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Applications · Time Series

Ji-Eun Choi, Jae-Hong Lee, Joon Hyuk Chang

Multivariate time-series forecasting (MTSF) learns from high-dimensional covariates with strong temporal dependence, periodic structure, and cross-variable correlations. While modern pipelines often mitigate non-stationarity through instance-wise normalization and decomposition, these interventions operate at the data level and do not directly control dependence that can emerge among the parameters during training. We study MTSF optimization from a parameter-decorrelation viewpoint. Modeling stochastic optimization as a Markov chain in parameter space and leveraging its stochastic differential equation interpretation, we use the per-step transition-variance induced by gradient noise as a tractable signal for optimization-induced dependence and update uncertainty. This signal can empirically inflate during training; we theoretically show that such inflation can degrade generalization diagnostics. Motivated by this mechanism, we propose transition-variance alignment (TVA), an architecture-agnostic procedure that regulates transition-variance by smoothly gating the step size based on the mismatch between an estimated noise scale and a chosen target. TVA maintains effective transition-variance near a prescribed scale without architectural changes, incurs negligible overhead, and integrates seamlessly with diverse methods. Across real-world multivariate benchmarks, TVA consistently improves forecasting accuracy.

Applications · Chemistry, Physics, and Earth Sciences

Matteo Rossi, Ryan Pederson, Miles Wang-Henderson, Benjamin Kaufman, Edward Williams, Carl Underkoffler, Owen Howell, Adrian Layer, Stephan Thaler, Narbe Mardirossian 等

We present CoarseBind, a foundation model for protein-ligand structure and binding affinity prediction that achieves 26$\times$ faster inference than state-of-the-art methods while improving affinity prediction accuracy by up to 20\%. Current deep learning approaches to structure-based drug design rely on expensive all-atom diffusion to generate 3D coordinates, creating inference bottlenecks that render large-scale compound screening computationally intractable. We challenge this paradigm with the hypothesis: full all-atom resolution is unnecessary for accurate small molecule pose and binding affinity prediction. CoarseBind tests this hypothesis through a coarse pocket-level representation (protein C$_\beta$ atoms and ligand heavy atoms only) within a multimodal architecture combining pretrained molecular encoders and ESM-2 protein embeddings that learns rich structural representations, which are used in a diffusion-free optimization module for pose generation and a binding affinity likelihood prediction module. On structure prediction benchmarks, CoarseBind matches diffusion-based baselines in ligand pose accuracy. For binding affinity, CoarseBind outperforms Boltz-2 by 16-20\% in Pearson correlation on both a public benchmark (CASP16) and a diverse private dataset (18 assays). The affinity module also provides well-calibrated uncertainty estimates, addressing a critical gap in compound prioritization for drug discovery. Furthermore, this module enables a continual learning framework and a hedged batch selection strategy that, in simulated drug discovery cycles, achieves 6$\times$ greater affinity improvement over greedy approaches.

Deep Learning · Self-Supervised Learning

Yongchao Huang

Joint Embedding Predictive Architectures (JEPA) offer a scalable paradigm for self-supervised learning by predicting latent representations rather than reconstructing high-entropy observations. However, existing formulations rely on deterministic regression objectives, which masks probabilistic semantics and limits its applicability in stochastic control. We introduce \emph{Variational JEPA (VJEPA)}, a probabilistic generalization that learns a predictive distribution over future latent states via a variational objective. We show that VJEPA unifies representation learning with Predictive State Representations (PSRs) and Bayesian filtering, establishing that sequential modeling does not require autoregressive observation likelihoods. Theoretically, we prove that VJEPA representations serve as sufficient information states for optimal control without pixel reconstruction, while providing formal guarantees for collapse avoidance. We further propose \emph{Bayesian JEPA (BJEPA)}, which extends the VJEPA framework to factorize predictive belief into a learned dynamics expert and a modular prior expert, enabling zero-shot task transfer and constraints satisfactions (e.g., goals, physics) via a Product of Experts. Empirically, VJEPA filters out high-variance nuisance distractors that cause representation collapse in generative baselines. By enabling principled uncertainty estimation (e.g. constructing credible intervals via sampling) while remaining likelihood-free regarding observations, VJEPA provides a foundational framework for scalable, robust, uncertainty-aware planning in high-dimensional, noisy environments.

Ruiqi Wu, Xuanhua He, Meng Cheng, Tianyu Yang, Yong Zhang, Zhuoliang Kang, Xunliang Cai, Xiaoming Wei, Chunle Guo, Chongyi Li 等

We propose **Infinite-World**, a robust interactive world model capable of maintaining coherent visual memory over **1000+ frames** in complex real-world environments. While existing world models can be efficiently optimized on synthetic data with perfect ground-truth, they lack an effective training paradigm for real-world videos due to noisy pose estimations and the scarcity of viewpoint revisits. To bridge this gap, we first introduce a **Hierarchical Pose-free Memory Compressor (HPMC)** that recursively distills historical latents into a fixed-budget representation. By jointly optimizing the compressor with the generative backbone, HPMC enables the model to autonomously anchor generations in the distant past with bounded computational cost, eliminating the need for explicit geometric priors. Second, we propose an **Uncertainty-aware Action Abstraction** module that discretizes continuous motion into a tri-state logic. This strategy maximizes the utilization of raw video data while shielding the deterministic action space from being corrupted by noisy trajectories, ensuring robust action-response learning. Furthermore, guided by insights from a pilot toy study, we employ a **Revisit-Dense Finetuning Strategy** using a compact, 30-minute dataset to efficiently activate the model’s long-range loop-closure capabilities. Extensive experiments, including objective metrics and user studies, demonstrate that Infinite-World achieves superior performance in visual quality, action controllability, and spatial consistency. Our code and data will be released.

Deep Learning · Graph Neural Networks

Chunhui Zhang, Pengqi Li, Lizhong Ding, Peng Yang, Changsheng Li, Ye Yuan, Guoren Wang

Graph learning has been increasingly deployed in critical and sensitive domains, raising pressing demands for trustworthiness-robustness, fairness, and beyond. However, these properties are often undermined by various perturbations, which induce distributional uncertainty and compromise the trustworthiness of graph learning. To address this, we propose DICT, a novel framework that models distributional uncertainty to achieve trustworthy graph learning. Specifically, DICT formulates a unified optimization objective that captures perturbation-induced distributional shifts in graph topology, node features, and labels, and minimizes the worst-case risk over the uncertainty set. However, directly optimizing this objective in its primal form leads to an infinite-dimensional problem. To make this problem tractable, we integrate strong duality and local Lipschitz continuity of the loss, reformulating the objective as a finite-dimensional min-max problem. We focus on robustness and fairness as primary instantiations of DICT because they are not only critical in real-world applications, but also provide transferable modeling principles for broader trustworthiness objectives. By formulating fairness in the form of an uncertainty set, DICT pioneers unified robustness and fairness within a single optimization framework. Extensive experiments across diverse benchmarks and backbones demonstrate that DICT consistently improves both robustness and fairness, validating the effectiveness and adaptability of the DICT framework.

Deep Learning · Large Language Models

Xingyuan Hua, Sheng Yue, Ju Ren

Recent advancements in agentic test-time scaling allow models to gather environmental feedback before committing to final actions. A key limitation of existing methods is that they typically employ undifferentiated exploration strategies, lacking the ability to adaptively distinguish when exploration is truly required. In this paper, we propose an exploration-aware reinforcement learning framework that enables LLM agents to adaptively explore only when uncertainty is high. Our method introduces a fine-grained reward function via variational inference that explicitly evaluates exploratory actions by estimating their potential to improve future decision-making, together with an exploration-aware grouping mechanism that separates exploratory actions from task-completion actions during optimization. By targeting informational gaps, this design allows agents to explore selectively and transition to execution as soon as the task context is clear. Empirically, we demonstrate that our approach achieves consistent improvements across a range of challenging text-based and GUI-based agent benchmarks.

Deep Learning · Large Language Models

Isha Puri, Mehul Damani, Idan Shenfeld, Marzyeh Ghassemi, Jacob Andreas, Yoon Kim

Large language models (LMs) are typically post-trained via RL to produce a single best answer per query, implicitly optimizing for modal correctness. While effective for benchmark accuracy, this approach is unideal for many applications of interest such as in medical diagnosis, which would benefit from models generating a set of plausible answers (ideally paired with uncertainty estimates).This paper describes a multi-answer reinforcement learning (RL) approach for enabling LMs to do this, where we modify the RL objective to train models to explicitly generate multiple candidate answers in a single forward pass, internalizing aspects of inference-time search into the model’s generative process. We instantiate this approach through Multi-Answer Reinforcement Learning with Verifiable Rewards (Multi-RLVR), which generalizes ordinary RLVR to the multi-answer case with a set-level reward. We further extend this approach to Multi-Answer Reinforcement Learning with Calibrated Rewards (Multi-RLCR) which adds a set-level Brier score-based calibration objective to enable LMs to output calibrated uncertainty estimates associated with each answer in the output set. Multi-answer training promotes explicit representation of alternative hypotheses rather than repeated generation of the dominant mode. Across question-answering and medical diagnostic benchmarks, we observe improved diversity, recall, and set-level calibration scores compared to single answer-trained baselines. We further observe that models trained with our approach are more token-efficient, requiring fewer tokens to generate multiple answers than competing approaches. These results position multi-answer RL as a principled and compute-efficient alternative to inference-time scaling.

Theory · Learning Theory

Yuxiang Luo, Chen Wang, Nan Tang

The high cost of fine-tuning LLMs poses a significant economic barrier; pre-hoc performance prediction offers a critical solution to substantially reduce this expense. However, the theoretical limits of pre-hoc performance prediction remain unexplored. We formulate it as a stochastic estimation problem under information constraints, decomposing prediction risk into two components: an \textbf{intrinsic limit} (static data-model compatibility) and a \textbf{reducible optimization variance}. We prove that optimization variance admits a necessary lower bound on its decay rate, implying fundamental constraints on how quickly uncertainty dissipates, regardless of the predictor used. Based on these dynamics, we derive a budget-optimal probing principle and introduce a predictability phase diagram that organizes tasks into three distinct regimes: Static-Sufficient, Dynamic-Critical, and Noise-Dominant. Extensive experiments on synthetic and real-world benchmarks validate these theoretical regimes and demonstrate the efficiency of our probing strategy.

Deep Learning · Generative Models and Autoencoders

Gongye Liu, Bo Yang, Zhi Yida, Zhizhou Zhong, Lei Ke, Didan Deng, Han Gao, Yongxiang Huang, Kaihao Zhang, Hongbo Fu 等

Preference optimization for diffusion models relies on reward functions that are both discriminative and computationally efficient. Vision-Language Models (VLMs) have emerged as powerful reward providers. However, their computation and memory cost can be substantial, and optimizing a latent diffusion generator through a pixel-space reward introduces a domain mismatch that complicates alignment. In this paper, we propose \textbf{DiNa-LRM}, a \textbf{di}ffusion-\textbf{na}tive \textbf{l}atent \textbf{r}eward \textbf{m}odel that formulates preference learning directly on noisy diffusion states. Our method introduces a noise-calibrated Thurstone likelihood with diffusion-noise-dependent uncertainty. DiNa-LRM leverages a pretrained latent diffusion backbone with a timestep-conditioned reward head, and supports inference-time noise ensembling, providing a diffusion-native mechanism for test-time scaling and robust rewarding. Across image alignment benchmarks, DiNa-LRM substantially outperforms existing diffusion-based reward baselines and achieves competitive performance compared to state-of-the-art VLMs while maintaining a substantially lower computational cost. In preference optimization, we demonstrate that DiNa-LRM improves preference optimization dynamics, enabling faster and more resource-efficient model alignment.

Deep Learning · Generative Models and Autoencoders

Luwei Tu, Jiawei Wu, Xing Luo, Zhi Jin

All-in-One Image Restoration (AiOIR) faces the fundamental challenge in reconciling conflicting optimization objectives across heterogeneous degradations. Existing methods are often constrained by coarse-grained control mechanisms or fixed mapping schedules, yielding suboptimal adaptation. To address this, we propose an Uncertainty-Aware Diffusion Bridge Model (UDBM), which innovatively reformulates AiOIR as a stochastic transport problem steered by pixel-wise uncertainty. By introducing a relaxed diffusion bridge formulation which replaces the strict terminal constraint with a relaxed constraint, we model the uncertainty of degradations while theoretically resolving the drift singularity inherent in standard diffusion bridges. Furthermore, we devise a dual modulation strategy: the noise schedule aligns diverse degradations into a shared high-entropy latent space, while the path schedule adaptively regulates the transport trajectory motivated by the viscous dynamics of entropy regularization. By effectively rectifying the transport geometry and dynamics, UDBM achieves state-of-the-art performance across diverse restoration tasks within a single inference step.

Deep Learning · Large Language Models

Nhi Nguyen, Shauli Ravfogel, Rajesh Ranganath

Large language models (LLMs) are increasingly deployed in high-stakes domains, where free-text explanations such as chain-of-thought and post-hoc rationales are used to justify model outputs. Yet it remains unclear whether these explanations are _sufficient_, i.e., if they contain enough information to explain the model’s output-generating process. We generalize classical sufficiency from feature attributions to arbitrary explanations and prove that explanation sufficiency is inherently relative to an input distribution, which must be explicitly defined for LLM explanations. We propose using the LLM itself to generate alternative inputs conditioned on an explanation, capturing its beliefs about possible inputs. We formalize _self-consistent sufficiency_ as a goal for free-text explanations and introduce an information-theoretic metric, SCSuff, that enables evaluation of free-text explanations without relying on predefined biases or shortcuts. Our experiments show that SCSuff aligns with targeted perturbation tests where applicable and demonstrate that explanation sufficiency can vary with the input distribution. We further find that SCSuff is uncorrelated with model size, accuracy, or uncertainty, suggesting that improving self-consistent sufficiency requires approaches beyond scaling or standard performance optimization.

Deep Learning · Large Language Models

Qingyue Zhang, Chang Chu, Tianren Peng, Qi Li, Xiangyang Luo, Zhihao Jiang, Shao-Lun Huang

LoRA has become a widely adopted method for PEFT, and its initialization methods have attracted increasing attention. However, existing methods have notable limitations: many methods do not incorporate target-domain data, while gradient-based methods exploit data only at a shallow level by relying on one-step gradient decomposition. In this paper, we establish a theoretical framework for data-aware LoRA initialization. Starting from minimizing the expectation of the parameter discrepancy between the fine-tuned and target models, we derive an optimization problem with two components: a bias term, which is related to the parameter distance between the fine-tuned and target models, and is approximated using a Fisher–gradient formulation to preserve anisotropy; and a variance term, which accounts for the uncertainty introduced by sampling stochasticity through the Fisher information. Solving this problem yields an optimal initialization strategy for LoRA, based on which we develop an efficient algorithm, LoRA-DA. Empirical results across multiple benchmarks demonstrate that LoRA-DA consistently improves final accuracy over existing initialization methods. Additional studies show faster, more stable convergence, robustness across ranks, and only a small initialization overhead for LoRA-DA. The source code will be released upon publication.

Deep Learning · Self-Supervised Learning

Moritz Gögl, Christopher Yau

The Joint-Embedding Predictive Architecture (JEPA) is often seen as a non-generative alternative to likelihood-based self-supervised learning, emphasizing prediction in representation space rather than reconstruction in observation space. We argue that the resulting separation from probabilistic generative modeling is largely rhetorical rather than structural: the canonical JEPA design–coupled encoders with a context-to-target predictor–mirrors the variational posteriors and learned conditional priors obtained when variational inference is applied to a particular class of coupled latent-variable models, and standard JEPA can be viewed as a deterministic specialization in which regularization is imposed via architectural and training heuristics rather than an explicit likelihood. Building on this view, we derive the Variational JEPA (Var-JEPA), which makes the latent generative structure explicit by optimizing a single Evidence Lower Bound (ELBO). This yields meaningful representations without ad-hoc anti-collapse regularizers and allows principled uncertainty quantification in the latent space. We instantiate the framework for tabular data (Var-T-JEPA) and achieve strong representation learning and downstream performance, consistently improving over T-JEPA while remaining competitive with strong raw-feature baselines.

Social Aspects · Accountability, Transparency, and Interpretability

Zakk Heile, Hayden McTavish, Varun Babbar, Margo Seltzer, Cynthia Rudin

Standard machine learning pipelines often admit many near-optimal models. These “Rashomon sets” pose a range of challenges and opportunities for uncertainty-aware, robust decision making. They allow users to incorporate domain knowledge and preferences that would otherwise be difficult to specify directly in an objective, and they quantify diversity among valid models for a given training dataset and objective function. However, computation of Rashomon sets, even for simple, interpretable model classes such as sparse decision trees, continues to require immense memory and runtime resources. We present PRAXIS, an algorithm to approximate this Rashomon set with orders of magnitude improvement in runtime and memory usage. We validate that PRAXIS regularly recovers almost all of the full Rashomon set. PRAXIS allows researchers and practitioners to scalably model the Rashomon set for real-world datasets.

Probabilistic Methods · Monte Carlo and Sampling Methods

Emanuel Sommer, David Rügamer

The practical adoption of sampling-based inference (SAI) in Bayesian neural networks (BNNs) remains limited, partly due to persistent misconceptions about the feasibility and efficiency of sampling. This position paper argues that SAI has achieved computational parity with optimization-based methods and is at the verge of superseding such methods for effective and efficient inference in BNNs. This development should be in the interest of the whole community, promoting BNNs as a principled paradigm with its long-standing yet unfulfilled promise of providing principled uncertainty quantification for neural networks. SAI can even do more—yielding superior prediction performance through model averaging, serving as the foundation for a plethora of possible downstream tasks, and providing crucial insights into the landscape of BNNs. In order to make such a change happen and unfold the potential of sampling, overcoming current misconceptions is a necessary first step. The next step is to realign research efforts toward addressing remaining challenges in SAI. In particular, the community must focus on two core problems: sufficient exploration of the posterior landscape and high-fidelity distillation of posterior samples for efficient downstream inference. By addressing conceptual and practical obstacles, we can unlock the full potential of SAI and establish it as a central tool in Bayesian deep learning.

Theory · Optimization

Jinyi Huang, Jinlong Lei, Guodong Shi

Distributionally Robust Optimization (DRO) is widely used to improve model robustness, with existing methods addressing either geometric perturbations (e.g., input shifts) or statistical contamination (e.g., heavy-tailed noise and outliers) effectively. However, these uncertainty sources often co-exist. Coupling them through a single divergence or optimal transport constraint conflates geometric displacement with loss-based outlierness, which often leads to the discarding of informative high-leverage samples. We introduce nested DRO, a bilevel formulation that combines optimal transport with an outer $\\phi$-divergence constraint to decouple geometric smoothing from statistical robustness. We prove that this structure naturally induces a geometry-invariant, loss-based reweighting mechanism that separates outlier suppression from transport-induced regularization. We derive a tractable strong dual for the resulting non-convex problem and show its equivalence to variance-regularized risk minimization, providing a rigorous theoretical justification for reweighting gains as a natural consequence of dualization. Empirical results on synthetic and real datasets demonstrate that nested DRO consistently outperforms geometry-coupled DRO baselines, particularly under heavy-tailed contamination where preserving high-leverage structure is crucial.

Reinforcement Learning · Policy Search

Soichiro Nishimori, Paavo Parmas, Sotetsu Koyamada, Tadashi Kozuno, Toshinori Kitamura, Shin Ishii, Yutaka Matsuo

In reinforcement learning (RL), agents benefit from exploration *only* because they repeatedly encounter similar states: trying different actions can improve performance or reduce uncertainty; without such retries, a greedy policy is optimal. We formalize this intuition with **ReMax**, an objective that evaluates a policy by the expected maximum return over $M$ samples ($M \in \mathbb{N}$), while accounting for return uncertainty. Optimizing this objective induces stochastic exploration as an emergent property, without explicit bonus terms. For efficient policy optimization, we derive a new policy-gradient formulation for ReMax and introduce **Re**Max **PPO** (**RePPO**), a PPO variant that optimizes ReMax while generalizing the discrete retry count $M$ to a continuous parameter $m > 0$, enabling fine-grained control of exploration. Empirically, RePPO promotes exploration—without any explicit exploration bonuses—on the MinAtar and Craftax benchmarks.

Reinforcement Learning · Everything Else

Yizhi Li, Qingshui Gu, Zhoufutu Wen, Ziniu Li, Ruibin Yuan, Tianshun Xing, Shuyue Guo, Tuney Zheng, 周欣, Xingwei Qu 等

Recent advancements in aligning large language models via reinforcement learning have achieved remarkable gains in solving complex reasoning problems, but at the cost of expensive on-policy rollouts and limited exploration of diverse reasoning paths. In this work, we introduce TreePO, involving a self-guided rollout algorithm that views sequence generation as a tree-structured searching process. Composed of dynamic tree sampling policy and fixed-length segment decoding, TreePO leverages local uncertainty to warrant additional branches. By amortizing computation across common prefixes and pruning low-value paths early, TreePO essentially reduces the per-update compute burden while preserving or enhancing exploration diversity. Key contributions include: (1) a segment-wise sampling algorithm that alleviates the KV cache burden through contiguous segments and spawns new branches along with an early-stop mechanism; (2) a tree-based segment-level advantage estimation that considers both global and local proximal policy optimization. and (3) analysis on the effectiveness of probability and quality-driven dynamic divergence and fallback strategy. We empirically validate the performance gain of \modelname on a set reasoning benchmarks and the efficiency saving of GPU hours from 22% up to 43% of the sampling design for the trained models, meanwhile showing up to 40% reduction at trajectory-level and 35% at token-level sampling compute for the existing models. While offering a free lunch of inference efficiency, TreePO reveals a practical path toward scaling RL-based post-training with fewer samples and less compute.

Reinforcement Learning · Deep RL

Shaojun Xu, Xiaoling Zhou, Yihan Lin, Yapeng Meng, Xinglong Ji, Luping Shi, Rong Zhao

Model-Based Reinforcement Learning (MBRL) leverages latent imagination for sample efficiency, yet remains constrained by **Historical Tethering**: imagination is typically initialized from observed states. This creates a learning asymmetry, where the world model’s manifold discovery outpaces the policy's sparse-reward optimization. We propose **Mind Dreamer (MD)**, a framework that operationalizes **Active Counterfactual Reasoning (ACR)** to transcend Markovian continuity. MD reformulates discovery as the minimization of a global Relay Manifold Expected Free Energy (R-EFE); by invoking a latent-space $do$-operator, MD utilizes an adversarial generator to synthesize non-continuous **latent jumps** to epistemic blind spots that are physically plausible yet cognitively challenging. To resolve the credit assignment paradox across these spatial ruptures, we derive the **Relay Value Function (RVF)** and **Relay Uncertainty Function (RUF)**. These potentials treat synthesized anchors as latent bridges, propagating pragmatic and epistemic value through a principled Bellman-style formulation. Notably, we prove that the Uncertainty propagation across discontinuities necessitates a quadratic discount $\gamma^2$, establishing a formal epistemic horizon. Theoretically, MD acts as an optimal importance sampler that expands the manifold's spectral gap, reducing the hitting time to critical bottleneck states. Empirically, MD achieves a **1.67$\times$ average speedup** over DreamerV3 on DeepMind Control Suite, reaching **8.8$\times$** in sparse-reward tasks.

Reinforcement Learning · Policy Search

Zachary Roch, George Atia, Yue Wang

Robust reinforcement learning (RL) under the average-reward criterion is essential for long-term decision-making, particularly when the environment may differ from its training dynamics. However, most existing studies focus on model-based settings and provide only asymptotic guarantees, hindering their principled understanding and practical deployment, especially in data-limited scenarios. We aim to close this gap by proposing a model-free algorithm, Robust Halpern Iteration (RHI). We first design our algorithm based on a black-box sampling oracle, which can estimate the worst-case performance accurately. We then derive the finite sample complexity of RHI under the generative model setting, assuming the sampling oracle. To concretely design such an oracle, we propose a $K$-order multi-level Monte-Carlo estimator, which is shown to have a lower bias compared to prior methods. We further instantiate our design for multiple uncertainty models, including KL and $\chi^2$ divergence sets, and show that our RHI algorithm achieves an $\varepsilon$-optimal robust policy with a sample complexity of $\tilde{\mathcal{O}}\left( \frac{SA\mathcal{H}^2}{\varepsilon^{(2+o(1))}}\right)$, where $S,A$ are the number of states and actions, and $\mathcal{H}$ is the robust optimal span. Our result asymptotically matches the best complexity in robust average reward RL.