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Probabilistic Methods · Bayesian Models and Methods

Katarzyna Kobalczyk, Zhiyuan Jerry Lin, Benjamin Letham, Zhuokai Zhao, Maximilian Balandat, Eytan Bakshy

Many real-world optimization problems are guided by complex, subjective preferences that are difficult to express as explicit closed-form objectives. In response, we introduce Language-in-the-Loop Optimization (LILO), a Bayesian optimization (BO) framework that employs a large language model (LLM) to translate free-form natural language feedback and prior knowledge from a decision maker into structured preference signals, going beyond the restrictive scalar or pairwise feedback formats typically assumed in preferential BO. The LLM-derived preferences are integrated by a Gaussian process proxy model, enabling principled acquisition-driven exploration with calibrated uncertainty. By placing the LLM in a supporting role rather than as the optimizer itself, LILO preserves the sample efficiency and stability of BO while providing a flexible and expressive feedback interface. Across synthetic and real-world benchmarks, LILO consistently outperforms both conventional preference-based BO methods and LLM-only optimizers, with particularly strong gains in feedback-limited regimes.

Reinforcement Learning · Multi-agent

Zhibo Deng, Feng Liang, Yong Zhang, Xiaoxi Zhang, Xiping Hu

In multi-agent reinforcement learning (MARL), communication enables agents to mitigate partial observability and stochasticity through information sharing, but large-scale systems inherently lead to a rapidly growing number of pairwise interactions. Previous studies often struggle to simultaneously achieve scalability and task adaptivity in large-scale multi-agent communication. To address this challenge, we propose a scalable communication scheme for large-scale MARL, termed $\textit{Sparse tOpology-aware Pairwise Scoring}$ (SOPS). We argue that scalable MARL communication requires decoupling scalability from task-adaptive link allocation. To ensure scalability, we constrain communication to an exponential-graph backbone with a small diameter, which preserves rapid potential information mixing while keeping per-agent candidates logarithmic. On top of this constraint, we learn a task-conditioned probabilistic subgraph distribution via a pairwise scoring network over agent states and edge-type embeddings to allocate sparse links for maximizing return, optimized end-to-end through differentiable Gumbel-Sigmoid reparameterization. Evaluation results show that SOPS significantly outperforms existing state-of-the-art methods across cooperative benchmarks of diverse scales and exhibits robust zero-shot transfer capabilities.

Applications · Health / Medicine

Haoyang Luan, Gufeng Yu, Letian Chen, Zhenran Xiao, Yueshan Huang, Junkun Guo, Yang Yang

The *de novo* generation of high-affinity epitopes tailored to specific major histocompatibility complex (MHC) proteins is a pivotal challenge in computational immunotherapy. However, current methods struggle to effectively integrate the MHC context into the generation process, and often fail to guarantee high binding affinity due to the neglect of discriminative signals from non-binders. To bridge these gaps, we present **EpiCoCo**, a probabilistic framework for **Epi**tope generation via MHC-context **Co**-modeling and **Co**ntrastive affinity learning. EpiCoCo treats the pMHC complex as a dynamic, co-adaptive system by operating on the joint E(3) graph. In addition, we introduce Contrastive Affinity Guidance (CAG), an inference mechanism that leverages the gradient difference between learned high- and low-affinity distributions. CAG actively drives the generation trajectory towards high-affinity manifolds while utilizing repulsive signals to filter out candidates with poor binding potential. Extensive evaluations demonstrate that EpiCoCo achieves a mean binding free energy of -45.20 REU, a 23% improvement over the state-of-the-art, while maintaining high structural plausibility. The results validate that context co-modeling and negative-informed guidance are essential for generating valid, high-potency immunotherapeutics.

Reinforcement Learning · Everything Else

Yannik Schnitzer, Mathias Jackermeier, Alessandro Abate, David Parker

Multi-task reinforcement learning trains generalist policies that can execute multiple tasks. While recent years have seen significant progress, existing approaches rarely provide formal performance guarantees, which are indispensable when deploying policies in safety-critical settings. We present an approach for computing high-confidence guarantees on the performance of a multi-task policy on tasks not seen during training. Concretely, we introduce a new generalisation bound that composes (i) per-task lower confidence bounds from finitely many rollouts with (ii) task-level generalisation from finitely many sampled tasks, yielding a high-confidence guarantee for new tasks drawn from the same arbitrary and unknown distribution. Across state-of-the-art multi-task RL methods, we show that the guarantees are theoretically sound and informative at realistic sample sizes.

Applications · Time Series

Hanyin Cheng, Jingrong Zhou, Yang Shu, Chenjuan Guo

Probabilistic forecasting with exogenous variables is vital for decision-making but remains underexplored compared to deterministic methods. We propose KITE, a knowledge-guided probabilistic modeling framework designed to bridge this gap by addressing two key bottlenecks: (1) topological disparity in sampling initialization and (2) spurious covariate correlations during the iterative conditional generation process. KITE introduces a *History-Conditional Manifold* to construct an informative source distribution from historical dynamics, effectively anchoring the starting point closer to the target space. Additionally, a *Knowledge-Guided Conditioning* module is developed to regularize variable interactions using statistical priors, suppressing spurious correlations and enhancing the robustness of covariate conditioning. Extensive experiments demonstrate that KITE outperforms state-of-the-art methods in both deterministic and probabilistic forecasting.

Reinforcement Learning · Policy Search

Joseph Cotnareanu, Chiara Roverato, Han Zhou, Didier Chételat, Yingxue Zhang, Mark Coates

Recent efforts to improve the reasoning abilities of Large Language Models (LLMs) have focused on integrating formal logic solvers within neurosymbolic frameworks. A key challenge is that formal solvers lack commonsense world knowledge, preventing them from making reasoning steps that humans find obvious. Prior methods address this by using LLMs to supply missing commonsense assumptions, but these approaches implicitly assume universal agreement on such commonsense facts. In reality, commonsense beliefs vary across individuals. We propose a probabilistic framework for abductive commonsense reasoning that explicitly models this variation, aiming to determine whether most people would judge a statement as true or false. We introduce Probabilistic Abductive CommonSense (PACS), a novel algorithm that uses an LLM and a formal solver to sample proofs as observations of individuals’ distinct commonsense beliefs, and aggregates conclusions across these samples. Empirically, PACS outperforms chain-of-thought reasoning, prior neurosymbolic methods, and search-based approaches across multiple benchmarks.

Theory · Probabilistic Methods

Achref Doula

Conformal prediction converts point predictions into set-valued predictions with coverage guarantees under exchangeability between calibration and deployment data. We study *conformal calibration transfer*, where this requirement fails because labeled calibration is available only in a source space, while prediction sets are needed in a target space linked to the source through *unlabeled paired* observations (e.g., paired modalities or sensor changes). We propose Transported Conformal Calibration (TCC): we transport labeled source calibration into the target space using the paired data, and then correct residual post-transport mismatch using only unlabeled target inputs. We instantiate this correction with two complementary methods: **TCC-KS**, which uses a label-free uncertainty surrogate to detect mismatch and adjust calibration conservatively, and **weighted-TCC**, which reweights transported calibration toward the target domain for improved efficiency when weights are stable. We provide finite-sample target-domain coverage guarantees that adapt to an observable measure of mismatch. Across CIFAR-100-C, Tiny-ImageNet-C, and SEN12MS, we show reliable target-domain coverage transfer without labeled target calibration data, with label-free diagnostics that predict when correction is needed.

Probabilistic Methods · Bayesian Models and Methods

Sherman Khoo, Dennis Prangle, Song Liu, Mark Beaumont

Simulation-based inference (SBI) enables amortized Bayesian inference by first training a neural posterior estimator (NPE) on prior-simulator pairs, typically through low-dimensional summary statistics, which can then be cheaply reused for fast inference by querying it on new test observations. Because NPE is estimated under the training data distribution, it is susceptible to misspecification when observations deviate from the training distribution. Many robust SBI approaches address this by modifying NPE training or introducing error models, coupling robustness to the inference network and compromising amortization and modularity. We introduce minimum-distance summaries, a plug-in robust NPE method that adapts queried test-time summaries independently of the pretrained NPE. Leveraging the maximum mean discrepancy (MMD) as a distance between observed data and a summary-conditional predictive distribution, the adapted summary inherits strong robustness properties from the MMD. We demonstrate that the algorithm can be implemented efficiently with random Fourier feature approximations, yielding a lightweight, model-free test-time adaptation procedure. We provide theoretical guarantees for the robustness of our algorithm and empirically evaluate it on a range of synthetic and real-world tasks, demonstrating substantial robustness gains with minimal additional overhead.

Social Aspects · Everything Else

Yizhou Min, Yizhou Lu, Lanqi Li, Zhen Zhang, Jiaye Teng

Conformal prediction (CP) has become a cornerstone of distribution-free uncertainty quantification, conventionally evaluated by its coverage and interval length. This work critically examines the sufficiency of these standard metrics. We demonstrate that the interval length might be deceptively improved through a counter-intuitive approach termed Prejudicial Trick (PT), while the coverage remains valid. Specifically, for any given test sample, PT probabilistically returns an interval, which is either null or constructed using an adjusted confidence level, thereby preserving marginal coverage. While PT potentially yields a deceptively lower interval length, it introduces practical vulnerabilities: the same input can yield completely different prediction intervals across repeated runs of the algorithm. We formally derive the conditions under which PT achieves these misleading improvements and provide extensive empirical evidence across various regression and classification tasks. Furthermore, we introduce a new metric interval stability which helps detect whether a new CP method implicitly improves the length based on such PT-like techniques.

Probabilistic Methods · Bayesian Models and Methods

SongEun Kim, Seungyoo Lee, Edwin Fong, Hyungi Lee, Juho Lee

Large language models (LLMs) are often hypothesized to perform implicit Bayesian inference, yet a key coherence condition—the martingale property of predictive beliefs—has been shown to fail in controlled synthetic in-context learning settings. We revisit this question in a more typical usage regime: generic multiple-choice question answering. Exploiting the discrete answer space, we compute exact predictive distributions and study belief dynamics induced by autoregressive answer resampling. We introduce prompted predictive resampling (PPR), where an LLM generates a sequence of answers to the same question. Empirically, PPR reveals early-stage belief drift, indicating martingale violations. However, after sufficient resampling steps, the belief process self-stabilizes and converges to a coherent predictive distribution. Based on this observation, we further propose (i) a seed-answer prompting strategy to accelerate stabilization, and (ii) a self-consistency loss that amortizes early-stage drift into the model via fine-tuning. Experiments on multiple-choice QA benchmarks show that our methods substantially reduce belief drift and improve predictive coherence without sacrificing accuracy.

Probabilistic Methods · Variational Inference

Ananyapam De, Linus Bleistein, Anton Thielmann, Benjamin Säfken

Optimal Transport (OT) traditionally relies on a fixed ground cost to produce a single deterministic transport plan—a practice that overlooks the inherent variability and noise in real-world data. While recent sampling based approaches of OT offer a principled way to quantify this uncertainty, these are computationally prohibitive and struggle to scale. In this paper, we introduce Sinkhorn-parameterized Variational Inference, a first scalable variational framework for performing posterior inference over transport plans. Our key insight is that the Sinkhorn map can be treated as a differentiable reparameterization of the set of entropic plans. This enables the use of flexible generative models like normalizing flows to approximate distributions over transport plans while enforcing marginal constraints. We experimentally demonstrate that our method matches the quality of intensive sampling techniques at a fraction of the computational cost, scaling effectively to large-scale problems.

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.

Probabilistic Methods · Monte Carlo and Sampling Methods

Arran Carter, Sanghyeok Choi, Kirill Tamogashev, Víctor Elvira, Esmeralda S. Whitammer

Sampling from a distribution $p(x) \propto e^{-\mathcal{E}(x)}$ known up to a normalising constant is an important and challenging problem in statistics. Recent years have seen the rise of a new family of amortised sampling algorithms, commonly referred to as diffusion samplers, that enable fast and efficient sampling from an unnormalised density. Such algorithms have been widely studied for continuous-space sampling tasks; however, their application to problems in discrete space remains largely unexplored. Although some progress has been made in this area, discrete diffusion samplers do not take full advantage of ideas commonly used for continuous-space sampling. In this paper, we propose to bridge this gap by introducing off-policy training techniques for discrete diffusion samplers. We show that these techniques improve the performance of discrete samplers on both established and new synthetic benchmarks. Next, we generalise discrete diffusion samplers to the task of bridging between two arbitrary distributions, introducing data-to-energy Schrödinger bridge training for the discrete domain for the first time. Lastly, we showcase the application of the proposed diffusion samplers to data-free posterior sampling in the discrete latent spaces of image generative models.

Probabilistic Methods · Monte Carlo and Sampling Methods

Sanghyeok Choi, Sarthak Mittal, Víctor Elvira, Jinkyoo Park, Esmeralda S. Whitammer

This paper proposes a synergy of amortised and particle-based methods for sampling from distributions defined by unnormalised density functions. We state a connection between sequential Monte Carlo (SMC) and neural sequential samplers trained by maximum-entropy reinforcement learning (MaxEnt RL), wherein learnt sampling policies and value functions define proposal kernels and twist functions. Exploiting this connection, we introduce an off-policy RL training procedure for the sampler that uses samples from SMC -- using the learnt sampler as a proposal -- as a behaviour policy that better explores the target distribution. We describe techniques for stable joint training of proposals and twist functions and an adaptive weight tempering scheme to reduce training signal variance. Furthermore, building upon past attempts to use experience replay to guide the training of neural samplers, we derive a way to combine historical samples with annealed importance sampling weights within a replay buffer. On synthetic multi-modal targets (in both continuous and discrete spaces) and the Boltzmann distribution of alanine dipeptide conformations, we demonstrate improvements in approximating the true distribution as well as training stability compared to both amortised and Monte Carlo methods.

Deep Learning · Robustness

Sara Taheri, Majid Zamani

The growing use of machine learning in safety-critical settings heightens vulnerability to *adversarial attacks*. Existing defense mechanisms typically either lack formal guarantees or depend on restrictive assumptions about the model family, the threat model, or the poisoning budget, and many only offer point-wise certification. Importantly, they often overlook the inherent stochasticity of modern training pipelines, which undermines their practical reliability. We introduce a probabilistic framework that views gradient-based training as a *discrete-time stochastic dynamical system* and formulates poisoning robustness as a safety verification task. Leveraging *barrier certificates* (BCs), we derive sufficient conditions to probabilistically certify a robust radius against worst-case ${\ell}_p$-bounded poisoning, guaranteeing that the final model parameters remain within a safe set. For tractable computation, we represent BCs with neural networks and obtain *probably approximately correct* (PAC) guarantees through a *scenario convex problem*. Our method identifies the largest certified radius for which the trained model is probabilistically accurate with a specified confidence level. Experiments on MNIST, SVHN, and CIFAR-10 show that our framework offers formal robustness guarantees under stochastic training, while being model-agnostic and not requiring prior knowledge of the attack strategy.

Probabilistic Methods · Monte Carlo and Sampling Methods

Jinwoo Kim, Sékou-Oumar Kaba, Jiyun Park, Seunghoon Hong, Siamak Ravanbakhsh

We study the problem of transformation inversion on general Lie groups: a datum is transformed by an unknown group element, and the goal is to recover an inverse transformation that maps it back to the original data distribution. We take a probabilistic view and model the posterior over transformations as a Boltzmann distribution defined by an energy function on data space. To sample from this posterior, we introduce a diffusion process on Lie groups that keeps all updates on-manifold and only requires computations in the associated Lie alge- bra. Our method, Transformation-Inverting Energy Diffusion (TIED), relies on a new trivialized target-score identity that enables efficient score-based sampling of the transformation posterior. As a key application, we focus on test-time equivariance, where the objective is to improve the robustness of pretrained neural networks to input transformations. Experiments on image homographies and PDE symmetries demonstrate that TIED can restore transformed inputs to the training distribution at test time, showing improved performance over strong canonicalization and sampling baselines.

Probabilistic Methods · Monte Carlo and Sampling Methods

Giorgio Giannone, Guangxuan Xu, Nikhil Nayak, Rohan Awhad, Shivchander Sudalairaj, Kai Xu, Akash Srivastava

Inference-Time Scaling (ITS) improves language models by allocating more computation at generation time. Particle Filtering (PF) has emerged as a strong ITS method for complex mathematical reasoning tasks, but it is vulnerable when guided by process reward models, which often assign overconfident scores early in the reasoning process. This causes PF to suffer from premature exploitation: it myopically commits to locally promising trajectories, prunes potentially correct hypotheses, and converges to suboptimal solutions. This failure mode, known as particle impoverishment, is especially severe under constrained computational budgets. To address this, we analyze the problem and identify two root causes: a lack of diversity in the particle set due to overconfident resampling and consequent inability to assess the potential of a reasoning path. We introduce Entropic Particle Filtering (ePF), an algorithm that integrates two new techniques to solve these issues. The first technique, Entropic Annealing (EA), directly mitigates particle impoverishment by monitoring search diversity via entropy; when diversity drops, it intervenes by dynamically annealing the resampling distribution to preserve exploration. The second, an enhancement called Look-ahead Modulation (LaM), adds a predictive guide to evaluate a state's potential based on its successors. On several challenging math benchmarks, ePF significantly outperforms strong baselines and achieves up to a 50\% relative improvement in task reward. Together, these methods improve PF's resilience by balancing the exploration of diverse solution spaces with the exploitation of high-reward regions, ultimately leading to higher-quality solutions.

Theory · Probabilistic Methods

Youheng Zhu, Yiping Lu

Inference-time scaling has recently emerged as a powerful paradigm for improving the reasoning capability of large language models. Among various approaches, \emph{Sequential Monte Carlo (SMC)} has become a particularly important framework, enabling iterative generation, evaluation, rejection, and resampling of intermediate reasoning trajectories. A central component in this process is the \emph{reward model}, which evaluates partial solutions and guides the allocation of computation during inference. However, in practice, true reward models are never available. All deployed systems rely on \emph{approximate reward models}, raising a fundamental question: \emph{Why and when do approximate reward models suffice for effective inference-time scaling?} In this work, we provide a theoretical answer. We identify the \emph{Bellman error} of the approximate reward model as the key quantity governing the effectiveness of SMC-based inference-time scaling. For a reasoning process of length $T$, we show that if the Bellman error of the approximate reward model is bounded by $O(1/T)$, then combining this reward model with SMC reduces the computational complexity of reasoning from exponential in $T$ to polynomial in $T$. This yields an \emph{exponential improvement} in inference efficiency despite using only approximate rewards.

Zhenyu Wu, Yao Huang, Shouwei Ruan, Xingxing Wei

Text-to-image diffusion models have achieved remarkable success in generating high-quality images, yet existing safety mechanisms exhibit critical cross-seed instability where defense performance varies significantly under different random seed conditions. This instability stems from the fact that a single malicious prompt generates diverse harmful variants across different noise initializations, forming complex distributional clusters that current methods cannot adequately address. We investigate extending Noise Contrastive Alignment (NCA) to diffusion models due to its native capability of handling multiple negative samples through probabilistic weighting, but our theoretical analysis reveals two fundamental flaws in direct extension: gradient reversal caused by positive regularization terms that paradoxically penalize safe content generation, and uniform suppression of harmful samples that ignores severity variations. To tackle these issues, we propose Noise Contrastive Diffusion (NCD), which incorporates targeted algorithmic modifications including elimination of problematic regularization and introduction of pairwise regularization mechanisms that establish individualized preference relationships between safe and harmful variants. Extensive experiments further demonstrate that NCD achieves superior cross-seed stability, reducing attack success rates (ASRs) from 11.1% to 6.2% compared to SOTA methods at the seed level while maintaining exceptional generation quality, exhibiting robust resistance against sophisticated jailbreak prompts and strong generalizability across different T2I architectures. WARNING: This paper may contain examples of harmful texts and images.

Theory · Probabilistic Methods

Binglin Li, Matthew Reed, Seong-Tae Kim

Compositional data analysis has gained increasing attention due to the widespread occurrence of simplex-valued data, including microbiome data. However, existing kernel or distance-based nonparametric two-sample tests are often designed for Euclidean data and rely on square-root or log-transformations, motivating the need for a unified framework for nonparametric two-sample testing applicable to both compositional and directional data. We propose a studentized spherical harmonic energy distance-based two-sample test over a fixed dimensional underlying space, incorporating U-statistics theory and recent developments of studentization in the context of compositional and directional data. We establish asymptotic normality of our studentized test statistics constructed via spherical harmonics theory, avoiding the need for permutation or bootstrap tests. Simulations demonstrate convergence to the limiting distribution, empirical size control, and improved power in certain scenarios. Our proposed framework paves a new direction for nonparametric testing in non-Euclidean data analysis.