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10 papers in the last four weeks, up 233% on the four weeks before. 0.1% of all new papers.

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Latest papers 76

Sep 30, 2026cs.CL

Bayesian Fine-tuning Yields Language Models that are as Bayesian as their Beliefs Allow

Language models (LMs) are increasingly used for tasks that require reasoning about hidden variables from a few observations, for which Bayesian inference is the normatively correct solution. While supervised fine-tuning of an LM on the outputs of an optimal

\textit{Bayesian}

model leads to near-Bayesian behavior, standard supervised fine-tuning (SFT) on the true answers for the task falls short of it. But behavior alone does not tell us

\textit{why}

tuning on a

\textit{Bayesian}

or an

\textit{oracle}

(true answers) signal differs: whether the resulting LM represents Bayesian beliefs, acts on them, or turns them into a choice the way Bayes' rule does. To compare them, we formulate increasingly demanding requirements for an LM to count as a Bayesian decision maker, spanning its behavior, representations, and computations, and test them on a flight recommendation task. The Bayes-trained LM acts Bayesian, encodes quantities of Bayes' rule in its middle layers, and uses the encoded belief for the recommendation to a certain extent. The oracle-trained LM differs from it both in the beliefs it holds and whether it reads beliefs out into recommendations. Exchanging beliefs between the LMs transfers a part of the Bayesian advantage. Bayes fine-tuning thus installs usable Bayesian beliefs in an LM for reasoning under uncertainty in a way standard SFT on oracle answers cannot, highlighting the advantage of nuanced supervision.

Polina Tsvilodub, Andreas Waldis, Linlu Qiu +2

University of Tübingen · Massachusetts Institute of Technology · New York University

Large Language Model Fine-Tuning Model Fine-Tuning Bayesian Bayesian Inference Journey

Sep 30, 2026stat.ML

BayesNDE: Bayesian Generative Modeling for Neural Density Estimation

Density estimation is a fundamental problem in statistics and machine learning. In this work, we introduce BayesNDE, a neural density estimator based on Bayesian generative modeling. BayesNDE learns a Bayesian generative model and evaluates its density without requiring invertible networks or Jacobian-determinant computation. For each observation, it infers a sample-specific latent posterior to construct an adaptive proposal that focuses computation on regions contributing most to its density. Bridge sampling then combines samples from this proposal with separate posterior samples to estimate the density. Experiments on nonlinear and multimodal synthetic datasets show improved estimation of density values and better recovery of the density structure compared to the state-of-the-art neural density estimators. Applications to real-world datasets further demonstrate improved anomaly detection. Together, these results highlight BayesNDE as a flexible and effective neural density estimator, demonstrating how posterior inference can turn generative models into tools for density estimation. The code and tutorials are available at https://github.com/liuq-lab/BayesNDE.

Chenglin Li, Qiao Liu

Department of Biostatistics, Yale University New Haven, Connecticut, USA

Density Ratio Estimation Bayesian Generative Models

Sep 28, 2026cs.LG

Gaussian Neural Networks

Gaussian neural networks (GaNNs) are proposed as a novel regularization mechanism for neural networks. From a Bayesian perspective standard regularization techniques can be viewed as imposing priors over weight-space. Assuming priors over activation-space remains a largely unexplored possibility. GaNNs assume such priors. They do this by treating activities from earlier layers like signals with Gaussian noise and predicting the properties of the noise distribution using an additional unsupervised loss. While training, the unsupervised loss acts as a penalty on unexpected activities, allowing greater weight updates in less surprising directions. The paper demonstrates the superiority of Gaussian neural networks over standard neural networks on a variety of classification and regression tasks. We also investigate the ability of GaNNs to quantify uncertainty.

Peter Kuhn, Victoria Heusinger-Heß

Fraunhofer Institute for High-Speed Dynamics, Ernst-Mach-Institut, EMI, Germany

Bayesian Neural Networks Neural Network Regularization Bayesian Loss Function

Sep 28, 2026stat.ML

Singularities of Non-negative Matrix Factorization and their application to Bayesian inference

Non-negative matrix factorization (NMF) is a singular statistical model whose Bayesian asymptotics are governed by the real log canonical threshold (RLCT). We study the local geometry of the factorization map and derive an upper bound for the RLCT of NMF. Let

H

be the model inner dimension and

H_0

the non-negative rank of the true

M\times N

matrix. Assuming that the true matrix admits a strictly positive factorization of inner dimension

H_0

in the interior of the parameter domain, we prove, for smooth positive priors, that

λ\leq \{(H-H_0)\min(M,N)+H_0(M+N-H_0)\}/2

. This bound strictly improves the previous bound when

H_0\geq3

. The proof uses a local analytic normal form that separates independent linear coordinates from a residual matrix product. When

H=H_0

also equals the ordinary rank of the true matrix, we obtain the exact value

λ=H_0(M+N-H_0)/2

. Under the standard assumptions of singular learning theory, these results bound the leading coefficients of the expected Bayesian generalization error and the Bayesian free energy.

Naoki Hayashi, Yota Maeda, Yasushi Esaki

Toyota Central R&D Labs., Inc.

Nonnegative Matrix Factorization Spectral Norm Bayesian Inference Bayesian Singularity Matrix Multiplication+1

Sep 27, 2026cs.LG

ICMAPE: In-Context Multiagent Pure Exploration

In some multi-agent systems, the quantity to be optimized is not an externally specified reward but the information acquired about unknown properties of the environment as done in active sequential hypothesis testing (ASHT) problems. However, the ASHT literature tends to focus on finite single-agent problems with well-specified models, while there is currently a gap for practical multi-agent methods that can perform active sequential testing. We fill this gap with ICMAPE, a Bayesian learning-based framework for decentralized multi-agent pure-exploration driven by inference objectives. ICMAPE converts the fixed-confidence identification objective into a reward derived from inference confidence, so that standard reinforcement learning machinery can be applied to decentralized pure exploration. It jointly learns a centralized neural inference network that estimates a posterior distribution over hypotheses from global trajectory data, and decentralized policies that select actions from local observation histories and learn when to stop collecting data once the target confidence is reached. On two synthetic benchmarks and a Maryland nitrate concentration monitoring task based on real-world data, ICMAPE-TD3 achieves target accuracy with fewer exploration steps.

Xinyi Hu, Alessio Russo, Aldo Pacchiano

Boston University · Broad Institute of MIT and Harvard

Multi-Agent Planning Stochastic Exploration Exploration Two-Sample Testing Bayesian

Sep 27, 2026cs.LG

Future Information-Directed Sampling for Bayesian Nonstationary Bandits

Exploration--exploitation is a central trade-off in bandit learning. While classical algorithms such as upper confidence bound methods and Thompson Sampling effectively balance this trade-off in stationary environments, their exploration strategies mainly reduce uncertainty about the current optimal arm, which can be insufficient in nonstationary settings where future optimal arms may differ substantially from current ones. In this paper, we propose Future Information-Directed Sampling (FIDS), a new algorithm for Bayesian nonstationary bandits that explicitly explores to gather information about future optimal arms. We show that FIDS achieves regret comparable to Thompson Sampling up to a small constant factor, while being able to exploit predictive information structures that conventional exploration objectives fail to capture. To address the practical difficulty of posterior inference, we further propose a supervised-learning-based approximation framework that learns the FIDS policy from offline data, and demonstrate its effectiveness on synthetic benchmarks.

Yichen Song, Alessio Russo, Aldo Pacchiano

Boston University · Broad Institute of MIT and Harvard

Bandits Stochastic Exploration Bayesian Exploration

Sep 27, 2026stat.ME

ViBR-WM: Visual Bayesian Regression for World Modeling

Modeling temporal dependence and uncertainty is central to forecasting with world models. The Visual Bayesian Regression World Model combines visual features, physical histories and known covariates through interpretable regression, within a modular architecture supporting trend, seasonal and cycle dynamics. Visual compression reduces representation dimension, while Bayesian variable selection reduces active regression dimension. Posterior prediction combines forecasts across predictor subsets using their posterior probabilities as weights and accounts for parameter uncertainty and future disturbances. The model forecasts joint visual--physical states recursively and physical targets directly. Across four forecasting tasks spanning object motion, vegetation greenness and solar power, ViBR-WM achieves lower mean overall physical-target error than Temporal Straightening, ConvLSTM, PredRNN and SimVP on every task. Repeated fitting and resampling support these overall gains.

Jifan Li, Ning Ning

Department of Statistics, Texas A&M University College Station, TX 77843

World Models Future Video Prediction Posterior Predictive Distribution Temporal Dependence Bayesian Bayesian Networks+1

Sep 27, 2026stat.ML

A Statistical Perspective on Knowledge Distillation: Foundations, Classical Methods, and Large Language Model Extensions

Knowledge Distillation (KD) has emerged as a vital paradigm for transferring the capabilities of high-capacity models to efficient ``student'' counterparts, addressing critical challenges in computational cost, deployment constraints, and privacy-sensitive settings. Although KD is widely used in practice, it is often viewed primarily as an engineering technique, with a unified statistical perspective remaining less developed. This review bridges that gap by presenting a unified Bayesian formulation of KD that formulates teacher predictions as prior information. This provides a principled interpretation of how teacher information is incorporated into student learning and establishes a rigorous connection to uncertainty quantification. We demonstrate how this foundational lens reconciles classical distillation with modern extensions in generative and foundation-model systems, showing that contemporary developments remain rooted in these same statistical principles. By synthesizing theory with emerging methodologies and diverse applications, this review provides a conceptual roadmap and identifies critical open problems for the future of the field.

Luyang Fang, Haoran Lu, Jiazhang Cai +4

Department of Statistics, University of Georgia, Athens, Georgia 30602, USA · Department of Biostatistics, Boston University, Boston, Massachusetts 02118, USA

Knowledge Distillation Residual Distillation Teacher Statistical Inference Bayesian

Sep 17, 2026cs.LG

Expected Hypervolume Maximization for Multiobjective Optimization under Uncertainties

The problem of multiobjective optimization under uncertainties is often approached by taking the expectation of each objective. In this work, we propose instead to formulate this as a Bayesian decision problem and to rely on the expected value of the hypervolume, which is to be maximized with respect to a finite set of input points. We show that this can be performed using methods based on gradients in a stochastic optimization framework, provided that care is taken with respect to dominated points. Moreover, in the absence of readily available differentiable code, we propose to use Gaussian Processes as differentiable surrogate models, in order to perform the optimization. An additional contribution in this work are some active learning strategies, through acquisition functions which helps construct a surrogate model well-designed for the multiobjective optimization problem at stake. These strategies are compared on simple analytical problems to assess their performances.

Victor Trappler

Mines Saint-Étienne MSE, LIMOS, FAYOL-ENSMSE, FAYOL-ENSMSE · Departement GMI Institut Henri Fayol, Mines Saint-Etienne, Univ Clermont Auvergne, CNRS, UMR 6158 LIMOS F - 42023 Saint-Etienne France

Multi-Objective Optimization Stochastic Optimization Bayesian Uncertainty

Sep 14, 2026stat.AP

Nationally Consistent, Locally Incomplete: A Bayesian Remote-Sensing Audit of Rooftop Photovoltaic Registries

Tracking the energy transition requires reliable statistics on renewable deployment. Rooftop photovoltaics (PV) are especially hard to track, owing to their decentralised nature, and the resulting inaccuracies in official statistics are known but not quantified. Remote sensing offers an independent way to identify rooftop PV systems. We introduce a Bayesian framework to estimate the ground-truth rooftop PV capacity from remote sensing detections, turning an imperfect detector into an uncertainty-aware measurement instrument. Applied to France, the corrected detections estimate a capacity of 4.03 GWp [3.96--4.11] (99% credible interval) of rooftop PV below 36 kWp, matching the transmission system operator's connection data within 3.3% nationally, while identifying local under-reports of up to 61% of local capacity. We also document and quantify a significant truncation bias in French rooftop PV open data. Beyond France, the approach paves the way for more reliable estimates of rooftop PV capacity worldwide.

Gabriel Kasmi, Yves-Marie Saint-Drenan, Laurent Dubus +1

Centre Observation Impacts Energie (O.I.E.), MINES Paris, Universit´e PSL, Sophia-Antipolis, France · R´eseau de Transport d’Electricit´e (RTE), Paris La D´efense, France · Lead contact +1

Photovoltaic Remote Sensing Bayesian Incomplete Model Auditing

Sep 9, 2026stat.ML

A Unifying Perspective on Probabilities as Model Predictions

Although probabilistic statements are ubiquitous, foundational disagreements persist about their understanding, as exemplified by debates between Bayesians and frequentists; moreover, it is unclear when and why acting on them actually leads to desirable outcomes. Here, we argue that every probability is the output of a \emph{prediction method}, that is, it depends on both a particular way of constructing abstractions and a way of transforming them into predictions. Through this, we provide a unifying perspective on supposedly different kinds of probabilities and show that even supposedly objective ones are model-dependent. We demonstrate that when a finite calibration criterion is met, one can anticipate the distribution of utilities for a given policy and inform successful decision-making on finite sets of events. Based on the notion of prediction methods, inductive arguments, and the probability calculus, we explain the feasibility of the calibration criterion in many settings. Overall, we develop a coherent perspective on probabilities and their use, connecting key intuitions behind other interpretations along the way.

Benedikt Höltgen

Hasso Plattner Institute, University of Potsdam

Probability Bayesian Decisions Perspective

Sep 7, 2026stat.ME

Bayesian Matrix-Valued Graphs for Context-Dependent Multivariate Relationships

Many scientific graphs attach several variables to each node, so a single scalar edge weight cannot describe direction-dependent interactions. We model each edge by a symmetric positive-definite (SPD) matrix and infer a posterior over matrix-valued graph geometries, which we call the Bayesian matrix-valued graph (BMVG). We ask how these interactions reconfigure across contexts: how large the change is and which multivariate directions strengthen or weaken. The geodesic distance induced by the affine-invariant Riemannian metric (AIRM) quantifies deformation magnitude and generalized eigenvalues resolve its signed directions.Against fused graphical lasso, Bayesian multiple-GGM, and common principal components, BMVG is competitive on global precision recovery while retaining identifiable matrix-valued edge structure and accurately recovering edge-level deformation directions. In controlled known-truth experiments, it resolves structural change with increasing sample size, including orientation changes that leave ordinary eigenvalues unchanged. In one year of Bay Area weather data, the geometry of 12-hour change reconfigures spatial coupling about as much as whole seasons differ. In TCGA-BRCA, estrogen-receptor (ER)-associated reconfiguration concentrates on specific gene-module pairs and persists under graph-scaffold sparsification and removal of subgroup mean differences. These results establish posterior matrix-valued edge geometry as a unified framework for quantifying and interpreting context-dependent multivariate reconfiguration.

Papri Dey

Probabilistic Graphical Models Bayesian Principal Component Analysis Deformable Cnn

Sep 3, 2026math.NA

Learning Informative Prior with Infinite-Dimensional Continuous Normalizing Flow for Bayesian Inverse Problem

This paper addresses infinite-dimensional Bayesian inference for inverse problem of partial differential equations with model parameters in infinite-dimensional Hilbert space. To effectively incorporate prior information, we propose a novel continuous normalizing flows based infinite-dimensional model. Specifically, by introducing a well-defined neural ordinary differential equation in infinite-dimensional space, a simple reference measure can be transformed into a more complex measure which encodes the prior information. A corresponding theoretical framework is established to ensure the well-posedness of our proposed Bayesian prior in infinite-dimensional space. We also provide training methods of the prior for two distinct data settings, along with two sampling algorithms for the resulting Bayesian posterior. The proposed framework is applied to three representative inverse problems: the simple smooth inverse problem, inverse scattering problem, and the inverse heat conduction problem. Numerical experiments support the theoretical analysis and demonstrate the efficiency of the proposed algorithms.

Yang Zhao, Junxiong Jia, Tao Zhou

School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China · Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, 100190, China

Bayesian Inverse Problems Normalizing Flows Bayesian Inference Bayesian Diffusion Priors Inverse Design+2

Sep 1, 2026cs.AI

Consistency Without Alignment: Item-Sensitive Language Models Indistinguishable From Random

Item-sensitivity, defined as whether a model's choice depends on the specific input rather than on its own output prior, is widely reported as evidence of task competence. We show this evidence is necessary but not sufficient using a forced-choice signalling task abstracted from the board game Deception: Murder in Hong Kong. In this environment, the reference points against which a coordinate should be judged (a fit-maximising strategy, a posterior-maximising strategy, and uniform random selection) are all computable in closed form. Across seven language models, two model families, a post-training ablation, and three independent scoring rules, every one of 21 model-by-rule cells is reliably item-sensitive. Yet 8 of those 21 cells are not statistically distinguishable from a chooser that ignores the item and selects at random, and 5 score worse than random at describing the target. Item-sensitivity and distance from random correlate at only r = 0.30. We call this consistency without alignment and argue it generalises to any evaluation that relies on item-sensitivity, permutation consistency, or self-consistency without an independent reference for the measured quantity. We further find that a literal-similarity baseline with no pragmatics outperforms most tested language models, that adding a pragmatic layer over two baseline similarity sources moves choosers toward random rather than toward the Bayesian reference, and that a standard labelled multiple-choice format carries no measurable content signal here. All results represent the model side of a pre-registered instrument; a matched human condition is designed and piloted but not yet collected.

Cris Huynh

Independent researcher

Large Language Model Alignment Item Response Theory Language Modeling Deception Virtual Cell Bayesian

Aug 25, 2026cs.LG

Enhancing Bayesian Optimization and Active Learning Through Kernel Diversity

Hyperparameter selection remains a key challenge in Bayesian optimization (BO) and Bayesian active learning (AL), as model misspecification can lead to suboptimal performance, while more accurate fully Bayesian treatments typically rely on computationally expensive MCMC sampling. This paper proposes a unified framework, KENDO (Kernel ENsemble Disagreement-aware Operator), that integrates Ensemble Gaussian Processes (EGP) with disagreement-aware acquisition strategies. The central idea is to replace hyperparameter sampling with a kernel ensemble and adaptive Bayesian weighting, combined with disagreement-aware acquisition strategies. Within this unified framework, we instantiate KENDO-BO for BO and KENDO-AL for Bayesian AL, demonstrating that both arise from a common self-correcting mechanism with task-specific acquisition objectives. We further extend the approach to multi-objective optimization via random scalarization that preserves the single-optimizer conditioning structure. Thorough numerical tests on synthetic and real-world benchmarks across single-objective optimization, multi-objective optimization, and active learning demonstrate that (i) KENDO-BO achieves competitive or superior optimization performance compared to state-of-the-art methods while reducing computational overhead by up to

5\times

and (ii) KENDO-AL achieves superior predictive calibration over MCMC-based active learning baselines with up to

27\times

speedup.

Heng Zhang, Haotian Xiang, Konstantinos D. Polyzos +2

University of Georgia, Athens, GA, USA · University of California San Diego, La Jolla, CA, USA

Bayesian Optimization Active Learning Kernel Method Bayesian Diversity Disagreement

Aug 6, 2026cs.CV

Bayesian adaptively-weighted ensembles for few-shot abdominal segmentation

Few-shot learning has emerged as a promising approach for anatomical segmentation when labelled data are scarce. However, different few-shot learning algorithms exhibit complementary strengths and weaknesses, with performance varying across anatomical targets and institutions. Existing few-shot segmentation ensembles, that combine predictions from multiple algorithms, typically employ fixed weighting schemes and therefore cannot adjust model contributions according to the target domain. In this work, we propose a Bayesian adaptively-weighted ensemble framework for segmentation under label scarcity and domain shift. Multiple few-shot segmentation algorithms are first adapted using a small labelled support set. Bayesian optimisation is then used to automatically identify ensemble weights that maximise segmentation performance on a target-domain validation set. The learned weights are subsequently fixed and applied to combine predictions on previously unseen query images from the target domain. The proposed framework is evaluated on the Cross-institution Male Pelvic Structures dataset using held-out anatomical structures and institutions to simulate simultaneous label scarcity and institutional domain shift. Results demonstrate statistically significant improvements over individual few-shot learners, fixed-weight ensembles, training-from-scratch baselines and recent state-of-the-art ensembling approaches. By adapting model contributions to the target anatomy and institutional domain, the proposed framework provides a practical mechanism for deploying segmentation systems to new clinical sites under severe annotation constraints.

Abbas Al-Sabbagh, Shalom F. Mushtaq, Tomás M. da Silva +7

Centre for Bioengineering, School of Engineering and Materials Science, Queen Mary University of London, London, United Kingdom · Digital Environment Research Institute, Queen Mary University of London, London, United Kingdom · Institute of Biomedical Engineering, Department of Engineering Science, University of Oxford, Oxford, United Kingdom +1

Few-Shot Segmentation Semi-Supervised Medical Image Segmentation Few-Shot Learning Ensemble Target Domain Bayesian

Aug 3, 2026stat.ML

Private Generative Bootstrap via Blocking

With AI systems gaining more access to individuals' information, it is important to protect privacy when reporting statistical answers. Equally important is to privatize the reporting of uncertainty in such answers. To this end, we adopt a Bayesian likelihood-free framework and make simulation from the posterior private. In particular, we propose a new private instantiation of the Bayesian bootstrap using a blocking strategy. Rather than assigning idiosyncratic random weights to each individual, we randomly group individuals and assign a single weight to each group. By concealing individuals' contributions within a group, we fortify differential privacy gates. We harness amortized inference that decouples private learning from posterior sampling. A push-forward map from observation weights to posterior samples is learned privately by adding calibrated noise during training. Subsequent posterior draws require no additional privacy and computation budget. We call the resulting method the Private Generative Bayesian Bootstrap (PGBB). We establish a differential privacy guarantee, analyze convergence to the non-private blocked-bootstrap target, and quantify the discrepancy between the ordinary and blocked Bayesian-bootstrap posteriors. In addition, we derive data-free tuning of the block Dirichlet concentration parameter that restores posterior dispersion asymptotically. We also show a single fit of PGBB can support a family of loss-based decision rules simultaneously without additional privacy cost. In simulations and in applications to U.S. Census returns to schooling and U.S. natality birthweight quantiles, PGBB gives competitive private uncertainty quantification and improves over private Bayesian alternatives that require a specified data-generating model in common settings.

Jinwon Sohn, Veronika Ročková

Booth School of Business, University of Chicago

Model-Based Bootstrap Bayesian Posterior

Aug 1, 2026cs.AI

The Bayesian Reflex: A Predictive Coding Engine for Artificial Intelligence

Predictive coding offers a powerful theory of cortical computation, but corresponding scalable algorithmic implementations for artificial intelligence have remained elusive. This paper introduces the Bayesian reflex, a computational framework that directly instantiates predictive coding through three pillars: belief maintenance via hierarchical generative models, sequential Bayesian updating via prediction-error minimization, and uncertainty-driven action via active inference. We show that recent breakthroughs---ellipsoidal decomposition for exact

i.i.d.

sampling, recursive Gaussian processes for deep hierarchical inference, and derivative-aware Bayesian optimization---provide the missing algorithmic ingredients. The resulting framework enables mathematically principled, scalable, and brain-inspired continual learning, perception, and decision-making. We illustrate its versatility through applications ranging from climate model evaluation to prime number discovery, offering a blueprint for truly adaptive artificial intelligence.

Sourabh Bhattacharya

Interdisciplinary Statistical Research Unit Indian Statistical Institute, Kolkata

Predictive Coding Bayesian Neural Networks Brain-Inspired Synergistic Framework Probabilistic Inference Bayesian Human Visual Cortex

Jul 31, 2026cs.AI

A Generalized-Bayes Perspective on Counterfactual Explanations: Posterior-Based Decision-Making and Evaluation

Counterfactual explanations (CEs) enhance the interpretability of machine learning models by identifying the smallest change to an input required to obtain a desired output. Although CEs are conventionally formulated as a distance-minimization problem, the theoretical basis of this formulation has received limited attention. We show that a distance-minimization-based CE is mathematically equivalent to the maximum a posteriori (MAP) estimate of a Gibbs posterior within the generalized Bayes framework, specifically when a distance-based prior is used. We call this formulation the Distance-Prior Generalized Bayes CE (DP-GBCE). Building on this posterior perspective, we introduce two decision rules beyond MAP within a unified framework: a Bayes decision that minimizes expected decision loss and CVaR-CE, a risk-averse decision rule. We also propose an extension that uses Bayesian model weights to mix the posterior distributions of multiple models, thereby accounting for model multiplicity, where several models have comparable predictive performance. Finally, we define metrics for evaluating both individual CEs and the posterior distribution as a whole, and use experiments on simulated data and Google Trends data to quantify the trade-offs among the decision rules.

Keita Kinjo

Faculty of Business, Kyoritsu Women’s University

Counterfactual Explanation Bayesian Decisions Perspective

Jul 30, 2026physics.med-ph

Three-Photon Bayesian Imaging of Ortho-Positronium

PET provides functional images relying on two-photon coincidences from positron-electron annihilation. In human tissue, about 40% of annihilations are preceded by Ps formation, of which o-Ps component partially decays into three photons, with the remainder annihilating via pick-off or spin-exchange into two photons. This three-photon channel carries additional information about the surrounding micro-environment, including the three-to-two-photon yield ratio as a potential diagnostic marker. We propose the TRIO algorithm, a novel three-photon event-by-event image reconstruction algorithm formulated as a Bayesian maximum a posteriori inference problem. TRIO unifies time-based trilateration, energy-based reconstruction and, for the first time, a physics-informed prior derived from the QED description of Ps decay within a single probabilistic framework. In contrast to positronium lifetime imaging, which requires a prompt photon and is therefore restricted to specific radionuclides, TRIO relies solely on the three photons and is fully compatible with standard radionuclides such as 18F. Monte Carlo simulation modelled after the Siemens Biograph Quadra scanner demonstrates a mean position error of 1.62~cm, improving by approximately a factor of two over the time-based trilateration (3.05 cm) and by about an order of magnitude over energy-based reconstruction alone (18 cm). More importantly, the proposed Bayesian approach is compatible with existing TOF-PET scanners that can register three-photon annihilation coincidences.

L. Raczynski, W. Krzemien, A. Coussat +5

National Centre for Nuclear Research, Department of Complex Systems, 05-400 Otwock, Poland · National Centre for Nuclear Research, Department of High Energy Physics, 05-400 Otwock, Poland · INSA-Lyon, Université Claude Bernard Lyon 1, CNRS, Inserm, CREATIS UMR 5220, U1294, F-69373, Lyon, France +1

Single-Photon Avalanche Diode Positron Emission Tomography Bayesian

Jul 30, 2026stat.ML

Robust Wavelength Selection for Partial Least Squares Sugar Content Estimation Using Combinatorial Bayesian Optimization

Wavelength selection is one of the important preprocessing methods in near-infrared spectroscopy to improve prediction accuracy and interpretability of spectral data. We formulate wavelength-region selection for sugar content estimation as a binary black-box optimization problem and propose a method based on Bayesian optimization. The proposed method constructs a sparse quadratic surrogate model and sequentially extracts interested wavelength regions by Thompson sampling. Minimizing an acquisition function is performed as a quadratic unconstrained binary optimization problem by simulated or quantum annealing. Experiments show that the proposed method improves the prediction accuracy of partial least squares regression and yields more consistent wavelength regions than genetic-algorithm-based selection and simulated annealing. Under one-bit local perturbations, the selected wavelength regions show minimal fluctuations in root mean square errors between observed and predicted values of a validation set. This local stability suggests that our method converges to a smoother error landscape and avoids isolated overfitted solutions. These results indicate that combinatorial Bayesian optimization is a useful framework for robust feature selection in spectroscopic prediction tasks.

Mitsunobu Kanebako, Ami S. Koshikawa, Masaru Hitomi +4

Graduate School of Information Sciences, Tohoku University, Miyagi 980-8564, Japan · DIC Corporation, Tokyo 103-8233, Japan · Department of Physics, Institute of Science Tokyo, Tokyo 152-8551, Japan +2

Least Squares Laser-Induced Breakdown Spectroscopy Bayesian Optimization Infrared Bayesian

Jul 27, 2026cs.CV

ELECTRIC: Evidential Learning-Enhanced CT Reconstruction via Iterative Correction

Here we introduce ELECTRIC (Evidential Learning-Enhanced CT Reconstruction via Iterative Correction), a physics-guided Bayesian formulation. An evidential neural network provides an image proposal and an error-predictive epistemic-uncertainty surrogate. The latter is converted into an adaptive precision field and inserted into a Poisson-weighted MAP update. The resulting image-evidence-precision-reconstruction loop treats prior confidence as a learned state variable of iterative reconstruction. In addition to the formulation and theoretical analysis, we report two simulation studies on image slices from the AAPM Mayo Clinic Low-Dose CT dataset: a mechanism-validation pilot using transparent surrogate estimators, and a feasibility study in which a trained Normal-Inverse-Gamma evidential network drives the full closed loop. On held-out patients, the learned prior mean reduces reconstruction error by roughly 70 percent relative to filtered back-projection, the learned epistemic uncertainty is error-predictive and supports selective trust, and the physics-guided update restores measurement consistency while the adaptive-precision reconstruction matches or exceeds a validation-tuned fixed prior and remains markedly more robust to prior-strength misspecification. Together these results demonstrate the complete ELECTRIC closed-loop pipeline, while identifying formal uncertainty calibration and joint training as the principal directions for future work.

Ge Wang

Department of Biomedical Engineering Department of Electrical, Computer and Systems Engineering Department of Computer Science Rensselaer Polytechnic Institute, Troy, New York, USA

Image Reconstruction Evidential Uncertainty Cone-Beam Computed Tomography Bayesian

Jul 25, 2026cs.CV

Inverse Bayesian Inference for Extracting Lesion Dynamics from Longitudinal Spectral CT

Longitudinal medical imaging captures temporal evolution of lesions, yet extracting the underlying dynamical parameters governing this evolution remains challenging. We propose an inverse Bayesian framework for inferring lesion dynamics from longitudinal spectral CT. We decompose spectral feature (

x

) evolution into three components: \begin{equation*} \frac{dx_i}{dt} = A_i x_i + B \cdot n + C \cdot Δx_{\text{sat}} \end{equation*} where

A_i

captures intrinsic dynamics (lesion-autonomous evolution),

B

captures local environment tumour burden (organ tumour burden through satellite count coupling), and

C

captures environment/satellite state change (i.e., whether surrounding lesions move similarly or not). We demonstrate the framework on photon-counting NSCLC CT data from metastases, recovering distinct dynamical regimes: lung lesions exhibit significant satellite count coupling (

B=-0.34

,

p<0.05

) suggesting competitive dynamics, while liver lesions show synergistic satellite behaviour coupling (

C\approx+1.0

,

p<0.05

). Synthetic validation confirms parameter recovery, and cross-coupling analysis validates that our method detects non-zero coupling when present. This work establishes inverse dynamical inference as a principled methodology for extracting interpretable parameters from longitudinal imaging, moving beyond static feature extraction toward mechanistic characterisation of lesion behaviour. The code and data are available at: https://github.com/lukasf98/inverse-bayesian-inference

Lukas Förner, Melina Wördehoff, Julian Steffens +6

Dept. of diagnostic and interventional Radiology and Neuroradiology, University Hospital Augsburg, Germany · Digital Medicine, University Hospital Augsburg, Germany · Chair for Computer-Aided Medical Procedures and Augmented Reality, Technical University of Munich, Germany +5

Cone-Beam Computed Tomography Bayesian Inference Bayesian Multiple Satellite Systems

Jul 25, 2026cs.LG

Bayesian Complete-Pooling in Cross-Subject Classification for Motor Imagery Electroencephalogram

Brain-computer interfaces (BCIs) have long sought calibration-free operation, but classifiers are typically benchmarked by discrimination alone, blind to whether predicted probabilities are well calibrated - a meaningful gap given nonstationary electroencephalogram (EEG) signals and the risk of overconfident point-estimate classifiers under distribution shift. We conducted a large-scale study contrasting Bayesian complete-pooling models against frequentist baselines for cross-subject, left-hand versus right-hand motor imagery EEG classification across 20 datasets. Six frequentist pipelines were each paired with an analogous Bayesian pipeline sharing identical feature engineering, fit via Markov chain Monte Carlo posterior sampling. Our primary metric was the Brier score, decomposed into reliability and resolution, alongside AUROC for discrimination and Shannon entropy for sharpness. Each metric was analyzed via random-effects meta-analysis (REML, Knapp-Hartung adjustment), verified by leave-one-out influence analysis. Bayesian complete-pooling produced statistically but not practically significant improvements in reliability and increases in predictive uncertainty (lower sharpness); Brier score, resolution, and discrimination showed no significant differences. Between-study heterogeneity was low across all metrics, though the reliability result was sensitive to leave-one-out removal. We additionally profiled computational cost, finding that Bayesian pipelines consumed roughly thirteen times more energy than their frequentist counterparts, a cost that remains modest relative to common household appliances. These results suggest that Bayesian complete-pooling alone offers limited practical benefit for cross-subject motor imagery classification, and that partial-pooling across subjects and sessions is a more promising direction for future work.

Ethan Davis

University of Washington, USA

Brain-Computer Interface Electroencephalography Bayesian Generalized Linear Model

Jul 23, 2026physics.optics

Reliability-Aware Bayesian Optimization of 1310 nm PCSELs with FDTD Verification

Near 1310 nm photonic-crystal surface-emitting lasers (PCSELs) are attractive narrow-beam sources for optical communication and sensing, but their final design refinement is costly. Small geometry changes simultaneously shift the band-edge resonance, cavity leakage, far-field divergence, and the numerical stability of a high-

Q

decay fit, while every full-wave trial requires a time-domain simulation. We couple a commercial finite-difference time-domain solver to a reliability-aware Bayesian optimization (BO) loop over eight local design variables. Each completed simulation updates the surrogate used to choose the next geometry. Candidate ranking combines wavelength and beam-quality requirements with a reliability-adjusted metric

Q_{\mathrm{eff}}

derived from the solver-reported relative fit-error estimate

dQ/Q

. Across three 80-evaluation runs from the same reference model, BO produced 5--15 candidates per run that passed the joint filter. Designs reconstructed from fresh model copies retained

Q_{\mathrm{eff}}=4.33\times10^6

--

7.76\times10^6

, a 60--108-fold increase over the baseline metric, at 1308.23--1310.90~nm with approximately

0.84^{\circ}

divergence. Under equal budgets, BO gave the highest mean strict-filter yield (9.0 candidates), compared with differential evolution (7.0) and Latin-hypercube sampling (1.5), although the controls occasionally matched the peak

Q_{\mathrm{eff}}

. Field maps, resonance spectra, and local perturbations further identify an index-related wavelength handle and a hole-size-related leakage handle. The resulting FDTD budget produces a pool of wavelength-compatible, narrow-beam, and reproducible high-

Q

PCSEL candidates without trusting a single optimistic decay fit.

Jinglin Yu, Feiyang Wu, Longying Wen +3

School of Science and Engineering (SSE), The Chinese University of Hong Kong, Shenzhen, Shenzhen 518172, China · Nick Holonyak Micro and Nanotechnology Laboratory, University of Illinois Urbana-Champaign, Urbana, IL 61801 USA

Nanophotonic Bayesian Optimization Bayesian

Jul 23, 2026cs.LG

An Introduction to Bayesian and Frequentist Simulation-Based Inference with Machine Learning

Simulation-based inference (SBI) with machine learning is an increasingly important tool for solving inverse problems in science and engineering, including parameter inference and the inversion of detector effects. We provide an overview of the Bayesian and frequentist statistical frameworks, describe how machine-learning-based SBI methods, such as neural posterior estimation and neural likelihood estimation, can be used for parameter estimation within these frameworks, and show that the same methods can also be applied to Empirical Bayes or unfolding tasks. We also discuss how to validate inference results and the limitations of SBI with machine learning.

Maximilian Dax, Theo Heimel, Gilles Louppe

ELLIS Institute Tübingen, Max Planck Institute for Intelligent Systems, Tübingen AI Center, Tübingen, Germany · CP3, Université catholique de Louvain, Louvain-la-Neuve, Belgium · Montefiore Institute, University of Liège, Belgium

Bayesian Inference Bayesian Statistical Inference Inverse Problem

Jul 22, 2026stat.ML

Adaptive Bayesian Online Learning via Expert Aggregation

Bayesian online learning promises uncertainty-aware prediction on data streams, but its performance hinges on inferential choices, including learning rates, prior distributions and variational families, which are usually fixed before seeing the stream. We address this by treating Bayesian update rules as experts and aggregating the Bayesian experts according to sequential predictive losses. We prove that the resulting aggregate competes with the best expert in hindsight at an aggregation cost determined by how each expert's per-round performance is evaluated. We instantiate the framework in online conformal inference and Gaussian process regression. The conformal inference application yields a smoothed Bayesian counterpart of adaptive conformal inference with long-run randomized coverage, while the Gaussian process application gives an oracle inequality in cumulative predictive Kullback-Leibler risk and adaptation to unknown Hölder smoothness up to logarithmic factors. Experiments show that the aggregate tracks strong experts without oracle expert selection.

Jungbin Jun, Ilsang Ohn

Department of Statistics Inha University Incheon, 22212, South Korea

Learning-Augmented Algorithms Bayesian Conformal Inference Gaussian Process Experts

Jul 10, 2026cs.LG

Pitfalls and Remedies for Multi-Task Bayesian Optimization

Bayesian optimization routinely warm-starts a target experiment with data from related source tasks, and the multi-task Gaussian process is the textbook surrogate for the job. We revisit this default in a controlled setting and find that it misestimates the cross-task correlation even in the simplest non-trivial case, affinely related source and target tasks, where a working transfer learning method should obviously succeed. We trace the failure to two independent structural mechanisms. Per-task standardization, the textbook fix for the affine slice ambiguity, propagates a finite-sample alignment error into the recovered correlation. The marginal likelihood itself identifies the correlation only at a per-sample rate that a Gaussian process at non-overlapping designs further dilutes. We propose three conservative remedies that follow from the analysis: promoting per-task means and scales to model parameters, restricting the task covariance to non-negative correlations, and co-locating part of the source and target designs. Across synthetic multi-task problems and surrogate-based hyperparameter tuning transfer, these remedies recover the target-only baseline on the simple instances, while the broader failure persists on harder instances and across most rank-based and latent-context variants.

Carl Hvarfner, Sam Daulton, Max Balandat +1

Meta

Bayesian Optimization Gaussian Process Bayesian Cross-Task Interference Remediation

Jul 5, 2026cs.LG

How Many Initial Points Does Bayesian Optimization Need?

Bayesian Optimization (BO) generally begins with an initialization phase: a batch of

n_0

uninformed evaluations. The choice of

n_0

remains largely heuristic, and we empirically observe that the total cost (random initial points plus BO iterations needed to find the global optimum) is U-shaped in

n_0

, i.e., a practitioner wastes resources by selecting either too low or too high a value of

n_0

. We find this tradeoff persists across MLE, Bayesian MCMC, and exact GP hyperparameters, as well as across acquisition functions. Toward the latter, Thompson Sampling appears an exception, with both total cost and simple regret essentially

n_0

-agnostic, though higher in our experiments. We attribute this U-shape to the known boundary issue of variance-driven BO: BO burns early budget on corners of the hypercube before turning inward. We demonstrate this effect using a 3D BO trajectory where the exact hyperparameters are known. We conclude with practical recommendations: use multi-step lookahead BO where possible; otherwise use Thompson Sampling when

n_0

cannot be tuned, and a generously large

n_0

when it can.

Mujin Cheon, James Odgers, Dong-Yeun Koh +1

Korea Advanced Institute of Science & Technology (KAIST) · HayanMind Inc. · Technical University of Nuremberg (UTN) +3

Bayesian Optimization Thompson Sampling Bayesian Gaussian Process Shaping

Jun 30, 2026cs.LG

A Bayesian Filtering Approach for Learning Lagrangian Dynamics from Noisy Measurements

This paper proposes a Bayesian filtering-based approach for learning the dynamics of a physical system from partial, noisy measurements. We model the system dynamics using a Lagrangian mechanics formulation. As in Lagrangian neural networks (LNNs), we parameterize the kinetic and potential energies with neural networks. The unknown external forces in the Lagrangian formulation are modeled as white Gaussian noise. The corresponding Euler--Lagrange equations then yield a continuous-time stochastic state-space model (SSM) that describes the system dynamics. The neural network parameters and system states are then jointly learned via a maximum-likelihood method using Gaussian-approximation-based Bayesian filters. The effectiveness of the proposed method is demonstrated on pendulum and Duffing oscillator examples, and its performance is compared with conventional LNNs and with approximate Bayesian filters using known system models.

Kundan Kumar, Shreya Das, Simo Särkkä

Bayesian Filtering Lagrangian Methods Latent Dynamics Bayesian State Space Models Oscillatory Dynamics+2

Jun 29, 2026cs.LG

Transformer Architectures as Complete Bayes Processes: A Formal Proof in the Measure-Theoretic Kernel Framework

We present a complete formal proof that transformer architectures, when their internal update mechanisms satisfy a Bayes joint-distribution condition, implement exact Bayesian posterior inference. Working within the measure-theoretic kernel framework, we define a hierarchy of abstractions -- from the core Bayesian transformer, through semantic transformers with explicit update kernels, to full transformer blocks with QKV/attention/residual/MLP pipelines, and finally multilayer stacks -- and prove at each level that the Bayes joint semantics implies the update kernel equals the posterior almost everywhere. For the block-level architecture, we derive the explicit Bayes formula through Radon-Nikodym differentiation and prove its normalization. We additionally prove that the softmax attention mechanism induces a valid probability distribution over keys, establishing the bridge between the abstract kernel framework and concrete attention implementations. The framework makes no architectural assumptions beyond the Markov kernel structure and exposes explicit conditions under which a transformer block is provably Bayesian. In essence, when this joint distribution condition is satisfied, the forward computation of a Transformer is formally equivalent to a rigorous Bayesian posterior update.

Haobo Yang

Department of Computer Science and Engineering, SUSTech University

Transformer Architectures Bayesian Posterior Pac-Bayesian Theory Probability Measures

Jun 28, 2026cs.LG

Bayesian Best-Arm Identification with Abstention: A Polynomial-to-Exponential Phase Transition

We study the Bayesian fixed-budget best-arm identification problem in which a learner can abstain from making a terminal recommendation. Subject to an abstention budget

α

, we analyze the probability of undetected error--the risk of recommending a suboptimal arm without abstaining. Our central finding is that abstention induces a phase transition: without abstention, the error probability decays polynomially in the sampling budget

T

; in contrast, introducing any small positive abstention budget shifts this to an exponential decay. For Gaussian priors and rewards, in the regime

T\to\infty

followed by

α\downarrow0

, we establish exact matching information-theoretic lower bounds and algorithmic upper bounds on the optimal error exponent, which takes the form

\exp(-\frac{α^{2}T}{8κ_ν^{2}})

. The hardness parameter

κ_ν

represents the prior density of the top-two gap at zero, highlighting that nearly tied instances drive the fundamental error. We introduce an adaptive algorithm, PGWS, that successfully achieves this optimal exponent by expending its abstention budget on statistically ambiguous instances. We further demonstrate that this polynomial-to-exponential improvement is exclusively a Bayesian phenomenon--in the frequentist setting, abstention only affects lower-order exponent terms. We also extend our results beyond the Gaussian model.

Yuqi Huang, Yunlong Hou, Vincent Y. F. Tan

Department of Mathematics, National University of Singapore · Department of Electrical and Computer Engineering, National University of Singapore

Bayesian Token Budget Allocation Exponents Abstention Prior Knowledge Integration Recommendation

Jun 28, 2026cs.LG

BaRA: Bayesian Adaptive Rank Allocation for Parameter-Efficient Fine-Tuning

While Low-rank adaptation (LoRA) enables highly efficient fine-tuning by constraining task-specific updates to fixed low-rank subspaces, this rigid design limits representational flexibility and often results in overconfident predictions and miscalibrated uncertainty, especially in low-data regimes. Recent Bayesian LoRA variants improve uncertainty estimation by modeling posterior distributions over adaptation parameters. However, these approaches typically rely on fixed or heuristically determined ranks, overlooking the inherently context-dependent nature of adaptation capacity. In this paper, we propose BaRA, a Bayesian Adaptive Rank Allocation framework for parameter-efficient fine-tuning. Drawing inspiration from probabilistic topic models, BaRA dynamically allocates adaptation capacity by activating a sparse, context-dependent subset of disentangled latent factors, enabling instance-wise variation in effective rank. This Bayesian formulation provides principled, data-driven capacity control, mitigating over-parameterization while preserving expressiveness. Beyond the modeling contribution, we provide a complexity-theoretic generalization analysis showing that the generalization gap of BaRA depends on the learned joint effective rank

\bar{s}_{Φ,θ}

induced by the global-local gate, rather than the maximum rank

r

. This result explains why sparse adaptive rank allocation can reduce the effective hypothesis complexity while preserving input-dependent expressiveness. Extensive experiments on diverse natural language benchmarks demonstrate that BaRA consistently improves predictive performance, robustness, and uncertainty calibration compared to standard LoRA and existing Bayesian LoRA variants.

Zhibin Duan, Yuhong Wang, Jiahong Fu +3

National Key Lab of Radar Signal Processing, Xidian University, Xi’an, Shaanxi 710071, China · School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, China

Model Fine-Tuning Bayesian Representational Capacity Topic Modeling

Jun 22, 2026stat.ML

Action-BED: Task-Driven Bayesian Experimental Design with Singly Intractable Objectives

Bayesian experimental design (BED) has traditionally been based on maximising expected uncertainty reductions from prior to posterior. A major shortfall of this approach is that it leads to doubly intractable objectives that are difficult to optimise, while customising them to particular downstream tasks of interest can also be difficult. Following first principles decision theory, we demonstrate that BED can alternatively be formulated in terms of an expected future loss (EFL) on downstream actions, providing a simple and naturally task-driven framework. Critically, we then show that all such EFLs can be rearranged into singly intractable objectives that can be jointly optimised with respect to both the design policy and a downstream action policy using stochastic gradients, an approach we refer to as ACTION-BED. This formulation further sidesteps the need for any explicit posterior or marginal likelihood estimation and is naturally implicit, requiring only the ability to sample from the joint model over model parameters and data, and evaluate the downstream loss function. It thus allows design policies to be learned more effectively, efficiently, and simply than existing methods, while providing easy customisation to different downstream tasks and losses.

Tom Rossa, Angus Phillips, Tom Rainforth

Department of Statistics University of Oxford

Bayesian Experimental Design Bayesian Objective Functions Action Expert

Jun 21, 2026cs.RO

BLENDS: Bayesian Learning-Enhanced Deep Smoothing for GNSS-Denied Environments

Maintaining accurate navigation during GNSS outages remains a significant challenge for autonomous systems relying on low-cost inertial sensors. While classical smoothing methods, such as the two-filter smoother and Rauch-Tung-Striebel smoother, exploit measurements collected before and after an outage, their performance remains limited by the accuracy of conventional GNSS measurements. This paper presents Bayesian learning-enhanced navigation with deep smoothing (BLENDS), a transformer-based framework that augments Bayesian smoothing with learned covariance adaptation and state correction. The proposed method preserves the statistical foundations of Bayesian estimation while leveraging data-driven learning to improve navigation accuracy. Evaluations on the quadrotor dataset with GNSS outages demonstrate that BLENDS consistently outperforms both model-based smoothers, achieving up to 25.6% improvement in the position root mean square error while also reducing estimation uncertainty. Furthermore, BLENDS learns to compensate for the systematic bias between conventional GNSS positioning and RTK ground truth, enabling accuracy beyond that achievable with conventional GNSS measurements alone. The results demonstrate the potential of learning-enhanced Bayesian smoothing for resilient and high-accuracy navigation in GNSS-challenged environments.

Nadav Cohen, Itzik Klein

The Hatter Department of Marine Technologies University of Haifa Haifa, Israel

Global Navigation Satellite System Smoothing Empirical Bayes Bayesian

Jun 20, 2026cs.GT

Quantifying Theoretical AI Alignment Guarantees: Receiver-Utility Bounds in Bayesian Persuasion

Misalignment can change how information moves from an AI agent to a human user. We model this as an information advantage: the AI agent observes the world state, while the human receiver only knows a prior and must act after seeing the agent's signal. A strategic AI sender may withhold evidence or garble information in order to steer the human's decision. We ask how much useful information can still reach the human when the AI optimizes a misaligned objective. We study a Bayesian persuasion model in which the world state is a bit string, the human receiver wants to guess the bits correctly, and a single AI sender wants the receiver to guess as many bits as possible as

1

. For a prior

μ

, let

R_0(μ)

be the receiver's utility from using only the prior, and let

R_{\max}(μ)

be the largest receiver utility among signaling schemes that are optimal for the sender. We prove

R_{\max}(μ)/R_0(μ)\leq 3/2

. This bound improves for priors close to the independent product prior with the same marginals: if

μ(x)\geq (1-η)π_μ(x)

for every state

x

, then

R_{\max}(μ)\leq R_0(μ)+ηn

. We also give a six-bit prior for which

R_{\max}(μ)/R_0(μ)=39/31>5/4

, so no universal

5/4

bound is possible.

Eric Yachbes, Eva Tardos

Cornell University, United States

Artificial Intelligence Alignment Persuasion Information-Theoretic Limits Bayesian

Jun 19, 2026cs.LG

BASIL: Bayesian Application for Scientific Iteration and Learning

We introduce BASIL, a user-friendly desktop application for process optimization. BASIL employs a Bayesian approach, incorporating special acquisition functions that can be used to solve both single and multi-objective optimization problems. It provides a graphical interface that enables users to input their experimental parameters, optimization objectives, and legacy data. This is then used to build surrogate models, which are coupled with acquisition functions to guide and optimize a process towards a desired objective. To facilitate model building, BASIL provides a variety of predefined surrogate model templates. BASIL can be used to optimize any arbitrary experiment or process with known, user-defined input variables, optimization objectives, and defined output.

Kelvin P. Idanwekhai, Valeriia Kaneva, Stefano Menegatti +1

Department of Chemistry, UNC Chapel Hill, Chapel Hill, NC, USA · Laboratory for Molecular Modeling (MML), UNC Chapel Hill, Chapel Hill, NC, USA · Department of Chemical and Biomolecular Engineering, NC State University, Raleigh, NC, USA +1

Multi-Objective Optimization Prompt Optimization Bayesian Surrogate Models Scientific Discovery Clover

Jun 17, 2026astro-ph.IM

The Chandra-Gaia Catalog of Counterparts: Resolving ambiguous Gaia matches to X-ray sources in the Chandra Source Catalog using Machine Learning

We present a framework to cross-match sources from the Chandra Source Catalog (CSC v2.1) with optical sources from Gaia Data Release 3. Unlike purely spatial approaches, we use source properties such as magnitudes, colors, and distances to identify true counterparts, detect chance coincidences, and resolve ambiguities when multiple plausible candidates exist. We define a training set of high-confidence matches using NWAY, a Bayesian cross-matching framework that accounts for positional errors and source densities. We train a gradient-boosted classifier (LightGBM) on a variety of features from both catalogs. Of the ~

254

k unique X-ray sources, we find counterparts for ~

113

k sources, of which plausible multiple counterparts are found for ~

7

k. We find no counterparts for ~

20

k sources for which separation-based cross-matching does find a match, and attribute half of these to chance coincidences. We validate the pipeline on the Chandra Orion Ultradeep Project (COUP), where the machine-learning matches reproduce 95% of NWAY cross-matches without using any positional information. We release a catalog of the ~

113

k Chandra-Gaia counterparts, together with ~

7

k alternative matches and ~

20

k ambiguous NWAY associations, supporting future population studies of sources detectable by both Chandra and Gaia. We discuss limitations and provide a generalization of the framework that is applicable in other cross-matching scenarios.

V. Samuel Pérez-Díaz, Vinay L. Kashyap, Joshua D. Ingram +6

Center for Astrophysics | Harvard & Smithsonian, 60 Garden St, Cambridge MA 02138, USA · Harvard John A. Paulson School of Engineering and Applied Sciences, 150 Western Ave, Allston, MA 02134, USA · Universidad del Rosario, School of Engineering, Science and Technology, Cll. 12C No. 6-25, Bogot´a, Colombia +5

Jun 17, 2026cs.CL

BCL: Bayesian In-Context Learning Framework for Information Extraction

Existing information extraction (IE) tasks increasingly adopt in-context learning (ICL) with large language models. However, current approaches either show inconsistent performance across model scales or lack systematic optimization and generalizability. Building on this, we propose BCL (Bayesian In-Context Learning Framework for Information Extraction), the first optimization framework that uses particle filtering with Bayesian updates to systematically refine label representations across IE tasks. Through four steps initialization, observation, weight update, and resampling, BCL generalizes to both sequence labeling and relation classification paradigms. Extensive experiments demonstrate substantial and consistent improvements over existing approaches.

Haoliang Liu, Chengkun Cai, Xu Zhao +7

HiThink Research · University College London · University of Edinburgh +6

In-Context Learning Information Extraction Sequence Modeling Bayesian

Jun 12, 2026cs.LG

Structured Noise Adaptation for Sequential Bayesian Filtering with Embedded Latent Transfer Operators

Kalman filters based on the Embedded Latent Transfer Operators (ELTO) emerge as novel statistical tools for sequential state estimation. However, a critical limitation stems from their use of simplified noise models, which fail to dynamically adapt to non-stationary processes. To address this limitation, we introduce an ELTO-based Bayesian filtering approach with a new structured parameterization for the filter's noise model. This parameterization enables structured noise adaptation, which couples the data-driven learning of an optimal time-invariant noise model with dynamic parameter adaptation that responds to changes in dynamics within non-stationary processes. Empirical results show that our structured noise adaptation improves the filter's dynamic state estimation performance in noisy, time-varying environments.

Naichang Ke, Pongpisit Thanasutives, Yoshinobu Kawahara

The University of Osaka · RIKEN Center for Advanced Intelligence Project (AIP)

Bayesian Filtering State Estimation Noise-Aware Non-Stationarity Bayesian

Jun 10, 2026stat.ML

Phase Transitions in Attention: A Bayesian Theory of Copy Head Emergence

Attention is the key mechanism underlying in-context learning in transformers, and attention patterns have been observed empirically to emerge abruptly during training. We present a Bayesian theory of feature learning in attention; we then focus on how the copy subcircuit in the first layer of an induction head is learned by analyzing a single-layer softmax attention network trained on a copy task. We derive a closed-form posterior over the attention matrix and reduce it to a low-dimensional order parameter space. This reduction reveals a phase transition in the amount of training data, which we verify using both Bayesian sampling and standard training with Adam. We contrast our results with linear attention and find that softmax attention exhibits a \emph{first-order phase transition} while in linear attention an initial \emph{second-order phase transition} is followed by a smooth, continuous evolution toward the structured attention pattern (\emph{crossover}). Our work provides a first-principles theoretical account of the abrupt emergence of the copy subcircuit, reminiscent of the one observed in training large language models.

Itay Lavie, Kirsten Fischer, Andrey Lekov +3

Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel · John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA · Institute for Advanced Simulation (IAS-6), Computational and Systems Neuroscience, Jülich Research Center, Jülich 52428, Germany +3

Phase Transitions Emergence Bayesian Circuits

Jun 4, 2026cs.LG

Synthics: Synthetic Physics-like Datasets for Machine Learning

Representative data is fundamental in machine learning, as limited data hinders generalisation. Collecting sufficient real-world samples is often infeasible. Synthetic data generation offers a practical solution, but only if the generated data faithfully reflects the structure of real observations. In this paper, a method for generating synthetic regression datasets that structurally resemble physics equations from a given equation corpus is presented. The approach uses a Bayesian Probabilistic Context-Free Grammar to capture the underlying algebraic structure of the corpus, from which novel equations are sampled. To ensure the generated inputs lie within a physically meaningful domain, the applicability domain is characterised for each equation through non-intrusive probing, also recovering inter-variable constraints. Input sampling further mimics realistic experimental conditions by drawing from random sub-ranges of the valid domain with mixed uniform and truncated normal distributions. The generated data is statistically validated against the Feynman equation corpus using Kolmogorov-Smirnov tests. The generated equations match the corpus on all of the eight studied structural features, compared to only two for an unsmoothed purely probabilistic grammar, demonstrating that the Bayesian prior is essential for structural fidelity given the size of the corpus. In a downstream hyperparameter-tuning task, a gradient-boosted regressor tuned on the synthetic data picks, on average, the 6th-best configuration out of 20 on real data, matching the result of tuning on real data itself and substantially outperforming random expression trees (10th) and noise (19th).

Jari Vepsäläinen

Mechatronics Department of Energy and Mechanical Engineering School of Engineering Aalto University Finland

Synthetic Data Unified Path-Integral Update Bayesian Fidelity

Jun 3, 2026cs.LG

Generalized TV-- $\ell_p$ Structured Priors for Bayesian $T_1$ Mapping

We propose an extended family of structured spatial priors that incorporates the total variation (TV) function with

\ell_p

norms. The prior is proven to be proper and incorporated into a Bayesian regression framework to enable uncertainty quantification in

T_1

mapping, with posterior inference performed using the No-U-Turn Sampler (NUTS). This TV--

\ell_p

construction is proven to constitute a well-defined family of prior distributions, and it naturally enforces spatial consistency and smooth variations in the estimated parameter maps. The method was evaluated in comparison to maximum-likelihood estimation and several Bayesian alternative priors based on the uniform, Gamma, and bounded TV priors. The evaluation includes experiments on synthetic brain and cardiac

T_1

mapping datasets, as well as a real in-vivo breast

T_1

mapping dataset. The results show that the TV--

\ell_p

prior yields more concentrated posterior densities, indicating reduced uncertainty. It also consistently achieves lower variance and smaller (negative) bias, leading to more reliable estimates. Overall, embedding a TV-based structured penalty along with

\ell_p

norms in a prior in a Bayesian model improves spatial coherence in

T_1

maps and enhances uncertainty quantification, offering a robust approach for

T_1

mapping with uncertainties.

Disi Lin, Martin Berggren, Tommy Löfstedt

Department of Computing Science, Ume˚a University, Sweden

Bayesian Spatial Priors Prior Knowledge Integration

Jun 2, 2026cs.LG

Bayes-Sufficient Representations in Supervised Learning

Representation learning is often described as preserving the information in an input that is relevant for prediction. This work asks what relevance means for a fixed supervised decision problem. A representation is defined to be Bayes-sufficient for a joint distribution and loss if some prediction head can use it to implement a Bayes-optimal action rule. This makes the target information loss-dependent. In the almost-surely unique Bayes-action case, the relevant object is a Bayes quotient, which identifies inputs that require the same Bayes-optimal action. A representation is sufficient when it refines this quotient, and Bayes-minimal when it is informationally equivalent to it. The framework connects naturally to property elicitation: zero-one loss requires the Bayes class, squared loss the conditional mean, Brier loss the conditional probability in binary prediction, and log loss or strictly proper scoring rules the predictive distribution. Controlled finite experiments, learned neural bottleneck experiments, and a real-data iNaturalist taxonomic refinement experiment illustrate the distinction between sufficiency, minimality, and retained non-required information. For a fixed supervised problem, the distribution and the loss determine the Bayes action, the Bayes action determines the quotient, and the quotient determines the minimal information required for Bayes-optimal prediction.

Vasileios Sevetlidis

Athena Research Center, Kimmeria Campus, Xanthi, Greece · Democritus University of Thrace, Vas. Sofias Campus, Xanthi, Greece · International Hellenic University, Serres, Greece

Pac-Bayesian Theory Bayesian Representation Learning Semi-Supervised Learning Loss Function Relevance

Jun 2, 2026cs.LG

Bayesian Tensor Decomposition with Diffusion Model Prior

Low-rank tensor decomposition (TD) is usually effective on clean, fully observed data, but it often degrades under severe missingness or noise. Low-rankness is itself a useful but limited structural prior, and additional handcrafted priors (e.g., sparsity or smoothness) still fall short of capturing the rich statistics of real-world data. To compensate for this weak inductive bias under heavy corruption, one would like to inject a learned, data-driven prior; however, the state-of-the-art diffusion models are not readily compatible with current TD and tractable posterior inference. To address these challenges, we introduce DiffBCP, a hybrid-prior Bayesian CP decomposition framework that couples a cumulative shrinkage process prior over the CP factors for automatic rank selection with an off-the-shelf pre-trained diffusion model as an implicit data prior on the reconstructed tensor. To make posterior inference tractable despite the coupling among the likelihood, low-rank constraint, and diffusion prior, we develop a split Gibbs sampler: CP factors admit conjugate updates, while the diffusion block is sampled via low-rank-guided denoising. A noise-adaptive coupling schedule further reduces sensitivity to hand-tuned annealing. Experiments on image inpainting and denoising, including high-resolution out-of-distribution images, show consistent gains over Bayesian, nonlinear, and plug-and-play TD baselines.

Zerui Tao, Qibin Zhao

RIKEN Center for Advanced Intelligence Project (AIP), Tokyo, Japan.

Tensor Decomposition Diffusion Priors Low-Rank Structure Bayesian Posterior Decomposition+1

Jun 1, 2026stat.ML

ShaplEIG: Bayesian Experimental Design for Shapley Value Estimation

Shapley values are a principled attribution measure widely used in interpretable machine learning, but their exact computation scales exponentially with the number of players, motivating a wide range of approximation methods based on value function evaluations of sampled coalitions. This raises the question of whether approximation accuracy can be improved by adaptively selecting coalitions for evaluation based on previous evaluations. This is particularly relevant in settings where the value function is costly and the number of evaluations is severely limited, such as retraining-based feature importance, data valuation, and hyperparameter importance. For this purpose, we propose ShaplEIG, a Bayesian experimental design approach that approximates the expensive value function using a Gaussian process surrogate and adaptively selects coalitions based on their expected information gain about the Shapley values. By the linearity of the Shapley values in the value function, we show that the expected information gain is available in closed form. Furthermore, we propose an efficient computation scheme that reduces the complexity from exponential to polynomial in the number of players via elementary symmetric polynomials. In extensive experiments across diverse costly applications, our method consistently improves sample efficiency in the low-budget regime over state-of-the-art baselines.

David Rundel, Fabian Fumagalli, Maximilian Muschalik +2

Department of Statistics, LMU Munich, Munich, Germany · Munich Center for Machine Learning, Munich, Germany · Institute for Informatics, LMU Munich, Munich, Germany +2

Shapley Value Bayesian Experimental Design Shaping Value Functions Bayesian Approximation

Jun 1, 2026stat.ML

Bayesian meta-learning for modeling Alzheimer's disease progression

Predicting whether an individual with Alzheimer's disease will experience mild or severe disease progression is essential for personalized treatment. Typically, practitioners seek to predict the distribution of a discrete disease score, conditional on an individual's current MRI volume and their historical disease trajectory. Classical statistical regression models and single-task neural networks are not well-suited for this purpose because fitting separate models is infeasible (since each individual typically has few observations), while ignoring individual-level correlation leads to poor generalization. Meta-learning, in contrast, provides a natural avenue to dynamically predict distributions without retraining and model nonlinear relationships between the outcome and covariates. Motivated by this, we propose a Bayesian meta-learner that is trained on multiple individuals but tailors the predictive disease score distribution to each individual's historical data. Our model predicts on unseen individuals without retraining, scales linearly with the number of historical observations, and is guaranteed to be less overconfident when predicting long-term disease scores compared to its deterministic counterpart. On real-world data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database, our model achieves performance competitive with both single-task models and deterministic meta-learners, while substantially improving performance when predicting long-term disease progression.

Clara Hoffmann, Nadja Klein

Scientific Computing Center, Karlsruhe Institute of Technology, Germany

Alzheimer Readmission Prediction Meta-Learning Disease Bayesian

Jun 1, 2026math.OC

MINTS: Minimalist Thompson Sampling

The Bayesian paradigm offers principled tools for sequential decision-making under uncertainty, but its reliance on a probabilistic model for all parameters can hinder the incorporation of complex structural constraints. We introduce a minimalist Bayesian framework that places a prior only on the location of the optimum, while eliminating nuisance parameters through profile likelihood. This yields a generalized posterior that naturally accommodates structural constraints. As a direct instantiation, we develop MINimalist Thompson Sampling (MINTS). For multi-armed bandits with mean constraints, we establish near-optimal non-asymptotic regret guarantees and sharp almost-sure asymptotic regret characterizations. In particular, MINTS attains the classical Lai--Robbins constant in the unstructured setting and automatically adapts to unimodal structure, achieving the sharp constant determined only by the immediate neighbors of the optimal arm.

Kaizheng Wang

Department of IEOR and Data Science Institute, Columbia University.

Thompson Sampling Bayesian

May 31, 2026cs.LG

Optimal-Point Variance Reduction For Bayesian Optimization With Regret Guarantee

This paper studies a one-step lookahead Bayesian optimization (BO) method and its theoretical guarantee. Although the empirical effectiveness of one-step lookahead BO methods, such as entropy search, has been studied extensively, they often rely on computationally intractable approximations, and their regret guarantees remain underdeveloped. Thus, this paper proposes a one-step lookahead BO method called optimal-point variance reduction (OVR), which requires only posterior sampling and Monte Carlo approximations. We obtain a uniform error bound over an input domain for the Monte Carlo estimation in OVR. Furthermore, we show that the regularized OVR, with the slight modification to promote exploration, achieves a vanishing Bayesian expected simple regret upper bound. Finally, we demonstrate the effectiveness of OVR through numerical experiments.

Shion Takeno

1Nagoya University

Bayesian Optimization Variance Reduction Bayesian Variance Regret

May 28, 2026cs.LG

iLoRA: Bayesian Low-Rank Adaptation with Latent Interaction Graphs for Microbiome Diagnosis

Parameter-efficient adaptation has made LLMs practical for domain prediction, but standard LoRA still relies on a static low-rank update and does not expose the latent interactions that often drive scientific labels. We introduce iLoRA. To our knowledge, it is the first Bayesian graph-conditioned LoRA framework. It infers a latent interaction graph from the input and uses it to generate input-conditioned LoRA updates. As a result, iLoRA learns prediction and latent interaction structure jointly, rather than training a predictor and applying interaction analysis only post hoc. We instantiate this idea for microbiome diagnosis, where disease state can depend on both species-level abundance and microbe-microbe cross-talk, and evaluate it in two complementary settings: interactive QA with human-annotated graphs, which tests latent structure recovery, and multi-cohort IBD diagnosis, which tests biomedical utility. Across both settings, iLoRA improves over strong LoRA and Bayesian adaptation baselines, recovers graphs aligned with human annotations and cohort-level microbiome associations, and provides calibrated uncertainty with moderate graph-branch overhead.

Yang Song, Yixuan Zhang, Lingfa Meng +5

Section of Health Data Science & AI, Department of Public Health, University of Copenhagen, Copenhagen, Denmark · University of Copenhagen, Copenhagen, Denmark · Rutgers University, New Brunswick, NJ, USA +1

Bacterial Colony Counting Bayesian Networks Bayesian

May 28, 2026cs.LG

Kernel Renormalization in Bayesian Deep Neural Networks: the Equivalent Wishart Ansatz in the Proportional Regime

The scaling limit where both the size of the training set

P

and the width

N

of a deep neural network grow at the same rate, the so-called proportional-width regime, has been intensely studied for shallow, single-hidden-layer networks. However, extending these non-perturbative results from shallow architectures to deep non-linear networks has proven very challenging. Here we present an effective approximate approach to predict the generalization performance of Bayesian multi-layer perceptrons (MLPs) of fixed depth

L

on arbitrary high-dimensional data. We propose an equivalent Wishart Ansatz to capture the dominant stochastic fluctuations of the hierarchical empirical kernels of MLPs. This allows us to perform a large deviation analysis for the partition function of MLPs in the proportional limit, expressed in terms of a renormalized NNGP kernel. In this description, even strong representation learning in the proportional limit is encoded in at most

L

scalar order parameters, determined self-consistently. Extending the approach to convolutional architectures (CNNs), we identify a hierarchical local kernel renormalization mechanism, which allows to quantify more complex data-dependent transformations of the large-width kernel in CNNs due to finite-width effects. We test our effective theory against sampling experiments from the Bayesian posterior of finite deep neural networks with depths

L \sim O(10)

and

P\sim O(10^3)

on classic benchmark datasets, finding overall very good agreement together with two distinct types of systematic deviations.

Paolo Baglioni, Christian Keup, Vincenzo Zimbardo +4

1INFN, Sezione di Milano Bicocca, Piazza della Scienza 3, 20126, Milano, Italy · 2INFN, Gruppo Collegato di Parma, Parco Area delle Scienze 7/A, 43124 Parma, Italy · 3Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit`a degli Studi di Parma, Parco Area delle Scienze, 7/A 43124 Parma, Italy +2

Bayesian Neural Networks Renormalization Group Large Deviation Principle Bayesian

May 28, 2026cs.LG

On the Construction and Implications of Low-Loss Valleys in LoRA-based Bayesian Inference

While parameter-efficient fine-tuning methods like low-rank adaptation (LoRA) are standard for large language models, principled estimation of epistemic uncertainty remains challenging. Recent results in the LoRA regime suggest that discrete multi-mode approaches such as deep ensembles offer little benefit over single-mode methods. This contradicts broader observations in deep learning, where ensembling independent optima typically improves generalization, and linking these modes through continuous low-loss valleys further enhances Bayesian model averaging (BMA). Whether such structure exists in the LoRA space and whether it yields functional diversity missed by local or discrete methods has not been studied. We introduce LoRA-Curve, a segmented Bézier curve parameterization in the LoRA space, with two variants: a free configuration that jointly optimizes all control points, and an anchored configuration that connects independently fine-tuned LoRA optima. We prove pathwise continuity and Lipschitz regularity of the loss along the curve and empirically show, across reasoning and classification benchmarks with Qwen2.5 7B, that linear interpolation encounters loss barriers, while our anchored multi-segment curves connect independent optima through continuous low-loss valleys. Combined with flat-minima perturbations and a Jensen-Shannon divergence regularizer, LoRA-Curve yields measurably higher mutual information of the predictive distribution without sacrificing performance, and links continuous parameter-space traversal to functional diversity.

Daniel Dold, Emanuel Sommer, Julius Kobialka +2

HTWG Konstanz · LMU Munich · Munich Center for Machine Learning (MCML)

Parameter-Efficient Fine-Tuning Methods Anisotropic Loss Landscapes Bayesian Inference Bayesian Curves Ridge+1

May 27, 2026cs.LG

Thinned Mean Field Langevin Dynamics

Several important learning tasks can be formulated as minimizing an entropy-regularized objective over an appropriate space of probability distributions. Mean-field Langevin dynamics (MFLD) facilitate computation in this general context, casting the minimizer as the invariant distribution of a McKean--Vlasov process, which can be numerically discretized using

N

particles and thus simulated. However, simulating this interacting particle system has computational complexity of order

N^2

. Motivated by recent research into \emph{kernel thinning}, we propose \texttt{KT-MFLD}, in which each particle interacts only with a thinned particle coreset of size

\mathcal{O}(N^{\frac{1}{2}})

. \texttt{KT-MFLD} thus reduces the computational complexity to order

N^{\frac{3}{2}}

while, under mild regularity conditions, achieving the same convergence guarantees (up to logarithmic factors) as MFLD. Our theoretical analysis is empirically confirmed on tasks including the training of student-teacher neural networks, quantization with maximum mean discrepancy, and computation of predictively-oriented posteriors in a post-Bayesian framework.

Zonghao Chen, Heishiro Kanagawa, François-Xavier Briol +2

University College London · 2Newcastle University · 3The Alan Turing Institute +1

Mean-Field Limit Langevin Dynamics Kullback-Leibler Regularization Fokker--Planck Equation Geometry-Aware Uncertainty Coresets Bayesian

May 25, 2026cs.LG

Goal-driven Bayesian Optimal Experimental Design for Robust Decision-Making Under Model Uncertainty

Bayesian optimal experimental design (BOED) selects experiments to maximize information gain about model parameters. However, in decision-critical settings, reducing parameter uncertainty does not necessarily improve downstream decisions, as only specific parameter directions relevant to the objective truly matter. We propose GoBOED, a goal-driven BOED framework that directly optimizes experimental designs for a specified decision-making objective. GoBOED combines an amortized variational posterior surrogate with a differentiable convex decision layer, enabling gradient-based design optimization that is fully decision-focused. We theoretically show that GoBOED gradients are insensitive to parameter directions irrelevant to the decision objective, providing a formal justification for why goal-driven design achieves equivalent decision quality over a wider set of experimental designs than information-gain maximization. Empirically, across source localization, epidemic management, and pharmacokinetic control, GoBOED identifies designs that better align with downstream decision objectives and reveals that near-optimal design windows are substantially wider than those predicted by goal-agnostic BOED approaches.

Jinwoo Go, Xiaoning Qian, Byung-Jun Yoon

Computing & Data Sciences, Brookhaven National Laboratory, Upton, NY · Department of Electrical & Computer Engineering, Texas A&M University, College Station, TX · Department of Computer Science & Engineering, Texas A&M University, College Station, TX

Bayesian Experimental Design Bayesian Sequential Decision Making Pharmacokinetics

May 25, 2026cs.LG

Generalized Evidential Deep Learning: From a Bayesian Perspective

Evidential Deep Learning (EDL) has emerged as an efficient, sampling-free strategy for uncertainty estimation. A series of EDL variants have been proposed to address specific limitations of the original framework, achieving notable success. However, the underlying theoretical structure of EDL and the relationships among these variants have received limited systematic investigation. In this work, we establish a principled theoretical foundation for EDL by interpreting it within a generalized Bayesian framework that includes prior specification, posterior update, and training objective. We further characterize evidential uncertainty from a Bayesian distributional uncertainty viewpoint, established via asymptotic analysis. Building on this perspective, we further propose Generalized Evidential Deep Learning (GEDL), a unified and extensible framework that explicitly disentangles the roles of individual components and systematically relates GEDL to existing variants. Extensive experiments demonstrate that GEDL yields comparable results on classification, uncertainty estimation and OOD detections, with theoretical grounding.

Yuanye Liu, Yibo Gao, Yuanyang Chen +1

School of Data Science, Fudan University, Shanghai, China.

Evidential Uncertainty Uncertainty-Aware Classification Bayesian Neural Networks Bayesian Perspective

May 21, 2026cs.CV

MotionDPS: Motion-Compensated 3D Brain MRI Reconstruction

Magnetic resonance imaging (MRI) is highly susceptible to patient motion due to its relatively long acquisition times and the fact that data are acquired sequentially in k-space. Even small patient movements introduce phase inconsistencies across measurements, leading to severe artifacts such as blurring, ghosting, and geometric distortions that can compromise diagnostic quality. Retrospective motion compensation remains challenging, particularly in accelerated acquisitions, due to the ill-posed nature of the joint reconstruction and motion estimation problem. In this work, we propose a unified Bayesian framework for motion-compensated 3D MRI that jointly estimates the anatomical image, rigid-body motion parameters, and coil sensitivity maps directly from motion-corrupted k-space data. Our approach integrates pretrained 3D complex-valued score-based diffusion models as expressive anatomical image priors within a physics-based forward model. Inference is performed by alternating diffusion posterior image updates with efficient proximal optimization steps for motion and coil sensitivity estimation, enabling fully unsupervised reconstruction without the need for paired motion-free training data. Experiments on simulated and real-motion brain MRI datasets demonstrate that the proposed method achieves improved image quality and motion robustness compared to state-of-the-art classical and learning-based motion correction techniques, particularly in the presence of severe motion and high acceleration.

Antonio Ortiz-Gonzalez, Erich Kobler, Lukas Schletter +1

Life and Medical Sciences Institute, University of Bonn, Bonn, Germany · Institute for Machine Learning, LIT AI Lab, Department of Virtual Morphology, Clinical Research Institute Medical AI, Johannes Kepler University Linz, Linz, Austria · German Center for Neurodegenerative Diseases (DZNE), Bonn, Germany +1

Magnetic Resonance Imaging Reconstruction Magnetic Resonance Imaging 3D Generation Bayesian Posterior

May 19, 2026cs.CV

MedCRP-CL: Continual Medical Image Segmentation via Bayesian Nonparametric Semantic Modality Discovery

Medical image segmentation faces a fundamental challenge in continual learning: data arrives sequentially from heterogeneous sources, yet effective continual learning requires discovering which tasks share sufficient structure to benefit from joint learning. Existing methods either apply uniform constraints across all tasks, causing catastrophic forgetting when tasks conflict, or require predefined task groupings that cannot anticipate future task diversity. We introduce MedCRP-CL, a framework that performs online task structure discovery and structure-aware continual learning. Leveraging the Chinese Restaurant Process (CRP), our method dynamically infers task groupings from clinical text prompts as tasks arrive, without requiring predefined cluster counts or access to future tasks. We term these discovered groupings semantic modalities, as they capture finer-grained structure than physical imaging modalities by integrating anatomical region and pathological context. Guided by this discovered structure, we maintain semantic modality-specific LoRA adapters regularized by intra-modality EWC, ensuring parameter isolation across dissimilar task groups while facilitating knowledge transfer within similar ones. The framework is also replay-free, storing only aggregate statistics rather than raw patient data. Experiments on 16 medical segmentation tasks across four imaging modalities demonstrate that MedCRP-CL achieves 73.3% Dice score with only 4.1% forgetting, outperforming the best baseline by 8.0% while requiring 6

\times

fewer parameters. Code is available at https://github.com/zygao930/MedCRP-CL.

Ziyuan Gao

University College London, London, United Kingdom

Semi-Supervised Medical Image Segmentation Replay-Based Continual Learning Low-Rank Adaptation Adapters Bayesian

May 15, 2026cs.RO

Bayesian Networks for Path-Based Sensors: Gathering Information and Path Planning in Communication Denied Environments

A "path-based sensor" produces a single observation along a continuous path. For example, a boolean path-based sensor returns a single "1" if an event of interest is detected at any point along the path and a "0" otherwise. Notably, a "1" provides no direct information about where along the path the event(s) may have occurred. Previous work has demonstrated that observations from multiple path-based sensors can be fused to create a Bayesian belief map over the spatial locations of the underlying event or phenomenon. Moreover, path planning can employ Shannon information theory to accelerate the rate of convergence of the belief map. In this paper, we present a new method to update the belief map based on a path-based sensor observation, and then plan paths to increase information gain. In contrast to prior work that approximates the posterior by averaging over the alternative event histories, we introduce a Bayesian Network (BN) formulation that models the probabilistic relationships between the latent variables and path-based sensor measurements, enabling a more principled Bayesian belief update. We consider static hazard detection in a communication-denied environment as a representative problem setting. The event of a robot returning from its path corresponds to a path-based hazard sensor reading of "0" (hazard not detected), while a robot failing to return corresponds to a reading of "1" (hazard detected). We consider false positives and false negatives. We find that the new method leads to quicker convergence of the belief map than prior work in both single- and multi-robot cases.

Alkesh K. Srivastava, George P. Kontoudis, Donald Sofge +1

University of Maryland, College Park, MD, US. · Temple University, Philadelphia, PA, US. · Colorado School of Mines, Golden, CO, US. +1

Path Planning Bayesian Networks Event-Guided Sensor-Level Fusion Particle Filters Bayesian Robot Systems

May 13, 2026cs.LG

Uncertainty-Aware Prediction of Lung Tumor Growth from Sparse Longitudinal CT Data via Bayesian Physics-Informed Neural Networks

This work studies lung tumor growth prediction from sparse and irregular longitudinal computed tomography (CT) observations with measurement variability. A Bayesian physics-informed neural network is developed by combining Gompertz growth dynamics with low-dimensional Bayesian inference in the log-volume domain. The framework employs a two-stage inference strategy combining maximum a posteriori (MAP) estimation and Hamiltonian Monte Carlo (HMC) sampling to estimate posterior predictive distributions and uncertainty intervals. The method was evaluated on longitudinal data from the National Lung Screening Trial (30 patients). Results show that the model captures heterogeneous tumor growth patterns while maintaining reasonable prediction accuracy under limited observations. Compared with deterministic modeling approaches, the proposed approach additionally provides calibrated uncertainty estimates. The inferred posterior parameter correlations were consistent with expected biological growth behavior. The proposed framework achieved a cohort-level log-space RMSE of approximately 0.20 together with well-calibrated 95% credible interval coverage across 30 patients. These findings suggest that Bayesian physics-informed modeling may be useful for uncertainty-aware tumor growth assessment when only limited longitudinal follow-up scans are available.

Lingfei Kong, Haoran Ma

Department of Mathematics, Vanderbilt University, Nashville, TN, USA · John A. Paulson School of Engineering and Applied Science, Harvard University, Allston, MA, USA

Prognostics Tumor Bayesian Cone-Beam Computed Tomography Posterior Neural Network

May 13, 2026cs.CV

Bayesian In Vivo Tracking of Synapses using Joint Poisson Deconvolution and Diffeomorphic Registration

Synapses are densely packed submicron structures that dynamically reorganize during learning and memory formation. Longitudinal \textit{in vivo} imaging of fluorescently tagged synaptic receptors offers a promising opportunity to study large-scale synaptic dynamics and how these processes are disrupted in neurological disease. However, in vivo imaging with 2-photon microscopy uses low laser power and therefore suffers from low signal-to-noise ratio (SNR) and high shot noise, nonlinear tissue motion between days, nonstationary fluctuations in synaptic fluorescence, and significant blur induced by the microscope point spread function (PSF). Together, these factors make it challenging to detect and track synapses, especially in regions with high synaptic density. This paper presents a novel template-based framework for modeling synapses as varying luminance point sources that move under a nonlinear tissue deformation. Taking a unified Bayesian approach, we apply this model to microscopy data by deriving a posterior that incorporates a diffeomorphic mapping for domain warping, a Gaussian point spread function for the imaging process, and a Poisson observation model for raw photon counts. The Bayesian solution simultaneously: (1) Constructs a probabilistic template of synapse locations, (2) denoises and deconvolves the image data, (3) infers fluorescence intensities, (4) performs diffeomorphic image registration to correct for tissue motion, and (5) provides confidence regions for these parameter estimates. We demonstrate the framework on both a 2D+t simulated dataset and a 3D+t longitudinal \textit{in vivo} microscopy dataset of fluorescent synapses imaged in a mouse over two weeks.

Shashwat Kumar, Dominic M. Padova, Binish Narang +6

Department of Biomedical Engineering, Johns Hopkins University · Department of Neuroscience, Johns Hopkins University · Kavli Neuroscience Discovery Institute, Johns Hopkins University +2

Microscopy Synaptic Plasticity Image Registration Bayesian