Reward models learned from human preferences are central to aligning large language models (LLMs) via reinforcement learning from human feedback, yet they are often vulnerable to reward hacking due to noisy annotations and systematic biases such as response length or style. We propose Bayesian Non-Negative Reward Model (BNRM), a principled reward modeling framework that integrates non-negative factor analysis into Bradley–Terry (BT) preference model. BNRM represents rewards through a sparse, non-negative latent factor generative process that operates at two complementary levels: instance-specific latent variables induce disentangled reward representations, while sparsity over global latent factors acts as an implicit debiasing mechanism that suppresses spurious correlations. Together, this disentanglement-then-debiasing structure enables robust uncertainty-aware reward learning. To scale BNRM to modern LLMs, we develop an amortized variational inference network conditioned on deep model representations, allowing efficient end-to-end training. Extensive empirical results demonstrate that BNRM substantially mitigates reward over-optimization, improves robustness under distribution shifts, and yields more interpretable reward decompositions than strong baselines.
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General Machine Learning · Evaluation
Conditional generative models have recently achieved remarkable success in various applications. However, a suitable metric for evaluating the reliability of these models, which takes into account their inherent uncertainty, is still lacking. Existing metrics, which typically assess a single output, may fail to capture the variability or potential risks in generation. In this paper, we propose a novel evaluation metric called \emph{reliability score} based on conformal prediction, which measures the worst-case performance within the prediction set at a pre-specified confidence level. However, computing this score is challenging due to the high-dimensional nature of the output space and the nonconvexity of both the metric function and the prediction set. To efficiently compute this score, we introduce Conformal ReLiability (CReL), a framework that can \textbf{(i)} construct the prediction set with desired coverage; and \textbf{(ii)} accurately optimize the reliability score within the constructed prediction set. We provide theoretical results on coverage and demonstrate empirically that our method produces more informative prediction sets than existing approaches. Experiments on synthetic data and the image-to-text and text-to-image tasks further demonstrate the interpretability of our new metric, and the validity and effectiveness of our computational framework.
Reinforcement Learning · Batch/Offline
Offline reinforcement learning (RL) aims to optimize policies from pre-collected datasets. A bottleneck of this paradigm is managing epistemic uncertainty, which arises from limited data coverage (sample-level) and the ambiguity in identifying transition dynamics from finite data (model-level). To provide a unified quantification of these uncertainties, Bayesian RL has been proposed by treating the dynamics model as a random variable and maintaining a corresponding belief. Despite its theoretical appeal, policy optimization in Bayesian RL remains computationally challenging as it requires solving composite objectives with expectations. Prior methods either employ search-based techniques with poor computational scalability or impose restrictive posterior assumptions that sacrifice the adaptability of Bayesian RL. To address these limitations, we propose Posterior Hybrid Bayesian Belief (PhyB), which reformulates the expectation as a convex combination over a subset of dynamics models. Theoretical analysis demonstrates that the objective discrepancy induced by this approximation remains bounded. Based on PhyB, we develop an iterative regularized policy optimization algorithm that provides metric-agnostic guarantees for monotonic improvement until convergence. Empirical results demonstrate that PhyB achieves state-of-the-art performance on various benchmarks.
Applications · Health / Medicine
Understanding how cellular morphology, gene expression, and spatial context jointly shape tissue function is a central challenge in biology. Image-based spatial transcriptomics technologies now provide high-resolution measurements of cell images and gene expression profiles, but existing methods typically analyze these modalities in isolation or at limited resolution. We address the problem by introducing SPATIA, a multi-level generative and predictive model that learns unified, spatially aware representations by fusing morphology, gene expression, and spatial context from the cell to the tissue level. SPATIA also incorporates a novel spatially conditioned generative framework for predicting cell morphologies under perturbations. Specifically, we propose a confidence-aware flow matching objective that reweights weak optimal-transport pairs based on uncertainty. We further apply morphology-profile alignment to encourage biologically meaningful image generation, enabling the modeling of microenvironment-dependent phenotypic transitions. We assembled a multi-scale dataset consisting of 25.9 million cell-gene pairs across 17 tissues. We benchmark SPATIA against 18 models across 12 tasks, spanning categories such as phenotype generation, annotation, clustering, gene imputation, and cross-modal prediction. SPATIA achieves improved performance over state-of-the-art models, improving generative fidelity by 8\% and predictive accuracy by up to 3\%.
Deep Learning · Large Language Models
Agentic reasoning enables large reasoning models (LRMs) to dynamically acquire external knowledge, but yet optimizing the retrieval process remains challenging due to the lack of dense, principled reward signals. In this paper, we introduce *InfoReasoner*, a unified framework that incentivizes effective information seeking via a *synthetic semantic information gain reward*. Theoretically, we redefine information gain as uncertainty reduction over the model's belief states, establishing guarantees, including non-negativity, telescoping additivity, and channel monotonicity. Practically, to enable scalable optimization without manual retrieval annotations, we propose an output-aware intrinsic estimator that computes information gain directly from the model's output distributions using *semantic clustering via bidirectional textual entailment*. This intrinsic reward guides the policy to maximize epistemic progress, enabling efficient training via Group Relative Policy Optimxization (GRPO). Experiments across seven question-answering benchmarks demonstrate that InfoReasoner consistently outperforms strong retrieval-augmented baselines, achieving up to 5.4% average accuracy improvement. Our work provides a theoretically grounded and scalable path toward agentic reasoning with retrieval.
Optimization · Stochastic
Flatness of the loss landscape has been widely studied as an important perspective for understanding the behavior and generalization of deep learning algorithms. Motivated by this view, we propose Flatness-Aware Stochastic Gradient Langevin Dynamics (fSGLD), a first-order optimization method that biases learning its dynamics toward flat basins while retaining the computational and memory efficiency of SGD and SGLD. We provide a non-asymptotic theoretical analysis showing that fSGLD converges to a flatness-biased Gibbs distribution under a theoretically prescribed coupling between the noise scale $\sigma$ and the inverse temperature $\beta$, together with explicit excess risk guarantees. We empirically evaluate fSGLD across standard optimizer benchmarks, Bayesian image classification, uncertainty quantification, and out-of-distribution detection, demonstrating consistently strong performance and reliable uncertainty estimates. Additional experiments confirm the effectiveness of the theoretically prescribed $\beta$–$\sigma$ coupling compared to decoupled choices.
Deep Learning · Graph Neural Networks
Graph Mixture-of-Experts (Graph-MoE) offers a way to scale GNNs via adaptive capacity allocation, with the goal of allowing different experts to capture diverse graph patterns. Its effectiveness heavily depends on the coordination between routing decisions and expert specialization. However, through extensive empirical study, we identify two critical phenomena. First, discrimination loss occurs on both the expert and routing sides, where GNN experts become highly homogenized and the router collapses to a small subset of experts, failing to reflect diverse graph semantics. Second, routing uncertainty is prevalent, as existing routers produce uncertain expert assignments for most nodes, and such uncertainty exhibits a strong negative correlation with model performance. To address these issues, we propose C$^2$GMoE, a novel **G**raph-**MoE** framework featuring **C**ontrastive routing and **C**onfidence-aware fusion. We introduce a group-wise contrastive routing strategy that provides explicit guidance for routing optimization by aligning node-level routing decisions with semantic clusters while satisfying load-balancing constraints. Moreover, through a theoretical analysis of generalization error, we develop a confidence-aware fusion mechanism that adaptively reweights expert predictions according to their confidence. Extensive experiments across multiple benchmarks demonstrate the effectiveness of our proposed C$^2$GMoE.
Optimization · Everything Else
Many machine learning techniques rely on approximating a loss function's curvature, but this is notoriously hard to do at the scale of modern deep networks. Surprisingly, no previous work has exploited the curvature constraints that arise from well known weight-space symmetries in loss landscapes. By analytically averaging over group actions that leave the loss invariant, we construct structured Hessian approximations from single gradients that can be tractably estimated, stored, and inverted. The choice of user-specified symmetry group directly governs the trade-off between approximation accuracy and computational cost. Moreover, our framework provides a unifying theoretical lens for viewing existing methods; in particular, a specific choice of symmetry group recovers Shampoo/Muon-like curvature estimates. We validate our method on a range of network architectures, and deploy it to second-order optimization benchmarks, including a small language model. Our curvature estimation framework might find applications in other machine learning problems such as uncertainty estimation, continual learning, compression/pruning, training data attribution, and more.
Deep Learning · Large Language Models
Inference time optimization techniques, such as repeated sampling, have significantly advanced the reasoning capabilities of Large Language Models (LLMs). However, the critical role of model uncertainty remains largely underexplored in these optimization strategies. In this paper, we investigate the dynamics of confidence along reasoning trajectories and for first time reveal a surprising and unique pattern: correct answer traces tend to exhibit confidence improvement over time (positive confidence gain), while incorrect traces show attenuated or declining confidence as reasoning proceeds. Based on this observation, we propose Confidence Dynamic Gain (CDG) based voting, which incorporates how the confidence trajectory of the response evolves along the reasoning chain. Experiments across four open-source architectures (DeepSeek-R1, gpt-oss, Gemma-3, Qwen-QwQ) on the AIME24/25, HMMT25, and BRUMO25 benchmarks demonstrate that CDG yields a significant performance boost over baselines. These results demonstrate that our method provides a robust discriminative signal for improving answer selection in LLM reasoning. We also provide theoretical insights for this phenomenon. Code is in the supplementary material.
Theory · Learning Theory
This paper develops a finite-sample statistical theory for in-context learning (ICL), analyzed within a meta-learning framework that accommodates mixtures of diverse task types. We leverage a Bayes risk identity that separates the total ICL risk into two orthogonal components: Bayes Gap and Posterior Variance. The Bayes Gap quantifies how well the trained model approximates the Bayes-optimal in-context predictor. For a uniform-attention Transformer, we derive a non-asymptotic upper bound on this gap, which explicitly clarifies the dependence on the number of pretraining prompts and their context length. The Posterior Variance is a model-independent risk representing the intrinsic task uncertainty. Our key finding is that this term is determined solely by the difficulty of the true underlying task, while the uncertainty arising from the task mixture vanishes exponentially fast with only a few in-context examples. Together, these results provide a unified view of ICL: the uniform-attention Transformer selects the optimal meta-algorithm during pretraining and rapidly converges to the optimal algorithm for the true task at test time.
Reinforcement Learning · Everything Else
The key to building trustworthy Large Language Models (LLMs) lies in endowing them with inherent uncertainty expression capabilities to mitigate the hallucinations that restrict their high-stakes applications. However, existing RL paradigms such as GRPO often suffer from Advantage Bias due to binary decision spaces and static uncertainty rewards, inducing either excessive conservatism or overconfidence. To tackle this challenge, this paper unveils the root causes of reward hacking and overconfidence in current RL paradigms incorporating uncertainty-based rewards, based on which we propose the UnCertainty-Aware Policy Optimization (UCPO) framework. UCPO employs Ternary Advantage Decoupling to separate and independently normalize deterministic and uncertain rollouts, thereby eliminating advantage bias. Furthermore, a Dynamic Uncertainty Reward Adjustment mechanism is introduced to calibrate uncertainty weights in real-time according to model evolution and instance difficulty. Experimental results in mathematical reasoning and general tasks demonstrate that UCPO effectively resolves the reward imbalance, significantly enhancing model reliability and calibration beyond their knowledge boundaries.
Deep Learning · Large Language Models
As large language models evolve into tool-augmented agents, a central question remains unresolved: when is external tool use actually justified? Existing agent frameworks typically treat tools as ordinary actions and optimize for task success or reward, offering little principled distinction between epistemically necessary interaction and unnecessary delegation. This position paper argues that \textit{agents should invoke external tools only when epistemically necessary}. Here, epistemic necessity means that a task cannot be completed reliably via the agent’s internal reasoning over its current context, without any external interaction. We introduce the \textit{\textbf{Theory of Agent (ToA)}}, a framework that treats agents as making sequential decisions about whether remaining uncertainty should be resolved internally or delegated externally. From this perspective, common agent failure modes (e.g., overthinking and overacting) arise from miscalibrated decisions under uncertainty rather than deficiencies in reasoning or tool execution alone. We further discuss implications for training, evaluation, and agent design, highlighting that unnecessary delegation not only causes inefficiency but can impede the development of internal reasoning capability. Our position provides a normative criterion for tool use that complements existing decision-theoretic models and is essential for building agents that are not only correct, but increasingly intelligent.
Deep Learning · Generative Models and Autoencoders
Masked Diffusion Models (MDMs) offer greater flexibility in decoding order than autoregressive models but require careful path planning to achieve high-quality generation. While existing samplers typically greedily select positions with the lowest uncertainty, we identify their fundamental limitations through failure case analysis, showing they overlook the impact of current actions on subsequent steps and fail to optimize cumulative uncertainty. To bridge this gap, we propose the **Info-Gain Sampler**, a principled decoding framework that balances immediate costs with information gain. Our method features a simple but effective objective and an efficient implementation that ensures practical overhead is minimal. Extensive evaluations across diverse architectures and tasks (reasoning, coding, creative writing, and image generation) demonstrate that Info-Gain Sampler consistently outperforms existing samplers, significantly raising the performance ceiling of MDMs. For instance, it achieves a 5.5\% improvement in average accuracy on reasoning tasks and a 63.1\% win-rate in creative writing; notably, on reasoning tasks it reduces cumulative uncertainty from 78.4 to 48.6, outperforming the best baseline by a large margin.
Reinforcement Learning · Planning
*AlphaZero* and *MuZero* have demonstrated superhuman performance across a range of strategic tasks. Yet their reliance on maximizing expected returns limits their use in real-world settings, where even high-return policies may incur rare but catastrophic failures. We introduce *RiskZero* to address this limitation; the first *MuZero*-family method for risk-sensitive decision-making, and planning with *zero* prior knowledge of environment dynamics. *RiskZero* learns distributional quantities to estimate trajectory-level risk, guiding search toward policies that explicitly avoid rare but severe outcomes. We establish theoretical convergence to optimal, stationary risk-sensitive policies and validate our approach on environments designed to test risk-sensitive learning from pixels, as well as on larger-scale combinatorial tasks. Across all settings, *RiskZero* consistently outperforms state-of-the-art risk-sensitive baselines, and improves sample efficiency, providing a general framework for safer and reliable model-based reinforcement learning under uncertainty.
General Machine Learning · Methodology
Conformal Prediction (CP) provides rigorous finite-sample coverage guarantees, yet its statistical efficiency hinges critically on the size of the calibration set. In data-scarce regimes, CP often suffers from volatile quantile estimation, leading to overly conservative and wide prediction intervals. To address this, we propose Random Score Alignment-Conformal Prediction (RSA-CP), a simple framework designed to improve sample efficiency in small-sample CP. Instead of requiring the computationally intensive generation of full synthetic datasets, RSA-CP enhances calibration by directly aligning real scores with a high-resolution reference score distribution. By employing an optimal transport mapping, our framework refines "step-like" quantile increments through a globally optimal use of reference information. We provide theoretical guarantees establishing that RSA-CP maintains robust coverage without any distributional assumptions on the reference scores. Empirical evaluations demonstrate that RSA-CP consistently produces shorter and more precise prediction intervals while maintaining finite-sample coverage guarantees. Overall, RSA-CP offers a computationally efficient and theoretically grounded solution for robust uncertainty quantification under limited data.
General Machine Learning · Methodology
Multimodal Federated Learning (MMFL) addresses collaborative training across clients with heterogeneous modality configurations, where effective client selection becomes critical under the compounded challenges of modality, distribution, and quantity heterogeneity. Existing selection methods operate within a reactive paradigm, responding to current observations without anticipating how decisions influence future optimization trajectories. This myopic approach leads to suboptimal convergence when training dynamics shift rapidly under severe heterogeneity. We propose FedSSM, which reconceptualizes client selection as a proactive decision-making process by predicting training dynamics through decision-aware state space models. The prediction error yields a \emph{surprise} signal that quantifies uncertainty and governs adaptive participation budgets and exploration-exploitation trade-offs via counterfactual reasoning over candidate actions. For aggregation, we introduce trust-weighted fusion with modality-specific routing, where surprise calibrates sensitivity to client anomalies. Experiments on four multimodal benchmarks demonstrate that FedSSM achieves 2.5--4.5\% accuracy improvements over state-of-the-art methods while reducing communication rounds by over 30\%.
Reinforcement Learning · Everything Else
Robust reinforcement learning (RRL) aims to tackle unexpected environmental changes by optimizing policies against the worst case. However, RRL remains impractical due to the cost of the Max-Min optimization, where it suffers from the exhaustive query complexity for finding the worst-case (dubbed 'Min') within the environmental uncertainty set $\mathcal{U}$, i.e., $\mathcal{O}(|\mathcal{U}|)$. By viewing this via a lens of quantum perspective, we raise a pivotal question: *If we can query from the environment with quantum superpositions, is it possible to accelerate the Max-Min optimization of RRL?* Our answer is 'Yes'. Our method, called quantum robust inner minimization (QRIM), encodes the uncertainty set with quantum superposition and amplifies low-return cases, thus enabling RL for solving the robust (i.e., worst-case) Bellman equation. Importantly, QRIM achieves a quadratic speed-up in query complexity without altering the outer RL pipeline, i.e., $\mathcal{O}(\sqrt{|\mathcal{U}|})$. Validated through classical simulations to real quantum hardware execution, QRIM learns more robust policies with quadratically reduced queries than classical RL.
Reinforcement Learning · Policy Search
Aligning large language models (LLMs) with human preferences is commonly done via reinforcement learning from human feedback (RLHF) with Proximal Policy Optimization (PPO) or, more simply, via Direct Preference Optimization (DPO). While DPO is stable and RL-free, it treats preferences as flat winner vs. loser signals and is sensitive to noisy or brittle preferences arising from fragile chains of thought. We propose TUR-DPO, a topology- and uncertainty-aware variant of DPO that rewards how answers are derived, not only what they say, by eliciting lightweight reasoning topologies and combining semantic faithfulness, utility, and topology quality into a calibrated uncertainty signal. A small learnable reward is factorized over these signals and incorporated into an uncertainty-weighted DPO objective that remains RL-free and relies only on a fixed or moving reference policy. Empirically, across open 7–8B models and benchmarks spanning mathematical reasoning, factual question answering, summarization, and helpful/harmless dialogue, TUR-DPO improves judge win-rates, faithfulness, and calibration relative to DPO while preserving training simplicity and avoiding online rollouts. We further observe consistent gains in multimodal and long-context settings, and show that TUR-DPO matches or exceeds PPO on reasoning-centric tasks while maintaining operational simplicity.
Reinforcement Learning · Online
Reinforcement learning algorithms such as GRPO have driven recent advances in large language model (LLM) reasoning. While scaling the number of rollouts stabilizes training, existing approaches suffer from limited exploration on challenging prompts and leave informative feedback signals underexploited, due to context-independent rollout allocation across prompts (e.g., generating 16 rollouts per prompt) and relying heavily on sparse rewards. This paper presents XRPO (eXplore–eXploit GRPO), a unified framework that recasts policy optimization through the principled lens of rollout exploration–exploitation. To enhance exploration, XRPO introduces a mathematically grounded rollout allocator that adaptively prioritizes prompts with higher potential for uncertainty reduction. It further addresses stagnation on zero-reward prompts through an in-context seeding strategy that injects curated exemplars, steering the model into more difficult reasoning trajectories. To strengthen exploitation, XRPO develops a group-relative, novelty-aware advantage sharpening mechanism that leverages sequence likelihoods to amplify low-probability yet correct responses, thereby extending the policy’s reach beyond sparse rewards. Experiments across diverse math and coding benchmarks on both reasoning and non-reasoning models demonstrate that XRPO outperforms existing advances (e.g., GRPO and GSPO) up to 4% pass@1 and 6% cons@32, while accelerating training convergence by up to 2.7x.
General Machine Learning · Everything Else
Joint planning through language-based interactions is a key area of human-AI teaming. Planning problems in the open world often involve various aspects of incomplete information and unknowns, e.g., objects involved, human goals/intents -- thus leading to knowledge gaps in joint planning. We consider the problem of discovering optimal interaction strategies for AI agents to actively elicit human inputs in object-driven planning. To this end, we propose Minimal Information Neuro-Symbolic Tree (MINT) to reason about the impact of knowledge gaps and leverage self-play with MINT to optimize the AI agent’s elicitation strategies and queries. More precisely, MINT builds a symbolic tree by making propositions of possible human-AI interactions and by consulting a neural planning policy to estimate the uncertainty in planning outcomes caused by remaining knowledge gaps. Finally, we leverage LLM to search and summarize MINT’s reasoning process and curate a set of queries to optimally elicit human inputs for best planning performance. By considering a family of extended Markov decision processes with knowledge gaps, we analyze the return guarantee for a given MINT with active human elicitation. Our evaluation on three benchmarks involving unseen/unknown objects of increasing realism shows that MINT-based planning attains near-expert returns by issuing a limited number of questions per task while achieving significantly improved rewards and success rates.