arXiv:2606. 01468v1 Announce Type: cross Abstract: Due to their explicit priors and ability to model uncertainty, Bayesian methods have played a major role in dynamical latent variable modeling of single-cell neural recordings.
arXiv:2602.01176v2 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding physica...
arXiv:2512. 24116v3 Announce Type: replace-cross Abstract: Parton Distribution Functions (PDFs) play a central role in describing experimental data at colliders and provide insight into the structure of nucleons.
arXiv:2608. 19377v1 Announce Type: cross Abstract: Bayesian inference via Markov Chain Monte Carlo (MCMC) provides effective parameter estimation, but its real-time application in complex physical systems is hindered by heavy computational bottlenecks and extreme sensitivity to statistical noise.
The paper introduces a model calibration method using optimal transport to address discrepancies between simulation and experimental data in high-dimensional machine learning applications. Applied to jet tagging in particle physics, the technique calibrates a 128‑dimensional latent representation from a general‑purpose classifier, ensuring downstream derived quantities are properly calibrated. This enables more reliable use of foundation models for jet flavor analysis in LHC experiments and offers a general framework for correcting high‑dimensional simulations across scientific fields.
The paper introduces a structured posterior‑correction framework that blends a tractable Gaussian reference with data‑driven corrections learned via diffusion models. After applying mean correction and covariance calibration, the diffusion model focuses on a low‑dimensional subspace that captures discrepancies from the Gaussian reference, while the remaining space stays Gaussian. Experiments on three scientific inference tasks show that these corrections recover hidden modes, improve sample structure, and reduce prediction error compared to the Gaussian reference, with trade‑offs between accuracy and computational cost relative to full‑field generative models.
The paper investigates a systematic bias in Bayesian physics-informed neural networks (B-PINNs) caused by their typical collider structure, where independent physical and trajectory parameters become coupled through likelihoods on differential-equation residuals. The authors demonstrate that this modeling choice can drive the posterior away from true parameter values, even with a well-centered prior. They propose a hierarchical chain model that avoids this bias, though it introduces a doubly intractable inference problem, which they solve by discretizing the dynamics and applying particle MCMC. Analytical approximations and diagnostic criteria are derived to predict when standard B-PINNs remain reliable, and experiments confirm both the bias and the effectiveness of the chain formulation.
arXiv:2606. 13818v1 Announce Type: new Abstract: This thesis investigates how Bayesian principles can deepen our understanding of modern deep learning systems.
The paper introduces a scalable method for uncertainty quantification in neural networks by applying a low‑rank generalized Laplace approximation within a data‑informed active subspace. It constructs a local Gaussian posterior around pretrained weights, calibrates the prior variance via empirical Bayes, and compares two posterior scalings: standard Bayesian and mean‑loss scaling. The study finds that mean‑loss scaling yields a more stable, lower‑dimensional subspace and produces calibrated, coherent predictive confidence intervals, whereas standard scaling can cause posterior variance contraction and degrade predictive coherence.
arXiv:2610.19074v1 Announce Type: new Abstract: Reliable uncertainty quantification remains an important challenge in AI. Hierarchical Bayesian methods provide a principled framework for this by repr...
arXiv:2603. 22050v2 Announce Type: replace-cross Abstract: Supervised machine learning describes the practice of fitting a parameterized model to labeled input-output data.
The paper proposes pre-training uncertainty estimators on large, diverse materials science datasets to improve uncertainty quantification (UQ) for machine‑learned interatomic potentials (MLIPs). By evaluating these pre‑trained models on both in‑distribution and out‑of‑domain adsorption‑energy predictions, the authors demonstrate that zero‑shot UQ is viable and that fine‑tuning yields strong correlations between predicted uncertainty and actual prediction error, even on challenging datasets. This approach aims to provide foundational UQ models that enable broader, more reliable deployment of MLIPs across chemical space.