arXiv:2606. 30064v1 Announce Type: new Abstract: We introduce a data-driven probabilistic framework for learning systems based on Gibbs measures on hierarchical structures.
We introduce a data-driven probabilistic framework for learning systems based on Gibbs measures on hierarchical structures. Unlike standard empirical risk minimization, where a dataset is used to identify a single optimal parameter, our approach transforms the empirical loss function into an interaction potential defining an energy-based model.
The review explores how control theory, optimal transport, probabilistic inference, non‑equilibrium thermodynamics, and machine learning are interconnected through the optimization of free‑energy‑like functionals under dynamical or statistical constraints. It presents a conceptual thread linking these five fields and illustrates the ideas with applications in reinforcement learning, variational inference, and generative modeling. The article is written for readers without prior familiarity, beginning with physics principles.
arXiv:2606. 02232v1 Announce Type: new Abstract: Learning a Markov transition model is not merely conditional density estimation: the learned object must be a valid transition kernel before it is iterated in downstream dynamics.
arXiv:2512. 22088v3 Announce Type: replace-cross Abstract: The scaling law, a cornerstone of Large Language Model (LLM) development, predicts improvements in model performance with increasing computational resources.
Energy-Based Models (EBMs) provide an interpretable framework for generative modeling of scientific data, but poor Markov Chain Monte Carlo mixing often limits their reliability. We introduce a training algorithm based on Parallel Trajectory Tempering (PTT), which exploits the continuity of the optimization path to maintain equilibrium sampling throughout learning.
arXiv:2512. 11415v3 Announce Type: replace-cross Abstract: We show that nonequilibrium dynamics can play a constructive role in unsupervised machine learning by inducing the spontaneous emergence of latent-state cycles.
The paper investigates three operations on Gibbs probability measures: renormalization, normalized log-linear combination, and nesting (changing the reference measure). It shows that the measures produced by the second and third operations solve related optimization problems and that, for specific parameters, nesting one Gibbs measure into another is equivalent to log-linearly combining them. This equivalence has practical implications, such as enabling a one-shot federated learning system where clients’ locally trained Gibbs algorithms can be combined on a server to match the performance of a centrally trained Gibbs algorithm.
arXiv:2609.15894v1 Announce Type: cross Abstract: Some of the sharpest challenges in sampling from the energy functions of physical systems arise at phase transitions, where the density of states cha...
FrOGS is a hybrid discrete neural sampler that couples an autoregressive model with a continuous-time Markov chain, trained under a single shared loss to sample alloy configurations across many chemical conditions. It produces independent, unbiased configurations, estimates the partition function, and yields consistent thermodynamic observables on a common absolute free‑energy scale. The method matches exact results for the 2D Ising model and reproduces reference phase diagrams for AgPd and CuAu, avoiding mode collapse and correctly recovering the stability range of the CuAu$_3$ phase.
arXiv:2605. 15407v3 Announce Type: replace-cross Abstract: We consider amortized Bayesian inference for nonlinear inverse problems using only samples from the joint distribution of parameters and observations, including problems with unknown functions in a Banach space.
arXiv:2603. 11249v4 Announce Type: replace Abstract: Accurate prediction of phase equilibria remains a central challenge in chemical engineering.
The article reviews modern machine learning techniques for estimating the committor and related kinetic statistics from molecular dynamics simulations. It emphasizes self‑supervised methods that solve the underlying dynamical equations instead of relying on labeled data, and unifies various approaches—generator‑based PDEs, variational principles, Markov state models, dynamical Galerkin approximation, and neural networks—under a common operator framework. The review also discusses practical guidance for handling non‑Markovian effects, sampling strategies, and outlines future research directions such as connections to reinforcement learning and generative modeling.