Daily Papers

We present a reproducible, parameter-driven software workflow for optimizing approximate mutually unbiased basis (AMUB) configurations in arbitrary dimensions d using a Lie-algebra unitary parameterization. The workflow is designed for portable execution across CPU, Apple MPS, CUDA-capable GPU, and HPC backends, using a Taylor-series matrix exponential layer as an accelerator compatibility pathway. As a dimension-six case study, we optimize unanchored configurations across 100 random seeds for basis counts n = 3, 4, 5, 6 in complex128 and complex64 arithmetic. The workflow recovers exact three-basis configurations, identifies a recurrent four-basis partial-exact hub-and-triangle structure, and finds no near-exact pairs for n = 5 or n = 6 in the reported campaigns under the primary tolerance. As a hardware-execution check, we embed the representative d = 6, n = 4 transition unitaries into three-qubit 8x8 unitaries and execute the resulting circuits on the 156-qubit Heron processor ibm-marrakesh using subspace post-selection. The measured QPU pairwise losses are dominated by a hardware and compilation noise floor of approximately 0.02-0.08, associated with compiled circuits averaging 37 native CZ gates, which obscures the distinction between classically near-exact and defective pairs. The results provide a reproducible computational framework for exploring AMUB landscapes, together with an initial assessment of the challenges involved in executing optimized dimension-six unitaries on current quantum hardware.

A family of loss functions built on pair-based computation have been proposed in the literature which provide a myriad of solutions for deep metric learning. In this paper, we provide a general weighting framework for understanding recent pair-based loss functions. Our contributions are three-fold: (1) we establish a General Pair Weighting (GPW) framework, which casts the sampling problem of deep metric learning into a unified view of pair weighting through gradient analysis, providing a powerful tool for understanding recent pair-based loss functions; (2) we show that with GPW, various existing pair-based methods can be compared and discussed comprehensively, with clear differences and key limitations identified; (3) we propose a new loss called multi-similarity loss (MS loss) under the GPW, which is implemented in two iterative steps (i.e., mining and weighting). This allows it to fully consider three similarities for pair weighting, providing a more principled approach for collecting and weighting informative pairs. Finally, the proposed MS loss obtains new state-of-the-art performance on four image retrieval benchmarks, where it outperforms the most recent approaches, such as ABEKim_2018_ECCV and HTL by a large margin: 60.6% to 65.7% on CUB200, and 80.9% to 88.0% on In-Shop Clothes Retrieval dataset at Recall@1. Code is available at https://github.com/MalongTech/research-ms-loss.

Loss functions serve as the foundation of supervised learning and are often chosen prior to model development. To avoid potentially ad hoc choices of losses, statistical decision theory describes a desirable property for losses known as properness, which asserts that Bayes' rule is optimal. Recent works have sought to learn losses and models jointly. Existing methods do this by fitting an inverse canonical link function which monotonically maps R to [0,1] to estimate probabilities for binary problems. In this paper, we extend monotonicity to maps between R^{C-1} and the projected probability simplex Delta^{C-1} by using monotonicity of gradients of convex functions. We present {\sc LegendreTron} as a novel and practical method that jointly learns proper canonical losses and probabilities for multiclass problems. Tested on a benchmark of domains with up to 1,000 classes, our experimental results show that our method consistently outperforms the natural multiclass baseline under a t-test at 99% significance on all datasets with greater than 10 classes.

Most existing works focus on improving robustness against adversarial attacks bounded by a single l_p norm using adversarial training (AT). However, these AT models' multiple-norm robustness (union accuracy) is still low, which is crucial since in the real-world an adversary is not necessarily bounded by a single norm. The tradeoffs among robustness against multiple l_p perturbations and accuracy/robustness make obtaining good union and clean accuracy challenging. We design a logit pairing loss to improve the union accuracy by analyzing the tradeoffs from the lens of distribution shifts. We connect natural training (NT) with AT via gradient projection, to incorporate useful information from NT into AT, where we empirically and theoretically show it moderates the accuracy/robustness tradeoff. We propose a novel training framework RAMP, to boost the robustness against multiple l_p perturbations. RAMP can be easily adapted for robust fine-tuning and full AT. For robust fine-tuning, RAMP obtains a union accuracy up to 53.3% on CIFAR-10, and 29.1% on ImageNet. For training from scratch, RAMP achieves a union accuracy of 44.6% and good clean accuracy of 81.2% on ResNet-18 against AutoAttack on CIFAR-10. Beyond multi-norm robustness RAMP-trained models achieve superior universal robustness, effectively generalizing against a range of unseen adversaries and natural corruptions.

Practitioners commonly align large language models using pairwise preferences, i.e., given labels of the type response A is preferred to response B for a given input. Perhaps less commonly, methods have also been developed for binary feedback, i.e. training models given labels of type response A is good or bad. We show how an existing performant binary feedback method, the Cringe Loss (Adolphs et al., 2022), can be generalized to the pairwise preference setting using a simple soft margin extension. Pairwise Cringe Loss is straightforward to implement and efficient to train, and we find it outperforms state-of-the-art preference optimization algorithms such as PPO and DPO on the AlpacaFarm benchmark.

The fine-tuning of pre-trained large language models (LLMs) using reinforcement learning (RL) is generally formulated as direct policy optimization. This approach was naturally favored as it efficiently improves a pretrained LLM, seen as an initial policy. Another RL paradigm, Q-learning methods, has received far less attention in the LLM community while demonstrating major success in various non-LLM RL tasks. In particular, Q-learning effectiveness comes from its sample efficiency and ability to learn offline, which is particularly valuable given the high computational cost of sampling with LLMs. However, naively applying a Q-learning-style update to the model's logits is ineffective due to the specificity of LLMs. Our core contribution is to derive theoretically grounded loss functions from Bellman equations to adapt Q-learning methods to LLMs. To do so, we carefully adapt insights from the RL literature to account for LLM-specific characteristics, ensuring that the logits become reliable Q-value estimates. We then use this loss to build a practical algorithm, ShiQ for Shifted-Q, that supports off-policy, token-wise learning while remaining simple to implement. Finally, we evaluate ShiQ on both synthetic data and real-world benchmarks, e.g., UltraFeedback and BFCL-V3, demonstrating its effectiveness in both single-turn and multi-turn LLM settings

Softmax Loss (SL) is widely applied in recommender systems (RS) and has demonstrated effectiveness. This work analyzes SL from a pairwise perspective, revealing two significant limitations: 1) the relationship between SL and conventional ranking metrics like DCG is not sufficiently tight; 2) SL is highly sensitive to false negative instances. Our analysis indicates that these limitations are primarily due to the use of the exponential function. To address these issues, this work extends SL to a new family of loss functions, termed Pairwise Softmax Loss (PSL), which replaces the exponential function in SL with other appropriate activation functions. While the revision is minimal, we highlight three merits of PSL: 1) it serves as a tighter surrogate for DCG with suitable activation functions; 2) it better balances data contributions; and 3) it acts as a specific BPR loss enhanced by Distributionally Robust Optimization (DRO). We further validate the effectiveness and robustness of PSL through empirical experiments. The code is available at https://github.com/Tiny-Snow/IR-Benchmark.

Recent direct preference alignment algorithms (DPA), such as DPO, have shown great promise in aligning large language models to human preferences. While this has motivated the development of many new variants of the original DPO loss, understanding the differences between these recent proposals, as well as developing new DPA loss functions, remains difficult given the lack of a technical and conceptual framework for reasoning about the underlying semantics of these algorithms. In this paper, we attempt to remedy this by formalizing DPA losses in terms of discrete reasoning problems. Specifically, we ask: Given an existing DPA loss, can we systematically derive a symbolic expression that characterizes its semantics? How do the semantics of two losses relate to each other? We propose a novel formalism for characterizing preference losses for single model and reference model based approaches, and identify symbolic forms for a number of commonly used DPA variants. Further, we show how this formal view of preference learning sheds new light on both the size and structure of the DPA loss landscape, making it possible to not only rigorously characterize the relationships between recent loss proposals but also to systematically explore the landscape and derive new loss functions from first principles. We hope our framework and findings will help provide useful guidance to those working on human AI alignment.

Recent works have shown a reduction from contextual bandits to online regression under a realizability assumption [Foster and Rakhlin, 2020, Foster and Krishnamurthy, 2021]. In this work, we investigate the use of neural networks for such online regression and associated Neural Contextual Bandits (NeuCBs). Using existing results for wide networks, one can readily show a {O}(T) regret for online regression with square loss, which via the reduction implies a {O}(K T^{3/4}) regret for NeuCBs. Departing from this standard approach, we first show a O(log T) regret for online regression with almost convex losses that satisfy QG (Quadratic Growth) condition, a generalization of the PL (Polyak-\L ojasiewicz) condition, and that have a unique minima. Although not directly applicable to wide networks since they do not have unique minima, we show that adding a suitable small random perturbation to the network predictions surprisingly makes the loss satisfy QG with unique minima. Based on such a perturbed prediction, we show a {O}(log T) regret for online regression with both squared loss and KL loss, and subsequently convert these respectively to mathcal{O}(KT) and mathcal{O}(KL^* + K) regret for NeuCB, where L^* is the loss of the best policy. Separately, we also show that existing regret bounds for NeuCBs are Omega(T) or assume i.i.d. contexts, unlike this work. Finally, our experimental results on various datasets demonstrate that our algorithms, especially the one based on KL loss, persistently outperform existing algorithms.

Classical supply chain risk models treat node failures as statistically independent events, systematically underestimating cascade probabilities when supplier dependencies are strongly correlated. At n=40 nodes, the full correlated failure distribution requires O(2^n) classical samples, a regime where exact simulation demands 17.6 TB of memory and over 369,000 hours of computation on a standard workstation. We present QR-SPPS (Quantum-Native Retail Shock Propagation and Policy Stress Simulator), a three-algorithm quantum pipeline implemented using the Qiskit framework with the Aer statevector_simulator backend. First, a 40-node, 4-tier retail supply network is encoded as a 40-qubit Ising Hamiltonian using OpenFermion QubitOperator, where ZZ coupling terms encode correlated cascade probabilities structurally absent from classical Monte Carlo. Second, a hardware-efficient VQE circuit finds the ground-state stress distribution with zero error, detecting entangled cascade failures in 14/40 nodes with max|ΔP|=0.637 versus classical Monte Carlo. Third, we introduce the first application of ADAPT-VQE gradient screening to counterfactual macroeconomic policy evaluation: six crisis interventions are ranked in O(1) Qiskit operator evaluations per policy, a 287x speedup over sequential VQE re-optimisation. Fourth, Density-of-States QPE (DOS-QPE) reconstructs the full eigenspectrum via 32-step Trotter evolution and introduces a novel mapping of the Boltzmann catastrophe probability P_cat(T) to VIX-equivalent market volatility temperature, enabling direct integration into regulatory Value-at-Risk frameworks. Qiskit Aer scaling benchmarks confirm exponential classical intractability at 40 qubits.

We propose UCBMQ, Upper Confidence Bound Momentum Q-learning, a new algorithm for reinforcement learning in tabular and possibly stage-dependent, episodic Markov decision process. UCBMQ is based on Q-learning where we add a momentum term and rely on the principle of optimism in face of uncertainty to deal with exploration. Our new technical ingredient of UCBMQ is the use of momentum to correct the bias that Q-learning suffers while, at the same time, limiting the impact it has on the second-order term of the regret. For UCBMQ, we are able to guarantee a regret of at most O(H^3SAT+ H^4 S A ) where H is the length of an episode, S the number of states, A the number of actions, T the number of episodes and ignoring terms in poly-log(SAHT). Notably, UCBMQ is the first algorithm that simultaneously matches the lower bound of Ω(H^3SAT) for large enough T and has a second-order term (with respect to the horizon T) that scales only linearly with the number of states S.

Reinforcement learning with verifiable rewards (RLVR) is effective for training large language models on deterministic outcome reasoning tasks. Prior work shows RLVR works with few prompts, but prompt selection is often based only on training-accuracy variance, leading to unstable optimization directions and weaker transfer. We revisit prompt selection from a mechanism-level view and argue that an effective minibatch should provide both (i) a reliable positive anchor and (ii) explicit negative learning signals from rare failures. Based on this principle, we propose positive--negative pairing: at each update, we sample a hard-but-solvable q^{+} and an easy-but-brittle prompt q^{-}(high success rate but not perfect), characterized by low and high empirical success rates under multiple rollouts. We further introduce Weighted GRPO, which reweights binary outcomes at the pair level and uses group-normalized advantages to amplify rare successes on q^{+} into sharp positive guidance while turning rare failures on q^{-} into strong negative penalties. This bidirectional signal provides informative learning feedback for both successes and failures, improving sample efficiency without suppressing exploration. On Qwen2.5-Math-7B, a single paired minibatch per update consistently outperforms a GRPO baseline that selects two prompts via commonly used variance-based selection heuristics: AIME~2025 Pass@8 improves from 16.8 to 22.2, and AMC23 Pass@64 from 94.0 to 97.0, while remaining competitive with large-scale RLVR trained from a pool of 1209 training prompts. Similar gains are observed on Qwen2.5-Math-7B-Instruct.

Cross-entropy is a widely used loss function in applications. It coincides with the logistic loss applied to the outputs of a neural network, when the softmax is used. But, what guarantees can we rely on when using cross-entropy as a surrogate loss? We present a theoretical analysis of a broad family of loss functions, comp-sum losses, that includes cross-entropy (or logistic loss), generalized cross-entropy, the mean absolute error and other cross-entropy-like loss functions. We give the first H-consistency bounds for these loss functions. These are non-asymptotic guarantees that upper bound the zero-one loss estimation error in terms of the estimation error of a surrogate loss, for the specific hypothesis set H used. We further show that our bounds are tight. These bounds depend on quantities called minimizability gaps. To make them more explicit, we give a specific analysis of these gaps for comp-sum losses. We also introduce a new family of loss functions, smooth adversarial comp-sum losses, that are derived from their comp-sum counterparts by adding in a related smooth term. We show that these loss functions are beneficial in the adversarial setting by proving that they admit H-consistency bounds. This leads to new adversarial robustness algorithms that consist of minimizing a regularized smooth adversarial comp-sum loss. While our main purpose is a theoretical analysis, we also present an extensive empirical analysis comparing comp-sum losses. We further report the results of a series of experiments demonstrating that our adversarial robustness algorithms outperform the current state-of-the-art, while also achieving a superior non-adversarial accuracy.

The goal of face recognition (FR) can be viewed as a pair similarity optimization problem, maximizing a similarity set S^p over positive pairs, while minimizing similarity set S^n over negative pairs. Ideally, it is expected that FR models form a well-discriminative feature space (WDFS) that satisfies mathcal{S^p} > mathcal{S^n}. With regard to WDFS, the existing deep feature learning paradigms (i.e., metric and classification losses) can be expressed as a unified perspective on different pair generation (PG) strategies. Unfortunately, in the metric loss (ML), it is infeasible to generate negative pairs taking all classes into account in each iteration because of the limited mini-batch size. In contrast, in classification loss (CL), it is difficult to generate extremely hard negative pairs owing to the convergence of the class weight vectors to their center. This leads to a mismatch between the two similarity distributions of the sampled pairs and all negative pairs. Thus, this paper proposes a unified negative pair generation (UNPG) by combining two PG strategies (i.e., MLPG and CLPG) from a unified perspective to alleviate the mismatch. UNPG introduces useful information about negative pairs using MLPG to overcome the CLPG deficiency. Moreover, it includes filtering the similarities of noisy negative pairs to guarantee reliable convergence and improved performance. Exhaustive experiments show the superiority of UNPG by achieving state-of-the-art performance across recent loss functions on public benchmark datasets. Our code and pretrained models are publicly available.

We initiate the study of proper losses for evaluating generative models in the discrete setting. Unlike traditional proper losses, we treat both the generative model and the target distribution as black-boxes, only assuming ability to draw i.i.d. samples. We define a loss to be black-box proper if the generative distribution that minimizes expected loss is equal to the target distribution. Using techniques from statistical estimation theory, we give a general construction and characterization of black-box proper losses: they must take a polynomial form, and the number of draws from the model and target distribution must exceed the degree of the polynomial. The characterization rules out a loss whose expectation is the cross-entropy between the target distribution and the model. By extending the construction to arbitrary sampling schemes such as Poisson sampling, however, we show that one can construct such a loss.

Most value function learning algorithms in reinforcement learning are based on the mean squared (projected) Bellman error. However, squared errors are known to be sensitive to outliers, both skewing the solution of the objective and resulting in high-magnitude and high-variance gradients. To control these high-magnitude updates, typical strategies in RL involve clipping gradients, clipping rewards, rescaling rewards, or clipping errors. While these strategies appear to be related to robust losses -- like the Huber loss -- they are built on semi-gradient update rules which do not minimize a known loss. In this work, we build on recent insights reformulating squared Bellman errors as a saddlepoint optimization problem and propose a saddlepoint reformulation for a Huber Bellman error and Absolute Bellman error. We start from a formalization of robust losses, then derive sound gradient-based approaches to minimize these losses in both the online off-policy prediction and control settings. We characterize the solutions of the robust losses, providing insight into the problem settings where the robust losses define notably better solutions than the mean squared Bellman error. Finally, we show that the resulting gradient-based algorithms are more stable, for both prediction and control, with less sensitivity to meta-parameters.

We consider learning in an adversarial Markov Decision Process (MDP) where the loss functions can change arbitrarily over K episodes and the state space can be arbitrarily large. We assume that the Q-function of any policy is linear in some known features, that is, a linear function approximation exists. The best existing regret upper bound for this setting (Luo et al., 2021) is of order mathcal O(K^{2/3}) (omitting all other dependencies), given access to a simulator. This paper provides two algorithms that improve the regret to mathcal O(sqrt K) in the same setting. Our first algorithm makes use of a refined analysis of the Follow-the-Regularized-Leader (FTRL) algorithm with the log-barrier regularizer. This analysis allows the loss estimators to be arbitrarily negative and might be of independent interest. Our second algorithm develops a magnitude-reduced loss estimator, further removing the polynomial dependency on the number of actions in the first algorithm and leading to the optimal regret bound (up to logarithmic terms and dependency on the horizon). Moreover, we also extend the first algorithm to simulator-free linear MDPs, which achieves mathcal O(K^{8/9}) regret and greatly improves over the best existing bound mathcal O(K^{14/15}). This algorithm relies on a better alternative to the Matrix Geometric Resampling procedure by Neu & Olkhovskaya (2020), which could again be of independent interest.

Decentralized learning often involves a weighted global loss with heterogeneous node weights λ. We revisit two natural strategies for incorporating these weights: (i) embedding them into the local losses to retain a uniform weight (and thus a doubly stochastic matrix), and (ii) keeping the original losses while employing a λ-induced row-stochastic matrix. Although prior work shows that both strategies target the same λ-weighted global loss, it remains unclear whether the Euclidean-space guarantees are tight and what fundamentally differentiates their behaviors. To clarify this, we develop a weighted Hilbert-space framework L^2(λ;R^d) and obtain convergence rates that are strictly tighter than those from standard Euclidean analysis. In this geometry, the row-stochastic matrix becomes self-adjoint whereas the doubly stochastic one does not, creating additional penalty terms that amplify consensus error, thereby slowing convergence. Consequently, the difference in convergence arises not only from spectral gaps but also from these penalty terms. We then derive sufficient conditions under which the row-stochastic design converges faster even with a smaller spectral gap. Finally, by using a Rayleigh-quotient and Loewner-order eigenvalue comparison, we further obtain topology conditions that guarantee this advantage and yield practical topology-design guidelines.

Risk-averse reinforcement learning finds application in various high-stakes fields. Unlike classical reinforcement learning, which aims to maximize expected returns, risk-averse agents choose policies that minimize risk, occasionally sacrificing expected value. These preferences can be framed through utility theory. We focus on the specific case of the exponential utility function, where we can derive the Bellman equations and employ various reinforcement learning algorithms with few modifications. However, these methods suffer from numerical instability due to the need for exponent computation throughout the process. To address this, we introduce a numerically stable and mathematically sound loss function based on the Itakura-Saito divergence for learning state-value and action-value functions. We evaluate our proposed loss function against established alternatives, both theoretically and empirically. In the experimental section, we explore multiple financial scenarios, some with known analytical solutions, and show that our loss function outperforms the alternatives.

Current model quantization methods have shown their promising capability in reducing storage space and computation complexity. However, due to the diversity of quantization forms supported by different hardware, one limitation of existing solutions is that usually require repeated optimization for different scenarios. How to construct a model with flexible quantization forms has been less studied. In this paper, we explore a one-shot network quantization regime, named Elastic Quantization Neural Networks (EQ-Net), which aims to train a robust weight-sharing quantization supernet. First of all, we propose an elastic quantization space (including elastic bit-width, granularity, and symmetry) to adapt to various mainstream quantitative forms. Secondly, we propose the Weight Distribution Regularization Loss (WDR-Loss) and Group Progressive Guidance Loss (GPG-Loss) to bridge the inconsistency of the distribution for weights and output logits in the elastic quantization space gap. Lastly, we incorporate genetic algorithms and the proposed Conditional Quantization-Aware Accuracy Predictor (CQAP) as an estimator to quickly search mixed-precision quantized neural networks in supernet. Extensive experiments demonstrate that our EQ-Net is close to or even better than its static counterparts as well as state-of-the-art robust bit-width methods. Code can be available at https://github.com/xuke225/EQ-Net.git{https://github.com/xuke225/EQ-Net}.

Direct Alignment Algorithms (DAAs) simplify language model alignment by replacing reinforcement learning (RL) and reward modeling (RM) in Reinforcement Learning from Human Feedback (RLHF) with direct policy optimization. DAAs can be classified by their ranking losses (pairwise vs. pointwise), by the rewards used in those losses (e.g., likelihood ratios of policy and reference policy, or odds ratios), or by whether a Supervised Fine-Tuning (SFT) phase is required (two-stage vs. one-stage). We first show that one-stage methods underperform two-stage methods. To address this, we incorporate an explicit SFT phase and introduce the beta parameter, controlling the strength of preference optimization, into single-stage ORPO and ASFT. These modifications improve their performance in Alpaca Eval 2 by +3.46 (ORPO) and +8.27 (ASFT), matching two-stage methods like DPO. Further analysis reveals that the key factor is whether the approach uses pairwise or pointwise objectives, rather than the specific implicit reward or loss function. These results highlight the importance of careful evaluation to avoid premature claims of performance gains or overall superiority in alignment algorithms.

Unified vision-language models (UVLMs) must perform both understanding and generation within a single architecture, but these tasks rely on heterogeneous data and supervision, making it difficult to balance them during reinforcement learning (RL). We propose PairUni, a unified framework that reorganizes data into understanding-generation (UG) pairs and aligns optimization accordingly. We first use GPT-o3 to augment single-task data, generating captions for understanding samples and question-answer (QA) pairs for generation samples, forming aligned pairs from the same instance. Additionally, for each generation sample, we retrieve a semantically related understanding example to form a retrieved pair, linking different but related data points. These paired structures expose cross-task semantic correspondences and support consistent policy learning. To leverage this structure, we present Pair-GPRO, a pair-aware variant based on Group Relative Policy Optimization. It assigns a similarity score to each pair to modulate the advantage, strengthening learning from well-aligned examples and reducing task interference. We curate a high-quality dataset of 16K UG pairs named PairUG for RL fine-tuning and evaluate PairUni on the powerful Janus-Pro UVLMs. Our approach achieves balanced improvements on various UVLMs, outperforming strong UVLM RL baselines. Code: https://github.com/Haochen-Wang409/PairUni{github.com/Haochen-Wang409/PairUni}

The prevalent deployment of learning from human preferences through reinforcement learning (RLHF) relies on two important approximations: the first assumes that pairwise preferences can be substituted with pointwise rewards. The second assumes that a reward model trained on these pointwise rewards can generalize from collected data to out-of-distribution data sampled by the policy. Recently, Direct Preference Optimisation (DPO) has been proposed as an approach that bypasses the second approximation and learn directly a policy from collected data without the reward modelling stage. However, this method still heavily relies on the first approximation. In this paper we try to gain a deeper theoretical understanding of these practical algorithms. In particular we derive a new general objective called PsiPO for learning from human preferences that is expressed in terms of pairwise preferences and therefore bypasses both approximations. This new general objective allows us to perform an in-depth analysis of the behavior of RLHF and DPO (as special cases of PsiPO) and to identify their potential pitfalls. We then consider another special case for PsiPO by setting Psi simply to Identity, for which we can derive an efficient optimisation procedure, prove performance guarantees and demonstrate its empirical superiority to DPO on some illustrative examples.

Post-training alignment of video generation models with human preferences is a critical goal. Developing effective Reward Models (RMs) for this process faces significant methodological hurdles. Current data collection paradigms, reliant on in-prompt pairwise annotations, suffer from labeling noise. Concurrently, the architectural design of VLM-based RMs, particularly their output mechanisms, remains underexplored. Furthermore, RM is susceptible to reward hacking in post-training. To mitigate these limitations, we propose SoliReward, a systematic framework for video RM training. Our framework first sources high-quality, cost-efficient data via single-item binary annotations, then constructs preference pairs using a cross-prompt pairing strategy. Architecturally, we employ a Hierarchical Progressive Query Attention mechanism to enhance feature aggregation. Finally, we introduce a modified BT loss that explicitly accommodates win-tie scenarios. This approach regularizes the RM's score distribution for positive samples, providing more nuanced preference signals to alleviate over-focus on a small number of top-scoring samples. Our approach is validated on benchmarks evaluating physical plausibility, subject deformity, and semantic alignment, demonstrating improvements in direct RM evaluation metrics and in the efficacy of post-training on video generation models. Code and benchmark will be publicly available.

Cardinality-estimation (CE) research ranks estimators by q-error, yet it is well known that q-error is an imperfect proxy for query-plan quality. We give a measurement-driven account of when it is a good proxy and when it is not, and why. Modeling plan selection as an argmin over a piecewise-linear cost landscape, we find that plan regret (the cost of the chosen plan relative to the optimal, under true cardinalities) is governed by plan-cost geometry in a regime-dependent way. (i) For small errors, a true-point condition number kappa predicts regret and out-predicts q-error; its predictive power decays to zero as error grows, as a local linearization must. (ii) For large errors -- where deployed learned estimators operate -- an estimator-independent average-case sub-optimality measure ACS-infinity predicts which queries are regret-prone (Spearman rho ~ 0.54 on STATS-CEB), while q-error is nearly uninformative at the query level (rho ~ 0.05). (iii) The worst case is Haritsa's maximum sub-optimality (MSO). The three are one cost-ratio spectrum under three weightings. We prove a limit law ACS-infinity = sum_k r_k pi_k with cardinality-independent combinatorial weights, and validate every claim on STATS-CEB and JOB-light with four released estimators under pre-registered decision rules, and confirm on real PostgreSQL runtime that ACS-infinity predicts regret where q-error does not. The contribution is conceptual and empirical -- an average-case companion to worst-case robust query optimization, and a characterization of when an accuracy metric tracks plan quality -- rather than a new estimator. Code and the full pre-registration are public.

Recent mixed-policy optimization methods for LLM reasoning that interleave or blend supervised and reinforcement learning signals report improvements over the standard SFT-then-RL pipeline. We show that numerous recently published research papers rely on a faulty baseline caused by two distinct bugs: a CPU-offloaded optimizer bug in DeepSpeed that silently drops intermediate micro-batches during gradient accumulation (affecting multiple downstream frameworks including TRL, OpenRLHF and Llama-Factory), and a loss aggregation bug in OpenRLHF that incorrectly weights per-mini-batch losses. Together they suppress SFT performance, with the optimizer bug accounting for most of the gap and the loss aggregation bug contributing a smaller additional effect. Once corrected, the standard SFT-then-RL pipeline surpasses every published mixed-policy method we evaluate by +3.8 points on math benchmarks with Qwen2.5-Math-7B and by +22.2 points with Llama-3.1-8B. Even a truncated variant with just 50 RL steps outperforms mixed-policy methods on math benchmarks while using fewer FLOPs.

Quantization-aware training (QAT) is a leading technique for improving the accuracy of quantized neural networks. Previous work has shown that decomposing training into a full-precision (FP) phase followed by a QAT phase yields superior accuracy compared to QAT alone. However, the optimal allocation of compute between the FP and QAT phases remains unclear. We conduct extensive experiments with various compute budgets, QAT bit widths, and model sizes from 86.0M to 2.2B to investigate how different QAT durations impact final performance. We demonstrate that, contrary to previous findings, the loss-optimal ratio of QAT to FP training increases with the total amount of compute. Moreover, the optimal fraction can be accurately predicted for a wide range of model sizes and quantization widths using the tokens-per-parameter-byte statistic. From experimental data, we derive a loss scaling law that predicts both optimal QAT ratios and final model performance across different QAT/FP compute allocation strategies and QAT bit widths. We use the scaling law to make further predictions, which we verify experimentally, including which QAT bit width is optimal under a given memory constraint and how QAT accuracy with different bit widths compares to full-precision model accuracy. Additionally, we propose a novel cooldown and QAT fusion approach that performs learning rate decay jointly with quantization-aware training, eliminating redundant full-precision model updates and achieving significant compute savings. These findings provide practical insights into efficient QAT planning and enable the training of higher-quality quantized models with the same compute budget.

We propose a simple pairwise sigmoid loss for image-text pre-training. Unlike standard contrastive learning with softmax normalization, the sigmoid loss operates solely on image-text pairs and does not require a global view of the pairwise similarities for normalization. The sigmoid loss simultaneously allows further scaling up the batch size, while also performing better at smaller batch sizes. With only four TPUv4 chips, we can train a Base CLIP model at 4k batch size and a Large LiT model at 20k batch size, the latter achieves 84.5% ImageNet zero-shot accuracy in two days. This disentanglement of the batch size from the loss further allows us to study the impact of examples vs pairs and negative to positive ratio. Finally, we push the batch size to the extreme, up to one million, and find that the benefits of growing batch size quickly diminish, with a more reasonable batch size of 32k being sufficient. We hope our research motivates further explorations in improving the quality and efficiency of language-image pre-training.

Dueling bandits is a prominent framework for decision-making involving preferential feedback, a valuable feature that fits various applications involving human interaction, such as ranking, information retrieval, and recommendation systems. While substantial efforts have been made to minimize the cumulative regret in dueling bandits, a notable gap in the current research is the absence of regret bounds that account for the inherent uncertainty in pairwise comparisons between the dueling arms. Intuitively, greater uncertainty suggests a higher level of difficulty in the problem. To bridge this gap, this paper studies the problem of contextual dueling bandits, where the binary comparison of dueling arms is generated from a generalized linear model (GLM). We propose a new SupLinUCB-type algorithm that enjoys computational efficiency and a variance-aware regret bound tilde Obig(dsum_{t=1^Tsigma_t^2} + dbig), where sigma_t is the variance of the pairwise comparison in round t, d is the dimension of the context vectors, and T is the time horizon. Our regret bound naturally aligns with the intuitive expectation in scenarios where the comparison is deterministic, the algorithm only suffers from an tilde O(d) regret. We perform empirical experiments on synthetic data to confirm the advantage of our method over previous variance-agnostic algorithms.

Conditional image generation enhances text-to-image synthesis with structural, spatial, or stylistic priors, but current methods face challenges in handling conflicts between sources. These include 1) input-level conflicts, where the conditioning image contradicts the text prompt, and 2) model-bias conflicts, where generative biases disrupt alignment even when conditions match the text. Addressing these conflicts requires nuanced solutions, which standard supervised fine-tuning struggles to provide. Preference-based optimization techniques like Direct Preference Optimization (DPO) show promise but are limited by gradient entanglement between text and condition signals and lack disentangled training data for multi-constraint tasks. To overcome this, we propose a bidirectionally decoupled DPO framework (BideDPO). Our method creates two disentangled preference pairs-one for the condition and one for the text-to reduce gradient entanglement. The influence of pairs is managed using an Adaptive Loss Balancing strategy for balanced optimization. We introduce an automated data pipeline to sample model outputs and generate conflict-aware data. This process is embedded in an iterative optimization strategy that refines both the model and the data. We construct a DualAlign benchmark to evaluate conflict resolution between text and condition. Experiments show BideDPO significantly improves text success rates (e.g., +35%) and condition adherence. We also validate our approach using the COCO dataset. Project Pages: https://limuloo.github.io/BideDPO/.

Off-policy, value-based reinforcement learning methods such as Q-learning are appealing because they can learn from arbitrary experience, including data collected by older policies or other agents. In practice, however, bootstrapping makes long-horizon learning brittle: estimation errors at later states propagate backward through temporal-difference (TD) updates and can compound over time. We propose long-horizon Q-learning (LQL), which introduces a principled backstop against compounding error when learning the optimal action-value function. LQL builds on a prior optimality tightening observation: any realized action sequence lower-bounds what the optimal policy can achieve in expectation, so acting optimally earlier should not be worse than following the observed actions for several steps before switching to optimal behavior. Our contribution is to turn this inequality into a practical stabilization mechanism for Q-learning by using a hinge loss to penalize violations of these bounds. Importantly, LQL computes these penalties using network outputs already produced for the TD error, requiring no auxiliary networks and no additional forward passes relative to Q-learning. When combined with multiple state-of-the-art methods on a range of online and offline-to-online benchmarks, LQL consistently outperforms both 1-step TD and n-step TD learning at similar runtime.

We propose training fitted Q-iteration with log-loss (FQI-LOG) for batch reinforcement learning (RL). We show that the number of samples needed to learn a near-optimal policy with FQI-LOG scales with the accumulated cost of the optimal policy, which is zero in problems where acting optimally achieves the goal and incurs no cost. In doing so, we provide a general framework for proving small-cost bounds, i.e. bounds that scale with the optimal achievable cost, in batch RL. Moreover, we empirically verify that FQI-LOG uses fewer samples than FQI trained with squared loss on problems where the optimal policy reliably achieves the goal.

In multi-task learning (MTL), gradient balancing has recently attracted more research interest than loss balancing since it often leads to better performance. However, loss balancing is much more efficient than gradient balancing, and thus it is still worth further exploration in MTL. Note that prior studies typically ignore that there exist varying improvable gaps across multiple tasks, where the improvable gap per task is defined as the distance between the current training progress and desired final training progress. Therefore, after loss balancing, the performance imbalance still arises in many cases. In this paper, following the loss balancing framework, we propose two novel improvable gap balancing (IGB) algorithms for MTL: one takes a simple heuristic, and the other (for the first time) deploys deep reinforcement learning for MTL. Particularly, instead of directly balancing the losses in MTL, both algorithms choose to dynamically assign task weights for improvable gap balancing. Moreover, we combine IGB and gradient balancing to show the complementarity between the two types of algorithms. Extensive experiments on two benchmark datasets demonstrate that our IGB algorithms lead to the best results in MTL via loss balancing and achieve further improvements when combined with gradient balancing. Code is available at https://github.com/YanqiDai/IGB4MTL.

IoU losses are surrogates that directly optimize the Jaccard index. In semantic segmentation, leveraging IoU losses as part of the loss function is shown to perform better with respect to the Jaccard index measure than optimizing pixel-wise losses such as the cross-entropy loss alone. The most notable IoU losses are the soft Jaccard loss and the Lovasz-Softmax loss. However, these losses are incompatible with soft labels which are ubiquitous in machine learning. In this paper, we propose Jaccard metric losses (JMLs), which are identical to the soft Jaccard loss in a standard setting with hard labels, but are compatible with soft labels. With JMLs, we study two of the most popular use cases of soft labels: label smoothing and knowledge distillation. With a variety of architectures, our experiments show significant improvements over the cross-entropy loss on three semantic segmentation datasets (Cityscapes, PASCAL VOC and DeepGlobe Land), and our simple approach outperforms state-of-the-art knowledge distillation methods by a large margin. Code is available at: https://github.com/zifuwanggg/JDTLosses{https://github.com/zifuwanggg/JDTLosses}.

Post-training quantization (PTQ) has emerged as a widely adopted technique for compressing and accelerating Large Language Models (LLMs). The major challenge in LLM quantization is that uneven and heavy-tailed data distributions can expand the quantization range, thereby reducing bit precision for most values. Recent methods attempt to eliminate outliers and balance inter-channel differences by employing linear transformations; however, they remain heuristic and are often overlook optimizing the data distribution across the entire quantization space.In this paper, we introduce Quantization Space Utilization Rate (QSUR), a novel metric that effectively assesses the quantizability of transformed data by measuring the space utilization of the data in the quantization space. We complement QSUR with mathematical derivations that examine the effects and limitations of various transformations, guiding our development of Orthogonal and Scaling Transformation-based Quantization (OSTQuant). OSQuant employs a learnable equivalent transformation, consisting of an orthogonal transformation and a scaling transformation, to optimize the distributions of weights and activations across the entire quantization space. Futhermore, we propose the KL-Top loss function, designed to mitigate noise during optimization while retaining richer semantic information within the limited calibration data imposed by PTQ. OSTQuant outperforms existing work on various LLMs and benchmarks. In the W4-only setting, it retains 99.5\% of the floating-point accuracy. In the more challenging W4A4KV4 configuration, OSTQuant reduces the performance gap by 32\% on the LLaMA-3-8B model compared to state-of-the-art methods. https://github.com/BrotherHappy/OSTQuant{https://github.com/BrotherHappy/OSTQuant}.

Reinforcement Learning from Verifiable Rewards (RLVR) has emerged as the standard paradigm for improving reasoning capability of large language models, while Multi-Token Prediction (MTP) has been a widely adopted module in pretraining. Combining them is a natural approach, yet current RL practices detach MTP gradients because joint training degrades the performance. We revisit this failure from an optimization perspective. We show that the per-step effect of MTP on the RL objective can be decomposed into two terms: a first-order correlation and a second-order perturbation penalty. This decomposition unifies three MTP training regimes: Detach, Cross-Entropy loss, and Policy loss, and explains why each succeeds or fails. Further analysis of policy loss reveals that, although it aligns with intuition, performance still degrades: the correlation term decays while the quadratic penalty persists. Guided by the analysis, we propose Optimal Coefficient Calibration (OCC), an adaptive scheme that tracks the optimal coefficient online via a log-probability proxy at negligible cost. Across six competition-level mathematical reasoning benchmarks, OCC consistently matches or exceeds the detach baseline, delivering improved joint MTP-RL training performance.

The realization of scalable fault-tolerant quantum computing is expected to hinge on quantum error-correcting codes. In the quest for more efficient quantum fault tolerance, a critical code parameter is the weight of measurements that extract information about errors to enable error correction: as higher measurement weights require higher implementation costs and introduce more errors, it is important in code design to optimize measurement weight. This underlies the surging interest in quantum low-density parity-check (qLDPC) codes, the study of which has primarily focused on the asymptotic (large-code-limit) properties. In this work, we introduce a versatile and computationally efficient approach to stabilizer code weight reduction based on reinforcement learning (RL), which produces new low-weight codes that substantially outperform the state of the art in practically relevant parameter regimes, extending significantly beyond previously accessible small distances. For example, our approach demonstrates savings in physical qubit overhead compared to existing results by 1 to 2 orders of magnitude for weight 6 codes and brings the overhead into a feasible range for near-future experiments. We also investigate the interplay between code parameters using our RL framework, offering new insights into the potential efficiency and power of practically viable coding strategies. Overall, our results demonstrate how RL can effectively advance the crucial yet challenging problem of quantum code discovery and thereby facilitate a faster path to the practical implementation of fault-tolerant quantum technologies.

Pairwise human preference prediction is central to evaluating code-generation systems, where quality often depends on task-specific trade-offs beyond functional correctness. While rubric-based LLM judges improve interpretability by decomposing evaluation into explicit criteria, most existing pipelines remain pointwise: they score each response independently and derive preferences by comparing aggregated scores. We show that this design is poorly matched to pairwise code preference prediction and can underperform a strong monolithic judge. We propose CriterAlign, a criterion-centric framework that adapts rubric-based judging to pairwise preference evaluation through direct criterion-level pairwise judgments, tie-driven criterion refinement, swap-consistency filtering, and final pairwise synthesis. We further introduce Human-Preference-Aligned Guidance (HPAG), synthesized offline from training examples by extracting recurring rationale gaps between human preferences and monolithic judge predictions, and injected into the criterion generator, criterion judge, and final judge. On BigCodeReward, CriterAlign improves a Qwen2.5-VL-32B monolithic judge from 60.4% to 66.3% accuracy, with ablations confirming the contributions of pairwise criterion design and HPAG.

Decoupled loss has been a successful reinforcement learning (RL) algorithm to deal with the high data staleness under the asynchronous RL setting. Decoupled loss improves coupled-loss style of algorithms' (e.g., PPO, GRPO) learning stability by introducing a proximal policy to decouple the off-policy corrections (importance weight) from the controlling policy updates (trust region). However, the proximal policy requires an extra forward pass through the network at each training step, creating a computational bottleneck for large language models. We observe that since the proximal policy only serves as a trust region anchor between the behavior and target policies, we can approximate it through simple interpolation without explicit computation. We call this approach A-3PO (APproximated Proximal Policy Optimization). A-3PO eliminates this overhead, reducing training time by 18% while maintaining comparable performance. Code & off-the-shelf example are available at: https://github.com/inclusionAI/AReaL/blob/main/docs/algorithms/prox_approx.md

Layer-wise PTQ is a promising technique for compressing large language models (LLMs), due to its simplicity and effectiveness without requiring retraining. However, recent progress in this area is saturating, underscoring the need to revisit its core limitations and explore further improvements. We address this challenge by identifying a key limitation of existing layer-wise PTQ methods: the growth of quantization errors across layers significantly degrades performance, particularly in low-bit regimes. To address this fundamental issue, we propose Quantization Error Propagation (QEP), a general, lightweight, and scalable framework that enhances layer-wise PTQ by explicitly propagating quantization errors and compensating for accumulated errors. QEP also offers a tunable propagation mechanism that prevents overfitting and controls computational overhead, enabling the framework to adapt to various architectures and resource budgets. Extensive experiments on several LLMs demonstrate that QEP-enhanced layer-wise PTQ achieves substantially higher accuracy than existing methods. Notably, the gains are most pronounced in the extremely low-bit quantization regime.

We present ITQ3_S (Interleaved Ternary Quantization -- Specialized), a novel 3-bit weight quantization format for LLMs integrating TurboQuant (TQ), a rotation-domain strategy based on the Fast Walsh-Hadamard Transform (FWHT). Conventional 3-bit methods suffer precision loss from heavy-tailed weight distributions and inter-channel outliers. ITQ3_S pre-rotates the weight space via FWHT before quantization, spreading outlier energy across the vector and inducing a near-Gaussian distribution amenable to uniform ternary coding. We derive a rigorous dequantization procedure fusing a 256-point Inverse FWHT into the CUDA shared-memory loading stage, ensuring reconstruction error is bounded exclusively by the ternary quantization grid with no additional error from the transform inversion. For any weight vector w in R^{256}, the reconstruction satisfies |mathbf{w} - w|_2 leq ε_q, strictly smaller than uniform 3-bit baselines that do not exploit rotation-induced distribution normalization. TurboQuant lacks a native CUDA kernel, precluding direct deployment; naively composing TQ with existing weight quantizers introduces domain mismatch errors that accumulate across layers, degrading quality below standard 3-bit baselines. ITQ3_S resolves this by co-designing the FWHT rotation and quantization kernel as a unified pipeline grounded in the IQ3_S weight format, with the inverse transform fused into the CUDA MMQ kernel. Empirically, on the NVIDIA RTX 5090 (Blackwell), ITQ3_S achieves perplexity competitive with FP16 while delivering throughput exceeding 1.5x that of 4-bit alternatives via optimized DP4A and Tensor Core scheduling. Our results establish ITQ3_S as a practical, mathematically grounded solution for high-fidelity LLM deployment on consumer hardware.

Mixed-precision quantization must decide which parts of a model to keep at higher precision. A common premise, shared by sensitivity-based methods such as HAWQ and CoopQ, is that the loss from quantizing a set of layers can be reconstructed from per-layer or pairwise sensitivities measured in isolation. We test this premise at the 4-bit weight-and-activation precisions now being deployed, treating the change in loss f(S) from quantizing a layer set S as a set function on the Boolean cube and analyzing it through two classical changes of basis. This analysis yields two findings. First, across configurations drawn from the deployment distribution, 85--93\% of the variance of f is explained by per-layer effects alone. Second, a monotone transform of a sum of per-layer terms reproduces f's ranking of configurations, misordering at most 2\% of pairs. We propose the coverage model f(S)=cbigl(1-prod_{iin S}(1-a_i)bigr), which reproduces the measured variance profile of f to within a few percent from its L fitted break-rates. This structure supports two predictors of a configuration's loss, each with L+1 parameters. The additive model is the optimal first-order predictor. By Parseval's identity its mean-squared error equals the variance of f left unexplained by per-layer effects, which we measure on full lattices, estimate out of sample at full-network scale, and report with every result as a certificate of how well any additive model can do. The coverage model itself is the second predictor. As allocators at matched memory, they attain the lowest KL divergence among the compared allocators on models from 30B to 355B parameters. Below four bits, the resulting allocations continue to solve code and reasoning tasks at budgets where allocations from gradient sensitivities no longer produce terminating generations.

Reinforcement Learning with Verifiable Rewards (RLVR) strengthens LLM reasoning, but training often oscillates between {entropy collapse} and {entropy explosion}. We trace both hazards to the mean baseline used in value-free RL (e.g., GRPO and DAPO), which improperly penalizes negative-advantage samples under reward outliers. We propose {Quantile Advantage Estimation} (QAE), replacing the mean with a group-wise K-quantile baseline. QAE induces a response-level, two-regime gate: on hard queries (p <= 1 - K) it reinforces rare successes, while on easy queries (p > 1 - K) it targets remaining failures. Under first-order softmax updates, we prove {two-sided entropy safety}, giving lower and upper bounds on one-step entropy change that curb explosion and prevent collapse. Empirically, this minimal modification stabilizes entropy, sparsifies credit assignment (with tuned K, roughly 80% of responses receive zero advantage), and yields sustained pass@1 gains on Qwen3-8B/14B-Base across AIME 2024/2025 and AMC 2023. These results identify {baseline design} -- rather than token-level heuristics -- as the primary mechanism for scaling RLVR.

Direct preference optimization (DPO), a widely adopted offline preference optimization algorithm, aims to align large language models (LLMs) with human-desired behaviors using pairwise preference data. However, the winning response and the losing response within pairwise data are generated isolatedly, leading to weak correlations between them as well as suboptimal alignment performance. To address this issue, we propose an effective framework named BMC, for bridging and modeling correlations in pairwise data. Firstly, we increase the consistency and informativeness of the pairwise preference signals by targeted modifications, synthesizing a pseudo winning response through improving the losing response based on the winning response. Secondly, we identify that DPO alone is insufficient to model these correlations and capture nuanced variations. Therefore, we propose learning token-level correlations by dynamically leveraging the policy model's confidence during training. Comprehensive experiments on QA, math, and instruction-following tasks demonstrate the effectiveness of our approach, significantly surpassing competitive baselines, including DPO. Additionally, our in-depth quantitative analysis reveals the reasons behind our method's superior performance over DPO and showcases its versatility to other DPO variants.

Large Language Models (LLMs) have demonstrated promising capabilities as automatic evaluators in assessing the quality of generated natural language. However, LLMs still exhibit biases in evaluation and often struggle to generate coherent evaluations that align with human assessments. In this work, we first conduct a systematic study of the misalignment between LLM evaluators and human judgement, revealing that existing calibration methods aimed at mitigating biases are insufficient for effectively aligning LLM evaluators. Inspired by the use of preference data in RLHF, we formulate the evaluation as a ranking problem and introduce Pairwise-preference Search (PairS), an uncertainty-guided search method that employs LLMs to conduct pairwise comparisons and efficiently ranks candidate texts. PairS achieves state-of-the-art performance on representative evaluation tasks and demonstrates significant improvements over direct scoring. Furthermore, we provide insights into the role of pairwise preference in quantifying the transitivity of LLMs and demonstrate how PairS benefits from calibration.

Offline reinforcement learning (RL) has progressed with return-conditioned supervised learning (RCSL), but its lack of stitching ability remains a limitation. We introduce Q-Aided Conditional Supervised Learning (QCS), which effectively combines the stability of RCSL with the stitching capability of Q-functions. By analyzing Q-function over-generalization, which impairs stable stitching, QCS adaptively integrates Q-aid into RCSL's loss function based on trajectory return. Empirical results show that QCS significantly outperforms RCSL and value-based methods, consistently achieving or exceeding the maximum trajectory returns across diverse offline RL benchmarks.

In this paper, we focus on the task of conditional image generation, where an image is synthesized according to user instructions. The critical challenge underpinning this task is ensuring both the fidelity of the generated images and their semantic alignment with the provided conditions. To tackle this issue, previous studies have employed supervised perceptual losses derived from pre-trained models, i.e., reward models, to enforce alignment between the condition and the generated result. However, we observe one inherent shortcoming: considering the diversity of synthesized images, the reward model usually provides inaccurate feedback when encountering newly generated data, which can undermine the training process. To address this limitation, we propose an uncertainty-aware reward modeling, called Ctrl-U, including uncertainty estimation and uncertainty-aware regularization, designed to reduce the adverse effects of imprecise feedback from the reward model. Given the inherent cognitive uncertainty within reward models, even images generated under identical conditions often result in a relatively large discrepancy in reward loss. Inspired by the observation, we explicitly leverage such prediction variance as an uncertainty indicator. Based on the uncertainty estimation, we regularize the model training by adaptively rectifying the reward. In particular, rewards with lower uncertainty receive higher loss weights, while those with higher uncertainty are given reduced weights to allow for larger variability. The proposed uncertainty regularization facilitates reward fine-tuning through consistency construction. Extensive experiments validate the effectiveness of our methodology in improving the controllability and generation quality, as well as its scalability across diverse conditional scenarios. Code will soon be available at https://grenoble-zhang.github.io/Ctrl-U-Page/.

We study a new non-stochastic federated multi-armed bandit problem with multiple agents collaborating via a communication network. The losses of the arms are assigned by an oblivious adversary that specifies the loss of each arm not only for each time step but also for each agent, which we call ``doubly adversarial". In this setting, different agents may choose the same arm in the same time step but observe different feedback. The goal of each agent is to find a globally best arm in hindsight that has the lowest cumulative loss averaged over all agents, which necessities the communication among agents. We provide regret lower bounds for any federated bandit algorithm under different settings, when agents have access to full-information feedback, or the bandit feedback. For the bandit feedback setting, we propose a near-optimal federated bandit algorithm called FEDEXP3. Our algorithm gives a positive answer to an open question proposed in Cesa-Bianchi et al. (2016): FEDEXP3 can guarantee a sub-linear regret without exchanging sequences of selected arm identities or loss sequences among agents. We also provide numerical evaluations of our algorithm to validate our theoretical results and demonstrate its effectiveness on synthetic and real-world datasets

Off-policy reinforcement learning of pretrained flow policies remains challenging due to the instability of optimization arising from the multi-step sampling process. Recently, Q-learning with Adjoint Matching (QAM) addressed this issue by reformulating into a memoryless stochastic optimal control (SOC) problem with a learned critic. However, QAM inherits a fundamental fragility of critic-guided improvement: small critic errors are amplified when critics are ill-conditioned, often leading to model collapse. This paper introduces Trust Region Q-Adjoint Matching (TRQAM), a stable off-policy fine-tuning algorithm that adaptively controls the path-space KL with pretrained flow policies through projected dual descent. Specifically, we optimize the trust-region parameter λ in SOC dynamics, and theoretically show that the path-space KL can be represented by a closed-form function of λ. As a result, our method can precisely control the exact deviation from pretrained flow policies, achieving stable off-policy RL. Through experiments on 50 OGBench tasks, TRQAM consistently outperforms prior arts in both offline RL and offline-to-online RL. In particular, TRQAM achieves an overall success rate of 68% in offline RL, substantially improves the strongest baseline at 46%.

As quantum hardware scales toward fault tolerant operation, the demand for correct quantum error correction (QEC) circuits far outpaces manual design capacity. AI agents offer a promising path to automating this synthesis, yet no benchmark exists to measure their progress on the specialized task of generating QEC circuits. We introduce StabilizerBench, a benchmark suite of 192 stabilizer codes spanning 12 families, 4-196 qubits, and distances 2-21, organized into three tasks of increasing difficulty: state preparation circuit generation, circuit optimization under semantic constraints, and fault tolerant circuit synthesis. Although motivated by QEC, stabilizer circuits exercise core competencies required for general quantum programming, including gate decomposition, qubit routing, and semantic preserving transformations, while admitting efficient verification via the Gottesman Knill theorem, enabling the benchmark to scale to large codes without the exponential cost of full unitary comparison. We define a unified generator weighted scoring system with two tiers: a capability score measuring breadth of success and a quality score capturing circuit merit. We also introduce continuous fault tolerance and optimization metrics that grade error resilience and circuit improvements beyond binary pass or fail. Following the design of classical benchmarks such as SWE-bench, StabilizerBench specifies inputs, verification oracles, and scoring but leaves prompts and agent strategies open. We evaluate three frontier AI agents and find the benchmark discriminates across models and tasks with substantial headroom for improvement.

Post-training quantization (PTQ) of large language models (LLMs) to extremely low bit-widths remains challenging due to the fundamental trade-off between computational efficiency and model expressiveness. While existing ultra-low-bit PTQ methods rely on binary approximations or complex compensation mechanisms, they suffer from either limited representational capacity or computational overhead that undermines their efficiency gains. We introduce PTQ to Trit-Planes (PTQTP), the first ternary-weight PTQ framework that decomposes weight matrices into structured ternary {-1, 0, 1} trit-planes using 2x1.58-bit representation. PTQTP achieves multiplication-free inference, identical to 1-bit quantization, while maintaining superior expressiveness through its novel structured decomposition. Our approach provides: (1) a theoretically grounded progressive approximation algorithm ensuring global weight consistency; (2) model-agnostic deployment across diverse modern LLMs without architectural modifications; and (3) uniform ternary operations that eliminate the need for mixed-precision or compensation schemes. Comprehensive experiments across LLaMA3.x and Qwen3 model families (0.6B-70B parameters) demonstrate that PTQTP significantly outperforms existing low-bit PTQ methods, achieving 82.4% mathematical reasoning retention versus 0% for competing approaches. PTQTP approaches and sometimes surpasses 1.58-bit quantization-aware training performance while requiring only single-hour quantization compared to 10-14 GPU days for training-based methods. These results establish PTQTP as a practical solution for efficient LLM deployment in resource-constrained environments.

Best-of-N (BoN) sampling, a common strategy for test-time scaling of Large Language Models (LLMs), relies on reward models to select the best candidate solution from multiple generations. However, traditional reward models often assign arbitrary and inconsistent scores, limiting their effectiveness. To address this, we propose a Pairwise Reward Model (Pairwise RM) combined with a knockout tournament for BoN sampling. Instead of assigning absolute scores, given one math problem, Pairwise RM evaluates two candidate solutions' correctness simultaneously. This approach eliminates the need for arbitrary scoring and enables cross-validation of solutions through parallel comparison. In the knockout tournament, Pairwise RM conducts pairwise comparisons between candidate solutions and eliminates the incorrect ones iteratively. We construct \ourdataset, a large-scale dataset of 443K pairwise comparisons derived from NumiaMath and annotated using gemini-1.5-flash, and train the Pairwise RM via supervised fine-tuning. Experiments on MATH-500 and the Olympiad Bench demonstrate significant improvements over traditional discriminative reward models. And a 40\% to 60\% relative improvement is achieved on the top 50\% challenging problems.

We propose a penalized nonparametric approach to estimating the quantile regression process (QRP) in a nonseparable model using rectifier quadratic unit (ReQU) activated deep neural networks and introduce a novel penalty function to enforce non-crossing of quantile regression curves. We establish the non-asymptotic excess risk bounds for the estimated QRP and derive the mean integrated squared error for the estimated QRP under mild smoothness and regularity conditions. To establish these non-asymptotic risk and estimation error bounds, we also develop a new error bound for approximating C^s smooth functions with s >0 and their derivatives using ReQU activated neural networks. This is a new approximation result for ReQU networks and is of independent interest and may be useful in other problems. Our numerical experiments demonstrate that the proposed method is competitive with or outperforms two existing methods, including methods using reproducing kernels and random forests, for nonparametric quantile regression.

We provide evidence of quantum kernel advantage under noiseless simulation in binary insurance classification on MIMIC-CXR chest radiographs using quantum support vector machines (QSVM) with frozen embeddings from three medical foundation models (MedSigLIP-448, RAD-DINO, ViT-patch32). We propose a two-tier fair comparison framework in which both classifiers receive identical PCA-q features. At Tier 1 (untuned QSVM vs. untuned linear SVM, C = 1 both sides), QSVM wins minority-class F1 in all 18 tested configurations (17 at p < 0.001, 1 at p < 0.01). The classical linear kernel collapses to majority-class prediction on 90-100% of seeds at every qubit count, while QSVM maintains non-trivial recall. At q = 11 (MedSigLIP-448 plateau center), QSVM achieves mean F1 = 0.343 vs. classical F1 = 0.050 (F1 gain = +0.293, p < 0.001) without hyperparameter tuning. Under Tier 2 (untuned QSVM vs. C-tuned RBF SVM), QSVM wins all seven tested configurations (mean gain +0.068, max +0.112). Eigenspectrum analysis reveals quantum kernel effective rank reaches 69.80 at q = 11, far exceeding linear kernel rank, while classical collapse remains C-invariant. A full qubit sweep reveals architecture-dependent concentration onset across models. Code: https://github.com/sebasmos/qml-medimage

Transformers have achieved great success in pluralistic image inpainting recently. However, we find existing transformer based solutions regard each pixel as a token, thus suffer from information loss issue from two aspects: 1) They downsample the input image into much lower resolutions for efficiency consideration, incurring information loss and extra misalignment for the boundaries of masked regions. 2) They quantize 256^3 RGB pixels to a small number (such as 512) of quantized pixels. The indices of quantized pixels are used as tokens for the inputs and prediction targets of transformer. Although an extra CNN network is used to upsample and refine the low-resolution results, it is difficult to retrieve the lost information back.To keep input information as much as possible, we propose a new transformer based framework "PUT". Specifically, to avoid input downsampling while maintaining the computation efficiency, we design a patch-based auto-encoder P-VQVAE, where the encoder converts the masked image into non-overlapped patch tokens and the decoder recovers the masked regions from inpainted tokens while keeping the unmasked regions unchanged. To eliminate the information loss caused by quantization, an Un-Quantized Transformer (UQ-Transformer) is applied, which directly takes the features from P-VQVAE encoder as input without quantization and regards the quantized tokens only as prediction targets. Extensive experiments show that PUT greatly outperforms state-of-the-art methods on image fidelity, especially for large masked regions and complex large-scale datasets. Code is available at https://github.com/liuqk3/PUT

Most progress in recent coder models has been driven by supervised fine-tuning (SFT), while the potential of reinforcement learning (RL) remains largely unexplored, primarily due to the lack of reliable reward data/model in the code domain. In this paper, we address this challenge by leveraging automated large-scale test-case synthesis to enhance code model training. Specifically, we design a pipeline that generates extensive (question, test-cases) pairs from existing code data. Using these test cases, we construct preference pairs based on pass rates over sampled programs to train reward models with Bradley-Terry loss. It shows an average of 10-point improvement for Llama-3.1-8B-Ins and 5-point improvement for Qwen2.5-Coder-7B-Ins through best-of-32 sampling, making the 7B model on par with 236B DeepSeek-V2.5. Furthermore, we conduct reinforcement learning with both reward models and test-case pass rewards, leading to consistent improvements across HumanEval, MBPP, BigCodeBench, and LiveCodeBench (V4). Notably, we follow the R1-style training to start from Qwen2.5-Coder-base directly and show that our RL training can improve model on HumanEval-plus by over 25\% and MBPP-plus by 6\% for merely 80 optimization steps. We believe our results highlight the huge potential of reinforcement learning in coder models.

Reinforcement learning problems typically define the goal as maximizing the expected value of a scalar reward function. But, pairwise preferences are often easier to specify than scalar rewards, and they express certain goals that scalar rewards cannot. Methods for reinforcement learning with pairwise preferences have thus received growing interest. Unfortunately, these methods are inefficient in problems with long time horizons, and they lack guarantees on the performance of Markov policies relative to history-dependent policies, which bridge the theory and practice of reinforcement learning. We therefore propose the Markov decision contest as a new problem model for reinforcement learning with pairwise preferences. We prove that stationary Markov policies are optimal among all history-dependent policies, that solving a Markov decision contest exactly is in P, and that a simple iterative algorithm converges to an optimal policy at a sublinear rate. Lastly, in a set of high-dimensional decision problems with long time horizons, we show that our approximate algorithm is significantly more learning-efficient than prior work.

We show that reinforcement learning with verifiable reward using one training example (1-shot RLVR) is effective in incentivizing the math reasoning capabilities of large language models (LLMs). Applying RLVR to the base model Qwen2.5-Math-1.5B, we identify a single example that elevates model performance on MATH500 from 36.0% to 73.6%, and improves the average performance across six common mathematical reasoning benchmarks from 17.6% to 35.7%. This result matches the performance obtained using the 1.2k DeepScaleR subset (MATH500: 73.6%, average: 35.9%), which includes the aforementioned example. Similar substantial improvements are observed across various models (Qwen2.5-Math-7B, Llama3.2-3B-Instruct, DeepSeek-R1-Distill-Qwen-1.5B), RL algorithms (GRPO and PPO), and different math examples (many of which yield approximately 30% or greater improvement on MATH500 when employed as a single training example). In addition, we identify some interesting phenomena during 1-shot RLVR, including cross-domain generalization, increased frequency of self-reflection, and sustained test performance improvement even after the training accuracy has saturated, a phenomenon we term post-saturation generalization. Moreover, we verify that the effectiveness of 1-shot RLVR primarily arises from the policy gradient loss, distinguishing it from the "grokking" phenomenon. We also show the critical role of promoting exploration (e.g., by adding entropy loss with an appropriate coefficient) in 1-shot RLVR training. As a bonus, we observe that applying entropy loss alone, without any outcome reward, significantly enhances Qwen2.5-Math-1.5B's performance on MATH500 by 27.4%. These findings can inspire future work on RLVR data efficiency and encourage a re-examination of both recent progress and the underlying mechanisms in RLVR. Our code, model, and data are open source at https://github.com/ypwang61/One-Shot-RLVR

Q-learning played a foundational role in the field reinforcement learning (RL). However, TD algorithms with off-policy data, such as Q-learning, or nonlinear function approximation like deep neural networks require several additional tricks to stabilise training, primarily a large replay buffer and target networks. Unfortunately, the delayed updating of frozen network parameters in the target network harms the sample efficiency and, similarly, the large replay buffer introduces memory and implementation overheads. In this paper, we investigate whether it is possible to accelerate and simplify off-policy TD training while maintaining its stability. Our key theoretical result demonstrates for the first time that regularisation techniques such as LayerNorm can yield provably convergent TD algorithms without the need for a target network or replay buffer, even with off-policy data. Empirically, we find that online, parallelised sampling enabled by vectorised environments stabilises training without the need for a large replay buffer. Motivated by these findings, we propose PQN, our simplified deep online Q-Learning algorithm. Surprisingly, this simple algorithm is competitive with more complex methods like: Rainbow in Atari, PPO-RNN in Craftax, QMix in Smax, and can be up to 50x faster than traditional DQN without sacrificing sample efficiency. In an era where PPO has become the go-to RL algorithm, PQN reestablishes off-policy Q-learning as a viable alternative.

Modeling human preferences is crucial for aligning foundation models with human values. Traditional reward modeling methods, such as the Bradley-Terry (BT) reward model, fall short in expressiveness, particularly in addressing intransitive preferences. Although supervised pair preference models (PairPM) can express general preferences, their implementation is highly ad-hoc and cannot guarantee a consistent preference probability of compared pairs. Additionally, they impose high computational costs due to their quadratic query complexity when comparing multiple responses. In this paper, we introduce preference representation learning, an approach that embeds responses into a latent space to capture intricate preference structures efficiently, achieving linear query complexity. Additionally, we propose preference score-based General Preference Optimization (GPO), which generalizes reward-based reinforcement learning from human feedback. Experimental results show that our General Preference representation model (GPM) outperforms the BT reward model on the RewardBench benchmark with a margin of up to 5.6% and effectively models cyclic preferences where any BT reward model behaves like a random guess. Furthermore, evaluations on downstream tasks such as AlpacaEval2.0 and MT-Bench, following the language model post-training with GPO and our general preference model, reveal substantial performance improvements with margins up to 9.3%. These findings indicate that our method may enhance the alignment of foundation models with nuanced human values. The code is available at https://github.com/general-preference/general-preference-model.

Offline preference optimization allows fine-tuning large models directly from offline data, and has proved effective in recent alignment practices. We propose generalized preference optimization (GPO), a family of offline losses parameterized by a general class of convex functions. GPO enables a unified view over preference optimization, encompassing existing algorithms such as DPO, IPO and SLiC as special cases, while naturally introducing new variants. The GPO framework also sheds light on how offline algorithms enforce regularization, through the design of the convex function that defines the loss. Our analysis and experiments reveal the connections and subtle differences between the offline regularization and the KL divergence regularization intended by the canonical RLHF formulation. In a controlled setting akin to Gao et al 2023, we also show that different GPO variants achieve similar trade-offs between regularization and performance, though the optimal values of hyper-parameter might differ as predicted by theory. In all, our results present new algorithmic toolkits and empirical insights to alignment practitioners.

We seek to understand fundamental tradeoffs between the accuracy of prior information that a learner has on a given problem and its learning performance. We introduce the notion of prioritized risk, which differs from traditional notions of minimax and Bayes risk by allowing us to study such fundamental tradeoffs in settings where reality does not necessarily conform to the learner's prior. We present a general reduction-based approach for extending classical minimax lower-bound techniques in order to lower bound the prioritized risk for statistical estimation problems. We also introduce a novel generalization of Fano's inequality (which may be of independent interest) for lower bounding the prioritized risk in more general settings involving unbounded losses. We illustrate the ability of our framework to provide insights into tradeoffs between prior information and learning performance for problems in estimation, regression, and reinforcement learning.

Cross-entropy loss has long been the standard choice for training deep neural networks, yet it suffers from interpretability limitations, unbounded weight growth, and inefficiencies that can contribute to costly training dynamics. The harmonic loss is a distance-based alternative grounded in Euclidean geometry that improves interpretability and mitigates phenomena such as grokking, or delayed generalization on the test set. However, the study of harmonic loss remains narrow: only Euclidean distance is explored, and no systematic evaluation of computational efficiency or sustainability was conducted. We extend harmonic loss by systematically investigating a broad spectrum of distance metrics as replacements for the Euclidean distance. We comprehensively evaluate distance-tailored harmonic losses on both vision backbones and large language models. Our analysis is framed around a three-way evaluation of model performance, interpretability, and sustainability. On vision tasks, cosine distances provide the most favorable trade-off, consistently improving accuracy while lowering carbon emissions, whereas Bray-Curtis and Mahalanobis further enhance interpretability at varying efficiency costs. On language models, cosine-based harmonic losses improve gradient and learning stability, strengthen representation structure, and reduce emissions relative to cross-entropy and Euclidean heads. Our code is available at: https://anonymous.4open.science/r/rethinking-harmonic-loss-5BAB/.

We compare two strategies for compressing the KV cache in transformer inference: rank reduction (discard dimensions) and quantization (keep all dimensions, reduce precision). At matched storage budgets across five models (124M-14B, MHA and GQA), we find that quantization consistently outperforms rank reduction by 4-364 PPL depending on model and compression level. The gap persists even when rank reduction is combined with quantization in hybrid baselines, and it grows with GQA aggressiveness. On LAMBADA, INT4 matches FP16 accuracy (+0.23 PPL on Mistral 7B, +0.58 on GPT-2) while rank-32 at identical storage collapses to 0.4%. We trace this gap to a structural asymmetry: under softmax attention routing, removing a dimension can flip which token is attended (a discrete failure), while quantization noise is bounded and typically preserves score ordering. We formalize this via a perturbation result showing projection damage exceeds quantization damage by 3 x 2^(2b) per direction under the softmax Fisher metric. A basis ablation confirms the finding is basis-independent (spread <0.4 PPL), establishing that the advantage comes from preserving dimensions, not from a better coordinate system. Joint K+V INT4 quantization achieves 75% total KV reduction at only +0.18 PPL on Mistral 7B.

In this work, we present a variety of novel information-theoretic generalization bounds for learning algorithms, from the supersample setting of Steinke & Zakynthinou (2020)-the setting of the "conditional mutual information" framework. Our development exploits projecting the loss pair (obtained from a training instance and a testing instance) down to a single number and correlating loss values with a Rademacher sequence (and its shifted variants). The presented bounds include square-root bounds, fast-rate bounds, including those based on variance and sharpness, and bounds for interpolating algorithms etc. We show theoretically or empirically that these bounds are tighter than all information-theoretic bounds known to date on the same supersample setting.

Reinforcement Learning with Human Feedback (RLHF) has achieved great success in aligning large language models (LLMs) with human preferences. Prevalent RLHF approaches are reward-based, following the Bradley-Terry (BT) model assumption, which may not fully capture the complexity of human preferences. In this paper, we explore RLHF under a general preference framework and approach it from a game-theoretic perspective. Specifically, we formulate the problem as a two-player game and propose a novel algorithm, iterative Nash policy optimization (INPO). The key idea is to let the policy play against itself via no-regret learning, thereby approximating the Nash policy. Unlike previous methods, INPO bypasses the need for estimating the expected win rate for individual responses, which typically incurs high computational or annotation costs. Instead, we introduce a new loss objective that is directly minimized over a preference dataset. We provide theoretical analysis for our approach and demonstrate its effectiveness through experiments on various representative benchmarks. With an LLaMA-3-8B-based SFT model, INPO achieves a 41.5% length-controlled win rate on AlpacaEval 2.0 and a 38.3% win rate on Arena-Hard, showing substantial improvement over the state-of-the-art iterative algorithm [Dong et al., 2024] under the BT model assumption. Additionally, our ablation study highlights the benefits of incorporating KL regularization for response length control.

Post-training model quantization is a widely adopted technique for reducing the memory and computational costs of large language models (LLMs). However, most existing methods rely on uniform or heuristic bitwidth assignments, failing to account for the nonuniform sensitivity of weights to quantization noise. In this paper, we propose a novel framework for allocating quantization bitwidths based on sensitivity metrics derived from a Hessian proxy. We make key assumptions, which allow the layer/component-wise loss function to be expressed as an explicit function of the bitwidths. This enables a neat formulation of the bit allocation problem as a convex optimization task, whose closed-form solution adapts precision across weights to minimize the layer-wise quantization loss. Inspecting the solution provides several insights (such as the equal-loss structure), which are then exploited to design the proposed BAQ (Bit Allocation Quantization) algorithm. The proposed algorithm achieves a good trade-off between loss minimization and complexity and allows BAQ to be integrated into standard quantization pipelines with minimal overhead. Experimental results show that BAQ consistently outperforms GPTQ, achieving up to 56times lower perplexity at the same bitwidth on large language models ranging from 125M to 30B parameters. Leveraging our analytical results derived from solving the optimal bit allocation problem, we also provide a theoretical explanation for the observed gains. All codes of this paper are available at https://github.com/CSU-ModelCompression/BAQ.

Reinforcement learning (RL) post-training is crucial for LLM alignment and reasoning, but existing policy-based methods, such as PPO and DPO, can fall short of fixing shortcuts inherited from pre-training. In this work, we introduce Qsharp, a value-based algorithm for KL-regularized RL that guides the reference policy using the optimal regularized Q function. We propose to learn the optimal Q function using distributional RL on an aggregated online dataset. Unlike prior value-based baselines that guide the model using unregularized Q-values, our method is theoretically principled and provably learns the optimal policy for the KL-regularized RL problem. Empirically, Qsharp outperforms prior baselines in math reasoning benchmarks while maintaining a smaller KL divergence to the reference policy. Theoretically, we establish a reduction from KL-regularized RL to no-regret online learning, providing the first bounds for deterministic MDPs under only realizability. Thanks to distributional RL, our bounds are also variance-dependent and converge faster when the reference policy has small variance. In sum, our results highlight Qsharp as an effective approach for post-training LLMs, offering both improved performance and theoretical guarantees. The code can be found at https://github.com/jinpz/q_sharp.

Post-training paradigms for Large Language Models (LLMs), primarily Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL), face a fundamental dilemma: SFT provides stability (low variance) but suffers from high fitting bias, while RL enables exploration (low bias) but grapples with high gradient variance. Existing unified optimization strategies often employ naive loss weighting, overlooking the statistical conflict between these distinct gradient signals. In this paper, we provide a rigorous theoretical analysis of this bias-variance trade-off and propose DYPO (Dynamic Policy Optimization), a unified framework designed to structurally mitigate this conflict. DYPO integrates three core components: (1) a Group Alignment Loss (GAL) that leverages intrinsic group dynamics to significantly reduce RL gradient variance; (2) a Multi-Teacher Distillation mechanism that corrects SFT fitting bias via diverse reasoning paths; and (3) a Dynamic Exploitation-Exploration Gating mechanism that adaptively arbitrates between stable SFT and exploratory RL based on reward feedback. Theoretical analysis confirms that DYPO linearly reduces fitting bias and minimizes overall variance. Extensive experiments demonstrate that DYPO significantly outperforms traditional sequential pipelines, achieving an average improvement of 4.8\% on complex reasoning benchmarks and 13.3\% on out-of-distribution tasks. Our code is publicly available at https://github.com/Tocci-Zhu/DYPO.

Deep neural networks have achieved remarkable performance on a range of classification tasks, with softmax cross-entropy (CE) loss emerging as the de-facto objective function. The CE loss encourages features of a class to have a higher projection score on the true class-vector compared to the negative classes. However, this is a relative constraint and does not explicitly force different class features to be well-separated. Motivated by the observation that ground-truth class representations in CE loss are orthogonal (one-hot encoded vectors), we develop a novel loss function termed `Orthogonal Projection Loss' (OPL) which imposes orthogonality in the feature space. OPL augments the properties of CE loss and directly enforces inter-class separation alongside intra-class clustering in the feature space through orthogonality constraints on the mini-batch level. As compared to other alternatives of CE, OPL offers unique advantages e.g., no additional learnable parameters, does not require careful negative mining and is not sensitive to the batch size. Given the plug-and-play nature of OPL, we evaluate it on a diverse range of tasks including image recognition (CIFAR-100), large-scale classification (ImageNet), domain generalization (PACS) and few-shot learning (miniImageNet, CIFAR-FS, tiered-ImageNet and Meta-dataset) and demonstrate its effectiveness across the board. Furthermore, OPL offers better robustness against practical nuisances such as adversarial attacks and label noise. Code is available at: https://github.com/kahnchana/opl.

Offline preference optimization methods are efficient for large language models (LLMs) alignment. Direct Preference optimization (DPO)-like learning, one of the most popular approaches, stands out for its efficiency in reward modeling. However, these methods typically follow the convention to use Bradley-Terry (BT) reward modeling that faces several critical assumptions, including the requirement for pairwise training data, model distribution shifting, human rationality assumption, etc. To address these limitations, we propose a general framework for offline preference optimization methods, Adaptive Preference Optimization with Utility Anchor (UAPO), which introduces an anchoring function to estimate the uncertainties brought from preference data annotation. Our method enables training even in scenarios where the data is unpaired, significantly enhancing data utilization efficiency. Moreover, the anchor design makes UAPO more robust in the training process. Experimental results demonstrate that UAPO achieves competitive outcomes without the strict dependency on data pairing, paving the way for more flexible and effective preference optimization methods.

Cross-entropy loss and focal loss are the most common choices when training deep neural networks for classification problems. Generally speaking, however, a good loss function can take on much more flexible forms, and should be tailored for different tasks and datasets. Motivated by how functions can be approximated via Taylor expansion, we propose a simple framework, named PolyLoss, to view and design loss functions as a linear combination of polynomial functions. Our PolyLoss allows the importance of different polynomial bases to be easily adjusted depending on the targeting tasks and datasets, while naturally subsuming the aforementioned cross-entropy loss and focal loss as special cases. Extensive experimental results show that the optimal choice within the PolyLoss is indeed dependent on the task and dataset. Simply by introducing one extra hyperparameter and adding one line of code, our Poly-1 formulation outperforms the cross-entropy loss and focal loss on 2D image classification, instance segmentation, object detection, and 3D object detection tasks, sometimes by a large margin.

Aligning large language models with pointwise absolute rewards has so far required online, on-policy algorithms such as PPO and GRPO. In contrast, simpler methods that can leverage offline or off-policy data, such as DPO and REBEL, are limited to learning from preference pairs or relative signals. To bridge this gap, we introduce Quantile Reward Policy Optimization (QRPO), which learns from pointwise absolute rewards while preserving the simplicity and offline applicability of DPO-like methods. QRPO uses quantile rewards to enable regression to the closed-form solution of the KL-regularized RL objective. This reward yields an analytically tractable partition function, removing the need for relative signals to cancel this term. Moreover, QRPO scales with increased compute to estimate quantile rewards, opening a new dimension for pre-computation scaling. Empirically, QRPO consistently achieves top performance on chat and coding evaluations--reward model scores, AlpacaEval 2, and LeetCode--compared to DPO, REBEL, and SimPO across diverse datasets and 8B-scale models. Finally, we find that training with robust rewards instead of converting them to preferences induces less length bias.

We study dynamic regret minimization in non-stationary online learning, with a primary focus on follow-the-regularized-leader (FTRL) methods. FTRL is important for curved losses and for understanding adaptive optimizers such as Adam, yet existing dynamic regret analyses are less explored for FTRL. To address this, we build on the discounted-to-dynamic reduction and present a modular way to obtain dynamic regret bounds of FTRL-related problems. Specifically, we focus on two representative curved losses: linear regression and logistic regression. Our method not only simplifies existing proofs for the optimal dynamic regret of online linear regression, but also yields new dynamic regret guarantees for online logistic regression. Beyond online convex optimization, we apply the reduction to analyze the Adam optimizers, obtaining optimal convergence rates in stochastic, non-convex, and non-smooth settings. The reduction also enables a more detailed treatment of Adam with two discount parameters (β_1,β_2), leading to new results for both clipped and clip-free variants of Adam optimizers.

The emergence of quantum reinforcement learning (QRL) is propelled by advancements in quantum computing (QC) and machine learning (ML), particularly through quantum neural networks (QNN) built on variational quantum circuits (VQC). These advancements have proven successful in addressing sequential decision-making tasks. However, constructing effective QRL models demands significant expertise due to challenges in designing quantum circuit architectures, including data encoding and parameterized circuits, which profoundly influence model performance. In this paper, we propose addressing this challenge with differentiable quantum architecture search (DiffQAS), enabling trainable circuit parameters and structure weights using gradient-based optimization. Furthermore, we enhance training efficiency through asynchronous reinforcement learning (RL) methods facilitating parallel training. Through numerical simulations, we demonstrate that our proposed DiffQAS-QRL approach achieves performance comparable to manually-crafted circuit architectures across considered environments, showcasing stability across diverse scenarios. This methodology offers a pathway for designing QRL models without extensive quantum knowledge, ensuring robust performance and fostering broader application of QRL.

Recent advancements in reinforcement learning from human feedback have shown that utilizing fine-grained token-level reward models can substantially enhance the performance of Proximal Policy Optimization (PPO) in aligning large language models. However, it is challenging to leverage such token-level reward as guidance for Direct Preference Optimization (DPO), since DPO is formulated as a sequence-level bandit problem. To address this challenge, this work decomposes the sequence-level PPO into a sequence of token-level proximal policy optimization problems and then frames the problem of token-level PPO with token-level reward guidance, from which closed-form optimal token-level policy and the corresponding token-level reward can be derived. Using the obtained reward and Bradley-Terry model, this work establishes a framework of computable loss functions with token-level reward guidance for DPO, and proposes a practical reward guidance based on the induced DPO reward. This formulation enables different tokens to exhibit varying degrees of deviation from reference policy based on their respective rewards. Experiment results demonstrate that our method achieves substantial performance improvements over DPO, with win rate gains of up to 7.5 points on MT-Bench, 6.2 points on AlpacaEval 2, and 4.3 points on Arena-Hard. Code is available at https://github.com/dvlab-research/TGDPO.

Reinforcement learning is time-consuming for complex tasks due to the need for large amounts of training data. Recent advances in GPU-based simulation, such as Isaac Gym, have sped up data collection thousands of times on a commodity GPU. Most prior works used on-policy methods like PPO due to their simplicity and ease of scaling. Off-policy methods are more data efficient but challenging to scale, resulting in a longer wall-clock training time. This paper presents a Parallel Q-Learning (PQL) scheme that outperforms PPO in wall-clock time while maintaining superior sample efficiency of off-policy learning. PQL achieves this by parallelizing data collection, policy learning, and value learning. Different from prior works on distributed off-policy learning, such as Apex, our scheme is designed specifically for massively parallel GPU-based simulation and optimized to work on a single workstation. In experiments, we demonstrate that Q-learning can be scaled to tens of thousands of parallel environments and investigate important factors affecting learning speed. The code is available at https://github.com/Improbable-AI/pql.

Image Quality Assessment (IQA) predicts perceptual quality scores consistent with human judgments. Recent RL-based IQA methods built on MLLMs focus on generating visual quality descriptions and scores, ignoring two key reliability limitations: (i) although the model's prediction stability varies significantly across training samples, existing GRPO-based methods apply uniform advantage weighting, thereby amplifying noisy signals from unstable samples in gradient updates; (ii) most works emphasize text-grounded reasoning over images while overlooking the model's visual perception ability of image content. In this paper, we propose Q-Hawkeye, an RL-based reliable visual policy optimization framework that redesigns the learning signal through unified Uncertainty-Aware Dynamic Optimization and Perception-Aware Optimization. Q-Hawkeye estimates predictive uncertainty using the variance of predicted scores across multiple rollouts and leverages this uncertainty to reweight each sample's update strength, stabilizing policy optimization. To strengthen perceptual reliability, we construct paired inputs of degraded images and their original images and introduce an Implicit Perception Loss that constrains the model to ground its quality judgments in genuine visual evidence. Extensive experiments demonstrate that Q-Hawkeye outperforms state-of-the-art methods and generalizes better across multiple datasets. Our dataset and code are available at https://github.com/AMAP-ML/Q-Hawkeye.

Stepwise group-based RL is an attractive way to train long-horizon LLM agents without a learned critic: it reuses multiple sampled rollouts to estimate local advantages. Its weakness is less visible but more fundamental: every group-relative estimator assumes that the steps it compares are equivalent for credit assignment. We show that current agentic variants violate this assumption through a state-action credit mismatch. The observation-hash partition is overly fine on the state side, creating singleton groups with zero step-level signal, while a single within-group mean is too coarse on the action side, mixing state-value estimation with action-specific credit. We introduce BiPACE (Bisimulation-Guided Policy Optimization with Action Counterfactual Estimation), a drop-in advantage estimator that fixes both sides without adding a critic, auxiliary loss, or extra rollouts. BiGPO clusters steps by cosine distance in the actor's own hidden-state geometry, an empirical policy-induced proxy for bisimulation that substantially lowers the singleton rate left by observation hashing. PACE then recenters returns within each behavioral cluster using action-conditioned peer baselines; its Q-style instance estimates a local Q(s,a)-V(s) nonparametrically. On ALFWorld/Qwen2.5-7B, BiPACE_Q raises overall validation success from GiGPO's 90.8 to 97.1pm0.9 over three seeds, and crosses the 95% threshold on every seed, which GiGPO never does within the same budget. On Qwen2.5-1.5B it reaches 93.5pm1.2 versus GiGPO's 86.7, and on WebShop and TextCraft it improves over GRPO and GiGPO at both model scales. The measured BiPACE-specific overhead is 11.3% of a single training-step wall time. Yet it changes the estimator's comparison unit from surface identity to approximate behavioral equivalence plus action-side counterfactuals. The code is available at https://github.com/TianxiangZhao/BiPACE.

Quantum Machine Learning (QML) has surfaced as a pioneering framework addressing sequential control tasks and time-series modeling. It has demonstrated empirical quantum advantages notably within domains such as Reinforcement Learning (RL) and time-series prediction. A significant advancement lies in Quantum Recurrent Neural Networks (QRNNs), specifically tailored for memory-intensive tasks encompassing partially observable environments and non-linear time-series prediction. Nevertheless, QRNN-based models encounter challenges, notably prolonged training duration stemming from the necessity to compute quantum gradients using backpropagation-through-time (BPTT). This predicament exacerbates when executing the complete model on quantum devices, primarily due to the substantial demand for circuit evaluation arising from the parameter-shift rule. This paper introduces the Quantum Fast Weight Programmers (QFWP) as a solution to the temporal or sequential learning challenge. The QFWP leverages a classical neural network (referred to as the 'slow programmer') functioning as a quantum programmer to swiftly modify the parameters of a variational quantum circuit (termed the 'fast programmer'). Instead of completely overwriting the fast programmer at each time-step, the slow programmer generates parameter changes or updates for the quantum circuit parameters. This approach enables the fast programmer to incorporate past observations or information. Notably, the proposed QFWP model achieves learning of temporal dependencies without necessitating the use of quantum recurrent neural networks. Numerical simulations conducted in this study showcase the efficacy of the proposed QFWP model in both time-series prediction and RL tasks. The model exhibits performance levels either comparable to or surpassing those achieved by QLSTM-based models.

When safety is formulated as a limit of cumulative cost, safe reinforcement learning (RL) aims to learn policies that maximize return subject to the cost constraint in data collection and deployment. Off-policy safe RL methods, although offering high sample efficiency, suffer from constraint violations due to cost-agnostic exploration and estimation bias in cumulative cost. To address this issue, we propose Constrained Optimistic eXploration Q-learning (COX-Q), an off-policy safe RL algorithm that integrates cost-bounded online exploration and conservative offline distributional value learning. First, we introduce a novel cost-constrained optimistic exploration strategy that resolves gradient conflicts between reward and cost in the action space and adaptively adjusts the trust region to control the training cost. Second, we adopt truncated quantile critics to stabilize the cost value learning. Quantile critics also quantify epistemic uncertainty to guide exploration. Experiments on safe velocity, safe navigation, and autonomous driving tasks demonstrate that COX-Q achieves high sample efficiency, competitive test safety performance, and controlled data collection cost. The results highlight COX-Q as a promising RL method for safety-critical applications.

Learning to rank is a key component of many e-commerce search engines. In learning to rank, one is interested in optimising the global ordering of a list of items according to their utility for users.Popular approaches learn a scoring function that scores items individually (i.e. without the context of other items in the list) by optimising a pointwise, pairwise or listwise loss. The list is then sorted in the descending order of the scores. Possible interactions between items present in the same list are taken into account in the training phase at the loss level. However, during inference, items are scored individually, and possible interactions between them are not considered. In this paper, we propose a context-aware neural network model that learns item scores by applying a self-attention mechanism. The relevance of a given item is thus determined in the context of all other items present in the list, both in training and in inference. We empirically demonstrate significant performance gains of self-attention based neural architecture over Multi-LayerPerceptron baselines, in particular on a dataset coming from search logs of a large scale e-commerce marketplace, Allegro.pl. This effect is consistent across popular pointwise, pairwise and listwise losses.Finally, we report new state-of-the-art results on MSLR-WEB30K, the learning to rank benchmark.

Large language models (LLMs) are increasingly used as judges to replace costly human preference labels in pairwise evaluation. Despite their practicality, LLM judges remain prone to miscalibration and systematic biases. This paper proposes SCOPE (Selective Conformal Optimized Pairwise Evaluation), a framework for selective pairwise judging with finite-sample statistical guarantees. Under exchangeability, SCOPE calibrates an acceptance threshold such that the error rate among non-abstained judgments is at most a user-specified level α. To provide SCOPE with a bias-neutral uncertainty signal, we introduce Bidirectional Preference Entropy (BPE), which queries the judge under both response positions, aggregates the implied preference probabilities to enforce invariance to response order, and converts the aggregated probability into an entropy-based uncertainty score. Across MT-Bench, RewardBench, and Chatbot Arena, BPE improves uncertainty quality over standard confidence proxies, providing a stronger selection signal that enables SCOPE to consistently meet the target risk level while retaining good coverage across judge scales. In particular, at α= 0.10, SCOPE consistently satisfies the risk bound across all benchmarks and judge scales (empirical risk approx 0.097 to 0.099), while retaining substantial coverage, reaching 0.89 on RewardBench with Qwen-14B and 0.98 on RewardBench with Qwen-32B. Compared to naïve baselines, SCOPE accepts up to 2.4times more judgments on MT-Bench with Qwen-7B under the same target risk constraint, demonstrating that BPE enables reliable and high-coverage LLM-based evaluation.

While implicit feedback is foundational to modern recommender systems, factors such as human error, uncertainty, and ambiguity in user behavior inevitably introduce significant noise into this feedback, adversely affecting the accuracy and robustness of recommendations. To address this issue, existing methods typically aim to reduce the training weight of noisy feedback or discard it entirely, based on the observation that noisy interactions often exhibit higher losses in the overall loss distribution. However, we identify two key issues: (1) there is a significant overlap between normal and noisy interactions in the overall loss distribution, and (2) this overlap becomes even more pronounced when transitioning from pointwise loss functions (e.g., BCE loss) to pairwise loss functions (e.g., BPR loss). This overlap leads traditional methods to misclassify noisy interactions as normal, and vice versa. To tackle these challenges, we further investigate the loss overlap and find that for a given user, there is a clear distinction between normal and noisy interactions in the user's personal loss distribution. Based on this insight, we propose a resampling strategy to Denoise using the user's Personal Loss distribution, named PLD, which reduces the probability of noisy interactions being optimized. Specifically, during each optimization iteration, we create a candidate item pool for each user and resample the items from this pool based on the user's personal loss distribution, prioritizing normal interactions. Additionally, we conduct a theoretical analysis to validate PLD's effectiveness and suggest ways to further enhance its performance. Extensive experiments conducted on three datasets with varying noise ratios demonstrate PLD's efficacy and robustness.

Large language models (LLMs) fine-tuned with alignment techniques, such as reinforcement learning from human feedback, have been instrumental in developing some of the most capable AI systems to date. Despite their success, existing methods typically rely on simple binary labels, such as those indicating preferred outputs in pairwise preferences, which fail to capture the subtle differences in relative quality between pairs. To address this limitation, we introduce an approach called Margin Matching Preference Optimization (MMPO), which incorporates relative quality margins into optimization, leading to improved LLM policies and reward models. Specifically, given quality margins in pairwise preferences, we design soft target probabilities based on the Bradley-Terry model, which are then used to train models with the standard cross-entropy objective. Experiments with both human and AI feedback data demonstrate that MMPO consistently outperforms baseline methods, often by a substantial margin, on popular benchmarks including MT-bench and RewardBench. Notably, the 7B model trained with MMPO achieves state-of-the-art performance on RewardBench as of June 2024, outperforming other models of the same scale. Our analysis also shows that MMPO is more robust to overfitting, leading to better-calibrated models.

This paper provides a pair similarity optimization viewpoint on deep feature learning, aiming to maximize the within-class similarity s_p and minimize the between-class similarity s_n. We find a majority of loss functions, including the triplet loss and the softmax plus cross-entropy loss, embed s_n and s_p into similarity pairs and seek to reduce (s_n-s_p). Such an optimization manner is inflexible, because the penalty strength on every single similarity score is restricted to be equal. Our intuition is that if a similarity score deviates far from the optimum, it should be emphasized. To this end, we simply re-weight each similarity to highlight the less-optimized similarity scores. It results in a Circle loss, which is named due to its circular decision boundary. The Circle loss has a unified formula for two elemental deep feature learning approaches, i.e. learning with class-level labels and pair-wise labels. Analytically, we show that the Circle loss offers a more flexible optimization approach towards a more definite convergence target, compared with the loss functions optimizing (s_n-s_p). Experimentally, we demonstrate the superiority of the Circle loss on a variety of deep feature learning tasks. On face recognition, person re-identification, as well as several fine-grained image retrieval datasets, the achieved performance is on par with the state of the art.

Levin Tree Search (LTS) is a search algorithm that makes use of a policy (a probability distribution over actions) and comes with a theoretical guarantee on the number of expansions before reaching a goal node, depending on the quality of the policy. This guarantee can be used as a loss function, which we call the LTS loss, to optimize neural networks representing the policy (LTS+NN). In this work we show that the neural network can be substituted with parameterized context models originating from the online compression literature (LTS+CM). We show that the LTS loss is convex under this new model, which allows for using standard convex optimization tools, and obtain convergence guarantees to the optimal parameters in an online setting for a given set of solution trajectories -- guarantees that cannot be provided for neural networks. The new LTS+CM algorithm compares favorably against LTS+NN on several benchmarks: Sokoban (Boxoban), The Witness, and the 24-Sliding Tile puzzle (STP). The difference is particularly large on STP, where LTS+NN fails to solve most of the test instances while LTS+CM solves each test instance in a fraction of a second. Furthermore, we show that LTS+CM is able to learn a policy that solves the Rubik's cube in only a few hundred expansions, which considerably improves upon previous machine learning techniques.

In RL, given a prompt, we sample a group of completions from a model and score them. Two questions follow: which completions should gain probability mass, and how should the parameters move to realize that change? Standard policy-gradient methods answer both at once, so the update can overshoot or undershoot depending on the learning rate, clipping, and other optimizer choices. We introduce Target Policy Optimization (TPO), which separates the two questions. Given scored completions, TPO constructs a target distribution q_i propto p_i^{,old} exp(u_i) and fits the policy to it by cross-entropy. The loss gradient on sampled-completion logits is p^θ- q, which vanishes once the policy matches the target. On tabular bandits, transformer sequence tasks, and billion-parameter LLM RLVR, TPO matches PG, PPO, GRPO, and DG on easy tasks and substantially outperforms them under sparse reward. Code is available at https://github.com/JeanKaddour/tpo.

Reinforcement learning from human feedback (RLHF) has become a powerful post-training paradigm for aligning large language models with human preferences. A core challenge in RLHF is constructing accurate reward signals, where the conventional Bradley-Terry reward models (BT RMs) often suffer from sensitivity to data size and coverage, as well as vulnerability to reward hacking. Generative reward models (GenRMs) offer a more robust alternative by generating chain-of-thought (CoT) rationales followed by a final reward. However, existing GenRMs rely on shallow, vertically scaled reasoning, limiting their capacity to handle nuanced or complex (e.g., reasoning-intensive) tasks. Moreover, their pairwise preference outputs are incompatible with standard RLHF algorithms that require pointwise reward signals. In this work, we introduce Think-RM, a training framework that enables long-horizon reasoning in GenRMs by modeling an internal thinking process. Rather than producing structured, externally provided rationales, Think-RM generates flexible, self-guided reasoning traces that support advanced capabilities such as self-reflection, hypothetical reasoning, and divergent reasoning. To elicit these reasoning abilities, we first warm-up the models by supervised fine-tuning (SFT) over long CoT data. We then further improve the model's long-horizon abilities by rule-based reinforcement learning (RL). In addition, we propose a novel pairwise RLHF pipeline that directly optimizes policies using pairwise preference rewards, eliminating the need for pointwise reward conversion and enabling more effective use of Think-RM outputs. Experiments show that Think-RM achieves state-of-the-art results on RM-Bench, outperforming both BT RM and vertically scaled GenRM by 8%. When combined with our pairwise RLHF pipeline, it demonstrates superior end-policy performance compared to traditional approaches.

While scaling laws provide a reliable methodology for predicting train loss across compute scales for a single data distribution, less is known about how these predictions should change as we change the distribution. In this paper, we derive a strategy for predicting one loss from another and apply it to predict across different pre-training datasets and from pre-training data to downstream task data. Our predictions extrapolate well even at 20x the largest FLOP budget used to fit the curves. More precisely, we find that there are simple shifted power law relationships between (1) the train losses of two models trained on two separate datasets when the models are paired by training compute (train-to-train), (2) the train loss and the test loss on any downstream distribution for a single model (train-to-test), and (3) the test losses of two models trained on two separate train datasets (test-to-test). The results hold up for pre-training datasets that differ substantially (some are entirely code and others have no code at all) and across a variety of downstream tasks. Finally, we find that in some settings these shifted power law relationships can yield more accurate predictions than extrapolating single-dataset scaling laws.

Imbalanced data are frequently encountered in real-world classification tasks. Previous works on imbalanced learning mostly focused on learning with a minority class of few samples. However, the notion of imbalance also applies to cases where the minority class contains abundant samples, which is usually the case for industrial applications like fraud detection in the area of financial risk management. In this paper, we take a population-level approach to imbalanced learning by proposing a new formulation called ultra-imbalanced classification (UIC). Under UIC, loss functions behave differently even if infinite amount of training samples are available. To understand the intrinsic difficulty of UIC problems, we borrow ideas from information theory and establish a framework to compare different loss functions through the lens of statistical information. A novel learning objective termed Tunable Boosting Loss is developed which is provably resistant against data imbalance under UIC, as well as being empirically efficient verified by extensive experimental studies on both public and industrial datasets.

Few-shot learning is a challenging area of research that aims to learn new concepts with only a few labeled samples of data. Recent works based on metric-learning approaches leverage the meta-learning approach, which is encompassed by episodic tasks that make use a support (training) and query set (test) with the objective of learning a similarity comparison metric between those sets. Due to the lack of data, the learning process of the embedding network becomes an important part of the few-shot task. Previous works have addressed this problem using metric learning approaches, but the properties of the underlying latent space and the separability of the difference classes on it was not entirely enforced. In this work, we propose two different loss functions which consider the importance of the embedding vectors by looking at the intra-class and inter-class distance between the few data. The first loss function is the Proto-Triplet Loss, which is based on the original triplet loss with the modifications needed to better work on few-shot scenarios. The second loss function, which we dub ICNN loss is based on an inter and intra class nearest neighbors score, which help us to assess the quality of embeddings obtained from the trained network. Our results, obtained from a extensive experimental setup show a significant improvement in accuracy in the miniImagenNet benchmark compared to other metric-based few-shot learning methods by a margin of 2%, demonstrating the capability of these loss functions to allow the network to generalize better to previously unseen classes. In our experiments, we demonstrate competitive generalization capabilities to other domains, such as the Caltech CUB, Dogs and Cars datasets compared with the state of the art.

Reinforcement Learning with Verifiable Rewards (RLVR) is commonly based on group sampling to estimate advantages and stabilize policy updates. In practice, large group sizes are not feasible due to computational limits, which biases learning toward trajectories that are already likely. Smaller groups often miss rare-correct trajectories while still containing mixed rewards, concentrating probability on common solutions. We derive the probability that updates miss rare-correct modes as a function of group size, showing non-monotonic behavior, and characterize how updates redistribute mass within the correct set, revealing that unsampled-correct mass can shrink even as total correct mass grows. Motivated by this analysis, we propose a difficulty-aware advantage scaling coefficient, inspired by Focal loss, that down-weights updates on high-success prompts. The lightweight modification can be directly integrated into any group-relative RLVR algorithm such as GRPO, DAPO, and CISPO. On Qwen2.5-7B across in-domain and out-of-domain benchmarks, our method improves pass@256 from 64.1 rightarrow 70.3 (GRPO), 69.3 rightarrow 72.5 (DAPO), and 73.2 rightarrow 76.8 (CISPO), while preserving or improving pass@1, without increasing group size or computational cost.

Score- and flow-matching models often rely on preference-based reinforcement learning for two purposes: aligning with subjective preferences and, surprisingly, recovering properties such as visual realism and coherent object structure that matching-based training is intended to learn from the data itself. We argue that this reflects a structural mismatch. Matching losses measure ell_2 regression error on the velocity or score field under training-time marginals, a proxy poorly aligned with the visual and semantic properties that determine sample quality at inference. Given a reward aligned with these properties, RL sidesteps the mismatch by evaluating the model on its own samples and following the reward landscape directly. The challenge is to obtain such a reward without relying on human preferences, which are expensive and conflate data realism with annotator inclinations. We propose Discriminator-Guided RL (DRL). DRL trains a discriminator to separate data from base-model samples in a pretrained representation space and uses its logit as the reward in KL-regularized RL. The pretrained space restricts the discriminator to perceptually meaningful directions, and the logit estimates the log-likelihood ratio between data and model, which is the optimal reward for targeting the data distribution. Across SiT, JiT, REPA, and RAE, DRL reduces guidance-free FID (e.g., 9.38 to 2.62 on SiT) and semantic-space FD (e.g., 88.2 to 19.3 on DINOv3 for SiT), with consistent gains across all backbones, and improves human-preference rewards without training on them. It also yields a better Pareto frontier between preference reward and image fidelity under subsequent preference-based post-training, increasing alignment while reducing low-level artifacts such as oversaturation and excessive brightness.

As LLMs advance, post-training reinforcement learning (RL) increasingly relies on multi-dimensional rewards to cultivate comprehensive capabilities. This shift demands new algorithms capable of optimizing diverse and potentially competing objectives simultaneously. To address this, existing methods such as Group reward-Decoupled Policy Optimization (GDPO) decompose the overall score into independent reward groups, then compute the RL loss separately within each group. However, this strategy still encounters multi-reward conflicts: a single rollout can yield positive advantages on certain reward dimensions but negative ones on others, causing opposing signals to cancel each other out during aggregation, further hindering RL training efficiency. Inspired by Dynamic sAmpling Policy Optimization (DAPO), which improves RL training efficiency by filtering out ineffective rollouts with near-zero advantages, we propose Group-Dynamic reward-Decoupled Policy Optimization (GD^2PO). Specifically, GD^2PO employs a conflict-aware filtering mechanism to mask out rollouts suffering from severe reward-wise disagreement. By preventing conflicting signals from canceling each other out, this masking strategy preserves and enhances the magnitude of effective RL advantages, thereby significantly accelerating learning efficiency. Furthermore, we introduce query-level reweighting to dynamically adjust the update intensity of each query based on its overall reward consensus. Experiments on various multi-reward scenarios, including tool calling and human preference alignment, demonstrate that GD^2PO consistently and significantly outperforms existing baselines. The code is available at https://github.com/Qwen-Applications/GD2PO.

Pairwise re-ranking models predict which of two documents is more relevant to a query and then aggregate a final ranking from such preferences. This is often more effective than pointwise re-ranking models that directly predict a relevance value for each document. However, the high inference overhead of pairwise models limits their practical application: usually, for a set of k documents to be re-ranked, preferences for all k^2-k comparison pairs excluding self-comparisons are aggregated. We investigate whether the efficiency of pairwise re-ranking can be improved by sampling from all pairs. In an exploratory study, we evaluate three sampling methods and five preference aggregation methods. The best combination allows for an order of magnitude fewer comparisons at an acceptable loss of retrieval effectiveness, while competitive effectiveness is already achieved with about one third of the comparisons.

Constraint handling remains a key bottleneck in quantum combinatorial optimization. While slack-variable-based encodings are straightforward, they significantly increase qubit counts and circuit depth, challenging the scalability of quantum solvers. In this work, we investigate a suite of Lagrangian-based optimization techniques including dual ascent, bundle methods, cutting plane approaches, and augmented Lagrangian formulations for solving constrained combinatorial problems on quantum simulators and hardware. Our framework is applied to three representative NP-hard problems: the Travelling Salesman Problem (TSP), the Multi-Dimensional Knapsack Problem (MDKP), and the Maximum Independent Set (MIS). We demonstrate that MDKP and TSP, with their inequality-based or degree-constrained structures, allow for slack-free reformulations, leading to significant qubit savings without compromising performance. In contrast, MIS does not inherently benefit from slack elimination but still gains in feasibility and objective quality from principled Lagrangian updates. We benchmark these methods across classically hard instances, analyzing trade-offs in qubit usage, feasibility, and optimality gaps. Our results highlight the flexibility of Lagrangian formulations as a scalable alternative to naive QUBO penalization, even when qubit savings are not always achievable. This work provides practical insights for deploying constraint-aware quantum optimization pipelines, with applications in logistics, network design, and resource allocation.

Adapting reasoning models to new tasks during post-training with only output-level supervision stalls under reinforcement learning from verifiable rewards (RLVR) when the initial success probability p_0 is small. Using the Tsallis q-logarithm, we define a loss family J_Q that interpolates between RLVR (at q{=}0, the exploitation pole) and the log-marginal-likelihood over latent trajectories (at q{=}1, the density-estimation pole). All members share the same per-example gradient direction, differing only by a scalar amplification P_{θ^{-q}} that reweights each instance independently of the learning rate. This amplification is the mechanism that addresses cold-start stalling: under gradient flow, the exploitation pole requires Ω(1{p_0}) time to escape cold start, while the density-estimation pole escapes in Θbig(log(1{p_0})big); intermediate q trades escape speed against noise memorization. Because P_θ is intractable, we derive two Monte Carlo estimators from the two factorizations of the gradient: Gradient-Amplified RL (GARL) samples from the prior and amplifies the RL gradient, and Posterior-Attenuated Fine-Tuning (PAFT) importance-resamples from the posterior and runs standard SFT. Both have bias Obig(q{M P_θ^{q+1}}big); GARL has lower variance, PAFT has semantically coherent gradients. On FinQA, HotPotQA, and MuSiQue, GARL at q{=}0.75 substantially mitigates cold-start stalling, escaping cold start where GRPO fails entirely. In warm start, GARL at low q dominates FinQA where training is stable; on HotPotQA and MuSiQue, GARL destabilizes during training, and PAFT at q{=}0.75 provides stable gradients (best overall on HotPotQA at 47.9 maj@16, +14.4 over GRPO).

This paper presents an advanced mathematical problem-solving framework, LLaMA-Berry, for enhancing the mathematical reasoning ability of Large Language Models (LLMs). The framework combines Monte Carlo Tree Search (MCTS) with iterative Self-Refine to optimize the reasoning path and utilizes a pairwise reward model to evaluate different paths globally. By leveraging the self-critic and rewriting capabilities of LLMs, Self-Refine applied to MCTS (SR-MCTS) overcomes the inefficiencies and limitations of conventional step-wise and greedy search algorithms by fostering a more efficient exploration of solution spaces. Pairwise Preference Reward Model~(PPRM), inspired by Reinforcement Learning from Human Feedback (RLHF), is then used to model pairwise preferences between solutions, utilizing an Enhanced Borda Count (EBC) method to synthesize these preferences into a global ranking score to find better answers. This approach addresses the challenges of scoring variability and non-independent distributions in mathematical reasoning tasks. The framework has been tested on general and advanced benchmarks, showing superior performance in terms of search efficiency and problem-solving capability compared to existing methods like ToT and rStar, particularly in complex Olympiad-level benchmarks, including GPQA, AIME24 and AMC23.

We propose Delta L Normalization, a simple yet effective loss aggregation method tailored to the characteristic of dynamic generation lengths in Reinforcement Learning with Verifiable Rewards (RLVR). Recently, RLVR has demonstrated strong potential in improving the reasoning capabilities of large language models (LLMs), but a major challenge lies in the large variability of response lengths during training, which leads to high gradient variance and unstable optimization. Although previous methods such as GRPO, DAPO, and Dr. GRPO introduce different loss normalization terms to address this issue, they either produce biased estimates or still suffer from high gradient variance. By analyzing the effect of varying lengths on policy loss both theoretically and empirically, we reformulate the problem as finding a minimum-variance unbiased estimator. Our proposed Delta L Normalization not only provides an unbiased estimate of the true policy loss but also minimizes gradient variance in theory. Extensive experiments show that it consistently achieves superior results across different model sizes, maximum lengths, and tasks. Our code will be made public at https://github.com/zerolllin/Delta-L-Normalization.

In this paper, we present SCOREQ, a novel approach for speech quality prediction. SCOREQ is a triplet loss function for contrastive regression that addresses the domain generalisation shortcoming exhibited by state of the art no-reference speech quality metrics. In the paper we: (i) illustrate the problem of L2 loss training failing at capturing the continuous nature of the mean opinion score (MOS) labels; (ii) demonstrate the lack of generalisation through a benchmarking evaluation across several speech domains; (iii) outline our approach and explore the impact of the architectural design decisions through incremental evaluation; (iv) evaluate the final model against state of the art models for a wide variety of data and domains. The results show that the lack of generalisation observed in state of the art speech quality metrics is addressed by SCOREQ. We conclude that using a triplet loss function for contrastive regression improves generalisation for speech quality prediction models but also has potential utility across a wide range of applications using regression-based predictive models.

Supervised low-level vision models rely on pixel-wise losses against paired references, yet paired training sets exhibit per-pair photometric inconsistency, say, different image pairs demand different global brightness, color, or white-balance mappings. This inconsistency enters through task-intrinsic photometric transfer (e.g., low-light enhancement) or unintended acquisition shifts (e.g., de-raining), and in either case causes an optimization pathology. Standard reconstruction losses allocate disproportionate gradient budget to conflicting per-pair photometric targets, crowding out content restoration. In this paper, we investigate this issue and prove that, under least-squares decomposition, the photometric and structural components of the prediction-target residual are orthogonal, and that the spatially dense photometric component dominates the gradient energy. Motivated by this analysis, we propose Photometric Alignment Loss (PAL). This flexible supervision objective discounts nuisance photometric discrepancy via closed-form affine color alignment while preserving restoration-relevant supervision, requiring only covariance statistics and tiny matrix inversion with negligible overhead. Across 6 tasks, 16 datasets, and 16 architectures, PAL consistently improves metrics and generalization. The implementation is in the appendix.

In this paper, we study risk-sensitive Reinforcement Learning (RL), focusing on the objective of Conditional Value at Risk (CVaR) with risk tolerance tau. Starting with multi-arm bandits (MABs), we show the minimax CVaR regret rate is Omega(tau^{-1AK}), where A is the number of actions and K is the number of episodes, and that it is achieved by an Upper Confidence Bound algorithm with a novel Bernstein bonus. For online RL in tabular Markov Decision Processes (MDPs), we show a minimax regret lower bound of Omega(tau^{-1SAK}) (with normalized cumulative rewards), where S is the number of states, and we propose a novel bonus-driven Value Iteration procedure. We show that our algorithm achieves the optimal regret of widetilde O(tau^{-1SAK}) under a continuity assumption and in general attains a near-optimal regret of widetilde O(tau^{-1}SAK), which is minimax-optimal for constant tau. This improves on the best available bounds. By discretizing rewards appropriately, our algorithms are computationally efficient.

Offline reinforcement learning (RL) presents a promising approach for learning reinforced policies from offline datasets without the need for costly or unsafe interactions with the environment. However, datasets collected by humans in real-world environments are often noisy and may even be maliciously corrupted, which can significantly degrade the performance of offline RL. In this work, we first investigate the performance of current offline RL algorithms under comprehensive data corruption, including states, actions, rewards, and dynamics. Our extensive experiments reveal that implicit Q-learning (IQL) demonstrates remarkable resilience to data corruption among various offline RL algorithms. Furthermore, we conduct both empirical and theoretical analyses to understand IQL's robust performance, identifying its supervised policy learning scheme as the key factor. Despite its relative robustness, IQL still suffers from heavy-tail targets of Q functions under dynamics corruption. To tackle this challenge, we draw inspiration from robust statistics to employ the Huber loss to handle the heavy-tailedness and utilize quantile estimators to balance penalization for corrupted data and learning stability. By incorporating these simple yet effective modifications into IQL, we propose a more robust offline RL approach named Robust IQL (RIQL). Extensive experiments demonstrate that RIQL exhibits highly robust performance when subjected to diverse data corruption scenarios.

Reinforcement learning with verifiable rewards (RLVR) has become central to LLM reasoning, but its outcome-level rewards can make models more willing to give confident answers when evidence or reasoning is unreliable. Existing SFT or RL methods mainly teach LLMs to refuse or express uncertainty at the response level, which can overfit abstention behavior rather than improve reasoning reliability. To address this limitation, we propose Cognitive Pairwise Training (CPT), a cognitive mid-training alignment stage that turns pairwise comparisons over reasoning traces into a reusable alignment signal. By learning to distinguish trustworthy from flawed reasoning, CPT encourages the model to internalize a reasoning-quality discrimination boundary rather than memorize surface refusal patterns. Across five model scales and three model families, CPT improves the reasoning--metacognition trade-off. At 14B, CPT+RL outperforms the standard SFT+RL pipeline by +2.2 math-average points and +5.2 abstention-F1 points. Further analyses show that CPT improves trace quality and exhibits strong robustness and scalability across evaluation and training settings. Code and models are released at https://github.com/Tsinghua-dhy/CPT.

Online conformal prediction (OCP) seeks prediction intervals that achieve long-run 1-α coverage for arbitrary (possibly adversarial) data streams, while remaining as informative as possible. Existing OCP methods often require manual learning-rate tuning to work well, and may also require algorithm-specific analyses. Here, we develop a general regret-to-coverage theory for interval-valued OCP based on the (1-α)-pinball loss. Our first contribution is to identify linearized regret as a key notion, showing that controlling it implies coverage bounds for any online algorithm. This relies on a black-box reduction that depends only on the Fenchel conjugate of an upper bound on the linearized regret. Building on this theory, we propose UP-OCP, a parameter-free method for OCP, via a reduction to a two-asset portfolio selection problem, leveraging universal portfolio algorithms. We show strong finite-time bounds on the miscoverage of UP-OCP, even for polynomially growing predictions. Extensive experiments support that UP-OCP delivers consistently better size/coverage trade-offs than prior online conformal baselines.

In machine learning, the notion of multi-armed bandits refers to a class of online learning problems, in which an agent is supposed to simultaneously explore and exploit a given set of choice alternatives in the course of a sequential decision process. In the standard setting, the agent learns from stochastic feedback in the form of real-valued rewards. In many applications, however, numerical reward signals are not readily available -- instead, only weaker information is provided, in particular relative preferences in the form of qualitative comparisons between pairs of alternatives. This observation has motivated the study of variants of the multi-armed bandit problem, in which more general representations are used both for the type of feedback to learn from and the target of prediction. The aim of this paper is to provide a survey of the state of the art in this field, referred to as preference-based multi-armed bandits or dueling bandits. To this end, we provide an overview of problems that have been considered in the literature as well as methods for tackling them. Our taxonomy is mainly based on the assumptions made by these methods about the data-generating process and, related to this, the properties of the preference-based feedback.

We propose a fully data-driven approach to designing mutual information (MI) estimators. Since any MI estimator is a function of the observed sample from two random variables, we parameterize this function with a neural network (MIST) and train it end-to-end to predict MI values. Training is performed on a large meta-dataset of 625,000 synthetic joint distributions with known ground-truth MI. To handle variable sample sizes and dimensions, we employ a two-dimensional attention scheme ensuring permutation invariance across input samples. To quantify uncertainty, we optimize a quantile regression loss, enabling the estimator to approximate the sampling distribution of MI rather than return a single point estimate. This research program departs from prior work by taking a fully empirical route, trading universal theoretical guarantees for flexibility and efficiency. Empirically, the learned estimators largely outperform classical baselines across sample sizes and dimensions, including on joint distributions unseen during training. The resulting quantile-based intervals are well-calibrated and more reliable than bootstrap-based confidence intervals, while inference is orders of magnitude faster than existing neural baselines. Beyond immediate empirical gains, this framework yields trainable, fully differentiable estimators that can be embedded into larger learning pipelines. Moreover, exploiting MI's invariance to invertible transformations, meta-datasets can be adapted to arbitrary data modalities via normalizing flows, enabling flexible training for diverse target meta-distributions.

Physics-Informed Neural Networks (PINNs) often train slowly or fail to converge on challenging partial differential equations (PDEs), a behavior recently linked to severely ill-conditioned loss landscapes inherited from the underlying differential operator. We study PINNs augmented with a pointwise data-fidelity term, added at a few points in the domain to the standard residual and boundary losses. We show that this supervision term acts as an operator-level preconditioner: for suitable weights, our comparison bounds guarantee a substantially smaller condition number than under the standard PINN loss, independently of how the pointwise labels are obtained. For a broad class of PDEs admitting a Feynman-Kac (FK) representation, we generate such labels by Monte Carlo averages of the FK functional, resulting in what we call ``FK-PINNs", and using the excess risk decomposition approach, we derive non-asymptotic L^2(Ω)-error bounds for FK-PINNs with tanh activation trained by finitely many steps of gradient descent. Along the way, we establish pseudo-dimension bounds for first- and second-order derivatives of tanh neural networks, which are of independent interest and, to the best of our knowledge, new. Numerical experiments on Poisson, Schrödinger, mean exit time, and committor problems corroborate the theory, and show that FK-PINNs can successfully solve PDEs for which standard PINNs exhibit severe failure modes.

Reinforcement Learning from Human Feedback (RLHF) has emerged as a important paradigm for aligning large language models (LLMs) with human preferences during post-training. This framework typically involves two stages: first, training a reward model on human preference data, followed by optimizing the language model using reinforcement learning algorithms. However, current RLHF approaches may constrained by two limitations. First, existing RLHF frameworks often rely on Bradley-Terry models to assign scalar rewards based on pairwise comparisons of individual responses. However, this approach imposes significant challenges on reward model (RM), as the inherent variability in prompt-response pairs across different contexts demands robust calibration capabilities from the RM. Second, reward models are typically initialized from generative foundation models, such as pre-trained or supervised fine-tuned models, despite the fact that reward models perform discriminative tasks, creating a mismatch. This paper introduces Pairwise-RL, a RLHF framework that addresses these challenges through a combination of generative reward modeling and a pairwise proximal policy optimization (PPO) algorithm. Pairwise-RL unifies reward model training and its application during reinforcement learning within a consistent pairwise paradigm, leveraging generative modeling techniques to enhance reward model performance and score calibration. Experimental evaluations demonstrate that Pairwise-RL outperforms traditional RLHF frameworks across both internal evaluation datasets and standard public benchmarks, underscoring its effectiveness in improving alignment and model behavior.

A range of quantum algorithms, especially those leveraging variational parameterization and circuit-based optimization, are being studied as alternatives for solving classically intractable combinatorial optimization problems (COPs). However, their applicability is limited by hardware constraints, including shallow circuit depth, limited qubit counts, and noise. To mitigate these issues, we propose a hybrid classical--quantum framework based on graph shrinking to reduce the number of variables and constraints in QUBO formulations of COPs, while preserving problem structure. Our approach introduces three key ideas: (i) constraint-aware shrinking that prevents merges that will likely violate problem-specific feasibility constraints, (ii) a verification-and-repair pipeline to correct infeasible solutions post-optimization, and (iii) adaptive strategies for recalculating correlations and controlling the graph shrinking process. We apply our approach to three standard benchmark problems: Multidimensional Knapsack (MDKP), Maximum Independent Set (MIS), and the Quadratic Assignment Problem (QAP). Empirical results show that our approach improves solution feasibility, reduces repair complexity, and enhances quantum optimization quality on hardware-limited instances. These findings demonstrate a scalable pathway for applying near-term quantum algorithms to classically challenging constrained optimization problems.

Training generally capable agents that thoroughly explore their environment and learn new and diverse skills is a long-term goal of robot learning. Quality Diversity Reinforcement Learning (QD-RL) is an emerging research area that blends the best aspects of both fields -- Quality Diversity (QD) provides a principled form of exploration and produces collections of behaviorally diverse agents, while Reinforcement Learning (RL) provides a powerful performance improvement operator enabling generalization across tasks and dynamic environments. Existing QD-RL approaches have been constrained to sample efficient, deterministic off-policy RL algorithms and/or evolution strategies, and struggle with highly stochastic environments. In this work, we, for the first time, adapt on-policy RL, specifically Proximal Policy Optimization (PPO), to the Differentiable Quality Diversity (DQD) framework and propose additional improvements over prior work that enable efficient optimization and discovery of novel skills on challenging locomotion tasks. Our new algorithm, Proximal Policy Gradient Arborescence (PPGA), achieves state-of-the-art results, including a 4x improvement in best reward over baselines on the challenging humanoid domain.

Quantizing neural networks is one of the most effective methods for achieving efficient inference on mobile and embedded devices. In particular, mixed precision quantized (MPQ) networks, whose layers can be quantized to different bitwidths, achieve better task performance for the same resource constraint compared to networks with homogeneous bitwidths. However, finding the optimal bitwidth allocation is a challenging problem as the search space grows exponentially with the number of layers in the network. In this paper, we propose QBitOpt, a novel algorithm for updating bitwidths during quantization-aware training (QAT). We formulate the bitwidth allocation problem as a constraint optimization problem. By combining fast-to-compute sensitivities with efficient solvers during QAT, QBitOpt can produce mixed-precision networks with high task performance guaranteed to satisfy strict resource constraints. This contrasts with existing mixed-precision methods that learn bitwidths using gradients and cannot provide such guarantees. We evaluate QBitOpt on ImageNet and confirm that we outperform existing fixed and mixed-precision methods under average bitwidth constraints commonly found in the literature.

We present an experimental implementation of the multiplayer Quantum Volunteer's Dilemma on noisy intermediate-scale quantum (NISQ) hardware, executed on the ibm_kingston backend via Qiskit Runtime. The game is evaluated for N = 2 to 9 players under four transpiler optimization levels, with 20 independent repetitions per configuration and 2048 shots per circuit, including post-processing readout error correction via mthree. Target-state fidelity decays with system size but remains above 70% (corrected) through N = 9. With readout correction, the global average payoff reproduces the quantum theoretical benchmark exactly for N <= 6 and exceeds the classical Nash equilibrium across the full tested range. Optimization level 2 is selected as the reference configuration after gate count analysis reveals that levels 2 and 3 produce identical transpiled circuits, with level 2 achieving superior fidelity stability. A Hamming distance analysis of raw measurement counts shows that single-qubit errors dominate at small N, with multi-qubit contributions growing beyond N = 6. A calibration-based digital twin captures global payoff trends but exhibits a linear fidelity decay profile that diverges from the hardware behavior at large N, exposing the limits of first-order independent per-qubit noise models. These results demonstrate that aggregate quantum advantage in multiplayer games is robust to NISQ noise conditions across the full tested range, while the practical observability of state-level advantage is constrained to N <= 8 under post-processed readout correction.

The emergence of quantum computing poses significant risks to the security of modern communication networks as it breaks today's public-key cryptographic algorithms. Quantum Key Distribution (QKD) offers a promising solution by harnessing the principles of quantum mechanics to establish secure keys. However, practical QKD implementations remain vulnerable to hardware imperfections and advanced attacks such as Photon Number Splitting and Trojan-Horse attacks. In this work, we investigate the potential of quantum machine learning (QML) to detect QKD attacks. In particular, we propose a Hybrid Quantum Long Short-Term Memory (QLSTM) model to improve detection performance. By combining quantum-enhanced learning with classical deep learning, the model captures temporal patterns in QKD data, improving detection accuracy. To evaluate the proposed model, we introduce a QKD dataset that simulates typical operations along with multiple attack scenarios, including Intercept-and-Resend, Photon-Number Splitting, Trojan-Horse, Detector Blinding, and Combined attacks. The dataset includes Quantum Bit Error Rate (QBER), signal and decoy loss rates, and time-based metrics. Our results demonstrate the promising performance of the quantum machine learning approach compared to classical models. The proposed Hybrid QLSTM achieved an accuracy of 94.7% after 50 training epochs. The evaluation is conducted on a semi-realistic, simulation-generated decoy-state BB84 dataset, and the reported performance should be interpreted as a proof-of-concept rather than a final assessment on field-deployed QKD systems.

We present a methodology to price options and portfolios of options on a gate-based quantum computer using amplitude estimation, an algorithm which provides a quadratic speedup compared to classical Monte Carlo methods. The options that we cover include vanilla options, multi-asset options and path-dependent options such as barrier options. We put an emphasis on the implementation of the quantum circuits required to build the input states and operators needed by amplitude estimation to price the different option types. Additionally, we show simulation results to highlight how the circuits that we implement price the different option contracts. Finally, we examine the performance of option pricing circuits on quantum hardware using the IBM Q Tokyo quantum device. We employ a simple, yet effective, error mitigation scheme that allows us to significantly reduce the errors arising from noisy two-qubit gates.

In this paper, we propose a feature affinity (FA) assisted knowledge distillation (KD) method to improve quantization-aware training of deep neural networks (DNN). The FA loss on intermediate feature maps of DNNs plays the role of teaching middle steps of a solution to a student instead of only giving final answers in the conventional KD where the loss acts on the network logits at the output level. Combining logit loss and FA loss, we found that the quantized student network receives stronger supervision than from the labeled ground-truth data. The resulting FAQD is capable of compressing model on label-free data, which brings immediate practical benefits as pre-trained teacher models are readily available and unlabeled data are abundant. In contrast, data labeling is often laborious and expensive. Finally, we propose a fast feature affinity (FFA) loss that accurately approximates FA loss with a lower order of computational complexity, which helps speed up training for high resolution image input.

Solving NP-hard problems traditionally relies on heuristics, yet manually designing effective heuristics for complex problems remains a significant challenge. While recent advancements like FunSearch have shown that large language models (LLMs) can be integrated into evolutionary algorithms (EAs) for heuristic design, their potential is hindered by limitations in balancing exploitation and exploration. We introduce Quality-Uncertainty Balanced Evolution (QUBE), a novel approach that enhances LLM+EA methods by redefining the priority criterion within the FunSearch framework. QUBE employs the Quality-Uncertainty Trade-off Criterion (QUTC), based on our proposed Uncertainty-Inclusive Quality metric, to evaluate and guide the evolutionary process. Through extensive experiments on challenging NP-complete problems, QUBE demonstrates significant performance improvements over FunSearch and baseline methods. Our code are available at https://github.com/zzjchen/QUBE\_code.

Quantization has become a crucial step for the efficient deployment of deep neural networks, where floating point operations are converted to simpler fixed point operations. In its most naive form, it simply consists in a combination of scaling and rounding transformations, leading to either a limited compression rate or a significant accuracy drop. Recently, Gradient-based post-training quantization (GPTQ) methods appears to be constitute a suitable trade-off between such simple methods and more powerful, yet expensive Quantization-Aware Training (QAT) approaches, particularly when attempting to quantize LLMs, where scalability of the quantization process is of paramount importance. GPTQ essentially consists in learning the rounding operation using a small calibration set. In this work, we challenge common choices in GPTQ methods. In particular, we show that the process is, to a certain extent, robust to a number of variables (weight selection, feature augmentation, choice of calibration set). More importantly, we derive a number of best practices for designing more efficient and scalable GPTQ methods, regarding the problem formulation (loss, degrees of freedom, use of non-uniform quantization schemes) or optimization process (choice of variable and optimizer). Lastly, we propose a novel importance-based mixed-precision technique. Those guidelines lead to significant performance improvements on all the tested state-of-the-art GPTQ methods and networks (e.g. +6.819 points on ViT for 4-bit quantization), paving the way for the design of scalable, yet effective quantization methods.

In value-based reinforcement learning methods such as deep Q-learning, function approximation errors are known to lead to overestimated value estimates and suboptimal policies. We show that this problem persists in an actor-critic setting and propose novel mechanisms to minimize its effects on both the actor and the critic. Our algorithm builds on Double Q-learning, by taking the minimum value between a pair of critics to limit overestimation. We draw the connection between target networks and overestimation bias, and suggest delaying policy updates to reduce per-update error and further improve performance. We evaluate our method on the suite of OpenAI gym tasks, outperforming the state of the art in every environment tested.