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General Machine Learning · Probabilistic Methods

Zifan Wang, Alice Harting, Matthieu Barreau, Michael Zavlanos, Karl H. Johansson

Guidance of generative models is typically achieved by modifying the probability flow vector field through the addition of a guidance field. In this paper, we instead propose the Source-Guided Flow Matching (SGFM) framework, which modifies the source distribution directly while keeping the pre-trained vector field intact. This reduces the guidance problem to a well-defined problem of sampling from the source distribution. We theoretically show that SGFM recovers the desired target distribution exactly. Furthermore, we provide bounds on the Wasserstein error for the generated distribution when using an approximate sampler of the source distribution and an approximate vector field. The key benefit of our approach is that it allows the user to flexibly choose the sampling method depending on their specific problem. To illustrate this, we systematically compare different sampling methods and discuss conditions for asymptotically exact guidance. Moreover, our framework integrates well with optimal flow matching models since the straight transport map generated by the vector field is preserved. Experimental results on synthetic 2D benchmarks, physics-informed generative tasks, and imaging inverse problems demonstrate the effectiveness and flexibility of the proposed framework.

General Machine Learning · Probabilistic Methods

Bruno Viti, Elias Karabelas, Martin Holler

Most machine learning-based image segmentation models produce pixel-wise confidence scores that represent the model’s predicted probability for each class label at every pixel. While this information can be particularly valuable in high-stakes domains such as medical imaging, these scores are heuristic in nature and do not constitute rigorous quantitative uncertainty estimates. Conformal prediction (CP) provides a principled framework for transforming heuristic confidence scores into statistically valid uncertainty estimates. However, applying CP directly to image segmentation ignores the spatial correlations between pixels, a fundamental characteristic of image data. This can result in overly conservative and less interpretable uncertainty estimates. To address this, we propose CONSIGN (*Conformal Segmentation Informed by Spatial Groupings via Decomposition*), a CP-based method that incorporates spatial correlations to improve uncertainty quantification in image segmentation. Our method generates meaningful prediction sets that come with user-specified, high-probability error guarantees. It is compatible with any pre-trained segmentation model capable of generating multiple sample outputs. We evaluate CONSIGN against two CP baselines across three medical imaging datasets and two COCO dataset subsets, using three different pre-trained segmentation models. Results demonstrate that accounting for spatial structure significantly improves performance across multiple metrics and enhances the quality of uncertainty estimates.

Reinforcement Learning · Planning

Shenghua Wan, Le Gan, De-Chuan Zhan

Pre-training world models on large, action-free video datasets offers a promising path toward generalist agents, but a fundamental flaw undermines this paradigm. Prevailing methods train models to predict a single, deterministic future, an objective that is ill-posed for inherently stochastic environments where actions are unknown. We contend that a world model should instead learn a structured, probabilistic representation of the future where predictive uncertainty correctly scales with the temporal horizon. To achieve this, we introduce a pre-training framework, **H**orizon-c**A**librated **U**ncertainty **W**orld **M**odel (HAUWM), built on a probabilistic ensemble that predicts frames at randomly sampled future horizons. The core of our method is a Horizon-Calibrated Uncertainty (HCU) loss, which explicitly shapes the latent space by encouraging predictive variance to grow as the model projects further into the future. This approach yields a latent dynamics model that is not only predictive but also equipped with a reliable measure of temporal confidence. When fine-tuned for downstream control, our pre-trained model significantly outperforms state-of-the-art methods across a diverse suite of benchmarks, including MetaWorld, the DeepMind Control Suite, and RoboDesk. These results highlight the critical role of structured uncertainty in robust decision-making.

Deep Learning · Everything Else

Xiaoyang Yi, Li Peng, Yuru Bao, Jian Zhang

Federated learning (FL), as a privacy-preserving distributed machine learning paradigm, enables clients to collaboratively train a global model without sharing local data. However, in real-world scenarios, domain shift caused by different source clients leads to structural discrepancies in the feature space, resulting in performance degradation of the global model. Although existing prototype-based FL methods offer improvements in cross-domain feature alignment, they still struggle to adapt to dynamic semantic structures and fail to continuously respond to the changing semantic separability and variance structure during training. To address this, we propose FedPTE, an FL framework with prototype topology evolution. Specifically, FedPTE treats prototype clusters as variable topological units, employing Bayesian Gaussian Mixture Models and marginal likelihood ratios on the server to perform probabilistic inference, which enables adaptive structural adjustments. Meanwhile, FedPTE introduces a stability constraint mechanism to balance the adaptability of topological evolution and training stability. By conducting prototype topology-aware contrastive learning on clients, it enhances the discriminability and cross-domain consistency of features. Experimental results demonstrate that FedPTE achieves superior performance across multiple cross-domain datasets, showcasing its strong expressiveness and generalization capability in heterogeneous domains.

Applications · Everything Else

Penghai Zhao, Jinyu Tian, Qinghua Xing, Xin Zhang, Zheng Li, Jianjun Qian, Ming-Ming Cheng, Xiang Li

The ability to estimate the quality of scientific papers is central to how both humans and AI systems will advance scientific knowledge in the future. However, existing LLM-based estimation methods suffer from high inference cost, whereas the faster direct score regression approach is limited by scale inconsistencies. We present NAIPv2, a debiased and efficient framework for paper quality estimation. NAIPv2 employs pairwise learning within domain-year groups to reduce inconsistencies in reviewer ratings and introduces the Review Tendency Signal (RTS) as a probabilistic integration of reviewer scores and confidences. To support training and evaluation, we further construct NAIDv2, a large-scale dataset of 24,276 ICLR submissions enriched with metadata and detailed structured content. Trained on pairwise comparisons but enabling efficient pointwise prediction at deployment, NAIPv2 achieves state-of-the-art performance (78.2\% AUC, 0.432 Spearman), while maintaining scalable, linear-time efficiency at inference. Notably, on unseen NeurIPS submissions, it further demonstrates strong generalization, with predicted scores increasing consistently across decision categories from Rejected to Oral. These findings establish NAIPv2 as a debiased and scalable framework for automated paper quality estimation, marking a step toward future scientific intelligence systems.

Theory · Probabilistic Methods

Qiaochu Xu, Zi Yang, Ying Li, Michael Minyi Zhang, Pablo Olmos

Multi-output Gaussian processes (MOGPs) provide a Bayesian framework for modeling non-linear functions with multiple outputs, in which nonstationary kernels are essential for capturing input-dependent variations in observations. However, from a spectral (dual) perspective, existing nonstationary kernels inherit the inflexibility and over-parameterization of their spectral densities due to the restrictive spectral–kernel duality. To overcome this, we establish a generalized spectral–kernel duality that enables fully flexible matrix-valued spectral densities — albeit at the cost of quadratic parameter growth in the number of outputs. To achieve linear scaling while retaining sufficient expressiveness, we propose the multi-output low-rank nonstationary (MO-LRN) kernel: by modeling the spectral density through a low-rank matrix whose rows are independently parameterized by bivariate Gaussian mixtures. Experiments on synthetic and real-world datasets demonstrate that MO-LRN consistently outperforms existing MOGP kernels in regression, missing-data interpolation, and imputation tasks.

General Machine Learning · Probabilistic Methods

Wei Chen, Jiacheng Li, Shigui Li, Zhiqi Lin, Junmei Yang, John Paisley, Delu Zeng

Score-based methods are powerful across machine learning, but they face a paradox: theoretically path-independent, yet practically path-dependent. We resolve this by proving that practical training objectives differ from the ideal, ground-truth objective by a crucial, overlooked term: the path variance of the score function. We propose the MVP (**M**imum **V**ariance **P**ath) Principle to minimize this path variance. Our key contribution is deriving a closed-form expression for the variance, making optimization tractable. By parameterizing the path with a flexible Kumaraswamy Mixture Model, our method learns data-adaptive, low-variance paths without heuristic manual selection. This principled optimization of the complete objective yields more accurate and stable estimators, establishing new state-of-the-art results on challenging benchmarks and providing a general framework for optimizing score-based interpolation.

General Machine Learning · Probabilistic Methods

Wenbin Zhou, Agni Orfanoudaki, Shixiang Zhu

High-stakes decisions in healthcare, energy, and public policy have long depended on human expertise and heuristics, but are now increasingly supported by predictive and optimization-based tools. A prevailing paradigm in operations research is predict-then-optimize, where predictive models estimate uncertain inputs and optimization models recommend decisions. However, such approaches often sideline human judgment, creating a disconnect between algorithmic outputs and expert intuition that undermines trust and adoption in practice. To bridge this gap, we propose CREDO, a framework that, for any candidate decision proposed by human experts, provides a distribution-free upper bound on the probability of suboptimality---informed by both the optimization structure and the data distribution. By combining inverse optimization geometry with conformal generative prediction, CREDO delivers statistically rigorous yet practically interpretable risk certificates. This framework allows human decision-makers to audit and validate their decisions under uncertainty, strengthening the alignment between algorithmic tools and human intuition.

Deep Learning · Algorithms

Xinyi Yang, Liang Zeng, Heng Dong, Chao Yu, Xiaoran Wu, Huazhong Yang, Yu Wang, Milind Tambe, Tonghan Wang

As humans increasingly share environments with diverse agents powered by RL, LLMs, and beyond, the ability to explain agent policies in natural language is vital for reliable coexistence. We introduce a general-purpose framework that trains explanation-generating LLMs via reinforcement learning from AI feedback, with distributional rewards generated by generative continuous normalizing flows (CNFs). CNFs capture the pluralistic and probabilistic nature of human judgments about explanations. Moreover, under mild assumptions, CNFs provably bound deviations from true human reward distributions when trained on noisy proxy rewards from LLMs. We design a specialized CNF architecture that selectively attends to linguistic cues in decision context and explanations when generating rewards. Human and LLM evaluators find that our method delivers explanations that enable more accurate predictions of true agent decisions, exhibit greater logical soundness and actionability, and impose lower cognitive load than explanations trained with proxy LLM rewards or state-of-the-art RLHF and RLAIF baselines.

General Machine Learning · Probabilistic Methods

Jian Xu, Delu Zeng, Qibin Zhao, John Paisley

Deep Gaussian processes (DGPs) enable expressive hierarchical Bayesian modeling but pose substantial challenges for posterior inference, especially over inducing variables. Denoising diffusion variational inference (DDVI) addresses this by modeling the posterior as a time-reversed diffusion from a simple Gaussian prior. However, DDVI’s fixed unconditional starting distribution remains far from the complex true posterior, resulting in inefficient inference trajectories and slow convergence. In this work, we propose Diffusion Bridge Variational Inference (DBVI), a principled extension of DDVI that initiates the reverse diffusion from a learnable, data-dependent initial distribution. This initialization is parameterized via an amortized neural network and progressively adapted using gradients from the ELBO objective, reducing the posterior gap and improving sample efficiency. To enable scalable amortization, we design the network to operate on the inducing inputs $\mathbf{Z}^{(l)}$, which serve as structured, low-dimensional summaries of the dataset and naturally align with the inducing variables' shape. DBVI retains the mathematical elegance of DDVI—including Girsanov-based ELBOs and reverse-time SDEs—while reinterpreting the prior via a Doob-bridged diffusion process. We derive a tractable training objective under this formulation and implement DBVI for scalable inference in large-scale DGPs. Across regression, classification, and image reconstruction tasks, DBVI consistently outperforms DDVI and other variational baselines in predictive accuracy, convergence speed, and posterior quality.

Reinforcement Learning · Deep RL

Zhaoyu Chen, hongnan lin, Yongwei Nie, Fei Ma, Xuemiao Xu, Fei Yu, Chengjiang Long

Temporal Video Grounding (TVG) aims to localize video segments corresponding to a given textual query, which often describes human actions. However, we observe that current methods, usually optimizing for high temporal Intersection-over-Union (IoU), frequently struggle to accurately recognize or understand the underlying actions in both the video and query, thus reducing the effectiveness of these methods. To address this, we propose a novel TVG framework that integrates inversion-based TVG as auxiliary objectives to maintain the model's action understanding ability. We introduce three kinds of inversion TVG tasks derived from the original TVG annotations: (1) Verb Completion, predicting masked verbs (actions) in queries given video segments; (2) Action Recognition, identifying query-described actions; and (3) Video Description, generating descriptions containing query-relevant actions given video segments. These inversion tasks are entirely derived from the original TVG tasks and are probabilistically integrated with them within a reinforcement learning framework. By leveraging carefully designed reward functions, the model preserves its ability to understand actions, thereby improving the accuracy of temporal grounding. Experiments show our method outperforms state-of-the-art approaches, achieving a 7.1% improvement in R1@0.7 on Charades-STA for a 3B model.

Computer Vision · 3D Rendering & Reconstruction

YoungJoong Kwon, Yao He, Hee Jung Choi, Chen Geng, Zhengmao Liu, Jiajun Wu, Ehsan Adeli

We present a feed-forward human performance capture method that renders novel views of a performer from a monocular RGB stream. A key challenge in this setting is the lack of sufficient observations, especially for unseen regions. Assuming the subject moves continuously over time, we take advantage of the fact that more body parts become observable by maintaining a canonical space that is progressively updated with each incoming frame. This canonical space accumulates appearance information over time and serves as a context bank when direct observations are missing in the current live frame. To effectively utilize this context while respecting the deformation of the live state, we formulate the rendering process as probabilistic regression. This resolves conflicts between past and current observations, producing sharper reconstructions than deterministic regression approaches. Furthermore, it enables plausible synthesis even in regions with no prior observations. Experiments on both in-domain (4D-Dress) and out-of-distribution (MVHumanNet) datasets demonstrate the effectiveness of our approach.

General Machine Learning · Probabilistic Methods

Runyan Tan, Shuang Wu, Phillip Howard

Obtaining high-quality outputs from Large Language Models (LLMs) often depends upon the choice of a sampling-based decoding strategy to probabilistically choose the next token at each generation step. While a variety of such sampling methods have been proposed, their performance can be sensitive to the selection of hyperparameters which may require different settings depending upon the generation task and temperature configuration. In this work, we introduce $p\textrm{-less}$ sampling: an information-theoretic approach to sampling which dynamically sets a truncation threshold at each decoding step based on the entire token probability distribution. Unlike existing methods, $p\textrm{-less}$ sampling has no hyperparameters and consistently produces high-quality outputs as temperature increases. We provide theoretical perspectives on $p$-less sampling to ground our proposed method and conduct experiments to empirically validate its effectiveness across a range of math, logical reasoning, and creative writing tasks. Our results demonstrate how $p\textrm{-less}$ sampling consistently outperforms existing sampling approaches while exhibiting much less degradation in text quality at higher temperature values. We further show how $p$-less achieves greater inference-time efficiency than alternative methods through lower average token sampling times and shorter generation lengths, without sacrificing accuracy. Finally, we provide analyses to highlight the benefits of $p\textrm{-less}$ through qualitative examples, case studies, and diversity assessments.

General Machine Learning · Probabilistic Methods

Mohsen Hariri, Amirhossein Samandar, Michael Hinczewski, Vipin Chaudhary

Pass@$k$ is widely used to report performance for LLM reasoning, but it often yields unstable, misleading rankings, especially when the number of trials (samples) is limited and compute is constrained. We present a principled Bayesian evaluation framework that replaces Pass@$k$ and average accuracy over $N$ trials (avg@$N$) with posterior estimates of a model's underlying success probability and credible intervals, yielding stable rankings and a transparent decision rule for differences. Evaluation outcomes are modeled as categorical (not just 0/1) with a Dirichlet prior, giving closed-form expressions for the posterior mean and uncertainty of any weighted rubric and enabling the use of prior evidence when appropriate. Theoretically, under a uniform prior, the Bayesian posterior mean is order-equivalent to average accuracy (Pass@$1$), explaining its empirical robustness while adding principled uncertainty. Empirically, in simulations with known ground-truth success rates and on AIME'24/'25, HMMT, and BrUMO, the Bayesian/avg procedure achieves faster convergence and greater rank stability than Pass@$k$ and recent variants, enabling reliable comparisons at far smaller sample counts. The framework clarifies when observed gaps are statistically meaningful (non-overlapping credible intervals) versus noise, and it naturally extends to graded, rubric-based evaluations. Together, these results recommend replacing Pass@$k$ for LLM evaluation and ranking with a posterior-based, compute-efficient protocol that unifies binary and non-binary evaluation while making uncertainty explicit. Source code is available at https://github.com/mohsenhariri/scorio.

General Machine Learning · Probabilistic Methods

Mara Daniels, Liam Hodgkinson, Michael W Mahoney

Physics-informed machine learning (PIML) integrates prior physical information, often in the form of differential equation constraints, into the process of fitting ML models to physical data. Popular PIML approaches, including neural operators, physics-informed neural networks, and neural ordinary differential equations, are typically fit to objectives that simultaneously include both data and physical constraints. However, the multi-objective nature of this approach creates ambiguity in the measurement of model quality. This is related to a poor understanding of epistemic uncertainty, and it can lead to surprising failure modes, even when existing metrics suggest strong fits. Working within a Gaussian process regression framework, we introduce the Physics-Informed Log Evidence (PILE) score. Bypassing the ambiguities of test losses, the PILE score is a single, uncertainty-aware metric that provides a selection principle for hyperparameters of a physics-informed model. We show that PILE minimization yields excellent choices for a wide variety of model parameters, including kernel bandwidth, least squares regularization weights, and even kernel function selection. We also show that, prior to data acquisition, a special data-free case of the PILE score identifies a-priori kernel choices that are "well adapted" to a given PDE. Beyond the kernel setting, we anticipate that the PILE score can be extended to PIML at large, and we outline approaches to do so.

General Machine Learning · Representation Learning

Sungjun Lim, Kangjun Noh, Youngjun Choi, Heeyoung Lee, Kyungwoo Song

Text embeddings are essential components in modern NLP pipelines. Although numerous embedding models have been proposed, no single model consistently dominates across domains and tasks. This variability motivates the use of ensemble techniques to combine complementary strengths. However, most existing ensemble methods operate on deterministic embeddings and fail to account for model-specific uncertainty, limiting their robustness and reliability in downstream applications. To address these limitations, we propose Uncertainty-driven Embedding Convolution (UEC). UEC first transforms deterministic embeddings into probabilistic ones in a post-hoc manner. It then computes adaptive ensemble coefficients based on embedding uncertainty, derived from a principled surrogate-loss formulation. Additionally, UEC employs an uncertainty-aware similarity function that directly incorporates uncertainty into the similarity scoring, providing a theoretically grounded and efficient surrogate to distributional distances. Extensive experiments on diverse benchmarks demonstrate that UEC consistently improves both performance and robustness by leveraging principled uncertainty modeling.

Reinforcement Learning · Deep RL

Alfredo Reichlin, Adriano Pacciarelli, Danica Kragic, Miguel Vasco

Estimating the state of an environment from high-dimensional, multimodal, and noisy observations is a fundamental challenge in reinforcement learning (RL). Traditional approaches rely on probabilistic models to account for the uncertainty, but often require explicit noise assumptions, in turn limiting generalization. In this work, we contribute a novel method to learn a structured latent representation, in which distances between states directly correlate with the minimum number of actions required to transition between them. The proposed metric space formulation provides a geometric interpretation of uncertainty without the need for explicit probabilistic modeling. To achieve this, we introduce a multimodal latent transition model and a sensor fusion mechanism based on inverse distance weighting, allowing for the adaptive integration of multiple sensor modalities without prior knowledge of noise distributions. We empirically validate the approach on a range of multimodal RL tasks, demonstrating improved robustness to sensor noise and superior state estimation compared to baseline methods. Our experiments show enhanced performance of an RL agent via the learned representation, eliminating the need of explicit noise augmentation. The presented results suggest that leveraging transition-aware metric spaces provides a principled and scalable solution for robust state estimation in sequential decision-making.

Theory · Probabilistic Methods

Linye Li, Yufei Chen, Xiaodong Yue, Xujing Zhou, Qunjie Chen

Evidential Deep Learning (EDL) has emerged as a promising framework for uncertainty estimation in classification tasks by modeling predictive uncertainty with a Dirichlet prior. Despite its empirical success, prior work has primarily focused on the probabilistic properties of the Dirichlet distribution, leaving the role of optimization dynamics during training underexplored. In this paper, we revisit EDL through the lens of optimization and establish a non-trivial connection: minimizing the expected cross-entropy loss over the Dirichlet prior implicitly encourages solutions akin to multi-class Support Vector Machines, maximizing decision margins. Motivated by this observation, we introduce the \emph{optimization-consistency principle}, which deems an uncertainty measure valid if its value decreases as samples approach the global optimum of the training objective. This principle provides a new criterion for evaluating and designing uncertainty measures that are consistent with the optimization dynamics. Building on this foundation, we further propose a novel measure, \emph{Margin-aware Predictive Uncertainty (MPU)}, which directly captures the separation between target and non-target evidence. Extensive experiments on out-of-distribution detection and classification-with-rejection benchmarks demonstrate the effectiveness of our propositions.

Amirhossein Afsharrad, Ruida Zhou, Luca Viano, Sanjay Lall, Mohammad Ghavamzadeh

Reward modeling is crucial for aligning large language models with human preferences, yet current approaches lack a principled mathematical framework for leveraging ordinal preference data. When human annotators provide graded preferences on a Likert scale (e.g., significantly better, better, slightly better, negligibly better), existing methods typically apply ad-hoc heuristics, such as margin terms or scaling factors, to loss functions derived from binary preference models like Bradley-Terry. These approaches lack an underlying mathematical model for how ordinal preference data is generated. We present a theoretically grounded framework that formulates reward modeling with Likert scale preferences as a discrete ordinal regression problem. We derive two loss functions from this formulation: a negative log-likelihood loss and an all-threshold loss, both of which learn threshold parameters that naturally capture the ordinal structure of preferences. Unlike existing heuristic methods that manually specify fixed margins or scaling weights, our approach learns these parameters directly from data within a coherent probabilistic framework. Experimental results on multiple benchmarks demonstrate that our ordinal regression approach consistently achieves competitive or superior performance compared to existing heuristic methods across diverse evaluation categories including chat, reasoning, and safety tasks. Our work provides the first principled mathematical framework for incorporating Likert scale preferences into reward model training, moving beyond ad-hoc modifications of binary preference models to enable more effective utilization of fine-grained human feedback.

Shuai Wang, Malu Zhang, Yulin Jiang, Dehao Zhang, Ammar Belatreche, Yu Liang, Yimeng Shan, Zijian Zhou, Yang Yang, Haizhou Li

Spiking Neural Networks (SNNs) represent a promising paradigm for energy-efficient neuromorphic computing due to their bio-plausible and spike-driven characteristics. However, the robustness of SNNs in complex adversarial environments remains significantly constrained. In this study, we theoretically demonstrate that those threshold-neighboring spiking neurons are the key factors limiting the robustness of directly trained SNNs. We find that these neurons set the upper limits for the maximum potential strength of adversarial attacks and are prone to state-flipping under minor disturbances. To address this challenge, we propose a Threshold Guarding Optimization (TGO) method, which comprises two key aspects. First, we incorporate additional constraints into the loss function to move neurons' membrane potentials away from their thresholds. It increases SNNs' gradient sparsity, thereby reducing the theoretical upper bound of adversarial attacks. Second, we introduce noisy spiking neurons to transition the neuronal firing mechanism from deterministic to probabilistic, decreasing their state-flipping probability due to minor disturbances. Extensive experiments conducted in standard adversarial scenarios prove that our method significantly enhances the robustness of directly trained SNNs. These findings pave the way for advancing more reliable and secure neuromorphic computing in real-world applications.