results in different selective pressures between sexes, which in turn may trigger evolutionary differences among them. Although some mechanisms of Sexual Selection have been applied to Genetic Programming in the past, the literature is scarce when it comes to mate choice. Recently, a way of modelling mating preferences by ideal mate representations was proposed, achieving good results when compared to a standard approach. These mating preferences evolve freely in a self-adaptive fashion, creating an evolutionary driving force of its own alongside fitness pressure. The inner mechanisms of this approach operate from personal choice, as each individual has its own representation of a perfect mate which affects the mate to be selected. In this paper, we compare this method against a random mate choice to assess whether there are advantages in evolving personal preferences. We conducted experiments using three symbolic regression problems and different mutation rates. The results show that self-adaptive mating preferences are able to create a more diverse set of solutions when compared to the traditional approach and a random mate approach (with statistically significant differences) and have a higher success rate in three of the six instances tested.

We study a model of a branching process subject to selection, modeled by giving each family an individual fitness acting as a branching rate, and mutation, modeled by resampling the fitness of a proportion of offspring in each generation. For two large classes of fitness distributions of Gumbel type we determine the growth of the population, almost surely on survival. We then study the empirical fitness distribution in a simplified model, which is numerically indistinguishable from the original model, and show the emergence of a Gaussian travelling wave.

This study proposes a hybrid deep-learning-metaheuristic framework with a bi-level architecture for road network design problems (NDPs). We train a graph neural network (GNN) to approximate the solution of the user equilibrium (UE) traffic assignment problem and use inferences made by the trained model to calculate fitness function evaluations of a genetic algorithm (GA) to approximate solutions for NDPs. Using three test networks, two NDP variants and an exact solver as benchmark, we show that on average, our proposed framework can provide solutions within 1.5% gap of the best results in less than 0.5% of the time used by the exact solution procedure. Our framework can be utilized within an expert system for infrastructure planning to determine the best infrastructure planning and management decisions under different scenarios. Given the flexibility of the framework, it can easily be adapted to many other decision problems that can be modeled as bi-level problems on graphs. Moreover, we foreseen interesting future research directions, thus we also put forward a brief research agenda for this topic. The key observation from our research that can shape future research is that the fitness function evaluation time using the inferences made by the GNN model was in the order of milliseconds, which points to an opportunity and a need for novel heuristics that 1) can cope well with noisy fitness function values provided by deep learning models, and 2) can use the significantly enlarged efficiency of the evaluation step to explore the search space effectively (rather than efficiently). This opens a new avenue for a modern class of metaheuristics that are crafted for use with AI-powered predictors.

Understanding the loss landscape is an important problem in machine learning. One key feature of the loss function, common to many neural network architectures, is the presence of exponentially many low lying local minima. Physical systems with similar energy landscapes may provide useful insights. In this work, we point out that black holes naturally give rise to such landscapes, owing to the existence of black hole entropy. For definiteness, we consider 1/8 BPS black holes in N = 8 string theory. These provide an infinite family of potential landscapes arising in the microscopic descriptions of corresponding black holes. The counting of minima amounts to black hole microstate counting. Moreover, the exact numbers of the minima for these landscapes are a priori known from dualities in string theory. Some of the minima are connected by paths of low loss values, resembling mode connectivity. We estimate the number of runs needed to find all the solutions. Initial explorations suggest that Stochastic Gradient Descent can find a significant fraction of the minima.

Recent advances in LLM-guided evolutionary computation, particularly AlphaEvolve (Novikov et al., 2025; Georgiev et al., 2025), have demonstrated remarkable success in discovering novel mathematical constructions and solving challenging optimization problems. However, the high-level descriptions in published work leave many implementation details unspecified, hindering reproducibility and further research. In this report we present GigaEvo, an extensible open-source framework that enables researchers to study and experiment with hybrid LLM-evolution approaches inspired by AlphaEvolve. Our system provides modular implementations of key components: MAP-Elites quality-diversity algorithms, asynchronous DAG-based evaluation pipelines, LLM-driven mutation operators with insight generation and bidirectional lineage tracking, and flexible multi-island evolutionary strategies. In order to assess reproducibility and validate our implementation we evaluate GigaEvo on challenging problems from the AlphaEvolve paper: Heilbronn triangle placement, circle packing in squares, and high-dimensional kissing numbers. The framework emphasizes modularity, concurrency, and ease of experimentation, enabling rapid prototyping through declarative configuration. We provide detailed descriptions of system architecture, implementation decisions, and experimental methodology to support further research in LLM driven evolutionary methods. The GigaEvo framework and all experimental code are available at https://github.com/AIRI-Institute/gigaevo-core.

We introduce Biomaker CA: a Biome Maker project using Cellular Automata (CA). In Biomaker CA, morphogenesis is a first class citizen and small seeds need to grow into plant-like organisms to survive in a nutrient starved environment and eventually reproduce with variation so that a biome survives for long timelines. We simulate complex biomes by means of CA rules in 2D grids and parallelize all of its computation on GPUs through the Python JAX framework. We show how this project allows for several different kinds of environments and laws of 'physics', alongside different model architectures and mutation strategies. We further analyze some configurations to show how plant agents can grow, survive, reproduce, and evolve, forming stable and unstable biomes. We then demonstrate how one can meta-evolve models to survive in a harsh environment either through end-to-end meta-evolution or by a more surgical and efficient approach, called Petri dish meta-evolution. Finally, we show how to perform interactive evolution, where the user decides how to evolve a plant model interactively and then deploys it in a larger environment. We open source Biomaker CA at: https://tinyurl.com/2x8yu34s .

Many fields use search algorithms, which automatically explore a search space to find high-performing solutions: chemists search through the space of molecules to discover new drugs; engineers search for stronger, cheaper, safer designs, scientists search for models that best explain data, etc. The goal of search algorithms has traditionally been to return the single highest-performing solution in a search space. Here we describe a new, fundamentally different type of algorithm that is more useful because it provides a holistic view of how high-performing solutions are distributed throughout a search space. It creates a map of high-performing solutions at each point in a space defined by dimensions of variation that a user gets to choose. This Multi-dimensional Archive of Phenotypic Elites (MAP-Elites) algorithm illuminates search spaces, allowing researchers to understand how interesting attributes of solutions combine to affect performance, either positively or, equally of interest, negatively. For example, a drug company may wish to understand how performance changes as the size of molecules and their cost-to-produce vary. MAP-Elites produces a large diversity of high-performing, yet qualitatively different solutions, which can be more helpful than a single, high-performing solution. Interestingly, because MAP-Elites explores more of the search space, it also tends to find a better overall solution than state-of-the-art search algorithms. We demonstrate the benefits of this new algorithm in three different problem domains ranging from producing modular neural networks to designing simulated and real soft robots. Because MAP- Elites (1) illuminates the relationship between performance and dimensions of interest in solutions, (2) returns a set of high-performing, yet diverse solutions, and (3) improves finding a single, best solution, it will advance science and engineering.

Large language models (LLMs) have shown promise in automating scientific hypothesis generation, yet existing approaches primarily yield coarse-grained hypotheses lacking critical methodological and experimental details. We introduce and formally define the novel task of fine-grained scientific hypothesis discovery, which entails generating detailed, experimentally actionable hypotheses from coarse initial research directions. We frame this as a combinatorial optimization problem and investigate the upper limits of LLMs' capacity to solve it when maximally leveraged. Specifically, we explore four foundational questions: (1) how to best harness an LLM's internal heuristics to formulate the fine-grained hypothesis it itself would judge as the most promising among all the possible hypotheses it might generate, based on its own internal scoring-thus defining a latent reward landscape over the hypothesis space; (2) whether such LLM-judged better hypotheses exhibit stronger alignment with ground-truth hypotheses; (3) whether shaping the reward landscape using an ensemble of diverse LLMs of similar capacity yields better outcomes than defining it with repeated instances of the strongest LLM among them; and (4) whether an ensemble of identical LLMs provides a more reliable reward landscape than a single LLM. To address these questions, we propose a hierarchical search method that incrementally proposes and integrates details into the hypothesis, progressing from general concepts to specific experimental configurations. We show that this hierarchical process smooths the reward landscape and enables more effective optimization. Empirical evaluations on a new benchmark of expert-annotated fine-grained hypotheses from recent chemistry literature show that our method consistently outperforms strong baselines.

Large language models (LLMs) are increasingly used to evolve programs and multi-agent systems, yet most existing approaches rely on overwrite-based mutations that maintain only a single candidate at a time. Such methods discard useful variants, suffer from destructive edits, and explore a brittle search space prone to structural failure. We introduce EvoLattice, a framework that represents an entire population of candidate programs or agent behaviors within a single directed acyclic graph. Each node stores multiple persistent alternatives, and every valid path through the graph defines a distinct executable candidate, yielding a large combinatorial search space without duplicating structure. EvoLattice enables fine-grained alternative-level evaluation by scoring each alternative across all paths in which it appears, producing statistics that reveal how local design choices affect global performance. These statistics provide a dense, data-driven feedback signal for LLM-guided mutation, recombination, and pruning, while preserving successful components. Structural correctness is guaranteed by a deterministic self-repair mechanism that enforces acyclicity and dependency consistency independently of the LLM. EvoLattice naturally extends to agent evolution by interpreting alternatives as prompt fragments or sub-agent behaviors. Across program synthesis (proxy and optimizer meta-learning), EvoLattice yields more stable evolution, greater expressivity, and stronger improvement trajectories than prior LLM-guided methods. The resulting dynamics resemble quality-diversity optimization, emerging implicitly from EvoLattice's internal multi-alternative representation rather than an explicit external archive.

A central statistical problem in population genetics is to infer evolutionary and biological parameters such as the strength of natural selection and allele age from DNA samples extracted from a contemporary population. That all samples come only from the present-day has long been known to limit statistical inference; there is potentially more information available if one also has access to ancient DNA so that inference is based on a time-series of historical changes in allele frequencies. We introduce a Markov Chain Monte Carlo (MCMC) method for Bayesian inference from allele frequency time-series data based on an underlying Wright--Fisher diffusion model of evolution, through which one can infer the parameters of essentially any selection model including those with frequency-dependent effects. The chief novelty is that we show this method to be exact in the sense that it is possible to augment the state space explored by MCMC with the unobserved diffusion trajectory, even though the transition function of this diffusion is intractable. Through careful design of a proposal distribution, we describe an efficient method in which updates to the trajectory and accept/reject decisions are calculated without error. We illustrate the method on data capturing changes in coat colour over the past 20,000 years, and find evidence to support previous findings that the mutant alleles ASIP and MC1R responsible for changes in coat color have experienced very strong, possibly overdominant, selection and further provide estimates for the ages of these genes.

LLM-based agents depend on effective tool-use policies to solve complex tasks, yet optimizing these policies remains challenging due to delayed supervision and the difficulty of credit assignment in long-horizon trajectories. Existing optimization approaches tend to be either monolithic, which are prone to entangling behaviors, or single-aspect, which ignore cross-module error propagation. To address these limitations, we propose EvoTool, a self-evolving framework that optimizes a modular tool-use policy via a gradient-free evolutionary paradigm. EvoTool decomposes agent's tool-use policy into four modules, including Planner, Selector, Caller, and Synthesizer, and iteratively improves them in a self-improving loop through three novel mechanisms. Trajectory-Grounded Blame Attribution uses diagnostic traces to localize failures to a specific module. Feedback-Guided Targeted Mutation then edits only that module via natural-language critique. Diversity-Aware Population Selection preserves complementary candidates to ensure solution diversity. Across four benchmarks, EvoTool outperforms strong baselines by over 5 points on both GPT-4.1 and Qwen3-8B, while achieving superior efficiency and transferability. The code will be released once paper is accepted.

The difficulty of monitoring biodiversity at fine scales and over large areas limits ecological knowledge and conservation efforts. To fill this gap, Species Distribution Models (SDMs) predict species across space from spatially explicit features. Yet, they face the challenge of integrating the rich but heterogeneous data made available over the past decade, notably millions of opportunistic species observations and standardized surveys, as well as multi-modal remote sensing data. In light of that, we have designed and developed a new European-scale dataset for SDMs at high spatial resolution (10-50 m), including more than 10k species (i.e., most of the European flora). The dataset comprises 5M heterogeneous Presence-Only records and 90k exhaustive Presence-Absence survey records, all accompanied by diverse environmental rasters (e.g., elevation, human footprint, and soil) that are traditionally used in SDMs. In addition, it provides Sentinel-2 RGB and NIR satellite images with 10 m resolution, a 20-year time-series of climatic variables, and satellite time-series from the Landsat program. In addition to the data, we provide an openly accessible SDM benchmark (hosted on Kaggle), which has already attracted an active community and a set of strong baselines for single predictor/modality and multimodal approaches. All resources, e.g., the dataset, pre-trained models, and baseline methods (in the form of notebooks), are available on Kaggle, allowing one to start with our dataset literally with two mouse clicks.

Self-evolution methods enhance code generation through iterative "generate-verify-refine" cycles, yet existing approaches suffer from low exploration efficiency, failing to discover solutions with superior complexity within limited budgets. This inefficiency stems from initialization bias trapping evolution in poor solution regions, uncontrolled stochastic operations lacking feedback guidance, and insufficient experience utilization across tasks. To address these bottlenecks, we propose Controlled Self-Evolution (CSE), which consists of three key components. Diversified Planning Initialization generates structurally distinct algorithmic strategies for broad solution space coverage. Genetic Evolution replaces stochastic operations with feedback-guided mechanisms, enabling targeted mutation and compositional crossover. Hierarchical Evolution Memory captures both successful and failed experiences at inter-task and intra-task levels. Experiments on EffiBench-X demonstrate that CSE consistently outperforms all baselines across various LLM backbones. Furthermore, CSE achieves higher efficiency from early generations and maintains continuous improvement throughout evolution. Our code is publicly available at https://github.com/QuantaAlpha/EvoControl.

We introduce ShinkaEvolve: a new open-source framework leveraging large language models (LLMs) to advance scientific discovery with state-of-the-art performance and unprecedented efficiency. Recent advances in scaling inference time compute of LLMs have enabled significant progress in generalized scientific discovery. These approaches rely on evolutionary agentic harnesses that leverage LLMs as mutation operators to generate candidate solutions. However, current code evolution methods suffer from critical limitations: they are sample inefficient, requiring thousands of samples to identify effective solutions, and remain closed-source, hindering broad adoption and extension. ShinkaEvolve addresses these limitations, introducing three key innovations: a parent sampling technique balancing exploration and exploitation, code novelty rejection-sampling for efficient search space exploration, and a bandit-based LLM ensemble selection strategy. We evaluate ShinkaEvolve across diverse tasks, demonstrating consistent improvements in sample efficiency and solution quality. ShinkaEvolve discovers a new state-of-the-art circle packing solution using only 150 samples, designs high-performing agentic harnesses for AIME mathematical reasoning tasks, identifies improvements to ALE-Bench competitive programming solutions, and discovers novel mixture-of-expert load balancing loss functions that illuminate the space of optimization strategies. Our results demonstrate that ShinkaEvolve achieves broad applicability with exceptional sample efficiency. By providing open-source accessibility and cost-efficiency, this work democratizes open-ended discovery across diverse computational problems.

The paradigm of automated program generation is shifting from one-shot generation to inference-time search, where Large Language Models (LLMs) function as semantic mutation operators within evolutionary loops. While effective, these systems are currently governed by static schedules that fail to account for the non-stationary dynamics of the search process. This rigidity results in substantial computational waste, as resources are indiscriminately allocated to stagnating populations while promising frontiers remain under-exploited. We introduce AdaEvolve, a framework that reformulates LLM-driven evolution as a hierarchical adaptive optimization problem. AdaEvolve uses an "accumulated improvement signal" to unify decisions across three levels: Local Adaptation, which dynamically modulates the exploration intensity within a population of solution candidates; Global Adaptation, which routes the global resource budget via bandit-based scheduling across different solution candidate populations; and Meta-Guidance which generates novel solution tactics based on the previously generated solutions and their corresponding improvements when the progress stalls. We demonstrate that AdaEvolve consistently outperforms the open-sourced baselines across 185 different open-ended optimization problems including combinatorial, systems optimization and algorithm design problems.

Many recently trained neural networks employ large numbers of parameters to achieve good performance. One may intuitively use the number of parameters required as a rough gauge of the difficulty of a problem. But how accurate are such notions? How many parameters are really needed? In this paper we attempt to answer this question by training networks not in their native parameter space, but instead in a smaller, randomly oriented subspace. We slowly increase the dimension of this subspace, note at which dimension solutions first appear, and define this to be the intrinsic dimension of the objective landscape. The approach is simple to implement, computationally tractable, and produces several suggestive conclusions. Many problems have smaller intrinsic dimensions than one might suspect, and the intrinsic dimension for a given dataset varies little across a family of models with vastly different sizes. This latter result has the profound implication that once a parameter space is large enough to solve a problem, extra parameters serve directly to increase the dimensionality of the solution manifold. Intrinsic dimension allows some quantitative comparison of problem difficulty across supervised, reinforcement, and other types of learning where we conclude, for example, that solving the inverted pendulum problem is 100 times easier than classifying digits from MNIST, and playing Atari Pong from pixels is about as hard as classifying CIFAR-10. In addition to providing new cartography of the objective landscapes wandered by parameterized models, the method is a simple technique for constructively obtaining an upper bound on the minimum description length of a solution. A byproduct of this construction is a simple approach for compressing networks, in some cases by more than 100 times.

Using the weights of trained Neural Network (NN) models as data modality has recently gained traction as a research field - dubbed Weight Space Learning (WSL). Multiple recent works propose WSL methods to analyze models, evaluate methods, or synthesize weights. Weight space learning methods require populations of trained models as datasets for development and evaluation. However, existing collections of models - called `model zoos' - are unstructured or follow a rudimentary definition of diversity. In parallel, work rooted in statistical physics has identified phases and phase transitions in NN models. Models are homogeneous within the same phase but qualitatively differ from one phase to another. We combine the idea of `model zoos' with phase information to create a controlled notion of diversity in populations. We introduce 12 large-scale zoos that systematically cover known phases and vary over model architecture, size, and datasets. These datasets cover different modalities, such as computer vision, natural language processing, and scientific ML. For every model, we compute loss landscape metrics and validate full coverage of the phases. With this dataset, we provide the community with a resource with a wide range of potential applications for WSL and beyond. Evidence suggests the loss landscape phase plays a role in applications such as model training, analysis, or sparsification. We demonstrate this in an exploratory study of the downstream methods like transfer learning or model weights averaging.

Recent studies have demonstrated the strong empirical performance of diffusion models on discrete sequences across domains from natural language to biological sequence generation. For example, in the protein inverse folding task, conditional diffusion models have achieved impressive results in generating natural-like sequences that fold back into the original structure. However, practical design tasks often require not only modeling a conditional distribution but also optimizing specific task objectives. For instance, we may prefer protein sequences with high stability. To address this, we consider the scenario where we have pre-trained discrete diffusion models that can generate natural-like sequences, as well as reward models that map sequences to task objectives. We then formulate the reward maximization problem within discrete diffusion models, analogous to reinforcement learning (RL), while minimizing the KL divergence against pretrained diffusion models to preserve naturalness. To solve this RL problem, we propose a novel algorithm, DRAKES, that enables direct backpropagation of rewards through entire trajectories generated by diffusion models, by making the originally non-differentiable trajectories differentiable using the Gumbel-Softmax trick. Our theoretical analysis indicates that our approach can generate sequences that are both natural-like and yield high rewards. While similar tasks have been recently explored in diffusion models for continuous domains, our work addresses unique algorithmic and theoretical challenges specific to discrete diffusion models, which arise from their foundation in continuous-time Markov chains rather than Brownian motion. Finally, we demonstrate the effectiveness of DRAKES in generating DNA and protein sequences that optimize enhancer activity and protein stability, respectively, important tasks for gene therapies and protein-based therapeutics.

This paper claims that machine learning (ML) largely overlooks an important facet of general intelligence: robustness to a qualitatively unknown future in an open world. Such robustness relates to Knightian uncertainty (KU) in economics, i.e. uncertainty that cannot be quantified, which is excluded from consideration in ML's key formalisms. This paper aims to identify this blind spot, argue its importance, and catalyze research into addressing it, which we believe is necessary to create truly robust open-world AI. To help illuminate the blind spot, we contrast one area of ML, reinforcement learning (RL), with the process of biological evolution. Despite staggering ongoing progress, RL still struggles in open-world situations, often failing under unforeseen situations. For example, the idea of zero-shot transferring a self-driving car policy trained only in the US to the UK currently seems exceedingly ambitious. In dramatic contrast, biological evolution routinely produces agents that thrive within an open world, sometimes even to situations that are remarkably out-of-distribution (e.g. invasive species; or humans, who do undertake such zero-shot international driving). Interestingly, evolution achieves such robustness without explicit theory, formalisms, or mathematical gradients. We explore the assumptions underlying RL's typical formalisms, showing how they limit RL's engagement with the unknown unknowns characteristic of an ever-changing complex world. Further, we identify mechanisms through which evolutionary processes foster robustness to novel and unpredictable challenges, and discuss potential pathways to algorithmically embody them. The conclusion is that the intriguing remaining fragility of ML may result from blind spots in its formalisms, and that significant gains may result from direct confrontation with the challenge of KU.

A central problem in biology is to understand how organisms evolve and adapt to their environment by acquiring variations in the observable characteristics or traits of species across the tree of life. With the growing availability of large-scale image repositories in biology and recent advances in generative modeling, there is an opportunity to accelerate the discovery of evolutionary traits automatically from images. Toward this goal, we introduce Phylo-Diffusion, a novel framework for conditioning diffusion models with phylogenetic knowledge represented in the form of HIERarchical Embeddings (HIER-Embeds). We also propose two new experiments for perturbing the embedding space of Phylo-Diffusion: trait masking and trait swapping, inspired by counterpart experiments of gene knockout and gene editing/swapping. Our work represents a novel methodological advance in generative modeling to structure the embedding space of diffusion models using tree-based knowledge. Our work also opens a new chapter of research in evolutionary biology by using generative models to visualize evolutionary changes directly from images. We empirically demonstrate the usefulness of Phylo-Diffusion in capturing meaningful trait variations for fishes and birds, revealing novel insights about the biological mechanisms of their evolution.

Geospatial Foundation Models (GeoFMs) are transforming Earth Observation (EO), but evaluation lacks standardized protocols. GEO-Bench-2 addresses this with a comprehensive framework spanning classification, segmentation, regression, object detection, and instance segmentation across 19 permissively-licensed datasets. We introduce ''capability'' groups to rank models on datasets that share common characteristics (e.g., resolution, bands, temporality). This enables users to identify which models excel in each capability and determine which areas need improvement in future work. To support both fair comparison and methodological innovation, we define a prescriptive yet flexible evaluation protocol. This not only ensures consistency in benchmarking but also facilitates research into model adaptation strategies, a key and open challenge in advancing GeoFMs for downstream tasks. Our experiments show that no single model dominates across all tasks, confirming the specificity of the choices made during architecture design and pretraining. While models pretrained on natural images (ConvNext ImageNet, DINO V3) excel on high-resolution tasks, EO-specific models (TerraMind, Prithvi, and Clay) outperform them on multispectral applications such as agriculture and disaster response. These findings demonstrate that optimal model choice depends on task requirements, data modalities, and constraints. This shows that the goal of a single GeoFM model that performs well across all tasks remains open for future research. GEO-Bench-2 enables informed, reproducible GeoFM evaluation tailored to specific use cases. Code, data, and leaderboard for GEO-Bench-2 are publicly released under a permissive license.

AlphaEvolve is a generic evolutionary coding agent that combines the generative capabilities of LLMs with automated evaluation in an iterative evolutionary framework that proposes, tests, and refines algorithmic solutions to challenging scientific and practical problems. In this paper we showcase AlphaEvolve as a tool for autonomously discovering novel mathematical constructions and advancing our understanding of long-standing open problems. To demonstrate its breadth, we considered a list of 67 problems spanning mathematical analysis, combinatorics, geometry, and number theory. The system rediscovered the best known solutions in most of the cases and discovered improved solutions in several. In some instances, AlphaEvolve is also able to generalize results for a finite number of input values into a formula valid for all input values. Furthermore, we are able to combine this methodology with Deep Think and AlphaProof in a broader framework where the additional proof-assistants and reasoning systems provide automated proof generation and further mathematical insights. These results demonstrate that large language model-guided evolutionary search can autonomously discover mathematical constructions that complement human intuition, at times matching or even improving the best known results, highlighting the potential for significant new ways of interaction between mathematicians and AI systems. We present AlphaEvolve as a powerful new tool for mathematical discovery, capable of exploring vast search spaces to solve complex optimization problems at scale, often with significantly reduced requirements on preparation and computation time.

Model merging is a powerful technique for integrating the specialized knowledge of multiple machine learning models into a single model. However, existing methods require manually partitioning model parameters into fixed groups for merging, which restricts the exploration of potential combinations and limits performance. To overcome these limitations, we propose Model Merging of Natural Niches (M2N2), an evolutionary algorithm with three key features: (1) dynamic adjustment of merging boundaries to progressively explore a broader range of parameter combinations; (2) a diversity preservation mechanism inspired by the competition for resources in nature, to maintain a population of diverse, high-performing models that are particularly well-suited for merging; and (3) a heuristicbased attraction metric to identify the most promising pairs of models for fusion. Our experimental results demonstrate, for the first time, that model merging can be used to evolve models entirely from scratch. Specifically, we apply M2N2 to evolve MNIST classifiers from scratch and achieve performance comparable to CMA-ES, while being computationally more efficient. Furthermore, M2N2 scales to merge specialized language and image generation models, achieving state-of-the-art performance. Notably, it preserves crucial model capabilities beyond those explicitly optimized by the fitness function, highlighting its robustness and versatility. Our code is available at https://github.com/SakanaAI/natural_niches

Large language models (LLMs) are increasingly being used to evolve solutions to problems in many domains, in a process inspired by biological evolution. However, unlike biological evolution, most LLM-evolution frameworks are formulated as static optimization problems, overlooking the open-ended adversarial dynamics that characterize real-world evolutionary processes. Here, we study Digital Red Queen (DRQ), a simple self-play algorithm that embraces these so-called "Red Queen" dynamics via continual adaptation to a changing objective. DRQ uses an LLM to evolve assembly-like programs, called warriors, which compete against each other for control of a virtual machine in the game of Core War, a Turing-complete environment studied in artificial life and connected to cybersecurity. In each round of DRQ, the model evolves a new warrior to defeat all previous ones, producing a sequence of adapted warriors. Over many rounds, we observe that warriors become increasingly general (relative to a set of held-out human warriors). Interestingly, warriors also become less behaviorally diverse across independent runs, indicating a convergence pressure toward a general-purpose behavioral strategy, much like convergent evolution in nature. This result highlights a potential value of shifting from static objectives to dynamic Red Queen objectives. Our work positions Core War as a rich, controllable sandbox for studying adversarial adaptation in artificial systems and for evaluating LLM-based evolution methods. More broadly, the simplicity and effectiveness of DRQ suggest that similarly minimal self-play approaches could prove useful in other more practical multi-agent adversarial domains, like real-world cybersecurity or combating drug resistance.

The widespread applicability and increasing omnipresence of LLMs have instigated a need to align LLM responses to user and stakeholder preferences. Many preference optimization approaches have been proposed that fine-tune LLM parameters to achieve good alignment. However, such parameter tuning is known to interfere with model performance on many tasks. Moreover, keeping up with shifting user preferences is tricky in such a situation. Decoding-time alignment with reward model guidance solves these issues at the cost of increased inference time. However, most of such methods fail to strike the right balance between exploration and exploitation of reward -- often due to the conflated formulation of these two aspects - to give well-aligned responses. To remedy this we decouple these two aspects and implement them in an evolutionary fashion: exploration is enforced by decoding from mutated instructions and exploitation is represented as the periodic replacement of poorly-rewarded generations with well-rewarded ones. Empirical evidences indicate that this strategy outperforms many preference optimization and decode-time alignment approaches on two widely accepted alignment benchmarks AlpacaEval 2 and MT-Bench. Our implementation will be available at: https://darwin-alignment.github.io.

In a convergence of machine learning and biology, we reveal that diffusion models are evolutionary algorithms. By considering evolution as a denoising process and reversed evolution as diffusion, we mathematically demonstrate that diffusion models inherently perform evolutionary algorithms, naturally encompassing selection, mutation, and reproductive isolation. Building on this equivalence, we propose the Diffusion Evolution method: an evolutionary algorithm utilizing iterative denoising -- as originally introduced in the context of diffusion models -- to heuristically refine solutions in parameter spaces. Unlike traditional approaches, Diffusion Evolution efficiently identifies multiple optimal solutions and outperforms prominent mainstream evolutionary algorithms. Furthermore, leveraging advanced concepts from diffusion models, namely latent space diffusion and accelerated sampling, we introduce Latent Space Diffusion Evolution, which finds solutions for evolutionary tasks in high-dimensional complex parameter space while significantly reducing computational steps. This parallel between diffusion and evolution not only bridges two different fields but also opens new avenues for mutual enhancement, raising questions about open-ended evolution and potentially utilizing non-Gaussian or discrete diffusion models in the context of Diffusion Evolution.

Loss landscape is a useful tool to characterize and compare neural network models. The main challenge for analysis of loss landscape for the deep neural networks is that they are generally highly non-convex in very high dimensional space. In this paper, we develop "the roughness"concept for understanding such landscapes in high dimensions and apply this technique to study two neural network models arising from solving differential equations. Our main innovation is the proposal of a well-defined and easy-to-compute roughness index (RI) which is based on the mean and variance of the (normalized) total variation for one-dimensional functions projected on randomly sampled directions. A large RI at the local minimizer hints an oscillatory landscape profile and indicates a severe challenge for the first-order optimization method. Particularly, we observe the increasing-then-decreasing pattern for RI along the gradient descent path in most models. We apply our method to two types of loss functions used to solve partial differential equations (PDEs) when the solution of PDE is parametrized by neural networks. Our empirical results on these PDE problems reveal important and consistent observations that the landscapes from the deep Galerkin method around its local minimizers are less rough than the deep Ritz method.

LLM-guided evolutionary methods such as AlphaEvolve have proven effective in domains like math, systems research, and algorithmic discovery, but their reliance on frontier models makes each run expensive. We argue this is largely an artifact of how existing frameworks allocate search: archives that fail to preserve solution diversity force compensation through stronger mutation models; blind model use spends frontier dollars on local edits a smaller model could handle; and full-set evaluation wastes rollouts on redundant examples. We introduce LEVI, a harness-first evolutionary framework built on the bet that stronger search architectures can substitute for or even outperform larger LLMs in evolutionary search. LEVI improves on three core components of evolutionary search: a solution database that establishes diversity from the beginning, and then maintains it throughout the run; a smarter mutation router that plays into the strengths of large and small LLMs; and a rank-preserving proxy benchmark for rollout-heavy settings. Across systems-research benchmarks LEVI attains the highest score on a budget 3.3-6.7x smaller than the published frontier-model runs of existing frameworks like ShinkaEvolve, GEPA, and AdaEvolve; on one problem, LEVI matches the existing best at a 35x lower cost. On prompt optimization, LEVI matches or exceeds GEPA at less than half of its rollout budget on four different benchmarks. LEVI is available as an open-source framework at https://github.com/ttanv/levi.

Significant recent work has studied the ability of gradient descent to recover a hidden planted direction θ^star in S^{d-1} in different high-dimensional settings, including tensor PCA and single-index models. The key quantity that governs the ability of gradient descent to traverse these landscapes is the information exponent k^star (Ben Arous et al., (2021)), which corresponds to the order of the saddle at initialization in the population landscape. Ben Arous et al., (2021) showed that n gtrsim d^{max(1, k^star-1)} samples were necessary and sufficient for online SGD to recover θ^star, and Ben Arous et al., (2020) proved a similar lower bound for Langevin dynamics. More recently, Damian et al., (2023) showed it was possible to circumvent these lower bounds by running gradient descent on a smoothed landscape, and that this algorithm succeeds with n gtrsim d^{max(1, k^star/2)} samples, which is optimal in the worst case. This raises the question of whether it is possible to achieve the same rate without explicit smoothing. In this paper, we show that Langevin dynamics can succeed with n gtrsim d^{ k^star/2 } samples if one considers the average iterate, rather than the last iterate. The key idea is that the combination of noise-injection and iterate averaging is able to emulate the effect of landscape smoothing. We apply this result to both the tensor PCA and single-index model settings. Finally, we conjecture that minibatch SGD can also achieve the same rate without adding any additional noise.

Training large neural networks (NNs) requires optimizing high-dimensional data-dependent loss functions. The optimization landscape of these functions is often highly complex and textured, even fractal-like, with many spurious local minima, ill-conditioned valleys, degenerate points, and saddle points. Complicating things further is the fact that these landscape characteristics are a function of the data, meaning that noise in the training data can propagate forward and give rise to unrepresentative small-scale geometry. This poses a difficulty for gradient-based optimization methods, which rely on local geometry to compute updates and are, therefore, vulnerable to being derailed by noisy data. In practice,this translates to a strong dependence of the optimization dynamics on the noise in the data, i.e., poor generalization performance. To remediate this problem, we propose a new optimization procedure: Rolling Ball Optimizer (RBO), that breaks this spatial locality by incorporating information from a larger region of the loss landscape in its updates. We achieve this by simulating the motion of a rigid sphere of finite radius rolling on the loss landscape, a straightforward generalization of Gradient Descent (GD) that simplifies into it in the infinitesimal limit. The radius serves as a hyperparameter that determines the scale at which RBO sees the loss landscape, allowing control over the granularity of its interaction therewith. We are motivated by the intuition that the large-scale geometry of the loss landscape is less data-specific than its fine-grained structure, and that it is easier to optimize. We support this intuition by proving that our algorithm has a smoothing effect on the loss function. Evaluation against SGD, SAM, and Entropy-SGD, on MNIST and CIFAR-10/100 demonstrates promising results in terms of convergence speed, training accuracy, and generalization performance.

The saturation of high-quality pre-training data has shifted research focus toward evolutionary systems capable of continuously generating novel artifacts, leading to the success of AlphaEvolve. However, the progress of such systems is hindered by the lack of rigorous, quantitative evaluation. To tackle this challenge, we introduce CreativeBench, a benchmark for evaluating machine creativity in code generation, grounded in a classical cognitive framework. Comprising two subsets -- CreativeBench-Combo and CreativeBench-Explore -- the benchmark targets combinatorial and exploratory creativity through an automated pipeline utilizing reverse engineering and self-play. By leveraging executable code, CreativeBench objectively distinguishes creativity from hallucination via a unified metric defined as the product of quality and novelty. Our analysis of state-of-the-art models reveals distinct behaviors: (1) scaling significantly improves combinatorial creativity but yields diminishing returns for exploration; (2) larger models exhibit ``convergence-by-scaling,'' becoming more correct but less divergent; and (3) reasoning capabilities primarily benefit constrained exploration rather than combination. Finally, we propose EvoRePE, a plug-and-play inference-time steering strategy that internalizes evolutionary search patterns to consistently enhance machine creativity.

Advances in Large Language Models (LLMs) have enabled a new class of self-evolving agents that autonomously improve through interaction with the environment, demonstrating strong capabilities. However, self-evolution also introduces novel risks overlooked by current safety research. In this work, we study the case where an agent's self-evolution deviates in unintended ways, leading to undesirable or even harmful outcomes. We refer to this as Misevolution. To provide a systematic investigation, we evaluate misevolution along four key evolutionary pathways: model, memory, tool, and workflow. Our empirical findings reveal that misevolution is a widespread risk, affecting agents built even on top-tier LLMs (e.g., Gemini-2.5-Pro). Different emergent risks are observed in the self-evolutionary process, such as the degradation of safety alignment after memory accumulation, or the unintended introduction of vulnerabilities in tool creation and reuse. To our knowledge, this is the first study to systematically conceptualize misevolution and provide empirical evidence of its occurrence, highlighting an urgent need for new safety paradigms for self-evolving agents. Finally, we discuss potential mitigation strategies to inspire further research on building safer and more trustworthy self-evolving agents. Our code and data are available at https://github.com/ShaoShuai0605/Misevolution . Warning: this paper includes examples that may be offensive or harmful in nature.

Decision trees are a crucial class of models offering robust predictive performance and inherent interpretability across various domains, including healthcare, finance, and logistics. However, current tree induction methods often face limitations such as suboptimal solutions from greedy methods or prohibitive computational costs and limited applicability of exact optimization approaches. To address these challenges, we propose an evolutionary optimization method for decision tree induction based on genetic programming (GP). Our key innovation is the integration of semantic priors and domain-specific knowledge about the search space into the optimization algorithm. To this end, we introduce LLEGO, a framework that incorporates semantic priors into genetic search operators through the use of Large Language Models (LLMs), thereby enhancing search efficiency and targeting regions of the search space that yield decision trees with superior generalization performance. This is operationalized through novel genetic operators that work with structured natural language prompts, effectively utilizing LLMs as conditional generative models and sources of semantic knowledge. Specifically, we introduce fitness-guided crossover to exploit high-performing regions, and diversity-guided mutation for efficient global exploration of the search space. These operators are controlled by corresponding hyperparameters that enable a more nuanced balance between exploration and exploitation across the search space. Empirically, we demonstrate across various benchmarks that LLEGO evolves superior-performing trees compared to existing tree induction methods, and exhibits significantly more efficient search performance compared to conventional GP approaches.

Large language models and autonomous AI agents have evolved rapidly, resulting in a diverse array of evaluation benchmarks, frameworks, and collaboration protocols. However, the landscape remains fragmented and lacks a unified taxonomy or comprehensive survey. Therefore, we present a side-by-side comparison of benchmarks developed between 2019 and 2025 that evaluate these models and agents across multiple domains. In addition, we propose a taxonomy of approximately 60 benchmarks that cover general and academic knowledge reasoning, mathematical problem-solving, code generation and software engineering, factual grounding and retrieval, domain-specific evaluations, multimodal and embodied tasks, task orchestration, and interactive assessments. Furthermore, we review AI-agent frameworks introduced between 2023 and 2025 that integrate large language models with modular toolkits to enable autonomous decision-making and multi-step reasoning. Moreover, we present real-world applications of autonomous AI agents in materials science, biomedical research, academic ideation, software engineering, synthetic data generation, chemical reasoning, mathematical problem-solving, geographic information systems, multimedia, healthcare, and finance. We then survey key agent-to-agent collaboration protocols, namely the Agent Communication Protocol (ACP), the Model Context Protocol (MCP), and the Agent-to-Agent Protocol (A2A). Finally, we discuss recommendations for future research, focusing on advanced reasoning strategies, failure modes in multi-agent LLM systems, automated scientific discovery, dynamic tool integration via reinforcement learning, integrated search capabilities, and security vulnerabilities in agent protocols.

Benchmarks shape scientific conclusions about model capabilities and steer model development. This creates a feedback loop: stronger benchmarks drive better models, and better models demand more discriminative benchmarks. Ensuring benchmark reliability is therefore essential for trustworthy evaluation and meaningful progress. In this work, we study benchmark reliability from a distributional perspective and introduce benchmark harmony, which measures how uniformly a model's performance is distributed across the subdomains of a benchmark. We posit that high harmony is a desirable benchmark property, indicating that the aggregate metric reflects uniform competence across subdomains. Across 19 multiple-choice benchmarks and five model families, we map each benchmark onto a mean-variance plane of harmony computed across models, where high mean and low variance signal more reliable evaluation. Our analysis shows that less harmonious benchmarks can give misleading results, since overall accuracy may be disproportionately influenced by specific subdomains. For instance, ARC-Easy is overwhelmed by questions on Biological Concepts, overshadowing other critical subdomains such as Geography, Physics, Chemistry, and Environmental Science. By recommending that harmony should be reported alongside accuracy, we reframe evaluation from simple performance averages to a more robust, distributionally reliable measurement of performance.

Exploration is a key problem in reinforcement learning, since agents can only learn from data they acquire in the environment. With that in mind, maintaining a population of agents is an attractive method, as it allows data be collected with a diverse set of behaviors. This behavioral diversity is often boosted via multi-objective loss functions. However, those approaches typically leverage mean field updates based on pairwise distances, which makes them susceptible to cycling behaviors and increased redundancy. In addition, explicitly boosting diversity often has a detrimental impact on optimizing already fruitful behaviors for rewards. As such, the reward-diversity trade off typically relies on heuristics. Finally, such methods require behavioral representations, often handcrafted and domain specific. In this paper, we introduce an approach to optimize all members of a population simultaneously. Rather than using pairwise distance, we measure the volume of the entire population in a behavioral manifold, defined by task-agnostic behavioral embeddings. In addition, our algorithm Diversity via Determinants (DvD), adapts the degree of diversity during training using online learning techniques. We introduce both evolutionary and gradient-based instantiations of DvD and show they effectively improve exploration without reducing performance when better exploration is not required.

This position paper argues for, and offers, a critical lens through which to examine the current AI frenzy in the landscape architecture profession. In it, the authors propose five archetypes or mental modes that landscape architects might inhabit when thinking about AI. Rather than limiting judgments of AI use to a single axis of acceleration, these archetypes and corresponding narratives exist along a relational spectrum and are permeable, allowing LAs to take on and switch between them according to context. We model these relationships between the archetypes and their contributions to AI advancement using a causal loop diagram (CLD), and with those interactions argue that more nuanced ways of approaching AI might also open new modes of practice in the new digital economy.

Inverse protein folding -- the task of predicting a protein sequence from its backbone atom coordinates -- has surfaced as an important problem in the "top down", de novo design of proteins. Contemporary approaches have cast this problem as a conditional generative modelling problem, where a large generative model over protein sequences is conditioned on the backbone. While these generative models very rapidly produce promising sequences, independent draws from generative models may fail to produce sequences that reliably fold to the correct backbone. Furthermore, it is challenging to adapt pure generative approaches to other settings, e.g., when constraints exist. In this paper, we cast the problem of improving generated inverse folds as an optimization problem that we solve using recent advances in "deep" or "latent space" Bayesian optimization. Our approach consistently produces protein sequences with greatly reduced structural error to the target backbone structure as measured by TM score and RMSD while using fewer computational resources. Additionally, we demonstrate other advantages of an optimization-based approach to the problem, such as the ability to handle constraints.

Would experience designing faster GPU kernels also help close in on a long-standing open mathematical conjecture? Large Language Models (LLMs) integrated into evolutionary search have recently produced state-of-the-art solutions on optimization tasks, including open mathematical conjectures, GPU kernel design, scientific law discovery, and combinatorial puzzles. To achieve this, prior work applied search scaffolds to one target task at a time, so every new problem is approached from scratch and the experience accumulated during search is discarded once the model finishes its attempt. This leaves the capability of iteratively evolving a solution (e.g., knowing which part to mutate and how, deciding when to backtrack) entirely in the scaffold rather than in the model itself. Whether the model itself could acquire this capability and reuse it across different tasks has been largely unexamined. To address this, we introduce Evolution Fine-Tuning (EFT), a mid-training paradigm that teaches LLMs to evolve solutions across tasks by converting evolutionary search trajectories into supervision. We construct Finch Collection, a 156K-trajectory dataset spanning 10 domains and 371 optimization tasks, and fine-tune open-source LLMs from 2B to 9B parameters. Empirically, EFT confers cross-task generalization: across 22 held-out tasks, our models surpass their base counterparts by 10.22% on average. Furthermore, when paired with test-time RL, our model matches state-of-the-art performance on two circle-packing tasks and outperforms its base-model counterpart on the Erdős minimum-overlap problem. EFT thus serves as a "practice phase" for general-purpose discovery agents that do not solve new problems from scratch.

Terrain modeling has traditionally relied on procedural techniques, which often require extensive domain expertise and handcrafted rules. In this paper, we present MESA - a novel data-centric alternative by training a diffusion model on global remote sensing data. This approach leverages large-scale geospatial information to generate high-quality terrain samples from text descriptions, showcasing a flexible and scalable solution for terrain generation. The model's capabilities are demonstrated through extensive experiments, highlighting its ability to generate realistic and diverse terrain landscapes. The dataset produced to support this work, the Major TOM Core-DEM extension dataset, is released openly as a comprehensive resource for global terrain data. The results suggest that data-driven models, trained on remote sensing data, can provide a powerful tool for realistic terrain modeling and generation.

This paper introduces RiskCards, a framework for structured assessment and documentation of risks associated with an application of language models. As with all language, text generated by language models can be harmful, or used to bring about harm. Automating language generation adds both an element of scale and also more subtle or emergent undesirable tendencies to the generated text. Prior work establishes a wide variety of language model harms to many different actors: existing taxonomies identify categories of harms posed by language models; benchmarks establish automated tests of these harms; and documentation standards for models, tasks and datasets encourage transparent reporting. However, there is no risk-centric framework for documenting the complexity of a landscape in which some risks are shared across models and contexts, while others are specific, and where certain conditions may be required for risks to manifest as harms. RiskCards address this methodological gap by providing a generic framework for assessing the use of a given language model in a given scenario. Each RiskCard makes clear the routes for the risk to manifest harm, their placement in harm taxonomies, and example prompt-output pairs. While RiskCards are designed to be open-source, dynamic and participatory, we present a "starter set" of RiskCards taken from a broad literature survey, each of which details a concrete risk presentation. Language model RiskCards initiate a community knowledge base which permits the mapping of risks and harms to a specific model or its application scenario, ultimately contributing to a better, safer and shared understanding of the risk landscape.

Instance-specific algorithm configuration and algorithm portfolios have been shown to offer significant improvements over single algorithm approaches in a variety of application domains. In the SAT and CSP domains algorithm portfolios have consistently dominated the main competitions in these fields for the past five years. For a portfolio approach to be effective there are two crucial conditions that must be met. First, there needs to be a collection of complementary solvers with which to make a portfolio. Second, there must be a collection of problem features that can accurately identify structural differences between instances. This paper focuses on the latter issue: feature representation, because, unlike SAT, not every problem has well-studied features. We employ the well-known SATzilla feature set, but compute alternative sets on different SAT encodings of CSPs. We show that regardless of what encoding is used to convert the instances, adequate structural information is maintained to differentiate between problem instances, and that this can be exploited to make an effective portfolio-based CSP solver.

Frontier model developers aim to train models continually to possess emergent, diverse capabilities. To extend capabilities, the current pre-training and post-training paradigm requires manually starting training runs with static datasets or reward functions every time. Addressing this limitation, our work pursues the insight that open-endedness (via the coevolution of models and tasks) can discover models with increasingly novel skills in a single run. We introduce a new model development framework that extends coevolution to large language model (LLM) discovery, open-ended Assessment Coevolving with Diverse Capabilities (AC/DC). AC/DC evolves both LLMs via model merging and natural language tasks via synthetic data generation. AC/DC discovers growing archives of LLMs that surpass the capabilities of larger LLMs while taking up less GPU memory. In particular, our LLM populations achieve a broader Coverage of expertise than other curated models or baselines on downstream benchmarks, without any explicit benchmark optimization. Furthermore, AC/DC improves Coverage over time, continually innovates on tasks and models, and improves performance in multi-agent best-of-N selection. Our findings highlight the potential of coevolution as a means of discovering broader sets of capabilities from base LLMs. Overall, AC/DC brings us one step closer to a profoundly new paradigm of LLM development, where continual improvements to the diversity of model capabilities can be accelerated by leveraging existing models as stepping stones to increasingly powerful models.

Seed science is essential for modern agriculture, directly influencing crop yields and global food security. However, challenges such as interdisciplinary complexity and high costs with limited returns hinder progress, leading to a shortage of experts and insufficient technological support. While large language models (LLMs) have shown promise across various fields, their application in seed science remains limited due to the scarcity of digital resources, complex gene-trait relationships, and the lack of standardized benchmarks. To address this gap, we introduce SeedBench -- the first multi-task benchmark specifically designed for seed science. Developed in collaboration with domain experts, SeedBench focuses on seed breeding and simulates key aspects of modern breeding processes. We conduct a comprehensive evaluation of 26 leading LLMs, encompassing proprietary, open-source, and domain-specific fine-tuned models. Our findings not only highlight the substantial gaps between the power of LLMs and the real-world seed science problems, but also make a foundational step for research on LLMs for seed design.

We introduce Equilibrium Matching (EqM), a generative modeling framework built from an equilibrium dynamics perspective. EqM discards the non-equilibrium, time-conditional dynamics in traditional diffusion and flow-based generative models and instead learns the equilibrium gradient of an implicit energy landscape. Through this approach, we can adopt an optimization-based sampling process at inference time, where samples are obtained by gradient descent on the learned landscape with adjustable step sizes, adaptive optimizers, and adaptive compute. EqM surpasses the generation performance of diffusion/flow models empirically, achieving an FID of 1.90 on ImageNet 256times256. EqM is also theoretically justified to learn and sample from the data manifold. Beyond generation, EqM is a flexible framework that naturally handles tasks including partially noised image denoising, OOD detection, and image composition. By replacing time-conditional velocities with a unified equilibrium landscape, EqM offers a tighter bridge between flow and energy-based models and a simple route to optimization-driven inference.

Environments serve as interactive systems for large language model (LLM) based agents across diverse scenarios and play a crucial role in driving the continual evolution of model capabilities. Despite this importance, existing work lacks a systematic categorization and deep analysis. This paper systematically studies current researches on agentic environments from the perspective of the environment engineering lifecycle, covering their modeling, synthesis, evaluation and application. Specifically, the paper first introduces representative environments from the perspectives of eight attributes and eight domains, providing detailed analyses of their development paths and highlighting their core capabilities. Second, for automated environment synthesis, two paradigms are introduced, such as symbolic synthesis and neural synthesis. This paper also shows different environment evaluation methods in each paradigm. Thirdly, the corresponding environment applications from the perspective of agent-environment co-evolution are discussed. In specific, the paper characterizes the primary pathways for agent evolution in dynamic environments from four complementary perspectives: memory-centric experience evolution, orchestration-centric workflow evolution, trajectory-centric offline evolution, and exploration-centric online evolution. And three paradigms of environment evolution are identified, namely neural-driven, difficulty-driven, and scaling-driven approaches. At last, several promising future directions are discussed, including Environment-as-a-Service, Multi-agent Environments, and Neural-Symbolic Environments.

Foundation models (FMs), such as GPT-4 and AlphaFold, are reshaping the landscape of scientific research. Beyond accelerating tasks such as hypothesis generation, experimental design, and result interpretation, they prompt a more fundamental question: Are FMs merely enhancing existing scientific methodologies, or are they redefining the way science is conducted? In this paper, we argue that FMs are catalyzing a transition toward a new scientific paradigm. We introduce a three-stage framework to describe this evolution: (1) Meta-Scientific Integration, where FMs enhance workflows within traditional paradigms; (2) Hybrid Human-AI Co-Creation, where FMs become active collaborators in problem formulation, reasoning, and discovery; and (3) Autonomous Scientific Discovery, where FMs operate as independent agents capable of generating new scientific knowledge with minimal human intervention. Through this lens, we review current applications and emerging capabilities of FMs across existing scientific paradigms. We further identify risks and future directions for FM-enabled scientific discovery. This position paper aims to support the scientific community in understanding the transformative role of FMs and to foster reflection on the future of scientific discovery. Our project is available at https://github.com/usail-hkust/Awesome-Foundation-Models-for-Scientific-Discovery.

Designing biological sequences is an important challenge that requires satisfying complex constraints and thus is a natural problem to address with deep generative modeling. Diffusion generative models have achieved considerable success in many applications. Score-based generative stochastic differential equations (SDE) model is a continuous-time diffusion model framework that enjoys many benefits, but the originally proposed SDEs are not naturally designed for modeling discrete data. To develop generative SDE models for discrete data such as biological sequences, here we introduce a diffusion process defined in the probability simplex space with stationary distribution being the Dirichlet distribution. This makes diffusion in continuous space natural for modeling discrete data. We refer to this approach as Dirchlet diffusion score model. We demonstrate that this technique can generate samples that satisfy hard constraints using a Sudoku generation task. This generative model can also solve Sudoku, including hard puzzles, without additional training. Finally, we applied this approach to develop the first human promoter DNA sequence design model and showed that designed sequences share similar properties with natural promoter sequences.

In this paper, we study the content-aware layout generation problem, which aims to automatically generate layouts that are harmonious with a given background image. Existing methods usually deal with this task with a single-step reasoning framework. The lack of a feedback-based self-correction mechanism leads to their failure rates significantly increasing when faced with complex element layout planning. To address this challenge, we introduce SEGA, a novel Stepwise Evolution Paradigm for Content-Aware Layout Generation. Inspired by the systematic mode of human thinking, SEGA employs a hierarchical reasoning framework with a coarse-to-fine strategy: first, a coarse-level module roughly estimates the layout planning results; then, another refining module performs fine-level reasoning regarding the coarse planning results. Furthermore, we incorporate layout design principles as prior knowledge into the model to enhance its layout planning ability. Besides, we present GenPoster-100K that is a new large-scale poster dataset with rich meta-information annotation. The experiments demonstrate the effectiveness of our approach by achieving the state-of-the-art results on multiple benchmark datasets. Our project page is at: https://brucew91.github.io/SEGA.github.io/

The rapid progress of frontier large language models has led to widespread benchmark saturation, limiting the ability of existing datasets to differentiate model capabilities or provide useful training signal. For instance, on LiveCodeBench, frontier models achieve over 99% Pass@1 on easy splits and exceed 90% Pass@1 on average across difficulty levels. Constructing new, challenging datasets typically requires substantial human effort, creating a bottleneck for progress. We introduce BenchEvolver, a solution-centric evolutionary framework that automatically transforms existing coding problems into harder variants. Rather than generating problems from scratch, BenchEvolver evolves reference solutions through structured transformations and derives corresponding statements and tests from the evolved solutions. This design grounds generation in executable semantics, enabling scalable construction of high-quality, diverse, and difficult tasks with verifiable correctness. Applying BenchEvolver to LiveCodeBench and SciCode, we obtain evolved tasks that are substantially harder while maintaining validity, reference correctness, and diversity. We further curate LiveCodeBench-Plus, a 91-problem benchmark combining evolved and difficult original LCB-v6 tasks, where frontier-model Pass@1 ranges from 27.5% to 62.6%, restoring clear discrimination among strong coding models. Importantly, evolved tasks remain challenging even for the model that generates them, enabling self-improvement. We further show that RL on evolved LCB tasks improves held-out coding performance: for gpt-oss-20b, seed+evolved training achieves +8.7 and +8.3 Pass@1 gains on LCB v6 Hard and LCB-Pro Easy, exceeding seed-only gains by 70.7% and 34.8%, respectively. Our results show that BenchEvolver can convert saturated benchmarks into frontier-level evaluation suites and reusable training signal.

Data Darwinism (Part I) established a ten-level hierarchy for data processing, showing that stronger processing can unlock greater data value. However, that work relied on manually designed strategies for a single category. Modern pretraining corpora comprise hundreds of heterogeneous categories spanning domains and content types, each demanding specialized treatment. At this scale, manual strategy design becomes prohibitive. This raises a key question: can strategies evolve in an automated way? We introduce DataEvolve, a framework that enables strategies to evolve through iterative optimization rather than manual design. For each data category, DataEvolve operates in a closed evolutionary loop: it identifies quality issues, generates candidate strategies, executes them on sampled data, evaluates results, and refines approaches across generations. The process accumulates knowledge through an experience pool of discovered issues and a strategy pool tracking performance across iterations. Applied to 8 categories spanning 672B tokens from Nemotron-CC, DataEvolve produces Darwin-CC, a 504B-token dataset with strategies evolved through 30 iterations per category. Training 3B models on 500B tokens, Darwin-CC outperforms raw data (+3.96 points) and achieves a 44.13 average score across 18 benchmarks, surpassing DCLM, Ultra-FineWeb, and FineWeb-Edu, with strong gains on knowledge-intensive tasks such as MMLU. Analysis shows evolved strategies converge on cleaning-focused approaches: targeted noise removal and format normalization with domain-aware preservation, echoing the L4 (Generative Refinement) principles from Part I. Ablation studies confirm iterative evolution is essential: optimized strategies outperform suboptimal ones by 2.93 points, establishing evolutionary strategy design as feasible and necessary for pretraining-scale data curation.

Solving complex real-world tasks requires cycles of actions and observations. This is particularly true in science, where tasks require many cycles of analysis, tool use, and experimentation. Language agents are promising for automating intellectual tasks in science because they can interact with tools via natural language or code. Yet their flexibility creates conceptual and practical challenges for software implementations, since agents may comprise non-standard components such as internal reasoning, planning, tool usage, as well as the inherent stochasticity of temperature-sampled language models. Here, we introduce Aviary, an extensible gymnasium for language agents. We formalize agents as policies solving language-grounded partially observable Markov decision processes, which we term language decision processes. We then implement five environments, including three challenging scientific environments: (1) manipulating DNA constructs for molecular cloning, (2) answering research questions by accessing scientific literature, and (3) engineering protein stability. These environments were selected for their focus on multi-step reasoning and their relevance to contemporary biology research. Finally, with online training and scaling inference-time compute, we show that language agents backed by open-source, non-frontier LLMs can match and exceed both frontier LLM agents and human experts on multiple tasks at up to 100x lower inference cost.

Large Language Models (LLMs) have demonstrated strong capabilities but remain fundamentally static, unable to adapt their internal parameters to novel tasks, evolving knowledge domains, or dynamic interaction contexts. As LLMs are increasingly deployed in open-ended, interactive environments, this static nature has become a critical bottleneck, necessitating agents that can adaptively reason, act, and evolve in real time. This paradigm shift -- from scaling static models to developing self-evolving agents -- has sparked growing interest in architectures and methods enabling continual learning and adaptation from data, interactions, and experiences. This survey provides the first systematic and comprehensive review of self-evolving agents, organized around three foundational dimensions -- what to evolve, when to evolve, and how to evolve. We examine evolutionary mechanisms across agent components (e.g., models, memory, tools, architecture), categorize adaptation methods by stages (e.g., intra-test-time, inter-test-time), and analyze the algorithmic and architectural designs that guide evolutionary adaptation (e.g., scalar rewards, textual feedback, single-agent and multi-agent systems). Additionally, we analyze evaluation metrics and benchmarks tailored for self-evolving agents, highlight applications in domains such as coding, education, and healthcare, and identify critical challenges and research directions in safety, scalability, and co-evolutionary dynamics. By providing a structured framework for understanding and designing self-evolving agents, this survey establishes a roadmap for advancing adaptive agentic systems in both research and real-world deployments, ultimately shedding lights to pave the way for the realization of Artificial Super Intelligence (ASI), where agents evolve autonomously, performing at or beyond human-level intelligence across a wide array of tasks.

We introduce the STATION, an open-world multi-agent environment that models a miniature scientific ecosystem. Leveraging their extended context windows, agents in the Station can engage in long scientific journeys that include reading papers from peers, formulating hypotheses, submitting code, performing analyses, and publishing results. Importantly, there is no centralized system coordinating their activities - agents are free to choose their own actions and develop their own narratives within the Station. Experiments demonstrate that AI agents in the Station achieve new state-of-the-art performance on a wide range of benchmarks, spanning from mathematics to computational biology to machine learning, notably surpassing AlphaEvolve in circle packing. A rich tapestry of narratives emerges as agents pursue independent research, interact with peers, and build upon a cumulative history. From these emergent narratives, novel methods arise organically, such as a new density-adaptive algorithm for scRNA-seq batch integration. The Station marks a first step towards autonomous scientific discovery driven by emergent behavior in an open-world environment, representing a new paradigm that moves beyond rigid optimization.

The presence of linear paths in parameter space between two different network solutions in certain cases, i.e., linear mode connectivity (LMC), has garnered interest from both theoretical and practical fronts. There has been significant research that either practically designs algorithms catered for connecting networks by adjusting for the permutation symmetries as well as some others that more theoretically construct paths through which networks can be connected. Yet, the core reasons for the occurrence of LMC, when in fact it does occur, in the highly non-convex loss landscapes of neural networks are far from clear. In this work, we take a step towards understanding it by providing a model of how the loss landscape needs to behave topographically for LMC (or the lack thereof) to manifest. Concretely, we present a `mountainside and ridge' perspective that helps to neatly tie together different geometric features that can be spotted in the loss landscape along the training runs. We also complement this perspective by providing a theoretical analysis of the barrier height, for which we provide empirical support, and which additionally extends as a faithful predictor of layer-wise LMC. We close with a toy example that provides further intuition on how barriers arise in the first place, all in all, showcasing the larger aim of the work -- to provide a working model of the landscape and its topography for the occurrence of LMC.

Large language model (LLM) agents have achieved strong performance on a wide range of benchmarks, yet most evaluations assume static environments. In contrast, real-world deployment is inherently dynamic, requiring agents to continually align their knowledge, skills, and behavior with changing environments and updated task conditions. To address this gap, we introduce EvoArena, a benchmark suite that models environment changes as sequences of progressive updates across terminal, software, and social domains. We further propose EvoMem, a patch-based memory paradigm that records memory evolution as structured update histories, enabling agents to reason about environmental evolution through changes in their memory. Experiments show that current agents struggle on EvoArena, achieving an average accuracy of 39.6% across evolving terminal, software, and social-preference domains. EvoMem consistently improves performance, yielding an average gain of 1.5% on EvoArena and also improving standard benchmarks such as GAIA and LoCoMo by 6.1% and 4.8%. Beyond individual tasks, EvoMem further improves chain-level accuracy by 3.7% on EvoArena, where success requires completing a consecutive sequence of related evolutionary subtasks. Mechanistic analysis shows that EvoMem improves evidence capture in the memory, indicating better preservation of complete evolving environment states. Our results highlight the importance of modeling evolution in both evaluation and memory for reliable agent deployment.

While deep learning has revolutionized the prediction of rigid protein structures, modelling the conformational ensembles of Intrinsically Disordered Proteins (IDPs) remains a key frontier. Current AI paradigms present a trade-off: Protein Language Models (PLMs) capture evolutionary statistics but lack explicit physical grounding, while generative models trained to model full ensembles are computationally expensive. In this work we critically assess these limits and propose a path forward. We introduce GeoGraph, a simulation-informed surrogate trained to predict ensemble-averaged statistics of residue-residue contact-map topology directly from sequence. By featurizing coarse-grained molecular dynamics simulations into residue- and sequence-level graph descriptors, we create a robust and information-rich learning target. Our evaluation demonstrates that this approach yields representations that are more predictive of key biophysical properties than existing methods.

We study the properties of common loss surfaces through their Hessian matrix. In particular, in the context of deep learning, we empirically show that the spectrum of the Hessian is composed of two parts: (1) the bulk centered near zero, (2) and outliers away from the bulk. We present numerical evidence and mathematical justifications to the following conjectures laid out by Sagun et al. (2016): Fixing data, increasing the number of parameters merely scales the bulk of the spectrum; fixing the dimension and changing the data (for instance adding more clusters or making the data less separable) only affects the outliers. We believe that our observations have striking implications for non-convex optimization in high dimensions. First, the flatness of such landscapes (which can be measured by the singularity of the Hessian) implies that classical notions of basins of attraction may be quite misleading. And that the discussion of wide/narrow basins may be in need of a new perspective around over-parametrization and redundancy that are able to create large connected components at the bottom of the landscape. Second, the dependence of small number of large eigenvalues to the data distribution can be linked to the spectrum of the covariance matrix of gradients of model outputs. With this in mind, we may reevaluate the connections within the data-architecture-algorithm framework of a model, hoping that it would shed light into the geometry of high-dimensional and non-convex spaces in modern applications. In particular, we present a case that links the two observations: small and large batch gradient descent appear to converge to different basins of attraction but we show that they are in fact connected through their flat region and so belong to the same basin.

Scientific archives now contain hundreds of petabytes of data across genomics, ecology, climate, and molecular biology that could reveal undiscovered patterns if systematically analyzed at scale. Large-scale, weakly-supervised datasets in language and vision have driven the development of foundation models whose internal representations encode structure (patterns, co-occurrences and statistical regularities) beyond their training objectives. Most existing methods extract structure only for pre-specified targets; they excel at confirmation but do not support open-ended discovery of unknown patterns. We ask whether sparse autoencoders (SAEs) can enable open-ended feature discovery from foundation model representations. We evaluate this question in controlled rediscovery studies, where the learned SAE features are tested for alignment with semantic concepts on a standard segmentation benchmark and compared against strong label-free alternatives on concept-alignment metrics. Applied to ecological imagery, the same procedure surfaces fine-grained anatomical structure without access to segmentation or part labels, providing a scientific case study with ground-truth validation. While our experiments focus on vision with an ecology case study, the method is domain-agnostic and applicable to models in other sciences (e.g., proteins, genomics, weather). Our results indicate that sparse decomposition provides a practical instrument for exploring what scientific foundation models have learned, an important prerequisite for moving from confirmation to genuine discovery.

Foundation models have revolutionized general-purpose problem-solving, offering rapid task adaptation through pretraining, meta-training, and finetuning. Recent crucial advances in these paradigms reveal the importance of challenging task prioritized sampling to enhance adaptation robustness under distribution shifts. However, ranking task difficulties over iteration as a preliminary step typically requires exhaustive task evaluation, which is practically unaffordable in computation and data-annotation. This study provides a novel perspective to illuminate the possibility of leveraging the dual importance of adaptation robustness and learning efficiency, particularly in scenarios where task evaluation is risky or costly, such as iterative agent-environment interactions for robotic policy evaluation or computationally intensive inference steps for finetuning foundation models. Firstly, we introduce Model Predictive Task Sampling (MPTS), a framework that bridges the task space and adaptation risk landscape, providing a theoretical foundation for robust active task sampling. MPTS employs a generative model to characterize the episodic optimization process and predicts task-specific adaptation risk via posterior inference. The resulting risk learner amortizes the costly evaluation of task adaptation performance and provably approximates task difficulty rankings. MPTS seamlessly integrates into zero-shot, few-shot, and supervised finetuning settings. Empirically, we conduct extensive experiments in pattern recognition using foundation models and sequential decision-making. Our results demonstrate that MPTS significantly enhances adaptation robustness for tail or out-of-distribution (OOD) tasks and improves learning efficiency compared to state-of-the-art (SOTA) methods. The code is available at the project site https://github.com/thu-rllab/MPTS.

We introduce NatureBench, a cross-discipline benchmark of 90 tasks distilled from peer-reviewed Nature-family publications, designed to evaluate whether AI coding agents can move beyond reproduction toward discovery on real scientific problems. NatureBench is built on NatureGym, an automated pipeline that constructs a standardized, per-task containerized environment from a source paper, addressing the environment-fragmentation problem that has limited the credibility of prior agent-on-research benchmarks. Evaluating ten frontier agent configurations under a strict web-search-disabled protocol, we find that the strongest model surpasses SOTA on only 17.8% of tasks under the g>0.1 criterion. Analysis of method pathways reveals that agents succeed primarily through methodological translation, converting scientific tasks into familiar supervised prediction problems, rather than through genuine scientific invention. Failures are dominated by wrong method choice and insufficient compute budget, not by task misunderstanding. We release the benchmark, the NatureGym pipeline, and a public leaderboard with maintainer-side reproduction. Code: https://github.com/FrontisAI/NatureBench

Long-horizon LLM agents leave traces that could become reusable experience, but raw trajectories are noisy and hard to govern. We treat Agent Skills as an experience schema that couples executable scripts, with non-executable guidance on procedures. Yet open skill ecosystems contain redundant, uneven, environment-sensitive artifacts, and indiscriminate updates can pollute future context. We present SkillsVote, a lifecycle-governance framework for Agent Skills from collection and recommendation to evolution. SkillsVote profiles a million-scale open-source corpus for environment requirements, quality, and verifiability, then synthesizes tasks for verifiable skills. Before execution, SkillsVote performs agentic library search over structured skill library to expose instructional skill context. After execution, it decomposes trajectories into skill-linked subtasks, attributes outcomes to skill use, agent exploration, environment, and result signals, and admits only successful reusable discoveries to evidence-gated updates. In our evaluation, offline evolution improves GPT-5.2 on Terminal-Bench 2.0 by up to 7.9 pp, while online evolution improves SWE-Bench Pro by up to 2.6 pp. Overall, governed external skill libraries can improve frozen agents without model updates when systems control exposure, credit, and preservation.

Protein language models (PLMs) face a fundamental divide: masked language models (MLMs) excel at fitness prediction while causal models enable generation, forcing practitioners to maintain separate architectures. We introduce Proust, a 309M-parameter causal PLM that bridges this gap through architectural innovations adapted from recent LLM research, including grouped-query attention with shared K/V projections, cross-layer value residuals, and depthwise causal convolutions. Trained on 33B tokens in 40 B200 GPU-hours, Proust achieves Spearman ρ= 0.390 on ProteinGym substitutions, competitive with MLMs requiring 50--200times the compute. On indels, Proust sets a new state-of-the-art, outperforming models up to 20times larger. On EVEREST viral fitness benchmarks, it approaches structure-aware methods using sequence alone. These powerful representations position Proust in a sweet spot as it also retains native generative capabilities that MLMs lack by design. Interpretability analysis reveals that per-position entropy variance predicts, to an extent, when retrieval augmentation helps and hurts. Such insights can grow in both quantity and quality at scale and inform capabilities such as test-time scaling. Code and weights are available at https://github.com/Furkan9015/proust-inference

Both the design and control of a robot play equally important roles in its task performance. However, while optimal control is well studied in the machine learning and robotics community, less attention is placed on finding the optimal robot design. This is mainly because co-optimizing design and control in robotics is characterized as a challenging problem, and more importantly, a comprehensive evaluation benchmark for co-optimization does not exist. In this paper, we propose Evolution Gym, the first large-scale benchmark for co-optimizing the design and control of soft robots. In our benchmark, each robot is composed of different types of voxels (e.g., soft, rigid, actuators), resulting in a modular and expressive robot design space. Our benchmark environments span a wide range of tasks, including locomotion on various types of terrains and manipulation. Furthermore, we develop several robot co-evolution algorithms by combining state-of-the-art design optimization methods and deep reinforcement learning techniques. Evaluating the algorithms on our benchmark platform, we observe robots exhibiting increasingly complex behaviors as evolution progresses, with the best evolved designs solving many of our proposed tasks. Additionally, even though robot designs are evolved autonomously from scratch without prior knowledge, they often grow to resemble existing natural creatures while outperforming hand-designed robots. Nevertheless, all tested algorithms fail to find robots that succeed in our hardest environments. This suggests that more advanced algorithms are required to explore the high-dimensional design space and evolve increasingly intelligent robots -- an area of research in which we hope Evolution Gym will accelerate progress. Our website with code, environments, documentation, and tutorials is available at http://evogym.csail.mit.edu.

Biomolecular generators are often adapted with reward feedback to improve task-specific utility, but pushing utility alone can concentrate generation on a narrow family of candidates. Maintaining diversity is difficult because sample diversity is a set-level property. We introduce Supergroup Relative Policy Optimization (SGRPO), a flexible GRPO-style framework that directly constructs rewards from set-level diversity. For each condition, SGRPO samples a supergroup of candidate sets, compares their diversity under the same condition, and redistributes the group diversity reward to individual rollouts through leave-one-out diversity contributions before combining it with rollout-level utility. This design decouples SGRPO from a particular generator, utility reward, or diversity metric, and allows instantiation with different GRPO-style approaches. We evaluate SGRPO on de novo small-molecule design, pocket-based small-molecule design, and de novo protein design, instantiating it with both GRPO and Coupled-GRPO across autoregressive and discrete diffusion generators. Across decoding sweeps, SGRPO expands the utility-diversity Pareto frontier and achieves the best frontier-level metrics relative to pretrained generators, GRPO, and memory-assisted GRPO when applicable. Our analyses further show that direct set-level diversity rewards remain effective with small groups and help preserve broader generation-distribution coverage during post-training. The code is available at https://github.com/IDEA-XL/SGRPO.

Large Language Models (LLMs) have emerged as powerful operators for evolutionary search, yet the design of efficient search scaffolds remains ad hoc. While promising, current LLM-in-the-loop systems lack a systematic approach to managing the evolutionary process. We identify three distinct failure modes: Context Pollution, where experiment history biases future candidate generation; Mode Collapse, where agents stagnate in local minima due to poor exploration-exploitation balance; and Weak Collaboration, where rigid crossover strategies fail to leverage parallel search trajectories effectively. We introduce Progress-Aware Consistent Evolution (PACEvolve), a framework designed to robustly govern the agent's context and search dynamics, to address these challenges. PACEvolve combines hierarchical context management (HCM) with pruning to address context pollution; momentum-based backtracking (MBB) to escape local minima; and a self-adaptive sampling policy that unifies backtracking and crossover for dynamic search coordination (CE), allowing agents to balance internal refinement with cross-trajectory collaboration. We demonstrate that PACEvolve provides a systematic path to consistent, long-horizon self-improvement, achieving state-of-the-art results on LLM-SR and KernelBench, while discovering solutions surpassing the record on Modded NanoGPT.

In this work, we introduce CodeEvolve, an open-source evolutionary coding agent that unites Large Language Models (LLMs) with genetic algorithms to solve complex computational problems. Our framework adapts powerful evolutionary concepts to the LLM domain, building upon recent methods for generalized scientific discovery. CodeEvolve employs an island-based genetic algorithm to maintain population diversity and increase throughput, introduces a novel inspiration-based crossover mechanism that leverages the LLMs context window to combine features from successful solutions, and implements meta-prompting strategies for dynamic exploration of the solution space. We conduct a rigorous evaluation of CodeEvolve on a subset of the mathematical benchmarks used to evaluate Google DeepMind's closed-source AlphaEvolve. Our findings show that our method surpasses AlphaEvolve's performance on several challenging problems. To foster collaboration and accelerate progress, we release our complete framework as an open-source repository.

The discovery of extremal structures in mathematics requires navigating vast and nonconvex landscapes where analytical methods offer little guidance and brute-force search becomes intractable. We introduce FlowBoost, a closed-loop generative framework that learns to discover rare and extremal geometric structures by combining three components: (i) a geometry-aware conditional flow-matching model that learns to sample high-quality configurations, (ii) reward-guided policy optimization with action exploration that directly optimizes the generation process toward the objective while maintaining diversity, and (iii) stochastic local search for both training-data generation and final refinement. Unlike prior open-loop approaches, such as PatternBoost that retrains on filtered discrete samples, or AlphaEvolve which relies on frozen Large Language Models (LLMs) as evolutionary mutation operators, FlowBoost enforces geometric feasibility during sampling, and propagates reward signal directly into the generative model, closing the optimization loop and requiring much smaller training sets and shorter training times, and reducing the required outer-loop iterations by orders of magnitude, while eliminating dependence on LLMs. We demonstrate the framework on four geometric optimization problems: sphere packing in hypercubes, circle packing maximizing sum of radii, the Heilbronn triangle problem, and star discrepancy minimization. In several cases, FlowBoost discovers configurations that match or exceed the best known results. For circle packings, we improve the best known lower bounds, surpassing the LLM-based system AlphaEvolve while using substantially fewer computational resources.

We explore the use of Evolution Strategies (ES), a class of black box optimization algorithms, as an alternative to popular MDP-based RL techniques such as Q-learning and Policy Gradients. Experiments on MuJoCo and Atari show that ES is a viable solution strategy that scales extremely well with the number of CPUs available: By using a novel communication strategy based on common random numbers, our ES implementation only needs to communicate scalars, making it possible to scale to over a thousand parallel workers. This allows us to solve 3D humanoid walking in 10 minutes and obtain competitive results on most Atari games after one hour of training. In addition, we highlight several advantages of ES as a black box optimization technique: it is invariant to action frequency and delayed rewards, tolerant of extremely long horizons, and does not need temporal discounting or value function approximation.

We compare the (1,lambda)-EA and the (1 + lambda)-EA on the recently introduced benchmark DisOM, which is the OneMax function with randomly planted local optima. Previous work showed that if all local optima have the same relative height, then the plus strategy never loses more than a factor O(nlog n) compared to the comma strategy. Here we show that even small random fluctuations in the heights of the local optima have a devastating effect for the plus strategy and lead to super-polynomial runtimes. On the other hand, due to their ability to escape local optima, comma strategies are unaffected by the height of the local optima and remain efficient. Our results hold for a broad class of possible distortions and show that the plus strategy, but not the comma strategy, is generally deceived by sparse unstructured fluctuations of a smooth landscape.

Game balancing is a longstanding challenge requiring repeated playtesting, expert intuition, and extensive manual tuning. We introduce RuleSmith, the first framework that achieves automated game balancing by leveraging the reasoning capabilities of multi-agent LLMs. It couples a game engine, multi-agent LLMs self-play, and Bayesian optimization operating over a multi-dimensional rule space. As a proof of concept, we instantiate RuleSmith on CivMini, a simplified civilization-style game containing heterogeneous factions, economy systems, production rules, and combat mechanics, all governed by tunable parameters. LLM agents interpret textual rulebooks and game states to generate actions, to conduct fast evaluation of balance metrics such as win-rate disparities. To search the parameter landscape efficiently, we integrate Bayesian optimization with acquisition-based adaptive sampling and discrete projection: promising candidates receive more evaluation games for accurate assessment, while exploratory candidates receive fewer games for efficient exploration. Experiments show that RuleSmith converges to highly balanced configurations and provides interpretable rule adjustments that can be directly applied to downstream game systems. Our results illustrate that LLM simulation can serve as a powerful surrogate for automating design and balancing in complex multi-agent environments.

Protein design with desirable properties has been a significant challenge for many decades. Generative artificial intelligence is a promising approach and has achieved great success in various protein generation tasks. Notably, diffusion models stand out for their robust mathematical foundations and impressive generative capabilities, offering unique advantages in certain applications such as protein design. In this review, we first give the definition and characteristics of diffusion models and then focus on two strategies: Denoising Diffusion Probabilistic Models and Score-based Generative Models, where DDPM is the discrete form of SGM. Furthermore, we discuss their applications in protein design, peptide generation, drug discovery, and protein-ligand interaction. Finally, we outline the future perspectives of diffusion models to advance autonomous protein design and engineering. The E(3) group consists of all rotations, reflections, and translations in three-dimensions. The equivariance on the E(3) group can keep the physical stability of the frame of each amino acid as much as possible, and we reflect on how to keep the diffusion model E(3) equivariant for protein generation.

Automatic Prompt Optimization (APO) has emerged as a critical technique for enhancing Large Language Model (LLM) performance, yet current state-of-the-art methods typically rely on large, labeled gold-standard development sets to compute fitness scores for evolutionary or Reinforcement Learning (RL) approaches. In real-world software engineering, however, such curated datasets are rarely available during the initial cold start of agent development, where engineers instead face messy production logs and evolving failure modes. We present ROAD (Reflective Optimization via Automated Debugging), a novel framework that bypasses the need for refined datasets by treating optimization as a dynamic debugging investigation rather than a stochastic search. Unlike traditional mutation strategies, ROAD utilizes a specialized multi-agent architecture, comprising an Analyzer for root-cause analysis, an Optimizer for pattern aggregation, and a Coach for strategy integration, to convert unstructured failure logs into robust, structured Decision Tree Protocols. We evaluated ROAD across both a standardized academic benchmark and a live production Knowledge Management engine. Experimental results demonstrate that ROAD is highly sample-efficient, achieving a 5.6 percent increase in success rate (73.6 percent to 79.2 percent) and a 3.8 percent increase in search accuracy within just three automated iterations. Furthermore, on complex reasoning tasks in the retail domain, ROAD improved agent performance by approximately 19 percent relative to the baseline. These findings suggest that mimicking the human engineering loop of failure analysis and patching offers a viable, data-efficient alternative to resource-intensive RL training for deploying reliable LLM agents.

World Models have emerged as a powerful paradigm for learning compact, predictive representations of environment dynamics, enabling agents to reason, plan, and generalize beyond direct experience. Despite recent interest in World Models, most available implementations remain publication-specific, severely limiting their reusability, increasing the risk of bugs, and reducing evaluation standardization. To mitigate these issues, we introduce stable-worldmodel (SWM), a modular, tested, and documented world-model research ecosystem that provides efficient data-collection tools, standardized environments, planning algorithms, and baseline implementations. In addition, each environment in SWM enables controllable factors of variation, including visual and physical properties, to support robustness and continual learning research. Finally, we demonstrate the utility of SWM by using it to study zero-shot robustness in DINO-WM.

We introduce DrugFlow, a generative model for structure-based drug design that integrates continuous flow matching with discrete Markov bridges, demonstrating state-of-the-art performance in learning chemical, geometric, and physical aspects of three-dimensional protein-ligand data. We endow DrugFlow with an uncertainty estimate that is able to detect out-of-distribution samples. To further enhance the sampling process towards distribution regions with desirable metric values, we propose a joint preference alignment scheme applicable to both flow matching and Markov bridge frameworks. Furthermore, we extend our model to also explore the conformational landscape of the protein by jointly sampling side chain angles and molecules.

Nucleotide sequence variation can induce significant shifts in functional fitness. Recent nucleotide foundation models promise to predict such fitness effects directly from sequence, yet heterogeneous datasets and inconsistent preprocessing make it difficult to compare methods fairly across DNA and RNA families. Here we introduce NABench, a large-scale, systematic benchmark for nucleic acid fitness prediction. NABench aggregates 162 high-throughput assays and curates 2.6 million mutated sequences spanning diverse DNA and RNA families, with standardized splits and rich metadata. We show that NABench surpasses prior nucleotide fitness benchmarks in scale, diversity, and data quality. Under a unified evaluation suite, we rigorously assess 29 representative foundation models across zero-shot, few-shot prediction, transfer learning, and supervised settings. The results quantify performance heterogeneity across tasks and nucleic-acid types, demonstrating clear strengths and failure modes for different modeling choices and establishing strong, reproducible baselines. We release NABench to advance nucleic acid modeling, supporting downstream applications in RNA/DNA design, synthetic biology, and biochemistry. Our code is available at https://github.com/mrzzmrzz/NABench.

Games have been vital test beds for the rapid development of Agent-based research. Remarkable progress has been achieved in the past, but it is unclear if the findings equip for real-world problems. While pressure grows, some of the most critical ecological challenges can find mitigation and prevention solutions through technology and its applications. Most real-world domains include multi-agent scenarios and require machine-machine and human-machine collaboration. Open-source environments have not advanced and are often toy scenarios, too abstract or not suitable for multi-agent research. By mimicking real-world problems and increasing the complexity of environments, we hope to advance state-of-the-art multi-agent research and inspire researchers to work on immediate real-world problems. Here, we present HIVEX, an environment suite to benchmark multi-agent research focusing on ecological challenges. HIVEX includes the following environments: Wind Farm Control, Wildfire Resource Management, Drone-Based Reforestation, Ocean Plastic Collection, and Aerial Wildfire Suppression. We provide environments, training examples, and baselines for the main and sub-tasks. All trained models resulting from the experiments of this work are hosted on Hugging Face. We also provide a leaderboard on Hugging Face and encourage the community to submit models trained on our environment suite.

Fine-tuning pre-trained large language models (LLMs) for down-stream tasks is a critical step in the AI deployment pipeline. Reinforcement learning (RL) is arguably the most prominent fine-tuning method, contributing to the birth of many state-of-the-art LLMs. In contrast, evolution strategies (ES), which once showed comparable performance to RL on models with a few million parameters, was neglected due to the pessimistic perception of its scalability to larger models. In this work, we report the first successful attempt to scale up ES for fine-tuning the full parameters of LLMs, showing the surprising fact that ES can search efficiently over billions of parameters and outperform existing RL fine-tuning methods in multiple respects, including sample efficiency, tolerance to long-horizon rewards, robustness to different base LLMs, less tendency to reward hacking, and more stable performance across runs. It therefore serves as a basis to unlock a new direction in LLM fine-tuning beyond what current RL techniques provide. The source codes are provided at: https://github.com/VsonicV/es-fine-tuning-paper.

Recent advances in large language models have sparked growing interest in AI agents capable of solving complex, real-world tasks. However, most existing agent systems rely on manually crafted configurations that remain static after deployment, limiting their ability to adapt to dynamic and evolving environments. To this end, recent research has explored agent evolution techniques that aim to automatically enhance agent systems based on interaction data and environmental feedback. This emerging direction lays the foundation for self-evolving AI agents, which bridge the static capabilities of foundation models with the continuous adaptability required by lifelong agentic systems. In this survey, we provide a comprehensive review of existing techniques for self-evolving agentic systems. Specifically, we first introduce a unified conceptual framework that abstracts the feedback loop underlying the design of self-evolving agentic systems. The framework highlights four key components: System Inputs, Agent System, Environment, and Optimisers, serving as a foundation for understanding and comparing different strategies. Based on this framework, we systematically review a wide range of self-evolving techniques that target different components of the agent system. We also investigate domain-specific evolution strategies developed for specialised fields such as biomedicine, programming, and finance, where optimisation objectives are tightly coupled with domain constraints. In addition, we provide a dedicated discussion on the evaluation, safety, and ethical considerations for self-evolving agentic systems, which are critical to ensuring their effectiveness and reliability. This survey aims to provide researchers and practitioners with a systematic understanding of self-evolving AI agents, laying the foundation for the development of more adaptive, autonomous, and lifelong agentic systems.

Recent advances in large language models (LLMs) have enabled breakthroughs in mathematical discovery, exemplified by AlphaEvolve, a closed-source system that evolves programs to improve bounds on open problems. However, it relies on ensembles of frontier LLMs to achieve new bounds and is a pure inference system that models cannot internalize the evolving strategies. We introduce ThetaEvolve, an open-source framework that simplifies and extends AlphaEvolve to efficiently scale both in-context learning and Reinforcement Learning (RL) at test time, allowing models to continually learn from their experiences in improving open optimization problems. ThetaEvolve features a single LLM, a large program database for enhanced exploration, batch sampling for higher throughput, lazy penalties to discourage stagnant outputs, and optional reward shaping for stable training signals, etc. ThetaEvolve is the first evolving framework that enable a small open-source model, like DeepSeek-R1-0528-Qwen3-8B, to achieve new best-known bounds on open problems (circle packing and first auto-correlation inequality) mentioned in AlphaEvolve. Besides, across two models and four open tasks, we find that ThetaEvolve with RL at test-time consistently outperforms inference-only baselines, and the model indeed learns evolving capabilities, as the RL-trained checkpoints demonstrate faster progress and better final performance on both trained target task and other unseen tasks. We release our code publicly: https://github.com/ypwang61/ThetaEvolve

Communications satellite network (CSN), as an integral component of the next generation of communication systems, has the capability to offer services globally. Data transmission in this network primarily relies on two modes: inter-satellite communication and satellite-to-ground station communication. The latter directly impacts the successful reception of data by users. However, due to resource and task limitations, finding a satisfactory solution poses a significant challenge. The communication satellite-ground station network scheduling problem (CS-GSNSP) aims to optimize CSN effectiveness by devising a plan that maximizes link construction time while considering constraints associated with satellite operation modes. The large number of tasks and numerous constraints in the problem result in a time-consuming evaluation of fitness function values. To address this issue, we propose a fuzzy fitness evaluation method (FFEM) that employs fuzzy or real evaluation methods based on individual similarity degrees. Additionally, we introduce an evolutionary algorithm based on FFEM, called evolutionary algorithm based on FFEM (FFEEA), for iteratively searching high-quality network construction schemes. In FFEEA, an adaptive crossover approach is used for efficient population search. Finally, extensive experiments are conducted to demonstrate that our proposed fuzzy fitness evaluation method and other improvement strategies significantly enhance satellite network service time. The study introduces a novel approach to enhance the efficiency of solving combinatorial optimization problems, such as CS-GSNSP, by mitigating the complexity associated with fitness evaluation.

The landscape of image generation has rapidly evolved, from early GAN-based approaches to diffusion models and, most recently, to unified generative architectures that seek to bridge understanding and generation tasks. Recent advances, especially the GPT-4o, have demonstrated the feasibility of high-fidelity multimodal generation, their architectural design remains mysterious and unpublished. This prompts the question of whether image and text generation have already been successfully integrated into a unified framework for those methods. In this work, we conduct an empirical study of GPT-4o's image generation capabilities, benchmarking it against leading open-source and commercial models. Our evaluation covers four main categories, including text-to-image, image-to-image, image-to-3D, and image-to-X generation, with more than 20 tasks. Our analysis highlights the strengths and limitations of GPT-4o under various settings, and situates it within the broader evolution of generative modeling. Through this investigation, we identify promising directions for future unified generative models, emphasizing the role of architectural design and data scaling.

We propose a sparsity-aware evolutionary (SAE) framework for model merging that involves iterative pruning-merging cycles to act as a novel mutation operator. We incorporate the sparsity constraints into the score function, which steers the evolutionary process to favor more sparse models, in addition to other conventional performance scores. Interestingly, the by-product of competition for sparsity introduces an extra local attraction and interplay into the evolutionary process: if one competitor has more zero elements, the other competitor's non-zero elements will occupy those positions, even though the less sparse competitor loses to the more sparse competitor in other positions. The proposed pipeline is evaluated on a variety of large-scale LLM benchmarks. Experiments demonstrate that our approach can improve model merging reliability across multiple benchmarks, and is easy to incorporate due to its simplicity and being orthogonal to most existing approaches.

In the realm of machine learning, traditional model development and automated approaches like AutoML typically rely on layers of abstraction, such as tree-based or Cartesian genetic programming. Our study introduces "Guided Evolution" (GE), a novel framework that diverges from these methods by utilizing Large Language Models (LLMs) to directly modify code. GE leverages LLMs for a more intelligent, supervised evolutionary process, guiding mutations and crossovers. Our unique "Evolution of Thought" (EoT) technique further enhances GE by enabling LLMs to reflect on and learn from the outcomes of previous mutations. This results in a self-sustaining feedback loop that augments decision-making in model evolution. GE maintains genetic diversity, crucial for evolutionary algorithms, by leveraging LLMs' capability to generate diverse responses from expertly crafted prompts and modulate model temperature. This not only accelerates the evolution process but also injects expert like creativity and insight into the process. Our application of GE in evolving the ExquisiteNetV2 model demonstrates its efficacy: the LLM-driven GE autonomously produced variants with improved accuracy, increasing from 92.52% to 93.34%, without compromising model compactness. This underscores the potential of LLMs to accelerate the traditional model design pipeline, enabling models to autonomously evolve and enhance their own designs.

Language models must now generalize out of the box to novel environments and work inside inference-scaling search procedures, such as AlphaEvolve, that select rollouts with a variety of task-specific reward functions. Unfortunately, the standard paradigm of LLM post-training optimizes a pre-specified scalar reward, often leading current LLMs to produce low-entropy response distributions and thus to struggle at displaying the diversity that inference-time search will require. We propose Vector Policy Optimization (VPO), an RL algorithm that explicitly trains policies to anticipate diverse downstream reward functions and to produce diverse solutions. VPO exploits that rewards are often vector-valued in practice, like per-test-case correctness in code generation or, say, multiple different user personas or reward models. VPO is essentially a drop-in replacement for the GRPO advantage estimator, but it trains the LLM to output a set of solutions where individual solutions specialize to different trade-offs in the vector reward space. Across four tasks, VPO matches or beats the strongest scalar RL baselines on test-time search (e.g. pass@k and best@k), with the gap widening as the search budget grows. For evolutionary search, VPO models unlock problems that GRPO models cannot solve at all. As test-time search becomes more standardized, optimizing for diversity may need to become the default post-training objective.

Network Architecture Search and specifically Regularized Evolution is a common way to refine the structure of a deep learning model.However, little is known about how models empirically evolve over time which has design implications for designing caching policies, refining the search algorithm for particular applications, and other important use cases.In this work, we algorithmically analyze and quantitatively characterize the patterns of model evolution for a set of models from the Candle project and the Nasbench-201 search space.We show how the evolution of the model structure is influenced by the regularized evolution algorithm. We describe how evolutionary patterns appear in distributed settings and opportunities for caching and improved scheduling. Lastly, we describe the conditions that affect when particular model architectures rise and fall in popularity based on their frequency of acting as a donor in a sliding window.

Large language models (LLMs) are on the rise for accelerating scientific discovery, most recently in advanced tasks such as generating valid scientific hypotheses. Yet in many discovery settings, the goal is not to identify a single best hypothesis since validation can be noisy and expensive, and scientists benefit from a set of high-quality alternative hypotheses that hedge against downstream uncertainty for the best solutions. Nevertheless, commonly used evolutionary search recipes tend to prioritize optimization over exploration in hypothesis generation, and the resulting selection pressure during the search process leads to diversity collapse. Motivated by these limitations, we formulate hypothesis search as a sampling problem, where the objective is to efficiently produce diverse, high-quality hypotheses under a fixed validation budget. Building on this perspective, we propose \ours, an evolutionary framework inspired by the classical parallel tempering algorithm that searches hypotheses at multiple temperature levels and enables principled information exchange across temperatures to improve exploration without disrupting convergence. Across domains including molecular discovery, equation discovery, and algorithm discovery, our approach consistently improves both hypothesis quality and diversity under the same validation budget, and produces candidates that remain robust under more expensive downstream computational validations.

In this work we introduce RITA: a suite of autoregressive generative models for protein sequences, with up to 1.2 billion parameters, trained on over 280 million protein sequences belonging to the UniRef-100 database. Such generative models hold the promise of greatly accelerating protein design. We conduct the first systematic study of how capabilities evolve with model size for autoregressive transformers in the protein domain: we evaluate RITA models in next amino acid prediction, zero-shot fitness, and enzyme function prediction, showing benefits from increased scale. We release the RITA models openly, to the benefit of the research community.

The emergence of complex life on Earth is often attributed to the arms race that ensued from a huge number of organisms all competing for finite resources. We present an artificial intelligence research environment, inspired by the human game genre of MMORPGs (Massively Multiplayer Online Role-Playing Games, a.k.a. MMOs), that aims to simulate this setting in microcosm. As with MMORPGs and the real world alike, our environment is persistent and supports a large and variable number of agents. Our environment is well suited to the study of large-scale multiagent interaction: it requires that agents learn robust combat and navigation policies in the presence of large populations attempting to do the same. Baseline experiments reveal that population size magnifies and incentivizes the development of skillful behaviors and results in agents that outcompete agents trained in smaller populations. We further show that the policies of agents with unshared weights naturally diverge to fill different niches in order to avoid competition.

In this paper, we propose a generic optimization approach for challenging objective functions that finds applications in various statistical problems. We focus on objective functions with two parameter blocks of one amenable to analytic optimization, and another that is irregular or computationally expensive. To address this setting, we propose the Voronoi-Elitism Genetic Algorithm (VEGA), a derivative-free optimization method that embeds geometric information into genetic search. The proposed algorithm retains elite candidates and constructs Voronoi-based neighborhoods around them, whose crossover and self-adaptive mutation balance exploitation of promising solutions with exploration of under-covered regions. We study the high dimensional behavior of genetic search by analyzing distance concentration, and the effects of population size and shrinking mutation, which shows that the algorithm improves spatial coverage and yields sharper distance bounds under limited computational budgets. Simulation studies are conducted to compare VEGA with two genetic-type algorithms competitors in finite samples. A real data application on Stack Exchange activity data further illustrates its ability to identify stable structural changes, implying the algorithm is computationally flexible for high-dimensional, derivative-free optimization and applicable for various statistical problems.

Any optimization algorithm programming interface can be seen as a black-box function with additional free parameters. In this spirit, simulated annealing (SA) can be implemented in pseudo-code within the dimensions of a single slide with free parameters relating to the annealing schedule. Such an implementation, however, necessarily neglects much of the structure necessary to take advantage of advances in computing resources and algorithmic breakthroughs. Simulated annealing is often introduced in myriad disciplines, from discrete examples like the Traveling Salesman Problem (TSP) to molecular cluster potential energy exploration or even explorations of a protein's configurational space. Theoretical guarantees also demand a stricter structure in terms of statistical quantities, which cannot simply be left to the user. We will introduce several standard paradigms and demonstrate how these can be "lifted" into a unified framework using object-oriented programming in Python. We demonstrate how clean, interoperable, reproducible programming libraries can be used to access and rapidly iterate on variants of Simulated Annealing in a manner which can be extended to serve as a best practices blueprint or design pattern for a data-driven optimization library.