Daily Papers

We propose PROSE-FD, a zero-shot multimodal PDE foundational model for simultaneous prediction of heterogeneous two-dimensional physical systems related to distinct fluid dynamics settings. These systems include shallow water equations and the Navier-Stokes equations with incompressible and compressible flow, regular and complex geometries, and different buoyancy settings. This work presents a new transformer-based multi-operator learning approach that fuses symbolic information to perform operator-based data prediction, i.e. non-autoregressive. By incorporating multiple modalities in the inputs, the PDE foundation model builds in a pathway for including mathematical descriptions of the physical behavior. We pre-train our foundation model on 6 parametric families of equations collected from 13 datasets, including over 60K trajectories. Our model outperforms popular operator learning, computer vision, and multi-physics models, in benchmark forward prediction tasks. We test our architecture choices with ablation studies.

Generative AI and large language models hold great promise in enhancing programming education by automatically generating individualized feedback for students. We investigate the role of generative AI models in providing human tutor-style programming hints to help students resolve errors in their buggy programs. Recent works have benchmarked state-of-the-art models for various feedback generation scenarios; however, their overall quality is still inferior to human tutors and not yet ready for real-world deployment. In this paper, we seek to push the limits of generative AI models toward providing high-quality programming hints and develop a novel technique, GPT4Hints-GPT3.5Val. As a first step, our technique leverages GPT-4 as a ``tutor'' model to generate hints -- it boosts the generative quality by using symbolic information of failing test cases and fixes in prompts. As a next step, our technique leverages GPT-3.5, a weaker model, as a ``student'' model to further validate the hint quality -- it performs an automatic quality validation by simulating the potential utility of providing this feedback. We show the efficacy of our technique via extensive evaluation using three real-world datasets of Python programs covering a variety of concepts ranging from basic algorithms to regular expressions and data analysis using pandas library.

Few-shot prompting is a surprisingly powerful way to use Large Language Models (LLMs) to solve various tasks. However, this approach struggles as the task complexity increases or when the individual reasoning steps of the task themselves are hard to learn, especially when embedded in more complex tasks. To address this, we propose Decomposed Prompting, a new approach to solve complex tasks by decomposing them (via prompting) into simpler sub-tasks that can be delegated to a library of prompting-based LLMs dedicated to these sub-tasks. This modular structure allows each prompt to be optimized for its specific sub-task, further decomposed if necessary, and even easily replaced with more effective prompts, trained models, or symbolic functions if desired. We show that the flexibility and modularity of Decomposed Prompting allows it to outperform prior work on few-shot prompting using GPT3. On symbolic reasoning tasks, we can further decompose sub-tasks that are hard for LLMs into even simpler solvable sub-tasks. When the complexity comes from the input length, we can recursively decompose the task into the same task but with smaller inputs. We also evaluate our approach on textual multi-step reasoning tasks: on long-context multi-hop QA task, we can more effectively teach the sub-tasks via our separate sub-tasks prompts; and on open-domain multi-hop QA, we can incorporate a symbolic information retrieval within our decomposition framework, leading to improved performance on both tasks. Datasets, Code and Prompts available at https://github.com/allenai/DecomP.

Large Language Model (LLM) agents, while proficient in the digital realm, face a significant gap in physical-world deployment due to the challenge of forming and maintaining a robust spatial mental model. We identify three core cognitive challenges hindering this transition: spatial reasoning, long-horizon state tracking via mental simulation, and active exploration under partial observation. To isolate and evaluate these faculties, we introduce CubeBench, a novel generative benchmark centered on the Rubik's Cube. CubeBench uses a three-tiered diagnostic framework that progressively assesses agent capabilities, from foundational state tracking with full symbolic information to active exploration with only partial visual data. Our experiments on leading LLMs reveal critical limitations, including a uniform 0.00% pass rate on all long-horizon tasks, exposing a fundamental failure in long-term planning. We also propose a diagnostic framework to isolate these cognitive bottlenecks by providing external solver tools. By analyzing the failure modes, we provide key insights to guide the development of more physically-grounded intelligent agents.

LLM-agent based binary code analysis has demonstrated significant potential across a wide range of software security scenarios, including vulnerability detection, malware analysis, etc. In agent workflow, however, retrieving the positive from thousands of stripped binary functions based on user query remains under-studied and challenging, as the absence of symbolic information distinguishes it from source code retrieval. In this paper, we introduce, BinSeek, the first two-stage cross-modal retrieval framework for stripped binary code analysis. It consists of two models: BinSeekEmbedding is trained on large-scale dataset to learn the semantic relevance of the binary code and the natural language description, furthermore, BinSeek-Reranker learns to carefully judge the relevance of the candidate code to the description with context augmentation. To this end, we built an LLM-based data synthesis pipeline to automate training construction, also deriving a domain benchmark for future research. Our evaluation results show that BinSeek achieved the state-of-the-art performance, surpassing the the same scale models by 31.42% in Rec@3 and 27.17% in MRR@3, as well as leading the advanced general-purpose models that have 16 times larger parameters.

Foundation models for time series analysis (TSA) have attracted significant attention. However, challenges such as training data scarcity and imbalance continue to hinder their development. Inspired by complex dynamic system theories, we design a series-symbol data generation mechanism, enabling the unrestricted creation of high-quality time series data paired with corresponding symbolic expressions. To leverage series-symbol data pairs with strong correlations, we develop SymTime, a pre-trained foundation model for enhancing time series representation using symbolic information. SymTime demonstrates competitive performance across five major TSA tasks when fine-tunes with downstream tasks, rivaling foundation models pre-trained on real-world datasets. This approach underscores the potential of series-symbol data generation and pretraining mechanisms in overcoming data scarcity and enhancing task performance. The code is available at https://github.com/wwhenxuan/SymTime.

We introduce CLaMP: Contrastive Language-Music Pre-training, which learns cross-modal representations between natural language and symbolic music using a music encoder and a text encoder trained jointly with a contrastive loss. To pre-train CLaMP, we collected a large dataset of 1.4 million music-text pairs. It employed text dropout as a data augmentation technique and bar patching to efficiently represent music data which reduces sequence length to less than 10%. In addition, we developed a masked music model pre-training objective to enhance the music encoder's comprehension of musical context and structure. CLaMP integrates textual information to enable semantic search and zero-shot classification for symbolic music, surpassing the capabilities of previous models. To support the evaluation of semantic search and music classification, we publicly release WikiMusicText (WikiMT), a dataset of 1010 lead sheets in ABC notation, each accompanied by a title, artist, genre, and description. In comparison to state-of-the-art models that require fine-tuning, zero-shot CLaMP demonstrated comparable or superior performance on score-oriented datasets.

Partitura is a lightweight Python package for handling symbolic musical information. It provides easy access to features commonly used in music information retrieval tasks, like note arrays (lists of timed pitched events) and 2D piano roll matrices, as well as other score elements such as time and key signatures, performance directives, and repeat structures. Partitura can load musical scores (in MEI, MusicXML, Kern, and MIDI formats), MIDI performances, and score-to-performance alignments. The package includes some tools for music analysis, such as automatic pitch spelling, key signature identification, and voice separation. Partitura is an open-source project and is available at https://github.com/CPJKU/partitura/.

Signage is an ubiquitous element of human environments, playing a critical role in both scene understanding and navigation. For autonomous systems to fully interpret human environments, effectively parsing and understanding signs is essential. We introduce the task of navigational sign understanding, aimed at extracting navigational cues from signs that convey symbolic spatial information about the scene. Specifically, we focus on signs capturing directional cues that point toward distant locations and locational cues that identify specific places. To benchmark performance on this task, we curate a comprehensive test set, propose appropriate evaluation metrics, and establish a baseline approach. Our test set consists of over 160 images, capturing signs with varying complexity and design across a wide range of public spaces, such as hospitals, shopping malls, and transportation hubs. Our baseline approach harnesses Vision-Language Models (VLMs) to parse navigational signs under these high degrees of variability. Experiments show that VLMs offer promising performance on this task, potentially motivating downstream applications in robotics. The code and dataset are available on Github.

Even though Transformers are extensively used for Natural Language Processing tasks, especially for machine translation, they lack an explicit memory to store key concepts of processed texts. This paper explores the properties of the content of symbolic working memory added to the Transformer model decoder. Such working memory enhances the quality of model predictions in machine translation task and works as a neural-symbolic representation of information that is important for the model to make correct translations. The study of memory content revealed that translated text keywords are stored in the working memory, pointing to the relevance of memory content to the processed text. Also, the diversity of tokens and parts of speech stored in memory correlates with the complexity of the corpora for machine translation task.

This paper introduces PDEformer, a neural solver for partial differential equations (PDEs) capable of simultaneously addressing various types of PDEs. We advocate representing the PDE in the form of a computational graph, facilitating the seamless integration of both symbolic and numerical information inherent in a PDE. A graph Transformer and an implicit neural representation (INR) are employed to generate mesh-free predicted solutions. Following pretraining on data exhibiting a certain level of diversity, our model achieves zero-shot accuracies on benchmark datasets that surpass those of adequately trained expert models. Additionally, PDEformer demonstrates promising results in the inverse problem of PDE coefficient recovery.

Generating structured ASCII art using computational techniques demands a careful interplay between aesthetic representation and computational precision, requiring models that can effectively translate visual information into symbolic text characters. Although Convolutional Neural Networks (CNNs) have shown promise in this domain, the comparative performance of deep learning architectures and classical machine learning methods remains unexplored. This paper explores the application of contemporary ML and DL methods to generate structured ASCII art, focusing on three key criteria: fidelity, character classification accuracy, and output quality. We investigate deep learning architectures, including Multilayer Perceptrons (MLPs), ResNet, and MobileNetV2, alongside classical approaches such as Random Forests, Support Vector Machines (SVMs) and k-Nearest Neighbors (k-NN), trained on an augmented synthetic dataset of ASCII characters. Our results show that complex neural network architectures often fall short in producing high-quality ASCII art, whereas classical machine learning classifiers, despite their simplicity, achieve performance similar to CNNs. Our findings highlight the strength of classical methods in bridging model simplicity with output quality, offering new insights into ASCII art synthesis and machine learning on image data with low dimensionality.

Large Language Models (LLMs) have demonstrated impressive reasoning capabilities, yet they struggle with spatial tasks that require mental simulation, such as mental rotation. This paper investigates whether equipping an LLM with an external ``Imagery Module'' -- a tool capable of rendering and rotating 3D models -- can bridge this gap, functioning as a ``cognitive prosthetic.'' We conducted experiments using a dual-module architecture in which a reasoning module (an MLLM) interacts with an imagery module on 3D model rotation tasks. Performance was lower than expected, with accuracy reaching at most 62.5%. Further investigation suggests that even when the burden of maintaining and manipulating a holistic 3D state is outsourced, the system still fails. This reveals that current frontier models lack the foundational visual-spatial primitives required to interface with imagery. Specifically, they lack: (1) the low-level sensitivity to extract spatial signals such as (a) depth, (b) motion, and (c) short-horizon dynamic prediction; and (2) the capacity to reason contemplatively over images, dynamically shifting visual focus and balancing imagery with symbolic and associative information.

The Information Bottleneck (IB) method frequently suffers from unstable optimization, characterized by abrupt representation shifts near critical points of the IB trade-off parameter, beta. In this paper, I introduce a novel approach to achieve stable and convex IB optimization through symbolic continuation and entropy-regularized trajectories. I analytically prove convexity and uniqueness of the IB solution path when an entropy regularization term is included, and demonstrate how this stabilizes representation learning across a wide range of eta values. Additionally, I provide extensive sensitivity analyses around critical points (beta) with statistically robust uncertainty quantification (95% confidence intervals). The open-source implementation, experimental results, and reproducibility framework included in this work offer a clear path for practical deployment and future extension of my proposed method.

Several adaptations of Transformers models have been developed in various domains since its breakthrough in Natural Language Processing (NLP). This trend has spread into the field of Music Information Retrieval (MIR), including studies processing music data. However, the practice of leveraging NLP tools for symbolic music data is not novel in MIR. Music has been frequently compared to language, as they share several similarities, including sequential representations of text and music. These analogies are also reflected through similar tasks in MIR and NLP. This survey reviews NLP methods applied to symbolic music generation and information retrieval studies following two axes. We first propose an overview of representations of symbolic music adapted from natural language sequential representations. Such representations are designed by considering the specificities of symbolic music. These representations are then processed by models. Such models, possibly originally developed for text and adapted for symbolic music, are trained on various tasks. We describe these models, in particular deep learning models, through different prisms, highlighting music-specialized mechanisms. We finally present a discussion surrounding the effective use of NLP tools for symbolic music data. This includes technical issues regarding NLP methods and fundamental differences between text and music, which may open several doors for further research into more effectively adapting NLP tools to symbolic MIR.

Neural networks adapt very well to distributed and continuous representations, but struggle to generalize from small amounts of data. Symbolic systems commonly achieve data efficient generalization by exploiting modularity to benefit from local and discrete features of a representation. These features allow symbolic programs to be improved one module at a time and to experience combinatorial growth in the values they can successfully process. However, it is difficult to design a component that can be used to form symbolic abstractions and which is adequately overparametrized to learn arbitrary high-dimensional transformations. I present Graph-based Symbolically Synthesized Neural Networks (G-SSNNs), a class of neural modules that operate on representations modified with synthesized symbolic programs to include a fixed set of local and discrete features. I demonstrate that the choice of injected features within a G-SSNN module modulates the data efficiency and generalization of baseline neural models, creating predictable patterns of both heightened and curtailed generalization. By training G-SSNNs, we also derive information about desirable semantics of symbolic programs without manual engineering. This information is compact and amenable to abstraction, but can also be flexibly recontextualized for other high-dimensional settings. In future work, I will investigate data efficient generalization and the transferability of learned symbolic representations in more complex G-SSNN designs based on more complex classes of symbolic programs. Experimental code and data are available at https://github.com/shlomenu/symbolically_synthesized_networks .

The coronavirus disease (COVID-19) has resulted in a pandemic crippling the a breadth of services critical to daily life. Segmentation of lung infections in computerized tomography (CT) slices could be be used to improve diagnosis and understanding of COVID-19 in patients. Deep learning systems lack interpretability because of their black box nature. Inspired by human communication of complex ideas through language, we propose a symbolic framework based on emergent languages for the segmentation of COVID-19 infections in CT scans of lungs. We model the cooperation between two artificial agents - a Sender and a Receiver. These agents synergistically cooperate using emergent symbolic language to solve the task of semantic segmentation. Our game theoretic approach is to model the cooperation between agents unlike Generative Adversarial Networks (GANs). The Sender retrieves information from one of the higher layers of the deep network and generates a symbolic sentence sampled from a categorical distribution of vocabularies. The Receiver ingests the stream of symbols and cogenerates the segmentation mask. A private emergent language is developed that forms the communication channel used to describe the task of segmentation of COVID infections. We augment existing state of the art semantic segmentation architectures with our symbolic generator to form symbolic segmentation models. Our symbolic segmentation framework achieves state of the art performance for segmentation of lung infections caused by COVID-19. Our results show direct interpretation of symbolic sentences to discriminate between normal and infected regions, infection morphology and image characteristics. We show state of the art results for segmentation of COVID-19 lung infections in CT.

In applications such as personal assistants, large language models (LLMs) must consider the user's personal information and preferences. However, LLMs lack the inherent ability to learn from user interactions. This paper explores capturing personal information from user prompts using ontology and knowledge-graph approaches. We use a subset of the KNOW ontology, which models personal information, to train the language model on these concepts. We then evaluate the success of knowledge capture using a specially constructed dataset. Our code and datasets are publicly available at https://github.com/HaltiaAI/paper-PTODSKC

Recent advances in methods focused on the grounding problem have resulted in techniques that can be used to construct a symbolic language associated with a specific domain. Inspired by how humans communicate complex ideas through language, we developed a generalized Symbolic Semantic (S^2) framework for interpretable segmentation. Unlike adversarial models (e.g., GANs), we explicitly model cooperation between two agents, a Sender and a Receiver, that must cooperate to achieve a common goal. The Sender receives information from a high layer of a segmentation network and generates a symbolic sentence derived from a categorical distribution. The Receiver obtains the symbolic sentences and co-generates the segmentation mask. In order for the model to converge, the Sender and Receiver must learn to communicate using a private language. We apply our architecture to segment tumors in the TCGA dataset. A UNet-like architecture is used to generate input to the Sender network which produces a symbolic sentence, and a Receiver network co-generates the segmentation mask based on the sentence. Our Segmentation framework achieved similar or better performance compared with state-of-the-art segmentation methods. In addition, our results suggest direct interpretation of the symbolic sentences to discriminate between normal and tumor tissue, tumor morphology, and other image characteristics.

As AI agents become increasingly autonomous, widely deployed in consequential contexts, and efficacious in bringing about real-world impacts, ensuring that their decisions are not only instrumentally effective but also normatively aligned has become critical. We introduce a neuro-symbolic reason-based containment architecture, Governor for Reason-Aligned ContainmEnt (GRACE), that decouples normative reasoning from instrumental decision-making and can contain AI agents of virtually any design. GRACE restructures decision-making into three modules: a Moral Module (MM) that determines permissible macro actions via deontic logic-based reasoning; a Decision-Making Module (DMM) that encapsulates the target agent while selecting instrumentally optimal primitive actions in accordance with derived macro actions; and a Guard that monitors and enforces moral compliance. The MM uses a reason-based formalism providing a semantic foundation for deontic logic, enabling interpretability, contestability, and justifiability. Its symbolic representation enriches the DMM's informational context and supports formal verification and statistical guarantees of alignment enforced by the Guard. We demonstrate GRACE on an example of a LLM therapy assistant, showing how it enables stakeholders to understand, contest, and refine agent behavior.

Despite their capabilities, Large Language Models (LLMs) remain opaque with limited understanding of their internal representations. Current interpretability methods, such as direct logit attribution (DLA) and sparse autoencoders (SAEs), provide restricted insight due to limitations such as the model's output vocabulary or unclear feature names. This work introduces Hyperdimensional Probe, a novel paradigm for decoding information from the LLM vector space. It combines ideas from symbolic representations and neural probing to project the model's residual stream into interpretable concepts via Vector Symbolic Architectures (VSAs). This probe combines the strengths of SAEs and conventional probes while overcoming their key limitations. We validate our decoding paradigm with controlled input-completion tasks, probing the model's final state before next-token prediction on inputs spanning syntactic pattern recognition, key-value associations, and abstract inference. We further assess it in a question-answering setting, examining the state of the model both before and after text generation. Our experiments show that our probe reliably extracts meaningful concepts across varied LLMs, embedding sizes, and input domains, also helping identify LLM failures. Our work advances information decoding in LLM vector space, enabling extracting more informative, interpretable, and structured features from neural representations.

As an important part of Music Information Retrieval (MIR), Symbolic Music Understanding (SMU) has gained substantial attention, as it can assist musicians and amateurs in learning and creating music. Recently, pre-trained language models have been widely adopted in SMU because the symbolic music shares a huge similarity with natural language, and the pre-trained manner also helps make full use of limited music data. However, the issue of bias, such as sexism, ageism, and racism, has been observed in pre-trained language models, which is attributed to the imbalanced distribution of training data. It also has a significant influence on the performance of downstream tasks, which also happens in SMU. To address this challenge, we propose Adversarial-MidiBERT, a symbolic music understanding model based on Bidirectional Encoder Representations from Transformers (BERT). We introduce an unbiased pre-training method based on adversarial learning to minimize the participation of tokens that lead to biases during training. Furthermore, we propose a mask fine-tuning method to narrow the data gap between pre-training and fine-tuning, which can help the model converge faster and perform better. We evaluate our method on four music understanding tasks, and our approach demonstrates excellent performance in all of them. The code for our model is publicly available at https://github.com/RS2002/Adversarial-MidiBERT.

We propose Hier-SLAM++, a comprehensive Neuro-Symbolic semantic 3D Gaussian Splatting SLAM method with both RGB-D and monocular input featuring an advanced hierarchical categorical representation, which enables accurate pose estimation as well as global 3D semantic mapping. The parameter usage in semantic SLAM systems increases significantly with the growing complexity of the environment, making scene understanding particularly challenging and costly. To address this problem, we introduce a novel and general hierarchical representation that encodes both semantic and geometric information in a compact form into 3D Gaussian Splatting, leveraging the capabilities of large language models (LLMs) as well as the 3D generative model. By utilizing the proposed hierarchical tree structure, semantic information is symbolically represented and learned in an end-to-end manner. We further introduce a novel semantic loss designed to optimize hierarchical semantic information through both inter-level and cross-level optimization. Additionally, we propose an improved SLAM system to support both RGB-D and monocular inputs using a feed-forward model. To the best of our knowledge, this is the first semantic monocular Gaussian Splatting SLAM system, significantly reducing sensor requirements for 3D semantic understanding and broadening the applicability of semantic Gaussian SLAM system. We conduct experiments on both synthetic and real-world datasets, demonstrating superior or on-par performance with state-of-the-art NeRF-based and Gaussian-based SLAM systems, while significantly reducing storage and training time requirements.

3D visual grounding (3DVG) is challenging because of the requirement of understanding on visual information, language and spatial relationships. While supervised approaches have achieved superior performance, they are constrained by the scarcity and high cost of 3D vision-language datasets. On the other hand, LLM/VLM based agents are proposed for 3DVG, eliminating the need for training data. However, these methods incur prohibitive time and token costs during inference. To address the challenges, we introduce a novel training-free symbolic framework for 3D visual grounding, namely Evolvable Symbolic Visual Grounder, that offers significantly reduced inference costs compared to previous agent-based methods while maintaining comparable performance. EaSe uses LLM generated codes to compute on spatial relationships. EaSe also implements an automatic pipeline to evaluate and optimize the quality of these codes and integrate VLMs to assist in the grounding process. Experimental results demonstrate that EaSe achieves 52.9% accuracy on Nr3D dataset and 49.2% Acc@0.25 on ScanRefer, which is top-tier among training-free methods. Moreover, it substantially reduces the inference time and cost, offering a balanced trade-off between performance and efficiency. Codes are available at https://github.com/OpenRobotLab/EaSe.

We present JASCO, a temporally controlled text-to-music generation model utilizing both symbolic and audio-based conditions. JASCO can generate high-quality music samples conditioned on global text descriptions along with fine-grained local controls. JASCO is based on the Flow Matching modeling paradigm together with a novel conditioning method. This allows music generation controlled both locally (e.g., chords) and globally (text description). Specifically, we apply information bottleneck layers in conjunction with temporal blurring to extract relevant information with respect to specific controls. This allows the incorporation of both symbolic and audio-based conditions in the same text-to-music model. We experiment with various symbolic control signals (e.g., chords, melody), as well as with audio representations (e.g., separated drum tracks, full-mix). We evaluate JASCO considering both generation quality and condition adherence, using both objective metrics and human studies. Results suggest that JASCO is comparable to the evaluated baselines considering generation quality while allowing significantly better and more versatile controls over the generated music. Samples are available on our demo page https://pages.cs.huji.ac.il/adiyoss-lab/JASCO.

The ability to extract structured information from unstructured sources-such as free-text documents and scientific literature-is critical for accelerating scientific discovery and knowledge synthesis. Large Language Models (LLMs) have demonstrated remarkable capabilities in various natural language processing tasks, including structured information extraction. However, their effectiveness often diminishes in specialized, domain-specific contexts that require nuanced understanding and expert-level domain knowledge. In addition, existing LLM-based approaches frequently exhibit poor transferability across tasks and domains, limiting their scalability and adaptability. To address these challenges, we introduce StructSense, a modular, task-agnostic, open-source framework for structured information extraction built on LLMs. StructSense is guided by domain-specific symbolic knowledge encoded in ontologies, enabling it to navigate complex domain content more effectively. It further incorporates agentic capabilities through self-evaluative judges that form a feedback loop for iterative refinement, and includes human-in-the-loop mechanisms to ensure quality and validation. We demonstrate that StructSense can overcome both the limitations of domain sensitivity and the lack of cross-task generalizability, as shown through its application to diverse neuroscience information extraction tasks.

Recent advancements have highlighted that Large Language Models (LLMs) are prone to hallucinations when solving complex reasoning problems, leading to erroneous results. To tackle this issue, researchers incorporate Knowledge Graphs (KGs) to improve the reasoning ability of LLMs. However, existing methods face two limitations: 1) they typically assume that all answers to the questions are contained in KGs, neglecting the incompleteness issue of KGs, and 2) they treat the KG as a static repository and overlook the implicit logical reasoning structures inherent in KGs. In this paper, we introduce SymAgent, an innovative neural-symbolic agent framework that achieves collaborative augmentation between KGs and LLMs. We conceptualize KGs as dynamic environments and transform complex reasoning tasks into a multi-step interactive process, enabling KGs to participate deeply in the reasoning process. SymAgent consists of two modules: Agent-Planner and Agent-Executor. The Agent-Planner leverages LLM's inductive reasoning capability to extract symbolic rules from KGs, guiding efficient question decomposition. The Agent-Executor autonomously invokes predefined action tools to integrate information from KGs and external documents, addressing the issues of KG incompleteness. Furthermore, we design a self-learning framework comprising online exploration and offline iterative policy updating phases, enabling the agent to automatically synthesize reasoning trajectories and improve performance. Experimental results demonstrate that SymAgent with weak LLM backbones (i.e., 7B series) yields better or comparable performance compared to various strong baselines. Further analysis reveals that our agent can identify missing triples, facilitating automatic KG updates.

Vector Symbolic Architectures (VSAs) have emerged as a novel framework for enabling interpretable machine learning algorithms equipped with the ability to reason and explain their decision processes. The basic idea is to represent discrete information through high dimensional random vectors. Complex data structures can be built up with operations over vectors such as the "binding" operation involving element-wise vector multiplication, which associates data together. The reverse task of decomposing the associated elements is a combinatorially hard task, with an exponentially large search space. The main algorithm for performing this search is the resonator network, inspired by Hopfield network-based memory search operations. In this work, we introduce a new variant of the resonator network, based on self-attention based update rules in the iterative search problem. This update rule, based on the Hopfield network with log-sum-exp energy function and norm-bounded states, is shown to substantially improve the performance and rate of convergence. As a result, our algorithm enables a larger capacity for associative memory, enabling applications in many tasks like perception based pattern recognition, scene decomposition, and object reasoning. We substantiate our algorithm with a thorough evaluation and comparisons to baselines.

Music Emotion Recognition involves the automatic identification of emotional elements within music tracks, and it has garnered significant attention due to its broad applicability in the field of Music Information Retrieval. It can also be used as the upstream task of many other human-related tasks such as emotional music generation and music recommendation. Due to existing psychology research, music emotion is determined by multiple factors such as the Timbre, Velocity, and Structure of the music. Incorporating multiple factors in MER helps achieve more interpretable and finer-grained methods. However, most prior works were uni-domain and showed weak consistency between arousal modeling performance and valence modeling performance. Based on this background, we designed a multi-domain emotion modeling method for instrumental music that combines symbolic analysis and acoustic analysis. At the same time, because of the rarity of music data and the difficulty of labeling, our multi-domain approach can make full use of limited data. Our approach was implemented and assessed using the publicly available piano dataset EMOPIA, resulting in a notable improvement over our baseline model with a 2.4% increase in overall accuracy, establishing its state-of-the-art performance.

Supervised approaches for learning spatio-temporal scene graphs (STSG) from video are greatly hindered due to their reliance on STSG-annotated videos, which are labor-intensive to construct at scale. Is it feasible to instead use readily available video captions as weak supervision? To address this question, we propose LASER, a neuro-symbolic framework to enable training STSG generators using only video captions. LASER employs large language models to first extract logical specifications with rich spatio-temporal semantic information from video captions. LASER then trains the underlying STSG generator to align the predicted STSG with the specification. The alignment algorithm overcomes the challenges of weak supervision by leveraging a differentiable symbolic reasoner and using a combination of contrastive, temporal, and semantics losses. The overall approach efficiently trains low-level perception models to extract a fine-grained STSG that conforms to the video caption. In doing so, it enables a novel methodology for learning STSGs without tedious annotations. We evaluate our method on three video datasets: OpenPVSG, 20BN, and MUGEN. Our approach demonstrates substantial improvements over fully-supervised baselines, achieving a unary predicate prediction accuracy of 27.78% (+12.65%) and a binary recall@5 of 0.42 (+0.22) on OpenPVSG. Additionally, LASER exceeds baselines by 7% on 20BN and 5.2% on MUGEN in terms of overall predicate prediction accuracy.

This paper presents AlphaSpace, a novel methodology designed to enhance the spatial reasoning capabilities of large language models (LLMs) for 3D Cartesian space navigation. AlphaSpace employs a semantics-based tokenization strategy, encoding height information through specialized semantic tokens, and integrates primarily symbolic synthetic reasoning data. This approach enables LLMs to accurately manipulate objects by positioning them at specific [x, y, z] coordinates. Experimental results demonstrate that AlphaSpace significantly outperforms existing models on manipulation subtasks, achieving a total accuracy of 66.67%, compared to 37.5% for GPT-4o and 29.17% for Claude 3.5 Sonnet.

We propose a fully spectral, neuro\-symbolic reasoning architecture that leverages Graph Signal Processing (GSP) as the primary computational backbone for integrating symbolic logic and neural inference. Unlike conventional reasoning models that treat spectral graph methods as peripheral components, our approach formulates the entire reasoning pipeline in the graph spectral domain. Logical entities and relationships are encoded as graph signals, processed via learnable spectral filters that control multi-scale information propagation, and mapped into symbolic predicates for rule-based inference. We present a complete mathematical framework for spectral reasoning, including graph Fourier transforms, band-selective attention, and spectral rule grounding. Experiments on benchmark reasoning datasets (ProofWriter, EntailmentBank, bAbI, CLUTRR, and ARC-Challenge) demonstrate improvements in logical consistency, interpretability, and computational efficiency over state\-of\-the\-art neuro\-symbolic models. Our results suggest that GSP provides a mathematically grounded and computationally efficient substrate for robust and interpretable reasoning systems.

Automated piano performance evaluation traditionally relies on symbolic (MIDI) representations, which capture note-level information but miss the acoustic nuances that characterize expressive playing. I propose using pre-trained audio foundation models, specifically MuQ and MERT, to predict 19 perceptual dimensions of piano performance quality. Using synthesized audio from PercePiano MIDI files (rendered via Pianoteq), I compare audio and symbolic approaches under controlled conditions where both derive from identical source data. The best model, MuQ layers 9-12 with Pianoteq soundfont augmentation, achieves R^2 = 0.537 (95% CI: [0.465, 0.575]), representing a 55% improvement over the symbolic baseline (R^2 = 0.347). Statistical analysis confirms significance (p < 10^-25) with audio outperforming symbolic on all 19 dimensions. I validate the approach through cross-soundfont generalization (R^2 = 0.534 +/- 0.075), difficulty correlation with an external dataset (rho = 0.623), and multi-performer consistency analysis. Analysis of audio-symbolic fusion reveals high error correlation (r = 0.738), explaining why fusion provides minimal benefit: audio representations alone are sufficient. I release the complete training pipeline, pretrained models, and inference code.

Visual reasoning, particularly spatial reasoning, is a challenging cognitive task that requires understanding object relationships and their interactions within complex environments, especially in robotics domain. Existing vision_language models (VLMs) excel at perception tasks but struggle with fine-grained spatial reasoning due to their implicit, correlation-driven reasoning and reliance solely on images. We propose a novel neuro_symbolic framework that integrates both panoramic-image and 3D point cloud information, combining neural perception with symbolic reasoning to explicitly model spatial and logical relationships. Our framework consists of a perception module for detecting entities and extracting attributes, and a reasoning module that constructs a structured scene graph to support precise, interpretable queries. Evaluated on the JRDB-Reasoning dataset, our approach demonstrates superior performance and reliability in crowded, human_built environments while maintaining a lightweight design suitable for robotics and embodied AI applications.

We propose a novel symbolic music representation and Generative Adversarial Network (GAN) framework specially designed for symbolic multitrack music generation. The main theme of symbolic music generation primarily encompasses the preprocessing of music data and the implementation of a deep learning framework. Current techniques dedicated to symbolic music generation generally encounter two significant challenges: training data's lack of information about chords and scales and the requirement of specially designed model architecture adapted to the unique format of symbolic music representation. In this paper, we solve the above problems by introducing new symbolic music representation with MusicLang chord analysis model. We propose our MMT-BERT architecture adapting to the representation. To build a robust multitrack music generator, we fine-tune a pre-trained MusicBERT model to serve as the discriminator, and incorporate relativistic standard loss. This approach, supported by the in-depth understanding of symbolic music encoded within MusicBERT, fortifies the consonance and humanity of music generated by our method. Experimental results demonstrate the effectiveness of our approach which strictly follows the state-of-the-art methods.

Learning musical structures and composition patterns is necessary for both music generation and understanding, but current methods do not make uniform use of learned features to generate and comprehend music simultaneously. In this paper, we propose PianoBART, a pre-trained model that uses BART for both symbolic piano music generation and understanding. We devise a multi-level object selection strategy for different pre-training tasks of PianoBART, which can prevent information leakage or loss and enhance learning ability. The musical semantics captured in pre-training are fine-tuned for music generation and understanding tasks. Experiments demonstrate that PianoBART efficiently learns musical patterns and achieves outstanding performance in generating high-quality coherent pieces and comprehending music. Our code and supplementary material are available at https://github.com/RS2002/PianoBart.

Given ample experimental data from a system governed by differential equations, it is possible to use deep learning techniques to construct the underlying differential operators. In this work we perform symbolic discovery of differential operators in a situation where there is sparse experimental data. This small data regime in machine learning can be made tractable by providing our algorithms with prior information about the underlying dynamics. Physics Informed Neural Networks (PINNs) have been very successful in this regime (reconstructing entire ODE solutions using only a single point or entire PDE solutions with very few measurements of the initial condition). We modify the PINN approach by adding a neural network that learns a representation of unknown hidden terms in the differential equation. The algorithm yields both a surrogate solution to the differential equation and a black-box representation of the hidden terms. These hidden term neural networks can then be converted into symbolic equations using symbolic regression techniques like AI Feynman. In order to achieve convergence of these neural networks, we provide our algorithms with (noisy) measurements of both the initial condition as well as (synthetic) experimental data obtained at later times. We demonstrate strong performance of this approach even when provided with very few measurements of noisy data in both the ODE and PDE regime.

Music composition represents the creative side of humanity, and itself is a complex task that requires abilities to understand and generate information with long dependency and harmony constraints. While demonstrating impressive capabilities in STEM subjects, current LLMs easily fail in this task, generating ill-written music even when equipped with modern techniques like In-Context-Learning and Chain-of-Thoughts. To further explore and enhance LLMs' potential in music composition by leveraging their reasoning ability and the large knowledge base in music history and theory, we propose ComposerX, an agent-based symbolic music generation framework. We find that applying a multi-agent approach significantly improves the music composition quality of GPT-4. The results demonstrate that ComposerX is capable of producing coherent polyphonic music compositions with captivating melodies, while adhering to user instructions.

The success of large language models (LLMs) for time series has been demonstrated in previous work. Utilizing a symbolic time series representation, one can efficiently bridge the gap between LLMs and time series. However, the remaining challenge is to exploit the semantic information hidden in time series by using symbols or existing tokens of LLMs, while aligning the embedding space of LLMs according to the hidden information of time series. The symbolic time series approximation (STSA) method called adaptive Brownian bridge-based symbolic aggregation (ABBA) shows outstanding efficacy in preserving salient time series features by modeling time series patterns in terms of amplitude and period while using existing tokens of LLMs. In this paper, we introduce a method, called LLM-ABBA, that integrates ABBA into large language models for various downstream time series tasks. By symbolizing time series, LLM-ABBA compares favorably to the recent state-of-the-art (SOTA) in UCR and three medical time series classification tasks. Meanwhile, a fixed-polygonal chain trick in ABBA is introduced to avoid obvious drifting during forecasting tasks by significantly mitigating the effects of cumulative error arising from misused symbols during the transition from symbols to numerical values. In time series regression tasks, LLM-ABBA achieves the new SOTA on Time Series Extrinsic Regression (TSER) benchmarks. LLM-ABBA also shows competitive forecasting capability compared to recent SOTA time series forecasting results. We believe this framework can also seamlessly extend to other time series tasks. Our simulation code is publicly available at: https://github.com/inEXASCALE/llm-abba

Though end-to-end neural approaches have recently been dominating NLP tasks in both performance and ease-of-use, they lack interpretability and robustness. We propose Binder, a training-free neural-symbolic framework that maps the task input to a program, which (1) allows binding a unified API of language model (LM) functionalities to a programming language (e.g., SQL, Python) to extend its grammar coverage and thus tackle more diverse questions, (2) adopts an LM as both the program parser and the underlying model called by the API during execution, and (3) requires only a few in-context exemplar annotations. Specifically, we employ GPT-3 Codex as the LM. In the parsing stage, with only a few in-context exemplars, Codex is able to identify the part of the task input that cannot be answerable by the original programming language, correctly generate API calls to prompt Codex to solve the unanswerable part, and identify where to place the API calls while being compatible with the original grammar. In the execution stage, Codex can perform versatile functionalities (e.g., commonsense QA, information extraction) given proper prompts in the API calls. Binder achieves state-of-the-art results on WikiTableQuestions and TabFact datasets, with explicit output programs that benefit human debugging. Note that previous best systems are all finetuned on tens of thousands of task-specific samples, while Binder only uses dozens of annotations as in-context exemplars without any training. Our code is available at https://github.com/HKUNLP/Binder .

Event coreference resolution is an important research problem with many applications. Despite the recent remarkable success of pretrained language models, we argue that it is still highly beneficial to utilize symbolic features for the task. However, as the input for coreference resolution typically comes from upstream components in the information extraction pipeline, the automatically extracted symbolic features can be noisy and contain errors. Also, depending on the specific context, some features can be more informative than others. Motivated by these observations, we propose a novel context-dependent gated module to adaptively control the information flows from the input symbolic features. Combined with a simple noisy training method, our best models achieve state-of-the-art results on two datasets: ACE 2005 and KBP 2016.

Modern business environments demand continuous reconfiguration of cross-functional processes, yet most enterprise systems remain organized around siloed departments, rigid workflows, and hard-coded automation. Meanwhile, large language models (LLMs) demonstrate strong capabilities in interpreting natural language and synthesizing unstructured information, but they lack deterministic, auditable execution of complex business logic. We introduce Autonomous Business System (AUTOBUS), a system that integrates LLM-based AI agents, predicate-logic programming, and business-semantics-centric enterprise data into a unified neuro-symbolic architecture for executing end-to-end business initiatives. AUTOBUS models a business initiative as a network of interrelated tasks with explicit pre- and post-conditions, required data, evaluation rules, and API-level actions. Enterprise data is organized as a knowledge graph, whose entities, relationships, and constraints are translated into logic facts and foundational rules that ground reasoning and ensure semantic consistency. Core AI agents synthesize task instructions, enterprise semantics, and available tools into task-specific logic programs, which are executed by a logic engine that enforces constraints, coordinates auxiliary tools, and produces deterministic outcomes. Humans specify task instructions, define and maintain business semantics and policies, curate tools, and supervise high-impact or ambiguous decisions, ensuring accountability and adaptability. We detail the AUTOBUS architecture, the structure of AI-generated logic programs, and the human-AI collaboration model and present a case study that demonstrates accelerated time to market in a data-rich organization. A reference implementation of the case study is available at https://github.com/cecilpang/autobus-paper.

While Large Language Model (LLM) agents are often approached from the angle of action planning/generation to accomplish a goal (e.g., given by language descriptions), their abilities to collaborate with each other to achieve a joint goal are not well explored. To address this limitation, this paper studies LLM agents in task collaboration, particularly under the condition of information asymmetry, where agents have disparities in their knowledge and skills and need to work together to complete a shared task. We extend Einstein Puzzles, a classical symbolic puzzle, to a table-top game. In this game, two LLM agents must reason, communicate, and act to satisfy spatial and relational constraints required to solve the puzzle. We apply a fine-tuning-plus-verifier framework in which LLM agents are equipped with various communication strategies and verification signals from the environment. Empirical results highlight the critical importance of aligned communication, especially when agents possess both information-seeking and -providing capabilities. Interestingly, agents without communication can still achieve high task performance; however, further analysis reveals a lack of true rule understanding and lower trust from human evaluators. Instead, by integrating an environment-based verifier, we enhance agents' ability to comprehend task rules and complete tasks, promoting both safer and more interpretable collaboration in AI systems. https://github.com/Roihn/EinsteinPuzzles

Music exists in various modalities, such as score images, symbolic scores, MIDI, and audio. Translations between each modality are established as core tasks of music information retrieval, such as automatic music transcription (audio-to-MIDI) and optical music recognition (score image to symbolic score). However, most past work on multimodal translation trains specialized models on individual translation tasks. In this paper, we propose a unified approach, where we train a general-purpose model on many translation tasks simultaneously. Two key factors make this unified approach viable: a new large-scale dataset and the tokenization of each modality. Firstly, we propose a new dataset that consists of more than 1,300 hours of paired audio-score image data collected from YouTube videos, which is an order of magnitude larger than any existing music modal translation datasets. Secondly, our unified tokenization framework discretizes score images, audio, MIDI, and MusicXML into a sequence of tokens, enabling a single encoder-decoder Transformer to tackle multiple cross-modal translation as one coherent sequence-to-sequence task. Experimental results confirm that our unified multitask model improves upon single-task baselines in several key areas, notably reducing the symbol error rate for optical music recognition from 24.58% to a state-of-the-art 13.67%, while similarly substantial improvements are observed across the other translation tasks. Notably, our approach achieves the first successful score-image-conditioned audio generation, marking a significant breakthrough in cross-modal music generation.

Against all attempts that consider virtuality as a substance (a parallel or alternative reality) or as a modality (like potentiality or possibility), we want to defend the pragmatic point of view that it is rather a dynamic cognitive and sensitive interaction with reality. More precisely, we show that the ``virtus'' is an operating capacity that produces simulations of real and fictional contexts to experiment with their effects. Based on Peirce's semiotics, we define virtual reality (VR) and augmented reality (AR) as mixed realities made of ``symbolic assemblies'', that is to say, structures of signs assembled by processes of computation and meaning (semiosis). We show that VR can be defined as a synesthetic experiment that does not reshape reality itself, but rather the senses and understanding we already have about it. In conclusion, we criticize David Chalmer's extended mind theory by distinguishing between knowledge and information, and we try to redefine AR as a hermeneutic device that extends not the mind itself, but the activity of thought by adding symbols to read in the world.

This paper addresses the problem of autonomous UAV search missions, where a UAV must locate specific Entities of Interest (EOIs) within a time limit, based on brief descriptions in large, hazard-prone environments with keep-out zones. The UAV must perceive, reason, and make decisions with limited and uncertain information. We propose NEUSIS, a compositional neuro-symbolic system designed for interpretable UAV search and navigation in realistic scenarios. NEUSIS integrates neuro-symbolic visual perception, reasoning, and grounding (GRiD) to process raw sensory inputs, maintains a probabilistic world model for environment representation, and uses a hierarchical planning component (SNaC) for efficient path planning. Experimental results from simulated urban search missions using AirSim and Unreal Engine show that NEUSIS outperforms a state-of-the-art (SOTA) vision-language model and a SOTA search planning model in success rate, search efficiency, and 3D localization. These results demonstrate the effectiveness of our compositional neuro-symbolic approach in handling complex, real-world scenarios, making it a promising solution for autonomous UAV systems in search missions.

Vision-Language Models (VLM) can support clinicians by analyzing medical images and engaging in natural language interactions to assist in diagnostic and treatment tasks. However, VLMs often exhibit "hallucinogenic" behavior, generating textual outputs not grounded in contextual multimodal information. This challenge is particularly pronounced in the medical domain, where we do not only require VLM outputs to be accurate in single interactions but also to be consistent with clinical reasoning and diagnostic pathways throughout multi-turn conversations. For this purpose, we propose a new alignment algorithm that uses symbolic representations of clinical reasoning to ground VLMs in medical knowledge. These representations are utilized to (i) generate GPT-4-guided visual instruction tuning data at scale, simulating clinician-VLM conversations with demonstrations of clinical reasoning, and (ii) create an automatic reward function that evaluates the clinical validity of VLM generations throughout clinician-VLM interactions. Our algorithm eliminates the need for human involvement in training data generation or reward model construction, reducing costs compared to standard reinforcement learning with human feedback (RLHF). We apply our alignment algorithm to develop Dr-LLaVA, a conversational VLM finetuned for analyzing bone marrow pathology slides, demonstrating strong performance in multi-turn medical conversations.

Large Language Models (LLMs) have emerged as transformative tools in artificial intelligence, capable of processing and understanding extensive human knowledge to enhance problem-solving across various domains. This paper explores the potential of LLMs to drive the discovery of symbolic solutions within scientific and engineering disciplines, where such solutions are crucial for advancing theoretical and practical applications. We propose a novel framework that utilizes LLMs in an evolutionary search methodology, augmented by a dynamic knowledge library that integrates and refines insights in an open-ended manner. This approach aims to tackle the dual challenges of efficiently navigating complex symbolic representation spaces and leveraging both existing and newly generated knowledge to foster open-ended innovation. By enabling LLMs to interact with and expand upon a knowledge library, we facilitate the continuous generation of novel solutions in diverse forms such as language, code, and mathematical expressions. Our experimental results demonstrate that this method not only enhances the efficiency of searching for symbolic solutions but also supports the ongoing discovery process, akin to human scientific endeavors. This study represents a first effort in conceptualizing the search for symbolic solutions as a lifelong, iterative process, marking a significant step towards harnessing AI in the perpetual pursuit of scientific and engineering breakthroughs. We have open-sourced our code and data, please visit https://github.com/pgg3/CoEvo for more information.

Long-term memory enables large language model agents to tackle complex tasks through historical interactions. However, existing frameworks encounter a fundamental dilemma between compressing redundant information efficiently and maintaining precise retrieval for downstream tasks. To bridge this gap, we propose MemFly, a framework grounded in information bottleneck principles that facilitates on-the-fly memory evolution for LLMs. Our approach minimizes compression entropy while maximizing relevance entropy via a gradient-free optimizer, constructing a stratified memory structure for efficient storage. To fully leverage MemFly, we develop a hybrid retrieval mechanism that seamlessly integrates semantic, symbolic, and topological pathways, incorporating iterative refinement to handle complex multi-hop queries. Comprehensive experiments demonstrate that MemFly substantially outperforms state-of-the-art baselines in memory coherence, response fidelity, and accuracy.

Chemical reasoning inherently integrates visual, textual, and symbolic modalities, yet existing benchmarks rarely capture this complexity, often relying on simple image-text pairs with limited chemical semantics. As a result, the actual ability of Multimodal Large Language Models (MLLMs) to process and integrate chemically meaningful information across modalities remains unclear. We introduce ChemVTS-Bench, a domain-authentic benchmark designed to systematically evaluate the Visual-Textual-Symbolic (VTS) reasoning abilities of MLLMs. ChemVTS-Bench contains diverse and challenging chemical problems spanning organic molecules, inorganic materials, and 3D crystal structures, with each task presented in three complementary input modes: (1) visual-only, (2) visual-text hybrid, and (3) SMILES-based symbolic input. This design enables fine-grained analysis of modality-dependent reasoning behaviors and cross-modal integration. To ensure rigorous and reproducible evaluation, we further develop an automated agent-based workflow that standardizes inference, verifies answers, and diagnoses failure modes. Extensive experiments on state-of-the-art MLLMs reveal that visual-only inputs remain challenging, structural chemistry is the hardest domain, and multimodal fusion mitigates but does not eliminate visual, knowledge-based, or logical errors, highlighting ChemVTS-Bench as a rigorous, domain-faithful testbed for advancing multimodal chemical reasoning. All data and code will be released to support future research.

In our opinion the exuberance surrounding the relative success of data-driven large language models (LLMs) is slightly misguided and for several reasons (i) LLMs cannot be relied upon for factual information since for LLMs all ingested text (factual or non-factual) was created equal; (ii) due to their subsymbolic na-ture, whatever 'knowledge' these models acquire about language will always be buried in billions of microfeatures (weights), none of which is meaningful on its own; and (iii) LLMs will often fail to make the correct inferences in several linguistic contexts (e.g., nominal compounds, copredication, quantifier scope ambi-guities, intensional contexts. Since we believe the relative success of data-driven large language models (LLMs) is not a reflection on the symbolic vs. subsymbol-ic debate but a reflection on applying the successful strategy of a bottom-up reverse engineering of language at scale, we suggest in this paper applying the effective bottom-up strategy in a symbolic setting resulting in symbolic, explainable, and ontologically grounded language models.

Multimodal Large Language Models (MLLMs) have demonstrated remarkable reasoning capabilities across modalities such as images and text. However, tabular data, despite being a critical real-world modality, remains relatively underexplored in multimodal learning. In this paper, we focus on the task of Tabular-Vision Multi-Modal Understanding (TVMU) and identify three core challenges: (1) high structural variability and data incompleteness in tables, (2) implicit and complex feature dependencies, and (3) significant heterogeneity in problem-solving pipelines across downstream tasks. To address these issues, we propose Thinking with Tables (TWT). TWT employs a program-aided code-based neuro-symbolic reasoning mechanism that facilitates key operations, such as information extraction and element modeling, by interacting with external environments. We evaluate TWT on eight representative datasets. Experimental results demonstrate that TWT consistently outperforms existing baselines by an average of 10\% in accuracy, achieving performance comparable to, or even surpassing, proprietary commercial SOTA LLMs on TVMU tasks. Models and codes are available at https://github.com/kunyang-YU/Thinking-with-Tables

Symbolic music datasets are important for music information retrieval and musical analysis. However, there is a lack of large-scale symbolic datasets for classical piano music. In this article, we create a GiantMIDI-Piano (GP) dataset containing 38,700,838 transcribed notes and 10,855 unique solo piano works composed by 2,786 composers. We extract the names of music works and the names of composers from the International Music Score Library Project (IMSLP). We search and download their corresponding audio recordings from the internet. We further create a curated subset containing 7,236 works composed by 1,787 composers by constraining the titles of downloaded audio recordings containing the surnames of composers. We apply a convolutional neural network to detect solo piano works. Then, we transcribe those solo piano recordings into Musical Instrument Digital Interface (MIDI) files using a high-resolution piano transcription system. Each transcribed MIDI file contains the onset, offset, pitch, and velocity attributes of piano notes and pedals. GiantMIDI-Piano includes 90% live performance MIDI files and 10\% sequence input MIDI files. We analyse the statistics of GiantMIDI-Piano and show pitch class, interval, trichord, and tetrachord frequencies of six composers from different eras to show that GiantMIDI-Piano can be used for musical analysis. We evaluate the quality of GiantMIDI-Piano in terms of solo piano detection F1 scores, metadata accuracy, and transcription error rates. We release the source code for acquiring the GiantMIDI-Piano dataset at https://github.com/bytedance/GiantMIDI-Piano

Symbolic music datasets with matched scores and performances are essential for many music information retrieval (MIR) tasks. Yet, existing resources often cover a narrow range of composers, lack performance variety, omit note-level alignments, or use inconsistent naming formats. This work presents PianoCoRe, a large-scale piano MIDI dataset that unifies and refines major open-source piano corpora. The dataset contains 250,046 performances of 5,625 pieces written by 483 composers, totaling 21,763 h of performed music. PianoCoRe is released in tiered subsets to support different applications: from large-scale analysis and pre-training (PianoCoRe-C and deduplicated PianoCoRe-B) to expressive performance modeling with note-level score alignment (PianoCoRe-A/A*). The note-aligned subset, PianoCoRe-A, provides the largest open-source collection of 157,207 performances aligned to 1,591 scores to date. In addition to the dataset, the contributions are: (1) a MIDI quality classifier for detecting corrupted and score-like transcriptions and (2) RAScoP, an alignment refinement pipeline that cleans temporal alignment errors and interpolates missing notes. The analysis shows that the refinement reduces temporal noise and eliminates tempo outliers. Moreover, an expressive performance rendering model trained on PianoCoRe demonstrates improved robustness to unseen pieces compared to models trained on raw or smaller datasets. PianoCoRe provides a ready-to-use foundation for the next generation of expressive piano performance research.

Music scores are written representations of music and contain rich information about musical components. The visual information on music scores includes notes, rests, staff lines, clefs, dynamics, and articulations. This visual information in music scores contains more semantic information than audio and symbolic representations of music. Previous music score datasets have limited sizes and are mainly designed for optical music recognition (OMR). There is a lack of research on creating a large-scale benchmark dataset for music modeling and generation. In this work, we propose MusicScore, a large-scale music score dataset collected and processed from the International Music Score Library Project (IMSLP). MusicScore consists of image-text pairs, where the image is a page of a music score and the text is the metadata of the music. The metadata of MusicScore is extracted from the general information section of the IMSLP pages. The metadata includes rich information about the composer, instrument, piece style, and genre of the music pieces. MusicScore is curated into small, medium, and large scales of 400, 14k, and 200k image-text pairs with varying diversity, respectively. We build a score generation system based on a UNet diffusion model to generate visually readable music scores conditioned on text descriptions to benchmark the MusicScore dataset for music score generation. MusicScore is released to the public at https://huggingface.co/datasets/ZheqiDAI/MusicScore.

Text-to-image (T2I) generation has seen significant growth over the past few years. Despite this, there has been little work on generating diagrams with T2I models. A diagram is a symbolic/schematic representation that explains information using structurally rich and spatially complex visualizations (e.g., a dense combination of related objects, text labels, directional arrows, connection lines, etc.). Existing state-of-the-art T2I models often fail at diagram generation because they lack fine-grained object layout control when many objects are densely connected via complex relations such as arrows/lines and also often fail to render comprehensible text labels. To address this gap, we present DiagrammerGPT, a novel two-stage text-to-diagram generation framework that leverages the layout guidance capabilities of LLMs (e.g., GPT-4) to generate more accurate open-domain, open-platform diagrams. In the first stage, we use LLMs to generate and iteratively refine 'diagram plans' (in a planner-auditor feedback loop) which describe all the entities (objects and text labels), their relationships (arrows or lines), and their bounding box layouts. In the second stage, we use a diagram generator, DiagramGLIGEN, and a text label rendering module to generate diagrams following the diagram plans. To benchmark the text-to-diagram generation task, we introduce AI2D-Caption, a densely annotated diagram dataset built on top of the AI2D dataset. We show quantitatively and qualitatively that our DiagrammerGPT framework produces more accurate diagrams, outperforming existing T2I models. We also provide comprehensive analysis including open-domain diagram generation, vector graphic diagram generation in different platforms, human-in-the-loop diagram plan editing, and multimodal planner/auditor LLMs (e.g., GPT-4Vision). We hope our work can inspire further research on diagram generation via T2I models and LLMs.

Symbolic anchoring is a crucial problem in the field of robotics, as it enables robots to obtain symbolic knowledge from the perceptual information acquired through their sensors. In cognitive-based robots, this process of processing sub-symbolic data from real-world sensors to obtain symbolic knowledge is still an open problem. To address this issue, this paper presents SAILOR, a framework for providing symbolic anchoring in the ROS 2 ecosystem. SAILOR aims to maintain the link between symbolic data and perceptual data in real robots over time, increasing the intelligent behavior of robots. It provides a semantic world modeling approach using two deep learning-based sub-symbolic robotic skills: object recognition and matching function. The object recognition skill allows the robot to recognize and identify objects in its environment, while the matching function enables the robot to decide if new perceptual data corresponds to existing symbolic data. This paper provides a description of the proposed method and the development of the framework, as well as its integration in MERLIN2 (a hybrid cognitive architecture fully functional in robots running ROS 2).

Many existing motion prediction approaches rely on symbolic perception outputs to generate agent trajectories, such as bounding boxes, road graph information and traffic lights. This symbolic representation is a high-level abstraction of the real world, which may render the motion prediction model vulnerable to perception errors (e.g., failures in detecting open-vocabulary obstacles) while missing salient information from the scene context (e.g., poor road conditions). An alternative paradigm is end-to-end learning from raw sensors. However, this approach suffers from the lack of interpretability and requires significantly more training resources. In this work, we propose tokenizing the visual world into a compact set of scene elements and then leveraging pre-trained image foundation models and LiDAR neural networks to encode all the scene elements in an open-vocabulary manner. The image foundation model enables our scene tokens to encode the general knowledge of the open world while the LiDAR neural network encodes geometry information. Our proposed representation can efficiently encode the multi-frame multi-modality observations with a few hundred tokens and is compatible with most transformer-based architectures. To evaluate our method, we have augmented Waymo Open Motion Dataset with camera embeddings. Experiments over Waymo Open Motion Dataset show that our approach leads to significant performance improvements over the state-of-the-art.

Large Language Models (LLMs) augmented with external tools have demonstrated remarkable capabilities in complex reasoning tasks. However, existing frameworks rely heavily on natural language reasoning to determine when tools can be invoked and whether their results should be committed, lacking formal guarantees for logical safety and verifiability. We present ToolGate, a forward execution framework that provides logical safety guarantees and verifiable state evolution for LLM tool calling. ToolGate maintains an explicit symbolic state space as a typed key-value mapping representing trusted world information throughout the reasoning process. Each tool is formalized as a Hoare-style contract consisting of a precondition and a postcondition, where the precondition gates tool invocation by checking whether the current state satisfies the required conditions, and the postcondition determines whether the tool's result can be committed to update the state through runtime verification. Our approach guarantees that the symbolic state evolves only through verified tool executions, preventing invalid or hallucinated results from corrupting the world representation. Experimental validation demonstrates that ToolGate significantly improves the reliability and verifiability of tool-augmented LLM systems while maintaining competitive performance on complex multi-step reasoning tasks. This work establishes a foundation for building more trustworthy and debuggable AI systems that integrate language models with external tools.

Retrieval Augmented Generation (RAG) has made significant strides in overcoming key limitations of large language models, such as hallucination, lack of contextual grounding, and issues with transparency. However, traditional RAG systems consist of three interconnected neural components - the retriever, re-ranker, and generator - whose internal reasoning processes remain opaque. This lack of transparency complicates interpretability, hinders debugging efforts, and erodes trust, especially in high-stakes domains where clear decision-making is essential. To address these challenges, we introduce the concept of Neurosymbolic RAG, which integrates symbolic reasoning using a knowledge graph with neural retrieval techniques. This new framework aims to answer two primary questions: (a) Can retrievers provide a clear and interpretable basis for document selection? (b) Can symbolic knowledge enhance the clarity of the retrieval process? We propose three methods to improve this integration. First is MAR (Knowledge Modulation Aligned Retrieval) that employs modulation networks to refine query embeddings using interpretable symbolic features, thereby making document matching more explicit. Second, KG-Path RAG enhances queries by traversing knowledge graphs to improve overall retrieval quality and interpretability. Lastly, Process Knowledge-infused RAG utilizes domain-specific tools to reorder retrieved content based on validated workflows. Preliminary results from mental health risk assessment tasks indicate that this neurosymbolic approach enhances both transparency and overall performance

Open-ended learning benefits immensely from the use of symbolic methods for goal representation as they offer ways to structure knowledge for efficient and transferable learning. However, the existing Hierarchical Reinforcement Learning (HRL) approaches relying on symbolic reasoning are often limited as they require a manual goal representation. The challenge in autonomously discovering a symbolic goal representation is that it must preserve critical information, such as the environment dynamics. In this paper, we propose a developmental mechanism for goal discovery via an emergent representation that abstracts (i.e., groups together) sets of environment states that have similar roles in the task. We introduce a Feudal HRL algorithm that concurrently learns both the goal representation and a hierarchical policy. The algorithm uses symbolic reachability analysis for neural networks to approximate the transition relation among sets of states and to refine the goal representation. We evaluate our approach on complex navigation tasks, showing the learned representation is interpretable, transferrable and results in data efficient learning.

The semantic matching capabilities of neural information retrieval can ameliorate synonymy and polysemy problems of symbolic approaches. However, neural models' dense representations are more suitable for re-ranking, due to their inefficiency. Sparse representations, either in symbolic or latent form, are more efficient with an inverted index. Taking the merits of the sparse and dense representations, we propose an ultra-high dimensional (UHD) representation scheme equipped with directly controllable sparsity. UHD's large capacity and minimal noise and interference among the dimensions allow for binarized representations, which are highly efficient for storage and search. Also proposed is a bucketing method, where the embeddings from multiple layers of BERT are selected/merged to represent diverse linguistic aspects. We test our models with MS MARCO and TREC CAR, showing that our models outperforms other sparse models

Maintaining legacy software requires many software and systems engineering hours. Assembly code programs, which demand low-level control over the computer machine state and have no variable names, are particularly difficult for humans to analyze. Existing conventional program translators guarantee correctness, but are hand-engineered for the source and target programming languages in question. Learned transpilation, i.e. automatic translation of code, offers an alternative to manual re-writing and engineering efforts. Automated symbolic program translation approaches guarantee correctness but struggle to scale to longer programs due to the exponentially large search space. Their rigid rule-based systems also limit their expressivity, so they can only reason about a reduced space of programs. Probabilistic neural language models (LMs) produce plausible outputs for every input, but do so at the cost of guaranteed correctness. In this work, we leverage the strengths of LMs and symbolic solvers in a neurosymbolic approach to learned transpilation for assembly code. Assembly code is an appropriate setting for a neurosymbolic approach, since assembly code can be divided into shorter non-branching basic blocks amenable to the use of symbolic methods. Guess & Sketch extracts alignment and confidence information from features of the LM then passes it to a symbolic solver to resolve semantic equivalence of the transpilation input and output. We test Guess & Sketch on three different test sets of assembly transpilation tasks, varying in difficulty, and show that it successfully transpiles 57.6% more examples than GPT-4 and 39.6% more examples than an engineered transpiler. We also share a training and evaluation dataset for this task.

Advances in diffusion, autoregressive, and hybrid models have enabled high-quality image synthesis for tasks such as text-to-image, editing, and reference-guided composition. Yet, existing benchmarks remain limited, either focus on isolated tasks, cover only narrow domains, or provide opaque scores without explaining failure modes. We introduce ImagenWorld, a benchmark of 3.6K condition sets spanning six core tasks (generation and editing, with single or multiple references) and six topical domains (artworks, photorealistic images, information graphics, textual graphics, computer graphics, and screenshots). The benchmark is supported by 20K fine-grained human annotations and an explainable evaluation schema that tags localized object-level and segment-level errors, complementing automated VLM-based metrics. Our large-scale evaluation of 14 models yields several insights: (1) models typically struggle more in editing tasks than in generation tasks, especially in local edits. (2) models excel in artistic and photorealistic settings but struggle with symbolic and text-heavy domains such as screenshots and information graphics. (3) closed-source systems lead overall, while targeted data curation (e.g., Qwen-Image) narrows the gap in text-heavy cases. (4) modern VLM-based metrics achieve Kendall accuracies up to 0.79, approximating human ranking, but fall short of fine-grained, explainable error attribution. ImagenWorld provides both a rigorous benchmark and a diagnostic tool to advance robust image generation.

We present AlphaApollo, a self-evolving agentic reasoning system that aims to address two bottlenecks in foundation model (FM) reasoning-limited model-intrinsic capacity and unreliable test-time iteration. AlphaApollo orchestrates multiple models with professional tools to enable deliberate, verifiable reasoning. It couples (i) a computation tool (Python with numerical and symbolic libraries) and (ii) a retrieval tool (task-relevant external information) to execute exact calculations and ground decisions. The system further supports multi-round, multi-model solution evolution via a shared state map that records candidates, executable checks, and feedback for iterative refinement. In evaluations on AIME 2024/2025 across multiple models, AlphaApollo delivers consistent gains: +5.15% Average@32 and +23.34% Pass@32 for Qwen2.5-14B-Instruct, and +8.91% Average@32 with +26.67% Pass@32 for Llama-3.3-70B-Instruct. Tool-use analysis shows that more than 80% of tool calls are successfully executed, with consistent outperformance of non-tool baselines, thereby lifting the capability ceiling of FMs. More empirical results and implementation details will be updated at https://github.com/tmlr-group/AlphaApollo.

Music transcription plays a pivotal role in Music Information Retrieval (MIR), particularly for stringed instruments like the guitar, where symbolic music notations such as MIDI lack crucial playability information. This contribution introduces the Fretting-Transformer, an encoderdecoder model that utilizes a T5 transformer architecture to automate the transcription of MIDI sequences into guitar tablature. By framing the task as a symbolic translation problem, the model addresses key challenges, including string-fret ambiguity and physical playability. The proposed system leverages diverse datasets, including DadaGP, GuitarToday, and Leduc, with novel data pre-processing and tokenization strategies. We have developed metrics for tablature accuracy and playability to quantitatively evaluate the performance. The experimental results demonstrate that the Fretting-Transformer surpasses baseline methods like A* and commercial applications like Guitar Pro. The integration of context-sensitive processing and tuning/capo conditioning further enhances the model's performance, laying a robust foundation for future developments in automated guitar transcription.

Robotic instruction following tasks require seamless integration of visual perception, task planning, target localization, and motion execution. However, existing task planning methods for instruction following are either data-driven or underperform in zero-shot scenarios due to difficulties in grounding lengthy instructions into actionable plans under operational constraints. To address this, we propose FlowPlan, a structured multi-stage LLM workflow that elevates zero-shot pipeline and bridges the performance gap between zero-shot and data-driven in-context learning methods. By decomposing the planning process into modular stages--task information retrieval, language-level reasoning, symbolic-level planning, and logical evaluation--FlowPlan generates logically coherent action sequences while adhering to operational constraints and further extracts contextual guidance for precise instance-level target localization. Benchmarked on the ALFRED and validated in real-world applications, our method achieves competitive performance relative to data-driven in-context learning methods and demonstrates adaptability across diverse environments. This work advances zero-shot task planning in robotic systems without reliance on labeled data. Project website: https://instruction-following-project.github.io/.

Classification of time series data is an important task for many application domains. One of the best existing methods for this task, in terms of accuracy and computation time, is MiniROCKET. In this work, we extend this approach to provide better global temporal encodings using hyperdimensional computing (HDC) mechanisms. HDC (also known as Vector Symbolic Architectures, VSA) is a general method to explicitly represent and process information in high-dimensional vectors. It has previously been used successfully in combination with deep neural networks and other signal processing algorithms. We argue that the internal high-dimensional representation of MiniROCKET is well suited to be complemented by the algebra of HDC. This leads to a more general formulation, HDC-MiniROCKET, where the original algorithm is only a special case. We will discuss and demonstrate that HDC-MiniROCKET can systematically overcome catastrophic failures of MiniROCKET on simple synthetic datasets. These results are confirmed by experiments on the 128 datasets from the UCR time series classification benchmark. The extension with HDC can achieve considerably better results on datasets with high temporal dependence without increasing the computational effort for inference.

Recent advances in general-purpose foundation models have stimulated the development of large biological sequence models. While natural language shows symbolic granularity (characters, words, sentences), biological sequences exhibit hierarchical granularity whose levels (nucleotides, amino acids, protein domains, genes) further encode biologically functional information. In this paper, we investigate the integration of cross-granularity knowledge from models through a case study of BiGCARP, a Pfam domain-level model for biosynthetic gene clusters, and ESM, an amino acid-level protein language model. Using representation analysis tools and a set of probe tasks, we first explain why a straightforward cross-model embedding initialization fails to improve downstream performance in BiGCARP, and show that deeper-layer embeddings capture a more contextual and faithful representation of the model's learned knowledge. Furthermore, we demonstrate that representations at different granularities encode complementary biological knowledge, and that combining them yields measurable performance gains in intermediate-level prediction tasks. Our findings highlight cross-granularity integration as a promising strategy for improving both the performance and interpretability of biological foundation models.

We introduce XiSort, a deterministic and reproducible sorting algorithm for floating-point sequences based on IEEE-754 total ordering and entropy minimization. XiSort guarantees bit-for-bit stability across runs and platforms by resolving tie-breaking via information-theoretic and symbolic methods. The algorithm supports both in-memory and external (out-of-core) operation, offering consistent performance on large datasets. We formalize a curved variant of the sorting metric that integrates into the Alpay Algebra framework, treating XiSort as a recursive operator with provable convergence and symbolic idempotence. This model preserves state-space closure while minimizing local disorder, interpretable as symbolic entropy. Empirical benchmarks demonstrate that XiSort achieves competitive throughput (e.g., sorting 10^8 doubles in approximately 12 seconds in-memory, and 100 GB at around 100 MB/s on SSDs), with applications in scientific computing, high-frequency finance, and reproducible numerical workflows. The results position XiSort as a principled tool for stable data alignment, symbolic preprocessing, and cross-platform float ordering. Keywords: deterministic sorting, IEEE-754, entropy minimization, symbolic algebra, reproducibility, external memory, Alpay Algebra, data pipelines

Faithfully summarizing the knowledge encoded by a deep neural network (DNN) into a few symbolic primitive patterns without losing much information represents a core challenge in explainable AI. To this end, Ren et al. (2023c) have derived a series of theorems to prove that the inference score of a DNN can be explained as a small set of interactions between input variables. However, the lack of generalization power makes it still hard to consider such interactions as faithful primitive patterns encoded by the DNN. Therefore, given different DNNs trained for the same task, we develop a new method to extract interactions that are shared by these DNNs. Experiments show that the extracted interactions can better reflect common knowledge shared by different DNNs.

Embodied agents face significant challenges when tasked with performing actions in diverse environments, particularly in generalizing across object types and executing suitable actions to accomplish tasks. Furthermore, agents should exhibit robustness, minimizing the execution of illegal actions. In this work, we present Egocentric Planning, an innovative approach that combines symbolic planning and Object-oriented POMDPs to solve tasks in complex environments, harnessing existing models for visual perception and natural language processing. We evaluated our approach in ALFRED, a simulated environment designed for domestic tasks, and demonstrated its high scalability, achieving an impressive 36.07% unseen success rate in the ALFRED benchmark and winning the ALFRED challenge at CVPR Embodied AI workshop. Our method requires reliable perception and the specification or learning of a symbolic description of the preconditions and effects of the agent's actions, as well as what object types reveal information about others. It is capable of naturally scaling to solve new tasks beyond ALFRED, as long as they can be solved using the available skills. This work offers a solid baseline for studying end-to-end and hybrid methods that aim to generalize to new tasks, including recent approaches relying on LLMs, but often struggle to scale to long sequences of actions or produce robust plans for novel tasks.

Chart understanding presents a critical test to the reasoning capabilities of Vision-Language Models (VLMs). Prior approaches face critical limitations: some rely on external tools, making them brittle and constrained by a predefined toolkit, while others fine-tune specialist models that often adopt a single reasoning strategy, such as text-based chain-of-thought (CoT). The intermediate steps of text-based reasoning are difficult to verify, which complicates the use of reinforcement-learning signals that reward factual accuracy. To address this, we propose a Code-as-Thought (CaT) approach to represent the visual information of a chart in a verifiable, symbolic format. Our key insight is that this strategy must be adaptive: a fixed, code-only implementation consistently fails on complex charts where symbolic representation is unsuitable. This finding leads us to introduce Visual Programmability: a learnable property that determines if a chart-question pair is better solved with code or direct visual analysis. We implement this concept in an adaptive framework where a VLM learns to choose between the CaT pathway and a direct visual reasoning pathway. The selection policy of the model is trained with reinforcement learning using a novel dual-reward system. This system combines a data-accuracy reward to ground the model in facts and prevent numerical hallucination, with a decision reward that teaches the model when to use each strategy, preventing it from defaulting to a single reasoning mode. Experiments demonstrate strong and robust performance across diverse chart-understanding benchmarks. Our work shows that VLMs can be taught not only to reason but also how to reason, dynamically selecting the optimal reasoning pathway for each task.

Radiology report generation (RRG) is a challenging task, as it requires a thorough understanding of medical images, integration of multiple temporal inputs, and accurate report generation. Effective interpretation of medical images, such as chest X-rays (CXRs), demands sophisticated visual-language reasoning to map visual findings to structured reports. Recent studies have shown that multimodal large language models (MLLMs) can acquire multimodal capabilities by aligning with pre-trained vision encoders. However, current approaches predominantly focus on single-image analysis or utilise rule-based symbolic processing to handle multiple images, thereby overlooking the essential temporal information derived from comparing current images with prior ones. To overcome this critical limitation, we introduce Libra, a temporal-aware MLLM tailored for CXR report generation using temporal images. Libra integrates a radiology-specific image encoder with a MLLM and utilises a novel Temporal Alignment Connector to capture and synthesise temporal information of images across different time points with unprecedented precision. Extensive experiments show that Libra achieves new state-of-the-art performance among the same parameter scale MLLMs for RRG tasks on the MIMIC-CXR. Specifically, Libra improves the RadCliQ metric by 12.9% and makes substantial gains across all lexical metrics compared to previous models.

Scalable Vector Graphics (SVGs) function both as visual images and as structured code that encode rich geometric and layout information, yet most methods rasterize them and discard this symbolic organization. At the same time, recent sentence embedding methods produce strong text representations but do not naturally extend to visual or structured modalities. We propose a training-free, instruction-guided multimodal embedding framework that uses a Multimodal Large Language Model (MLLM) to map text, raster images, and SVG code into an aligned embedding space. We control the direction of embeddings through modality-specific instructions and structural SVG cues, eliminating the need for learned projection heads or contrastive training. Our method has two key components: (1) Multimodal Explicit One-word Limitation (mEOL), which instructs the MLLM to summarize any multimodal input into a single token whose hidden state serves as a compact semantic embedding. (2) A semantic SVG rewriting module that assigns meaningful identifiers and simplifies nested SVG elements through visual reasoning over the rendered image, exposing geometric and relational cues hidden in raw code. Using a repurposed VGBench, we build the first text-to-SVG retrieval benchmark and show that our training-free embeddings outperform encoder-based and training-based multimodal baselines. These results highlight prompt-level control as an effective alternative to parameter-level training for structure-aware multimodal retrieval. Project page: https://scene-the-ella.github.io/meol/

Visual language models (VLMs) have attracted increasing interest in autonomous driving due to their powerful reasoning capabilities. However, existing VLMs typically utilize discrete text Chain-of-Thought (CoT) tailored to the current scenario, which essentially represents highly abstract and symbolic compression of visual information, potentially leading to spatio-temporal relationship ambiguity and fine-grained information loss. Is autonomous driving better modeled on real-world simulation and imagination than on pure symbolic logic? In this paper, we propose a spatio-temporal CoT reasoning method that enables models to think visually. First, VLM serves as a world model to generate unified image frame for predicting future world states: where perception results (e.g., lane divider and 3D detection) represent the future spatial relationships, and ordinary future frame represent the temporal evolution relationships. This spatio-temporal CoT then serves as intermediate reasoning steps, enabling the VLM to function as an inverse dynamics model for trajectory planning based on current observations and future predictions. To implement visual generation in VLMs, we propose a unified pretraining paradigm integrating visual generation and understanding, along with a progressive visual CoT enhancing autoregressive image generation. Extensive experimental results demonstrate the effectiveness of the proposed method, advancing autonomous driving towards visual reasoning.

Theory-of-Mind (ToM), the ability to infer others' perceptions and mental states, is fundamental to human interaction but remains a challenging task for Large Language Models (LLMs). While existing ToM reasoning methods show promise with reasoning via perceptual perspective-taking, they often rely excessively on LLMs, reducing their efficiency and limiting their applicability to high-order ToM reasoning, which requires multi-hop reasoning about characters' beliefs. To address these issues, we present EnigmaToM, a novel neuro-symbolic framework that enhances ToM reasoning by integrating a Neural Knowledge Base of entity states (Enigma) for (1) a psychology-inspired iterative masking mechanism that facilitates accurate perspective-taking and (2) knowledge injection that elicits key entity information. Enigma generates structured representations of entity states, which construct spatial scene graphs -- leveraging spatial information as an inductive bias -- for belief tracking of various ToM orders and enhancing events with fine-grained entity state details. Experimental results on multiple benchmarks, including ToMi, HiToM, and FANToM, show that EnigmaToM significantly improves ToM reasoning across LLMs of varying sizes, particularly excelling in high-order reasoning scenarios.

Knowledge Graph Embedding models have become an important area of machine learning.Those models provide a latent representation of entities and relations in a knowledge graph which can then be used in downstream machine learning tasks such as link prediction. The learning process of such models can be performed by contrasting positive and negative triples. While all triples of a KG are considered positive, negative triples are usually not readily available. Therefore, the choice of the sampling method to obtain the negative triples play a crucial role in the performance and effectiveness of Knowledge Graph Embedding models. Most of the current methods fetch negative samples from a random distribution of entities in the underlying Knowledge Graph which also often includes meaningless triples. Other known methods use adversarial techniques or generative neural networks which consequently reduce the efficiency of the process. In this paper, we propose an approach for generating informative negative samples considering available complementary knowledge about entities. Particularly, Pre-trained Language Models are used to form neighborhood clusters by utilizing the distances between entities to obtain representations of symbolic entities via their textual information. Our comprehensive evaluations demonstrate the effectiveness of the proposed approach on benchmark Knowledge Graphs with textual information for the link prediction task.

Mathematical symbols and descriptions appear in various forms across document section boundaries without explicit markup. In this paper, we present a new large-scale dataset that emphasizes extracting symbols and descriptions in scientific documents. Symlink annotates scientific papers of 5 different domains (i.e., computer science, biology, physics, mathematics, and economics). Our experiments on Symlink demonstrate the challenges of the symbol-description linking task for existing models and call for further research effort in this area. We will publicly release Symlink to facilitate future research.

Large Language Models (LLMs) have greatly propelled the progress in natural language(NL)-centric tasks based on NL interface. However, the NL form is not enough for world knowledge. Current works focus on this question by injecting specific symbolic knowledge into LLM, which ignore two critical challenges: the interrelations between various symbols and the balance between symbolic-centric and NL-centric capabilities. In this work, we tackle these challenges from both a data and framework perspective and introduce Symbol-LLM series models. First, we collect 34 symbolic tasks, covering ~20 different forms, which are unified to capture symbol interrelations. Then, a two-stage tuning framework succeeds in injecting symbolic knowledge without loss of the generality ability. Extensive experiments on both symbol- and NL-centric tasks demonstrate the balanced and superior performances of Symbol-LLM series models.

Current advances in Artificial Intelligence (AI) and Machine Learning (ML) have achieved unprecedented impact across research communities and industry. Nevertheless, concerns about trust, safety, interpretability and accountability of AI were raised by influential thinkers. Many have identified the need for well-founded knowledge representation and reasoning to be integrated with deep learning and for sound explainability. Neural-symbolic computing has been an active area of research for many years seeking to bring together robust learning in neural networks with reasoning and explainability via symbolic representations for network models. In this paper, we relate recent and early research results in neurosymbolic AI with the objective of identifying the key ingredients of the next wave of AI systems. We focus on research that integrates in a principled way neural network-based learning with symbolic knowledge representation and logical reasoning. The insights provided by 20 years of neural-symbolic computing are shown to shed new light onto the increasingly prominent role of trust, safety, interpretability and accountability of AI. We also identify promising directions and challenges for the next decade of AI research from the perspective of neural-symbolic systems.

Abstract symbolic writing systems are semiotic codes that are ubiquitous in modern society but are otherwise absent in the animal kingdom. Anthropological evidence suggests that the earliest forms of some writing systems originally consisted of iconic pictographs, which signify their referent via visual resemblance. While previous studies have examined the emergence and, separately, the evolution of pictographic writing systems through a computational lens, most employ non-naturalistic methodologies that make it difficult to draw clear analogies to human and animal cognition. We develop a multi-agent reinforcement learning testbed for emergent communication called a Signification Game, and formulate a model of inferential communication that enables agents to leverage visual theory of mind to communicate actions using pictographs. Our model, which is situated within a broader formalism for animal communication, sheds light on the cognitive and cultural processes that led to the development of early writing systems.

Symbolic equations are at the core of scientific discovery. The task of discovering the underlying equation from a set of input-output pairs is called symbolic regression. Traditionally, symbolic regression methods use hand-designed strategies that do not improve with experience. In this paper, we introduce the first symbolic regression method that leverages large scale pre-training. We procedurally generate an unbounded set of equations, and simultaneously pre-train a Transformer to predict the symbolic equation from a corresponding set of input-output-pairs. At test time, we query the model on a new set of points and use its output to guide the search for the equation. We show empirically that this approach can re-discover a set of well-known physical equations, and that it improves over time with more data and compute.

The advancement of machine learning and symbolic approaches have underscored their strengths and weaknesses in Natural Language Processing (NLP). While machine learning approaches are powerful in identifying patterns in data, they often fall short in learning commonsense and the factual knowledge required for the NLP tasks. Meanwhile, the symbolic methods excel in representing knowledge-rich data. However, they struggle to adapt dynamic data and generalize the knowledge. Bridging these two paradigms through hybrid approaches enables the alleviation of weaknesses in both while preserving their strengths. Recent studies extol the virtues of this union, showcasing promising results in a wide range of NLP tasks. In this paper, we present an overview of hybrid approaches used for NLP. Specifically, we delve into the state-of-the-art hybrid approaches used for a broad spectrum of NLP tasks requiring natural language understanding, generation, and reasoning. Furthermore, we discuss the existing resources available for hybrid approaches for NLP along with the challenges and future directions, offering a roadmap for future research avenues.

Assessing the capabilities of large language models (LLMs) is often challenging, in part, because it is hard to find tasks to which they have not been exposed during training. We take one step to address this challenge by turning to a new task: focusing on symbolic graphics programs, which are a popular representation for graphics content that procedurally generates visual data. LLMs have shown exciting promise towards program synthesis, but do they understand symbolic graphics programs? Unlike conventional programs, symbolic graphics programs can be translated to graphics content. Here, we characterize an LLM's understanding of symbolic programs in terms of their ability to answer questions related to the graphics content. This task is challenging as the questions are difficult to answer from the symbolic programs alone -- yet, they would be easy to answer from the corresponding graphics content as we verify through a human experiment. To understand symbolic programs, LLMs may need to possess the ability to imagine how the corresponding graphics content would look without directly accessing the rendered visual content. We use this task to evaluate LLMs by creating a large benchmark for the semantic understanding of symbolic graphics programs. This benchmark is built via program-graphics correspondence, hence requiring minimal human efforts. We evaluate current LLMs on our benchmark to elucidate a preliminary assessment of their ability to reason about visual scenes from programs. We find that this task distinguishes existing LLMs and models considered good at reasoning perform better. Lastly, we introduce Symbolic Instruction Tuning (SIT) to improve this ability. Specifically, we query GPT4-o with questions and images generated by symbolic programs. Such data are then used to finetune an LLM. We also find that SIT data can improve the general instruction following ability of LLMs.

In symbolic regression, the goal is to find an analytical expression that accurately fits experimental data with the minimal use of mathematical symbols such as operators, variables, and constants. However, the combinatorial space of possible expressions can make it challenging for traditional evolutionary algorithms to find the correct expression in a reasonable amount of time. To address this issue, Neural Symbolic Regression (NSR) algorithms have been developed that can quickly identify patterns in the data and generate analytical expressions. However, these methods, in their current form, lack the capability to incorporate user-defined prior knowledge, which is often required in natural sciences and engineering fields. To overcome this limitation, we propose a novel neural symbolic regression method, named Neural Symbolic Regression with Hypothesis (NSRwH) that enables the explicit incorporation of assumptions about the expected structure of the ground-truth expression into the prediction process. Our experiments demonstrate that the proposed conditioned deep learning model outperforms its unconditioned counterparts in terms of accuracy while also providing control over the predicted expression structure.

Harnessing the statistical power of neural networks to perform language understanding and symbolic reasoning is difficult, when it requires executing efficient discrete operations against a large knowledge-base. In this work, we introduce a Neural Symbolic Machine, which contains (a) a neural "programmer", i.e., a sequence-to-sequence model that maps language utterances to programs and utilizes a key-variable memory to handle compositionality (b) a symbolic "computer", i.e., a Lisp interpreter that performs program execution, and helps find good programs by pruning the search space. We apply REINFORCE to directly optimize the task reward of this structured prediction problem. To train with weak supervision and improve the stability of REINFORCE, we augment it with an iterative maximum-likelihood training process. NSM outperforms the state-of-the-art on the WebQuestionsSP dataset when trained from question-answer pairs only, without requiring any feature engineering or domain-specific knowledge.

Although the mapping between sound and meaning in human language is assumed to be largely arbitrary, research in cognitive science has shown that there are non-trivial correlations between particular sounds and meanings across languages and demographic groups, a phenomenon known as sound symbolism. Among the many dimensions of meaning, sound symbolism is particularly salient and well-demonstrated with regards to cross-modal associations between language and the visual domain. In this work, we address the question of whether sound symbolism is reflected in vision-and-language models such as CLIP and Stable Diffusion. Using zero-shot knowledge probing to investigate the inherent knowledge of these models, we find strong evidence that they do show this pattern, paralleling the well-known kiki-bouba effect in psycholinguistics. Our work provides a novel method for demonstrating sound symbolism and understanding its nature using computational tools. Our code will be made publicly available.

Humans interact with the environment using a combination of perception - transforming sensory inputs from their environment into symbols, and cognition - mapping symbols to knowledge about the environment for supporting abstraction, reasoning by analogy, and long-term planning. Human perception-inspired machine perception, in the context of AI, refers to large-scale pattern recognition from raw data using neural networks trained using self-supervised learning objectives such as next-word prediction or object recognition. On the other hand, machine cognition encompasses more complex computations, such as using knowledge of the environment to guide reasoning, analogy, and long-term planning. Humans can also control and explain their cognitive functions. This seems to require the retention of symbolic mappings from perception outputs to knowledge about their environment. For example, humans can follow and explain the guidelines and safety constraints driving their decision-making in safety-critical applications such as healthcare, criminal justice, and autonomous driving. This article introduces the rapidly emerging paradigm of Neurosymbolic AI combines neural networks and knowledge-guided symbolic approaches to create more capable and flexible AI systems. These systems have immense potential to advance both algorithm-level (e.g., abstraction, analogy, reasoning) and application-level (e.g., explainable and safety-constrained decision-making) capabilities of AI systems.

Small Language Models (SLMs) are attracting attention due to the high computational demands and privacy concerns of Large Language Models (LLMs). Some studies fine-tune SLMs using Chains of Thought (CoT) data distilled from LLMs, aiming to enhance their reasoning ability. Furthermore, Some CoT distillation methods introduce external symbolic knowledge into the generation process to improve the limited knowledge memory, reasoning ability and out-of-domain (OOD) generalization of SLMs. However, the introduction of symbolic knowledge increases computational overhead and introduces potential noise. In this paper, we introduce SKIntern, an innovative approach that empowers SLMs to internalize symbolic knowledge and few-shot examples gradually through a progressive fine-tuning process, guided by a predefined linear decay schedule under curriculum learning. By efficiently internalizing knowledge, SKIntern reduces computational overhead and speeds up the reasoning process by focusing solely on the question during inference. It outperforms state-of-the-art baselines by over 5\%, while reducing inference costs (measured in FLOPs) by up to 4times across a wide range of SLMs in both in-domain (ID) and out-of-domain (OOD) tasks. Our code will be available at https://github.com/Xnhyacinth/SKIntern.

Neuro-symbolic artificial intelligence (NSAI) represents a transformative approach in artificial intelligence (AI) by combining deep learning's ability to handle large-scale and unstructured data with the structured reasoning of symbolic methods. By leveraging their complementary strengths, NSAI enhances generalization, reasoning, and scalability while addressing key challenges such as transparency and data efficiency. This paper systematically studies diverse NSAI architectures, highlighting their unique approaches to integrating neural and symbolic components. It examines the alignment of contemporary AI techniques such as retrieval-augmented generation, graph neural networks, reinforcement learning, and multi-agent systems with NSAI paradigms. This study then evaluates these architectures against comprehensive set of criteria, including generalization, reasoning capabilities, transferability, and interpretability, therefore providing a comparative analysis of their respective strengths and limitations. Notably, the Neuro > Symbolic < Neuro model consistently outperforms its counterparts across all evaluation metrics. This result aligns with state-of-the-art research that highlight the efficacy of such architectures in harnessing advanced technologies like multi-agent systems.

We study syllogistic reasoning in LLMs from the logical and natural language perspectives. In process, we explore fundamental reasoning capabilities of the LLMs and the direction this research is moving forward. To aid in our studies, we use 14 large language models and investigate their syllogistic reasoning capabilities in terms of symbolic inferences as well as natural language understanding. Even though this reasoning mechanism is not a uniform emergent property across LLMs, the perfect symbolic performances in certain models make us wonder whether LLMs are becoming more and more formal reasoning mechanisms, rather than making explicit the nuances of human reasoning.

While Multimodal Large Language Models (MLLMs) have achieved remarkable success in interpreting natural scenes, their ability to process discrete symbols -- the fundamental building blocks of human cognition -- remains a critical open question. Unlike continuous visual data, symbols such as mathematical formulas, chemical structures, and linguistic characters require precise, deeper interpretation. This paper introduces a comprehensive benchmark to evaluate how top-tier MLLMs navigate these "discrete semantic spaces" across five domains: language, culture, mathematics, physics, and chemistry. Our investigation uncovers a counterintuitive phenomenon: models often fail at basic symbol recognition yet succeed in complex reasoning tasks, suggesting they rely on linguistic probability rather than true visual perception. By exposing this "cognitive mismatch", we highlight a significant gap in current AI capabilities: the struggle to truly perceive and understand the symbolic languages that underpin scientific discovery and abstract thought. This work offers a roadmap for developing more rigorous, human-aligned intelligent systems.

Symbolic regression (SR) is a powerful technique for discovering the underlying mathematical expressions from observed data. Inspired by the success of deep learning, recent efforts have focused on two categories for SR methods. One is using a neural network or genetic programming to search the expression tree directly. Although this has shown promising results, the large search space poses difficulties in learning constant factors and processing high-dimensional problems. Another approach is leveraging a transformer-based model training on synthetic data and offers advantages in inference speed. However, this method is limited to fixed small numbers of dimensions and may encounter inference problems when given data is out-of-distribution compared to the synthetic data. In this work, we propose DySymNet, a novel neural-guided Dynamic Symbolic Network for SR. Instead of searching for expressions within a large search space, we explore DySymNet with various structures and optimize them to identify expressions that better-fitting the data. With a topology structure like neural networks, DySymNet not only tackles the challenge of high-dimensional problems but also proves effective in optimizing constants. Based on extensive numerical experiments using low-dimensional public standard benchmarks and the well-known SRBench with more variables, our method achieves state-of-the-art performance in terms of fitting accuracy and robustness to noise.

Information theory, introduced by Shannon, has been extremely successful and influential as a mathematical theory of communication. Shannon's notion of information does not consider the meaning of the messages being communicated but only their probability. Even so, computational approaches regularly appeal to "information processing" to study how meaning is encoded and decoded in natural and artificial systems. Here, we contrast Shannon information theory with integrated information theory (IIT), which was developed to account for the presence and properties of consciousness. IIT considers meaning as integrated information and characterizes it as a structure, rather than as a message or code. In principle, IIT's axioms and postulates allow one to "unfold" a cause-effect structure from a substrate in a state, a structure that fully defines the intrinsic meaning of an experience and its contents. It follows that, for the communication of meaning, the cause-effect structures of sender and receiver must be similar.

Symbolic regression plays a crucial role in modern scientific research thanks to its capability of discovering concise and interpretable mathematical expressions from data. A grand challenge lies in the arduous search for parsimonious and generalizable mathematical formulas, in an infinite search space, while intending to fit the training data. Existing algorithms have faced a critical bottleneck of accuracy and efficiency over a decade when handling problems of complexity, which essentially hinders the pace of applying symbolic regression for scientific exploration across interdisciplinary domains. To this end, we introduce a parallelized tree search (PTS) model to efficiently distill generic mathematical expressions from limited data. Through a series of extensive experiments, we demonstrate the superior accuracy and efficiency of PTS for equation discovery, which greatly outperforms the state-of-the-art baseline models on over 80 synthetic and experimental datasets (e.g., lifting its performance by up to 99% accuracy improvement and one-order of magnitude speed up). PTS represents a key advance in accurate and efficient data-driven discovery of symbolic, interpretable models (e.g., underlying physical laws) and marks a pivotal transition towards scalable symbolic learning.

This paper addresses the problem of formalizing and quantifying the concept of "intensional inheritance" between two concepts. We begin by conceiving the intensional inheritance of W from F as the amount of information the proposition "x is F " provides about the proposition "x is W. To flesh this out, we consider concepts F and W defined by sets of properties left{F_{1}, F_{2}, ldots, F_{n}right} and left{W_{1}, W_{2}, ldots, W_{m}right} with associated degrees left{d_{1}, d_{2}, ldots, d_{n}right} and left{e_{1}, e_{2}, ldots, e_{m}right}, respectively, where the properties may overlap. We then derive formulas for the intensional inheritance using both Shannon information theory and algorithmic information theory, incorporating interaction information among properties. We examine a special case where all properties are mutually exclusive and calculate the intensional inheritance in this case in both frameworks. We also derive expressions for P(W mid F) based on the mutual information formula. Finally we consider the relationship between intensional inheritance and conventional set-theoretic "extensional" inheritance, concluding that in our information-theoretic framework, extensional inheritance emerges as a special case of intensional inheritance.

In an era where symbolic mathematical equations are indispensable for modeling complex natural phenomena, scientific inquiry often involves collecting observations and translating them into mathematical expressions. Recently, deep learning has emerged as a powerful tool for extracting insights from data. However, existing models typically specialize in either numeric or symbolic domains, and are usually trained in a supervised manner tailored to specific tasks. This approach neglects the substantial benefits that could arise from a task-agnostic unified understanding between symbolic equations and their numeric counterparts. To bridge the gap, we introduce SNIP, a Symbolic-Numeric Integrated Pre-training, which employs joint contrastive learning between symbolic and numeric domains, enhancing their mutual similarities in the pre-trained embeddings. By performing latent space analysis, we observe that SNIP provides cross-domain insights into the representations, revealing that symbolic supervision enhances the embeddings of numeric data and vice versa. We evaluate SNIP across diverse tasks, including symbolic-to-numeric mathematical property prediction and numeric-to-symbolic equation discovery, commonly known as symbolic regression. Results show that SNIP effectively transfers to various tasks, consistently outperforming fully supervised baselines and competing strongly with established task-specific methods, especially in few-shot learning scenarios where available data is limited.

The latest Deep Learning (DL) models for detection and classification have achieved an unprecedented performance over classical machine learning algorithms. However, DL models are black-box methods hard to debug, interpret, and certify. DL alone cannot provide explanations that can be validated by a non technical audience. In contrast, symbolic AI systems that convert concepts into rules or symbols -- such as knowledge graphs -- are easier to explain. However, they present lower generalisation and scaling capabilities. A very important challenge is to fuse DL representations with expert knowledge. One way to address this challenge, as well as the performance-explainability trade-off is by leveraging the best of both streams without obviating domain expert knowledge. We tackle such problem by considering the symbolic knowledge is expressed in form of a domain expert knowledge graph. We present the eXplainable Neural-symbolic learning (X-NeSyL) methodology, designed to learn both symbolic and deep representations, together with an explainability metric to assess the level of alignment of machine and human expert explanations. The ultimate objective is to fuse DL representations with expert domain knowledge during the learning process to serve as a sound basis for explainability. X-NeSyL methodology involves the concrete use of two notions of explanation at inference and training time respectively: 1) EXPLANet: Expert-aligned eXplainable Part-based cLAssifier NETwork Architecture, a compositional CNN that makes use of symbolic representations, and 2) SHAP-Backprop, an explainable AI-informed training procedure that guides the DL process to align with such symbolic representations in form of knowledge graphs. We showcase X-NeSyL methodology using MonuMAI dataset for monument facade image classification, and demonstrate that our approach improves explainability and performance.

Today's probabilistic language generators fall short when it comes to producing coherent and fluent text despite the fact that the underlying models perform well under standard metrics, e.g., perplexity. This discrepancy has puzzled the language generation community for the last few years. In this work, we posit that the abstraction of natural language generation as a discrete stochastic process--which allows for an information-theoretic analysis--can provide new insights into the behavior of probabilistic language generators, e.g., why high-probability texts can be dull or repetitive. Humans use language as a means of communicating information, aiming to do so in a simultaneously efficient and error-minimizing manner; in fact, psycholinguistics research suggests humans choose each word in a string with this subconscious goal in mind. We formally define the set of strings that meet this criterion: those for which each word has an information content close to the expected information content, i.e., the conditional entropy of our model. We then propose a simple and efficient procedure for enforcing this criterion when generating from probabilistic models, which we call locally typical sampling. Automatic and human evaluations show that, in comparison to nucleus and top-k sampling, locally typical sampling offers competitive performance (in both abstractive summarization and story generation) in terms of quality while consistently reducing degenerate repetitions.

What mathematical functions do neural network components learn? Symbolic distillation addresses this question by expressing neural network components with interpretable, closed-form mathematical expressions that expose the functional structure learned during training. We develop symbolic distillation as a systematic, architecture-agnostic methodology, and release our approach as the open-source SymTorch package - a PySR-powered library built natively for the PyTorch ecosystem. Applying this methodology across diverse architectures, we find that SymTorch is successful in the automated discovery of physical laws. Specifically, our approach (1) recovers pairwise interaction forces from graph neural networks trained on empirical n-body observations, (2) distills the exact closed-form PDE/ODE solutions of multiple physical systems, including the value of constants, from physics-informed neural networks trained on sparse data, and (3) uncovers the chaotic dynamics of the Lorenz system from high-dimensional data, ultimately outperforming the base neural network on downstream prediction tasks. We further demonstrate the utility of our framework for model interpretability by providing an optimized implementation of SLIME - a symbolic extension to the LIME explainability method. SLIME consistently outperforms LIME across predictive metrics across eight popular classification and regression benchmarks, while still providing an interpretable local symbolic model. Lastly, we investigate replacing transformer MLP layers with symbolic surrogates: replacing 1-7 layers with symbolic approximations yields 2-19\% throughput improvements and up to 18.7\% VRAM reduction, with the resulting hybrid models lying on the Pareto front of throughput versus perplexity among open-source LLMs of comparable scale.

This paper revisits datasets and evaluation criteria for Symbolic Regression, a task of expressing given data using mathematical equations, specifically focused on its potential for scientific discovery. Focused on a set of formulas used in the existing datasets based on Feynman Lectures on Physics, we recreate 120 datasets to discuss the performance of symbolic regression for scientific discovery (SRSD). For each of the 120 SRSD datasets, we carefully review the properties of the formula and its variables to design reasonably realistic sampling range of values so that our new SRSD datasets can be used for evaluating the potential of SRSD such as whether or not an SR method can (re)discover physical laws from such datasets. As an evaluation metric, we also propose to use normalized edit distances between a predicted equation and the ground-truth equation trees. While existing metrics are either binary or errors between the target values and an SR model's predicted values for a given input, normalized edit distances evaluate a sort of similarity between the ground-truth and predicted equation trees. We have conducted experiments on our new SRSD datasets using five state-of-the-art SR methods in SRBench and a simple baseline based on a recent Transformer architecture. The results show that we provide a more realistic performance evaluation and open up a new machine learning-based approach for scientific discovery. Our datasets and code repository are publicly available.

Symbolic regression (SR) aims to discover closed-form mathematical expressions that accurately describe data, offering interpretability and analytical insight beyond standard black-box models. Existing SR methods often rely on population-based search or autoregressive modeling, which struggle with scalability and symbolic consistency. We introduce LIES (Logarithm, Identity, Exponential, Sine), a fixed neural network architecture with interpretable primitive activations that are optimized to model symbolic expressions. We develop a framework to extract compact formulae from LIES networks by training with an appropriate oversampling strategy and a tailored loss function to promote sparsity and to prevent gradient instability. After training, it applies additional pruning strategies to further simplify the learned expressions into compact formulae. Our experiments on SR benchmarks show that the LIES framework consistently produces sparse and accurate symbolic formulae outperforming all baselines. We also demonstrate the importance of each design component through ablation studies.

The symbolic discovery of Ordinary Differential Equations (ODEs) from trajectory data plays a pivotal role in AI-driven scientific discovery. Existing symbolic methods predominantly rely on fixed, pre-collected training datasets, which often result in suboptimal performance, as demonstrated in our case study in Figure 1. Drawing inspiration from active learning, we investigate strategies to query informative trajectory data that can enhance the evaluation of predicted ODEs. However, the butterfly effect in dynamical systems reveals that small variations in initial conditions can lead to drastically different trajectories, necessitating the storage of vast quantities of trajectory data using conventional active learning. To address this, we introduce Active Symbolic Discovery of Ordinary Differential Equations via Phase Portrait Sketching (APPS). Instead of directly selecting individual initial conditions, our APPS first identifies an informative region within the phase space and then samples a batch of initial conditions from this region. Compared to traditional active learning methods, APPS mitigates the gap of maintaining a large amount of data. Extensive experiments demonstrate that APPS consistently discovers more accurate ODE expressions than baseline methods using passively collected datasets.

In this paper, we explain the inference logic of large language models (LLMs) as a set of symbolic concepts. Many recent studies have discovered that traditional DNNs usually encode sparse symbolic concepts. However, because an LLM has much more parameters than traditional DNNs, whether the LLM also encodes sparse symbolic concepts is still an open problem. Therefore, in this paper, we propose to disentangle the inference score of LLMs for dialogue tasks into a small number of symbolic concepts. We verify that we can use those sparse concepts to well estimate all inference scores of the LLM on all arbitrarily masking states of the input sentence. We also evaluate the transferability of concepts encoded by an LLM and verify that symbolic concepts usually exhibit high transferability across similar input sentences. More crucially, those symbolic concepts can be used to explain the exact reasons accountable for the LLM's prediction errors.

Discovering the underlying mathematical expressions describing a dataset is a core challenge for artificial intelligence. This is the problem of symbolic regression. Despite recent advances in training neural networks to solve complex tasks, deep learning approaches to symbolic regression are underexplored. We propose a framework that leverages deep learning for symbolic regression via a simple idea: use a large model to search the space of small models. Specifically, we use a recurrent neural network to emit a distribution over tractable mathematical expressions and employ a novel risk-seeking policy gradient to train the network to generate better-fitting expressions. Our algorithm outperforms several baseline methods (including Eureqa, the gold standard for symbolic regression) in its ability to exactly recover symbolic expressions on a series of benchmark problems, both with and without added noise. More broadly, our contributions include a framework that can be applied to optimize hierarchical, variable-length objects under a black-box performance metric, with the ability to incorporate constraints in situ, and a risk-seeking policy gradient formulation that optimizes for best-case performance instead of expected performance.

The AI community has been exploring a pathway to artificial general intelligence (AGI) by developing "language agents", which are complex large language models (LLMs) pipelines involving both prompting techniques and tool usage methods. While language agents have demonstrated impressive capabilities for many real-world tasks, a fundamental limitation of current language agents research is that they are model-centric, or engineering-centric. That's to say, the progress on prompts, tools, and pipelines of language agents requires substantial manual engineering efforts from human experts rather than automatically learning from data. We believe the transition from model-centric, or engineering-centric, to data-centric, i.e., the ability of language agents to autonomously learn and evolve in environments, is the key for them to possibly achieve AGI. In this work, we introduce agent symbolic learning, a systematic framework that enables language agents to optimize themselves on their own in a data-centric way using symbolic optimizers. Specifically, we consider agents as symbolic networks where learnable weights are defined by prompts, tools, and the way they are stacked together. Agent symbolic learning is designed to optimize the symbolic network within language agents by mimicking two fundamental algorithms in connectionist learning: back-propagation and gradient descent. Instead of dealing with numeric weights, agent symbolic learning works with natural language simulacrums of weights, loss, and gradients. We conduct proof-of-concept experiments on both standard benchmarks and complex real-world tasks and show that agent symbolic learning enables language agents to update themselves after being created and deployed in the wild, resulting in "self-evolving agents".

Progress in the task of symbolic music generation may be lagging behind other tasks like audio and text generation, in part because of the scarcity of symbolic training data. In this paper, we leverage the greater scale of audio music data by applying pre-trained MIR models (for transcription, beat tracking, structure analysis, etc.) to extract symbolic events and encode them into token sequences. To the best of our knowledge, this work is the first to demonstrate the feasibility of training symbolic generation models solely from auto-transcribed audio data. Furthermore, to enhance the controllability of the trained model, we introduce SymPAC (Symbolic Music Language Model with Prompting And Constrained Generation), which is distinguished by using (a) prompt bars in encoding and (b) a technique called Constrained Generation via Finite State Machines (FSMs) during inference time. We show the flexibility and controllability of this approach, which may be critical in making music AI useful to creators and users.

The trade-off between expressiveness and interpretability remains a core challenge when building human-centric predictive models for classification and decision-making. While symbolic rules offer interpretability, they often lack expressiveness, whereas neural networks excel in performance but are known for being black boxes. In this paper, we show a combination of Large Language Models (LLMs) and symbolic programs can bridge this gap. In the proposed LLM-based Symbolic Programs (LSPs), the pretrained LLM with natural language prompts provides a massive set of interpretable modules that can transform raw input into natural language concepts. Symbolic programs then integrate these modules into an interpretable decision rule. To train LSPs, we develop a divide-and-conquer approach to incrementally build the program from scratch, where the learning process of each step is guided by LLMs. To evaluate the effectiveness of LSPs in extracting interpretable and accurate knowledge from data, we introduce IL-Bench, a collection of diverse tasks, including both synthetic and real-world scenarios across different modalities. Empirical results demonstrate LSP's superior performance compared to traditional neurosymbolic programs and vanilla automatic prompt tuning methods. Moreover, as the knowledge learned by LSP is a combination of natural language descriptions and symbolic rules, it is easily transferable to humans (interpretable), and other LLMs, and generalizes well to out-of-distribution samples.

We develop a general approach to distill symbolic representations of a learned deep model by introducing strong inductive biases. We focus on Graph Neural Networks (GNNs). The technique works as follows: we first encourage sparse latent representations when we train a GNN in a supervised setting, then we apply symbolic regression to components of the learned model to extract explicit physical relations. We find the correct known equations, including force laws and Hamiltonians, can be extracted from the neural network. We then apply our method to a non-trivial cosmology example-a detailed dark matter simulation-and discover a new analytic formula which can predict the concentration of dark matter from the mass distribution of nearby cosmic structures. The symbolic expressions extracted from the GNN using our technique also generalized to out-of-distribution data better than the GNN itself. Our approach offers alternative directions for interpreting neural networks and discovering novel physical principles from the representations they learn.

One of the primary driving forces contributing to the superior performance of Large Language Models (LLMs) is the extensive availability of human-annotated natural language data, which is used for alignment fine-tuning. This inspired researchers to investigate self-training methods to mitigate the extensive reliance on human annotations. However, the current success of self-training has been primarily observed in natural language scenarios, rather than in the increasingly important neural-symbolic scenarios. To this end, we propose an environment-guided neural-symbolic self-training framework named ENVISIONS. It aims to overcome two main challenges: (1) the scarcity of symbolic data, and (2) the limited proficiency of LLMs in processing symbolic language. Extensive evaluations conducted on three distinct domains demonstrate the effectiveness of our approach. Additionally, we have conducted a comprehensive analysis to uncover the factors contributing to ENVISIONS's success, thereby offering valuable insights for future research in this area. Code will be available at https://github.com/xufangzhi/ENVISIONS.

Large Language Models (LLMs) are transforming scientific hypothesis generation and validation by enabling information synthesis, latent relationship discovery, and reasoning augmentation. This survey provides a structured overview of LLM-driven approaches, including symbolic frameworks, generative models, hybrid systems, and multi-agent architectures. We examine techniques such as retrieval-augmented generation, knowledge-graph completion, simulation, causal inference, and tool-assisted reasoning, highlighting trade-offs in interpretability, novelty, and domain alignment. We contrast early symbolic discovery systems (e.g., BACON, KEKADA) with modern LLM pipelines that leverage in-context learning and domain adaptation via fine-tuning, retrieval, and symbolic grounding. For validation, we review simulation, human-AI collaboration, causal modeling, and uncertainty quantification, emphasizing iterative assessment in open-world contexts. The survey maps datasets across biomedicine, materials science, environmental science, and social science, introducing new resources like AHTech and CSKG-600. Finally, we outline a roadmap emphasizing novelty-aware generation, multimodal-symbolic integration, human-in-the-loop systems, and ethical safeguards, positioning LLMs as agents for principled, scalable scientific discovery.

We present a novel method for symbolic regression (SR), the task of searching for compact programmatic hypotheses that best explain a dataset. The problem is commonly solved using genetic algorithms; we show that we can enhance such methods by inducing a library of abstract textual concepts. Our algorithm, called LaSR, uses zero-shot queries to a large language model (LLM) to discover and evolve concepts occurring in known high-performing hypotheses. We discover new hypotheses using a mix of standard evolutionary steps and LLM-guided steps (obtained through zero-shot LLM queries) conditioned on discovered concepts. Once discovered, hypotheses are used in a new round of concept abstraction and evolution. We validate LaSR on the Feynman equations, a popular SR benchmark, as well as a set of synthetic tasks. On these benchmarks, LaSR substantially outperforms a variety of state-of-the-art SR approaches based on deep learning and evolutionary algorithms. Moreover, we show that LaSR can be used to discover a novel and powerful scaling law for LLMs.

Large language models (LLMs) with memory are computationally universal. However, mainstream LLMs are not taking full advantage of memory, and the designs are heavily influenced by biological brains. Due to their approximate nature and proneness to the accumulation of errors, conventional neural memory mechanisms cannot support LLMs to simulate complex reasoning. In this paper, we seek inspiration from modern computer architectures to augment LLMs with symbolic memory for complex multi-hop reasoning. Such a symbolic memory framework is instantiated as an LLM and a set of SQL databases, where the LLM generates SQL instructions to manipulate the SQL databases. We validate the effectiveness of the proposed memory framework on a synthetic dataset requiring complex reasoning. The project website is available at https://chatdatabase.github.io/ .

Loop invariants are fundamental to reasoning about programs with loops. They establish properties about a given loop's behavior. When they additionally are inductive, they become useful for the task of formal verification that seeks to establish strong mathematical guarantees about program's runtime behavior. The inductiveness ensures that the invariants can be checked locally without consulting the entire program, thus are indispensable artifacts in a formal proof of correctness. Finding inductive loop invariants is an undecidable problem, and despite a long history of research towards practical solutions, it remains far from a solved problem. This paper investigates the capabilities of the Large Language Models (LLMs) in offering a new solution towards this old, yet important problem. To that end, we first curate a dataset of verification problems on programs with loops. Next, we design a prompt for exploiting LLMs, obtaining inductive loop invariants, that are checked for correctness using sound symbolic tools. Finally, we explore the effectiveness of using an efficient combination of a symbolic tool and an LLM on our dataset and compare it against a purely symbolic baseline. Our results demonstrate that LLMs can help improve the state-of-the-art in automated program verification.

Large Language Models (LLMs) have been successfully used in many natural-language tasks and applications including text generation and AI chatbots. They also are a promising new technology for concept-oriented deep learning (CODL). However, the prerequisite is that LLMs understand concepts and ensure conceptual consistency. We discuss these in this paper, as well as major uses of LLMs for CODL including concept extraction from text, concept graph extraction from text, and concept learning. Human knowledge consists of both symbolic (conceptual) knowledge and embodied (sensory) knowledge. Text-only LLMs, however, can represent only symbolic (conceptual) knowledge. Multimodal LLMs, on the other hand, are capable of representing the full range (conceptual and sensory) of human knowledge. We discuss conceptual understanding in visual-language LLMs, the most important multimodal LLMs, and major uses of them for CODL including concept extraction from image, concept graph extraction from image, and concept learning. While uses of LLMs for CODL are valuable standalone, they are particularly valuable as part of LLM applications such as AI chatbots.

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically learn embeddings in Euclidean vector spaces, which do not account for this property. For this purpose, we introduce a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincar\'e ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We introduce an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincar\'e embeddings outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability.

The symbolic architecture of non-ordinary consciousness remains largely unmapped in cognitive science and artificial intelligence. While conventional models prioritize rational coherence, altered states such as those induced by psychedelics reveal distinct symbolic regimes characterized by recursive metaphor, ego dissolution, and semantic destabilization. We present Glyph, a generative symbolic interface designed to simulate psilocybin-like symbolic cognition in large language models. Rather than modeling perception or mood, Glyph enacts symbolic transformation through recursive reentry, metaphoric modulation, and entropy-scaled destabilization -- a triadic operator formalized within a tensorial linguistic framework. Experimental comparison with baseline GPT-4o reveals that Glyph consistently generates high-entropy, metaphor-saturated, and ego-dissolving language across diverse symbolic prompt categories. These results validate the emergence of non-ordinary cognitive patterns and support a new paradigm for simulating altered consciousness through language. Glyph opens novel pathways for modeling symbolic cognition, exploring metaphor theory, and encoding knowledge in recursively altered semantic spaces.

How can we perform computations over natural language representations to solve tasks that require symbolic and numeric reasoning? We propose natural language embedded programs (NLEP) as a unifying framework for addressing math/symbolic reasoning, natural language understanding, and instruction following tasks. Our approach prompts a language model to generate full Python programs that define functions over data structures which contain natural language representations of structured knowledge. A Python interpreter then executes the generated code and prints the output. Despite using a task-general prompt, we find that this approach can improve upon strong baselines across a range of different tasks including math and symbolic reasoning, text classification, question answering, and instruction following. We further find the generated programs are often interpretable and enable post-hoc verification of the intermediate reasoning steps.

Semantic code search is the task of retrieving a code snippet given a textual description of its functionality. Recent work has been focused on using similarity metrics between neural embeddings of text and code. However, current language models are known to struggle with longer, compositional text, and multi-step reasoning. To overcome this limitation, we propose supplementing the query sentence with a layout of its semantic structure. The semantic layout is used to break down the final reasoning decision into a series of lower-level decisions. We use a Neural Module Network architecture to implement this idea. We compare our model - NS3 (Neuro-Symbolic Semantic Search) - to a number of baselines, including state-of-the-art semantic code retrieval methods, and evaluate on two datasets - CodeSearchNet and Code Search and Question Answering. We demonstrate that our approach results in more precise code retrieval, and we study the effectiveness of our modular design when handling compositional queries.