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Probabilistic Methods · Gaussian Processes

Masahiro Kohjima

Shuffled regression is the problem of learning regression functions from shuffled data where the correspondence between the input features and target response is unknown. This paper proposes a probabilistic model for shuffled regression called Gaussian Process Shuffled Regression (GPSR). By introducing Gaussian processes as a prior of regression functions in function space via the kernel function, GPSR can express a wide variety of functions in a nonparametric manner while quantifying the uncertainty of the prediction. By adopting the Bayesian evidence maximization framework and a theoretical analysis of the connection between the marginal likelihood/predictive distribution of GPSR and that of standard Gaussian process regression (GPR), we derive an easy-to-implement inference algorithm for GPSR that iteratively applies GPR and updates the input-output correspondence. To reduce computation costs and obtain closed-form solutions for correspondence updates, we also develop a sparse approximate variant of GPSR using its weight space formulation, which can be seen as Bayesian shuffled linear regression with random Fourier features. Experiments on benchmark datasets confirm the effectiveness of our GPSR proposal.

Computer Vision · Segmentation

Conghui Li, Chern Hong Lim, Xin Wang

While deep neural networks possess the capability to perform semantic segmentation, producing a single deterministic output limits reliability in safety-critical applications, caused by uncertainty and annotation variability. To address this, stochastic segmentation models using Conditional Variational Autoencoders (CVAE), Bayesian networks, and diffusion have been explored. However, existing approaches suffer from limited latent expressiveness and interpretability. Furthermore, our experiments showed that models like Probabilistic U-Net rely excessively on high latent variance, leading to posterior collapse. This work propose a novel framework by integrating Gaussian Mixture Model (GMM) with Normalizing Flow (NF) in CVAE for stochastic segmentation. GMM structures the latent space into meaningful semantic clusters, while NF captures feature deformations with quantified uncertainty. Our method stabilizes latent distributions through constrained variance and mean ranges. Experiments on LIDC, Crack500, and Cityscapes datasets show that our approach outperformed state-of-the-art in curvilinear structure and medical image segmentation.

Computer Vision · Image and Video Generation

Guanxiong Luo, Shoujin Huang

We propose ***self-diffusion***, a novel framework for solving inverse problems without relying on pretrained generative models. Traditional diffusion-based approaches require training a model on a clean dataset to learn to reverse the forward noising process. This model is then used to sample clean solutions---corresponding to posterior sampling from a Bayesian perspective---that are consistent with the observed data under a specific task. In contrast, self-diffusion introduces a self-contained iterative process that alternates between noising and denoising steps to progressively refine its estimate of the solution. At each step of self-diffusion, noise is added to the current estimate, and a self-denoiser, which is a single untrained convolutional network randomly initialized from scratch, is continuously trained for certain iterations via a data fidelity loss to predict the solution from the noisy estimate. Essentially, self-diffusion exploits the spectral bias of neural networks and modulates it through a scheduled noise process. Without relying on pretrained score functions or external denoisers, this approach still remains adaptive to arbitrary forward operators and noisy observations, making it highly flexible and broadly applicable. We demonstrate the effectiveness of our approach on a variety of linear inverse problems, showing that self-diffusion achieves competitive or superior performance compared to other methods.

Applications · Genetics, Cell Biology, etc

Hanlin Wu, Yuxuan Song, Zhe Zhang, Zhilong Zhang, Hao Zhou, Wei-Ying Ma, Jingjing Liu

Designing functional proteins is a critical yet challenging problem due to the intricate interplay between backbone structures, sequences, and side-chains. Current approaches often decompose protein design into separate tasks, which can lead to accumulated errors, while recent efforts increasingly focus on all-atom protein design. However, we observe that existing all-atom generation approaches suffering from an information shortcut issue, where models inadvertently infer sequences from side-chain information, compromising their ability to accurately learn sequence distributions. To address this, we introduce a novel rationalized information flow strategy to eliminate the information shortcut. Furthermore, motivated by the advantages of Bayesian flows over differential equation–based methods, we propose the first Bayesian flow formulation for protein backbone orientations by recasting orientation modeling as an equivalent hyperspherical generation problem with antipodal symmetry. To validate, our method delivers consistently exceptional performance in both peptide and antibody design tasks.

Probabilistic Methods · Bayesian Models and Methods

Sina Tootoonian, Andreas Schaefer

A common view of sensory processing is as probabilistic inference of latent causes from receptor activations. Standard approaches often assume these causes are \textit{a priori} independent, yet real-world generative factors are typically correlated. Representing such structured priors in neural systems poses architectural challenges, particularly when direct interactions between units representing latent causes are biologically implausible or computationally expensive. Inspired by the architecture of the olfactory bulb, we propose a novel circuit motif that enables inference with correlated priors without requiring direct interactions among latent cause units. The key insight lies in using \textit{sister cells}: neurons receiving shared receptor input but connected differently to local interneurons. The required interactions among latent units are implemented indirectly through their connections to the sister cells, such that correlated connectivity implies anti-correlation in the prior and vice versa. We use geometric arguments to construct connectivity that implements a given prior and to bound the number of causes for which such priors can be constructed. Using simulations, we demonstrate the efficacy of such priors for inference in noisy environments and compare the inference dynamics to those experimentally observed. Finally, we show how, under certain assumptions on latent representations, the prior used can be inferred from sister cell activations. While biologically grounded in the olfactory system, our mechanism generalises to other natural and artificial sensory systems and may inform the design of architectures for efficient inference under correlated latent structure.

Probabilistic Methods · Bayesian Models and Methods

Zongbo Han, Jialong Yang, Guangyu Wang, Junfan Li, Qianli Xu, Mike Zheng Shou, Changqing Zhang

Vision-language foundation models (VLMs), such as CLIP, exhibit remarkable performance across a wide range of tasks. However, deploying these models can be unreliable when significant distribution gaps exist between training and test data, while fine-tuning for diverse scenarios is often costly. Cache-based test-time adapters offer an efficient alternative by storing representative test samples to guide subsequent classifications. Yet, these methods typically employ naive cache management with limited capacity, leading to severe catastrophic forgetting when samples are inevitably dropped during updates. In this paper, we propose DOTA (DistributiOnal Test-time Adaptation), a simple yet effective method addressing this limitation. Crucially, instead of merely memorizing individual test samples, DOTA continuously estimates the underlying distribution of the test data stream. Test-time posterior probabilities are then computed using these dynamically estimated distributions via Bayes' theorem for adaptation. This distribution-centric approach enables the model to continually learn and adapt to the deployment environment. Extensive experiments validate that DOTA significantly mitigates forgetting and achieves state-of-the-art performance compared to existing methods.

Probabilistic Methods · Bayesian Models and Methods

Laurence Davies, Daniel MacKinlay, Rafael Oliveira, Scott SIsson

The expressiveness of flow-based models combined with stochastic variational inference (SVI) has expanded the application of optimization-based Bayesian inference to highly complex problems. However, despite the importance of multi-model Bayesian inference, defined over a transdimensional joint model and parameter space, flow-based SVI has been limited to problems defined over a fixed-dimensional parameter space. We introduce CoSMIC normalizing flows (COntextually-Specified Masking for Identity-mapped Components), an extension to neural autoregressive conditional normalizing flow architectures that enables use of a single amortized variational density for inference over a transdimensional (multi-model) conditional target distribution. We propose a combined stochastic variational transdimensional inference (VTI) approach to training CoSMIC flows using ideas from Bayesian optimization and Monte Carlo gradient estimation. Numerical experiments show the performance of VTI on challenging problems that scale to high-cardinality model spaces.

Applications · Neuroscience, Cognitive Science

A Sağtekin, Colin Bredenberg, Cristina Savin

How should feedback influence recurrent neural network (RNN) learning? One way to address the known limitations of backpropagation through time is to directly adjust neural activities during the learning process. However, it remains unclear how to effectively use feedback to shape RNN dynamics. Here, we introduce error forcing (EF), where the network activity is guided orthogonally toward the zero-error manifold during learning. This method contrasts with alternatives like teaching forcing, which impose stronger constraints on neural activity and thus induce larger feedback influence on circuit dynamics. Furthermore, EF can be understood from a Bayesian perspective as a form of approximate dynamic inference. Empirically, EF consistently outperforms other learning algorithms across several tasks and its benefits persist when additional biological constraints are taken into account. Overall, EF is a powerful temporal credit assignment mechanism and a promising candidate model for learning in biological systems.

General Machine Learning · Transfer, Multitask and Meta-learning

Tim Genewein, Kevin Li, Jordi Grau-Moya, Anian Ruoss, Laurent Orseau, Marcus Hutter

Prompting is one of the main ways to adapt a pretrained model to target tasks. Besides manually constructing prompts, many prompt optimization methods have been proposed in the literature. Method development is mainly empirically driven, with less emphasis on a conceptual understanding of prompting. In this paper we discuss how optimal prompting can be understood through a Bayesian view, which also implies some fundamental limitations of prompting that can only be overcome by tuning weights. The paper explains in detail how meta-trained neural networks behave as Bayesian predictors over the pretraining distribution, whose hallmark feature is rapid in-context adaptation. Optimal prompting can be studied formally as conditioning these Bayesian predictors, yielding criteria for target tasks where optimal prompting is and is not possible. We support the theory with educational experiments on LSTMs and Transformers, where we compare different versions of prefix-tuning and different weight-tuning methods. We also confirm that soft prefixes, which are sequences of real-valued vectors outside the token alphabet, can lead to very effective prompts for trained and even untrained networks by manipulating activations in ways that are not achievable by hard tokens. This adds an important mechanistic aspect beyond the conceptual Bayesian theory.

Probabilistic Methods · Bayesian Models and Methods

Mykola Lukashchuk, Raphaël Trésor, Wouter Nuijten, Ismail Senoz, Bert Vries

This paper introduces the Quotient Bayesian Learning Rule, an extension of natural-gradient Bayesian updates to probability models that fall outside the exponential family. Building on the observation that many heavy-tailed and otherwise non-exponential distributions arise as marginals of minimal exponential families, we prove that such marginals inherit a unique Fisher–Rao information geometry via the quotient-manifold construction. Exploiting this geometry, we derive the Quotient Natural Gradient algorithm, which takes steepest-descent steps in the well-structured covering space, thereby guaranteeing parameterization-invariant optimization in the target space. Empirical results on the Student-$t$ distribution confirm that our method converges more rapidly and attains higher-quality solutions than previous variants of the Bayesian Learning Rule. These findings position quotient geometry as a unifying tool for efficient and principled inference across a broad class of latent-variable models.

Raymond Li, Chuyuan Li, Gabriel Murray, Giuseppe Carenini

Large language models (LLMs) have demonstrated impressive generative capabilities, yet their inner mechanisms remain largely opaque. In this work, we introduce a novel approach to interpret LLMs generation process through the lens of an explicit Bayesian framework by inferring latent topic variables via variational inference. Specifically, we leverage a variational autoencoder-based neural topic model to dynamically approximate the posterior distribution over the high-level latent topic variables at each generation step. By reconstructing the LLM’s next-token predictions through these latent topics and maintaining a regularized latent space, our method yields interpretable and diverse topic representations but also has the ability to effectively captures semantic shifts throughout the text. We validate our approach on multiple datasets, showing that our latent topics outperform state-of-the-art topic models on intrinsic measures of coherence and diversity. Furthermore, we demonstrate the utility of our approach in downstream applications by using the inferred topic distributions to retrieve relevant demonstration examples for in-context learning, resulting in significant gains on classification and summarization tasks.

Iqra Zahid, Youcheng Sun, Riza Batista-Navarro

Authorship Attribution (AA) seeks to identify the author of a given text, yet existing methods often struggle with trustworthiness and interpretability, particularly across different domains, languages, and stylistic variations. These challenges arise from the absence of uncertainty quantification and the inability of current models to adapt to diverse authorship tasks. To address these limitations, we introduce BEDAA, a Bayesian-Enhanced DeBERTa framework that integrates Bayesian reasoning with transformer-based language models to enable uncertainty-aware and interpretable authorship attribution. BEDAA achieves up to 19.69% improvement in F1-score across multiple authorship attribution tasks, including binary, multiclass, and dynamic authorship detection. By incorporating confidence ranking, uncertainty decomposition, and probabilistic reasoning, BEDAA improves robustness while offering transparent decision-making processes. Furthermore, BEDAA extends beyond traditional AA by demonstrating its effectiveness in human vs. machine-generated text classification, code authorship detection, and cross-lingual attribution. These advances establish BEDAA as a generalised, interpretable, and adaptable framework for modern authorship attribution challenges.

Tianyi Alex Qiu, Fanzhi Zeng, Jiaming Ji, Dong Yan, Kaile Wang, Jiayi Zhou, Yang Han, Josef Dai, Xuehai Pan, Yaodong Yang

Existing alignment methods share a common topology of information flow, where reward information is collected from humans, modeled with preference learning, and used to tune language models. However, this shared topology has not been systematically characterized, nor have its alternatives been thoroughly explored, leaving the problems of low data efficiency and unreliable generalization unaddressed. As a solution, we introduce a theory of **reward generalization** in reinforcement learning from human feedback (RLHF), focusing on the **topology of information flow** at both macro and micro levels. At the macro level, we portray the RLHF information flow as an autoencoding process over behavior distributions, formalizing the RLHF objective of distributional consistency between human preference and model behavior. At the micro level, we present *induced Bayesian networks* to model the impact of dataset topologies on reward generalization. Combining analysis on both levels, we propose **reward modeling from tree-structured preference information**. It is shown to reduce reward uncertainty by up to \Theta(\log n/\log\log n) times compared to baselines, where n is the dataset size. Validation on three NLP tasks shows that it achieves an average win rate of 65% against baselines, thus improving reward generalization *for free* via topology design, while *reducing* the amount of data requiring annotation.

Chengkun Cai, Haoliang Liu, Xu Zhao, Zhongyu Jiang, Tianfang Zhang, Zongkai Wu, John Lee, Jenq-Neng Hwang, Lei Li

In the rapidly evolving field of image generation, achieving precise control over generated content and maintaining semantic consistency remain significant limitations, particularly concerning grounding techniques and the necessity for model fine-tuning. To address these challenges, we propose BayesGenie, an off-the-shelf approach that integrates Large Language Models (LLMs) with Bayesian Optimization to facilitate precise and user-friendly image editing. Our method enables users to modify images through natural language descriptions without manual area marking, while preserving the original image’s semantic integrity. Unlike existing techniques that require extensive pre-training or fine-tuning, our approach demonstrates remarkable adaptability across various LLMs through its model-agnostic design. BayesGenie employs an adapted Bayesian optimization strategy to automatically refine the inference process parameters, achieving high-precision image editing with minimal user intervention. Through extensive experiments across diverse scenarios, we demonstrate that our framework outperforms existing methods in both editing accuracy and semantic preservation, as validated using different LLMs including Claude3 and GPT-4.

Wei Li, Lujun Li, Mark G. Lee, Shengjie Sun, Lei Zhang, Wei Xue, Yike Guo

Large language models (LLMs) have revolutionized various domains with their remarkable capabilities, but their massive parameter sizes pose significant challenges for fine-tuning and inference, especially in resource-constrained environments. Conventional compression methods often result in substantial performance degradation within LLMs and struggle to restore model quality during fine-tuning. To address this challenge, we present Bayesian Knowledge Distillation (BayesKD), a novel distillation framework meticulously designed for compact LLMs in resource-constrained fine-tuning scenarios. Departing from conventional LLM distillation methods that introduce time-consuming paradigms and fail to generalize in compressed LLM fine-tuning scenarios, our BayesKD develops the Logits Dual-Scaling, Knowledge Alignment Module, and Bayesian Distillation Optimization. In particular, our Logits Dual-Scaling strategy adaptively aligns the strength of the teacher’s knowledge transfer, while the Knowledge Alignment Module bridges the gap between the teacher and student models by projecting their knowledge representations into a shared interval. Additionally, we employ Logits-Aware Bayesian Optimization to swiftly identify optimal settings based on these strategies, thereby enhancing model performance. Extensive experiments across diverse tasks demonstrate that BayesKD consistently outperforms baseline methods on various state-of-the-art LLMs, including LLaMA, Qwen2, Bloom, and Vicuna. Notably, our BayesKD achieves average accuracy gains of 2.99% and 4.05% over standard KD for the 8B parameter LLaMA and Qwen2 model. Codes are available in the supplementary materials.

Lang Gao, Jiahui Geng, Xiangliang Zhang, Preslav Nakov, Xiuying Chen

Jailbreaking in Large Language Models (LLMs) is a major security concern as it can deceive LLMs into generating harmful text. However, understanding of how jailbreaking works remains limited, hindering the development of effective defense strategies. To address this issue, we conduct a large-scale analysis of seven different jailbreak methods and identify that disagreements among methods stem from insufficient observation samples.We introduce the concept of a safety boundary and discover that jailbreaks shift harmful activations outside this boundary, where LLMs become less sensitive to harmful information. Our analysis reveals that low and middle layers play a critical role in these shifts, while deeper layers have a lesser impact.Building on these insights, we propose a novel defense mechanism called Activation Boundary Defense (ABD), which adaptively constrains activations within the safety boundary. To enhance its effectiveness, we use Bayesian optimization to selectively apply the defense to the low and middle layers.Experiments on several benchmark datasets demonstrate that ABD achieves an average Defense Success Rate (DSR) of over 98% against various jailbreak attacks, with less than a 2% impact on the model’s general capabilities.

Position · Methodology

Sam Bowyer, Laurence Aitchison, Desi Ivanova

Rigorous statistical evaluations of large language models (LLMs), including valid error bars and significance testing, are essential for meaningful and reliable performance assessment. Currently, when such statistical measures are reported, they typically rely on the Central Limit Theorem (CLT). In this position paper, we argue that while CLT-based methods for uncertainty quantification are appropriate when benchmarks consist of thousands of examples, they fail to provide adequate uncertainty estimates for LLM evaluations that rely on smaller, highly specialized benchmarks. In these small-data settings, we demonstrate that CLT-based methods perform very poorly, usually dramatically underestimating uncertainty (i.e. producing error bars that are too small). We give recommendations for alternative frequentist and Bayesian methods that are both easy to implement and more appropriate in these increasingly common scenarios.

Position · Methodology

Hanqi Yan, Linhai Zhang, Jiazheng Li, Zhenyi Shen, Yulan He

Large language models (LLMs) excel in many reasoning tasks but continue to face significant challenges, such as lack of robustness in reasoning, struggling with cross-task generalization, and inefficiencies in scaling up reasoning capabilities. Current training paradigms, including next-token prediction and reinforcement learning from human feedback, often fall short in adaptability to diverse reasoning tasks. Existing approaches, such as prompt optimization and iterative output refinement, offer performance improvement, but can be inefficient and lack effective generalization. To overcome these limitations, this position paper argues for a transformative shift in how LLMs approach reasoning. Drawing inspiration from cognitive science, particularly meta-reasoning theories such as Dual-Process Theory and Metacognitive Reasoning, we propose a Bayesian meta-reasoning framework for LLMs. Our approach integrates self-awareness, monitoring, evaluation, regulation, and meta-reflection, to enhance LLMs' ability to refine reasoning strategies and generalize across tasks. We revisit existing LLM reasoning methods, identify key challenges, and suggest directions for future research.

Probabilistic Methods · Everything Else

Markelle Kelly, Alex Boyd, Samuel Showalter, Mark Steyvers, Padhraic Smyth

Applications of machine learning often involve making predictions based on both model outputs and the opinions of human experts. In this context, we investigate the problem of querying experts for class label predictions, using as few human queries as possible, and leveraging the class probability estimates of pre-trained classifiers. We develop a general Bayesian framework for this problem, modeling expert correlation via a joint latent representation, enabling simulation-based inference about the utility of additional expert queries, as well as inference of posterior distributions over unobserved expert labels. We apply our approach to two real-world medical classification problems, as well as to CIFAR-10H and ImageNet-16H, demonstrating substantial reductions relative to baselines in the cost of querying human experts while maintaining high prediction accuracy.

Social Aspects · Privacy

Yusuke Yamasaki, Kenta Niwa, Daiki Chijiwa, Takumi Fukami, Takayuki Miura

We propose Plausible Token Amplification (PTA) to improve the accuracy of Differentially Private In-Context Learning (DP-ICL) using DP synthetic demonstrations. While Tang et al. empirically improved the accuracy of DP-ICL by limiting vocabulary space during DP synthetic demonstration generation, its theoretical basis remains unexplored. By interpreting ICL as implicit Bayesian inference on a concept underlying demonstrations, we not only provide theoretical evidence supporting Tang et al.'s empirical method but also introduce PTA, a refined method for modifying next-token probability distribution. Through the modification, PTA highlights tokens that distinctly represent the ground-truth concept underlying the original demonstrations. As a result, generated DP synthetic demonstrations guide the Large Language Model to successfully infer the ground-truth concept, which improves the accuracy of DP-ICL. Experimental evaluations on both synthetic and real-world text-classification datasets validated the effectiveness of PTA.