相关论文: Free Energy Minimization: A Unified Framework for …
We introduce two new particle-based algorithms for learning latent variable models via marginal maximum likelihood estimation, including one which is entirely tuning-free. Our methods are based on the perspective of marginal maximum…
Deep learning achieves remarkable generalization capability with overwhelming number of model parameters. Theoretical understanding of deep learning generalization receives recent attention yet remains not fully explored. This paper…
Federated learning (FL) enables collaborative model training across distributed devices while preserving data privacy. However, balancing energy efficiency and fair participation while ensuring high model accuracy remains challenging in…
We develop a novel data-driven approach to the inverse problem of classical statistical mechanics: given experimental data on the collective motion of a classical many-body system, how does one characterise the free energy landscape of that…
Graphical models trained using maximum likelihood are a common tool for probabilistic inference of marginal distributions. However, this approach suffers difficulties when either the inference process or the model is approximate. In this…
Estimating the free energy in molecular simulation requires, implicitly or explicitly, counting how many times the system is observed in a finite region. If the simulation is biased by an external potential, the weight of the configurations…
We investigate the impact of limited data on training pairwise energy-based models for inverse problems aimed at identifying interaction networks. Utilizing the Gaussian model as testbed, we dissect training trajectories across the…
Learning systems acquire structured internal representations from data, yet classical information-theoretic results state that deterministic transformations do not increase information. This raises a fundamental question: how can learning…
The uniform electron gas is a key model system in the description of matter, including dense plasmas and solid state systems. However, the simultaneous occurence of quantum, correlation, and thermal effects makes the theoretical description…
A maximum entropy-based framework is presented for the synthesis of projections from multiple Earth climate models. This identifies the most representative (most probable) model from a set of climate models -- as defined by specified…
We consider the minimum error entropy (MEE) criterion and an empirical risk minimization learning algorithm in a regression setting. A learning theory approach is presented for this MEE algorithm and explicit error bounds are provided in…
We present an approach that extends the theory of targeted free energy perturbation (TFEP) to calculate free energy differences and free energy surfaces at an accurate quantum mechanical level of theory from a cheaper reference potential.…
Machine Learning is becoming more prevalent in science and engineering, but many approaches do not provide meaningful uncertainty estimates and predictions may also violate known physical knowledge. We propose a Bayesian framework to embed…
Maximization of an expensive, unimodal function under random observations has been an important problem in hyperparameter tuning. It features expensive function evaluations (which means small budgets) and a high level of noise. We develop…
Machine unlearning refers to mechanisms that can remove the influence of a subset of training data upon request from a trained model without incurring the cost of re-training from scratch. This paper develops a unified PAC-Bayesian…
This paper outlines an energy-minimization finite-element approach to the computational modeling of equilibrium configurations for nematic liquid crystals under free elastic effects. The method targets minimization of the system free energy…
The framework of reinforcement learning or optimal control provides a mathematical formalization of intelligent decision making that is powerful and broadly applicable. While the general form of the reinforcement learning problem enables…
The free energy principle (FEP) is a mathematical framework that describes how biological systems self-organize and survive in their environment. This principle provides insights on multiple scales, from high-level behavioral and cognitive…
A learning machine, like all machines, is an open system driven far from thermal equilibrium by access to a low entropy source of free energy. We discuss the connection between machines that learn, with low probability of error, and the…
Energy-based models (EBMs) are generative models that are usually trained via maximum likelihood estimation. This approach becomes challenging in generic situations where the trained energy is non-convex, due to the need to sample the Gibbs…