Sampling from a target distribution induced by training data is central to Bayesian learning, with Stochastic Gradient Langevin Dynamics (SGLD) serving as a key tool for scalable posterior sampling and decentralized variants enabling learning when data are distributed across a network of agents. This paper introduces DIGing-SGLD, a decentralized SGLD algorithm designed for scalable Bayesian learning in multi-agent systems operating over time-varying networks. Existing decentralized SGLD methods are restricted to static network topologies, and many exhibit steady-state sampling bias caused by network effects, even when full batches are used. DIGing-SGLD overcomes these limitations by integrating Langevin-based sampling with the gradient-tracking mechanism of the DIGing algorithm, originally developed for decentralized optimization over time-varying networks, thereby enabling efficient and bias-free sampling without a central coordinator. To our knowledge, we provide the first finite-time non-asymptotic Wasserstein convergence guarantees for decentralized SGLD-based sampling over time-varying networks, with explicit constants. Under standard strong convexity and smoothness assumptions, DIGing-SGLD achieves geometric convergence to an $O(\sqrtη)$ neighborhood of the target distribution, where $η$ is the stepsize, with dependence on the target accuracy matching the best-known rates for centralized and static-network SGLD algorithms using constant stepsize. Numerical experiments on Bayesian linear and logistic regression validate the theoretical results and demonstrate the strong empirical performance of DIGing-SGLD under dynamically evolving network conditions.

This paper proposes a novel Bayesian framework for solving Poisson inverse problems by devising a Monte Carlo sampling algorithm which accounts for the underlying non-Euclidean geometry. To address the challenges posed by the Poisson likelihood -- such as non-Lipschitz gradients and positivity constraints -- we derive a Bayesian model which leverages exact and asymptotically exact data augmentations. In particular, the augmented model incorporates two sets of splitting variables both derived through a Bregman divergence based on the Burg entropy. Interestingly the resulting augmented posterior distribution is characterized by conditional distributions which benefit from natural conjugacy properties and preserve the intrinsic geometry of the latent and splitting variables. This allows for efficient sampling via Gibbs steps, which can be performed explicitly for all conditionals, except the one incorporating the regularization potential. For this latter, we resort to a Hessian Riemannian Langevin Monte Carlo (HRLMC) algorithm which is well suited to handle priors with explicit or easily computable score functions. By operating on a mirror manifold, this Langevin step ensures that the sampling satisfies the positivity constraints and more accurately reflects the underlying problem structure. Performance results obtained on denoising, deblurring, and positron emission tomography (PET) experiments demonstrate that the method achieves competitive performance in terms of reconstruction quality compared to optimization- and sampling-based approaches.

These properties are used implicitly in exact inference, but are difficult to harness for approximate inference.

In this work, we estimate the intrinsic dimension (iD) of the Radio Galaxy Zoo (RGZ) dataset using a score-based diffusion model. We examine how the iD estimates vary as a function of Bayesian neural network (BNN) energy scores, which measure how similar the radio sources are to the MiraBest subset of the RGZ dataset. We find that out-of-distribution sources exhibit higher iD values, and that the overall iD for RGZ exceeds those typically reported for natural image datasets. Furthermore, we analyse how iD varies across Fanaroff-Riley (FR) morphological classes and as a function of the signal-to-noise ratio (SNR). While no relationship is found between FR I and FR II classes, a weak trend toward higher SNR at lower iD. Future work using the RGZ dataset could make use of the relationship between iD and energy scores to quantitatively study and improve the representations learned by various self-supervised learning algorithms.

There has been a prevalence of applying AI software in both high-stakes public-sector and industrial contexts. However, the lack of transparency has raised concerns about whether these data-informed AI software decisions secure fairness against people of all racial, gender, or age groups. Despite extensive research on emerging fairness-aware AI software, up to now most efforts to solve this issue have been dedicated to binary classification tasks. Fairness in regression is relatively underexplored. In this work, we adopted a mutual information-based metric to assess separation violations. The metric is also extended so that it can be directly applied to both classification and regression problems with both binary and continuous sensitive attributes. Inspired by the Reweighing algorithm in fair classification, we proposed a FairReweighing pre-processing algorithm based on density estimation to ensure that the learned model satisfies the separation criterion. Theoretically, we show that the proposed FairReweighing algorithm can guarantee separation in the training data under a data independence assumption. Empirically, on both synthetic and real-world data, we show that FairReweighing outperforms existing state-of-the-art regression fairness solutions in terms of improving separation while maintaining high accuracy.

Multi-token prediction (MTP) is a prominent strategy to significantly speed up generation in large language models (LLMs), including byte-level LLMs, which are tokeniser-free but prohibitively slow. However, existing MTP methods often sacrifice expressiveness by assuming independence between future tokens. In this work, we investigate the trade-off between expressiveness and latency in MTP within the framework of probabilistic circuits (PCs). Our framework, named MTPC, allows one to explore different ways to encode the joint distributions over future tokens by selecting different circuit architectures, generalising classical models such as (hierarchical) mixture models, hidden Markov models and tensor networks. We show the efficacy of MTPC by retrofitting existing byte-level LLMs, such as EvaByte. Our experiments show that, when combined with speculative decoding, MTPC significantly speeds up generation compared to MTP with independence assumptions, while guaranteeing to retain the performance of the original verifier LLM. We also rigorously study the optimal trade-off between expressiveness and latency when exploring the possible parameterisations of MTPC, such as PC architectures and partial layer sharing between the verifier and draft LLMs.

Many tasks in machine learning can be described as or reduced to learning a probability distribution given a finite set of samples. A common approach is to minimize a statistical divergence between the (empirical) data distribution and a parameterized distribution, e.g., a normalizing flow (NF) or an energy-based model (EBM). In this context, the forward KL divergence is a ubiquitous due to its tractability, though its asymmetry may prevent capturing some properties of the target distribution. Symmetric alternatives involve brittle min-max formulations and adversarial training (e.g., generative adversarial networks) or evaluating the reverse KL divergence, as is the case for the symmetric Jeffreys divergence, which is challenging to compute from samples. This work sets out to develop a new approach to minimize the Jeffreys divergence. To do so, it uses a proxy model whose goal is not only to fit the data, but also to assist in optimizing the Jeffreys divergence of the main model. This joint training task is formulated as a constrained optimization problem to obtain a practical algorithm that adapts the models priorities throughout training. We illustrate how this framework can be used to combine the advantages of NFs and EBMs in tasks such as density estimation, image generation, and simulation-based inference.

Abstract--Motivated by the challenges of edge inference, we study a variant of the cascade bandit model in which each arm corresponds to an inference model with an associated accuracy and error probability. We analyse four decision-making policies--Explore-then-Commit, Action Elimination, Lower Confidence Bound (LCB), and Thompson Sampling--and provide sharp theoretical regret guarantees for each. Unlike in classical bandit settings, Explore-then-Commit and Action Elimination incur suboptimal regret because they commit to a fixed ordering after the exploration phase, limiting their ability to adapt. In contrast, LCB and Thompson Sampling continuously update their decisions based on observed feedback, achieving constant O(1) regret. Simulations corroborate these theoretical findings, highlighting the crucial role of adaptivity for efficient edge inference under uncertainty.

Lossless compression techniques are crucial in an era of rapidly growing data. Traditional universal compressors like gzip offer low computational overhead, high speed, and broad applicability across data distributions. However, they often lead to worse compression rates than modern neural compressors, which leverage large-scale training data to model data distributions more effectively. Despite their advantages, neural compressors struggle to generalize to unseen data. To address this limitation, we propose a novel framework that performs Test-Time Steering via a Weighted Product of Experts (wPoE). At inference, our method adaptively combines a universal compression model with a pretrained neural language model, ensuring the compression rate is at least as good as that of the best individual model. Extensive experiments demonstrate that our approach improves the performance of text compression without requiring fine-tuning. Furthermore, it seamlessly integrates with any autoregressive language model, providing a practical solution for enhancing text compression across diverse data distributions.

Vision-Language Models (VLMs), with their powerful content generation capabilities, have been successfully applied to data annotation processes. However, the VLM-generated labels exhibit dual limitations: low quality (i.e., label noise) and absence of error correction mechanisms. To enhance label quality, we propose Human-Corrected Labels (HCLs), a novel setting that efficient human correction for VLM-generated noisy labels. As shown in Figure 1(b), HCL strategically deploys human correction only for instances with VLM discrepancies, achieving both higher-quality annotations and reduced labor costs. Specifically, we theoretically derive a risk-consistent estimator that incorporates both human-corrected labels and VLM predictions to train classifiers. Besides, we further propose a conditional probability method to estimate the label distribution using a combination of VLM outputs and model predictions. Extensive experiments demonstrate that our approach achieves superior classification performance and is robust to label noise, validating the effectiveness of HCL in practical weak supervision scenarios. Code https://github.com/Lilianach24/HCL.git