arXiv Machine Learning

Recursive Gaussian Processes and the Bayesian Brain

arXiv:2608. 00503v1 Announce Type: cross Abstract: Predictive coding offers a powerful framework for cortical computation, yet scalable implementations that respect both Bayesian exactness and neurobiological constraints remain scarce.

arXiv Machine Learning
Sep 11

Bio-inspired Learning and Decision-Making with Probabilistic In-Memory Computing Hardware: Part 1

The article explores how biological learning and decision-making, often modeled as Bayesian processes, can be replicated in computing systems by leveraging noisy neural and synaptic dynamics for stochastic sampling. It proposes a biologically grounded framework where internal energy functions capture uncertainty over latent states and model parameters, enabling predictive coding networks to perform Markov chain Monte Carlo sampling. By drawing parallels between intrinsic biological noise and electrical noise in emerging probabilistic analogue memory technologies, the authors argue that analogue in‑memory computing hardware offers a massively scalable and energy‑efficient solution for probabilistic inference.

By Thomas Dalgaty, Eiji Kawasaki, Miguel de Prado, Devendra Vyas, Tommaso Salvatori
arXiv Machine Learning
Sep 14

Nonlinear Dimensionality Reduction Techniques for Bayesian Optimization

The paper investigates nonlinear dimensionality reduction for Bayesian optimisation (BO) by transforming high‑dimensional black‑box optimisation problems into a sequence of low‑dimensional latent‑space BO (LSBO) tasks. It extends earlier linear embedding approaches by using variational autoencoders (VAEs), deep metric loss, and adaptive retraining to better capture nonlinear structure, and couples LSBO with sequential domain reduction (SDR‑LSBO) to progressively narrow search domains. Experiments on GPU‑accelerated BoTorch with Matérn‑5/2 Gaussian‑process surrogates show that VAE‑based LSBO outperforms adaptive linear embeddings, and the authors provide a theoretical analysis of latent‑space error versus representation gap under PAC‑Bayes conditions.

By Luo Long, Coralia Cartis, Paz Fink Shustin
arXiv Machine Learning
Aug 19

Composing Flow-Matching Energies with Known Physics: Generation, OOD Detection, and Inversion on PDE Fields

The paper presents a method that combines flow‑matching models with energy‑based modeling to explicitly construct scalar energy functions for physical fields. These energies are derived from a matching regression objective on a linear Gaussian interpolation, avoiding variational approximations or extra MCMC steps, and can be used for energy‑corrected data generation, out‑of‑distribution detection, and posterior sampling in inverse problems. The approach enables general MCMC samplers that reduce PDE residuals and spectral distance, and it demonstrates that combining data‑driven and physics‑based energies improves OOD detection accuracy.

By Yixuan Sun, Anirban Samaddar, Sandeep Madireddy