arXiv:2606. 15443v1 Announce Type: cross Abstract: Physical learning methods train physical networks to perform computational tasks using only local update rules, exploiting the physics of the system to handle the global transfer of information.
arXiv:2606. 15444v1 Announce Type: cross Abstract: In this paper we show that the physical learning methods known as coupled learning (CL) and equilibrium propagation (EP) conserve a mass-like quantity in the trainable parameters in the continuous-time, small-nudging limit.
arXiv:2608. 00097v1 Announce Type: cross Abstract: Physical learning rules such as equilibrium propagation (EP), coupled learning (CL), and adjoint coupled learning (AL) train resistive networks through local measurements.
arXiv:2602. 03670v2 Announce Type: replace-cross Abstract: Equilibrium Propagation (EP) is a physics-inspired learning algorithm that uses stationary states of a dynamical system both for inference and learning.
arXiv:2607. 23940v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) solve differential equations by minimizing the residual of a nonlinear operator over a neural parameterization of the solution.
arXiv:2511. 01938v3 Announce Type: replace-cross Abstract: Grokking is a puzzling phenomenon in neural networks where full generalization occurs only after a substantial delay following the complete memorization of the training data.
arXiv:2401. 04013v2 Announce Type: replace Abstract: Deep learning models, such as wide neural networks, can be conceptualized as nonlinear dynamical physical systems characterized by a multitude of interacting degrees of freedom.
arXiv:2605. 23391v2 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) for coupled multiphysics systems suffer systematic accuracy degradation as inter-equation coupling strengthens.
arXiv:2606. 00340v1 Announce Type: new Abstract: We study optimal learning-rate selection in two-layer and three-layer linear neural networks trained to learn linear target functions.
arXiv:2606. 15551v1 Announce Type: new Abstract: The Edge of Stability (EoS) phenomenon, where gradient descent operates with sharpness exceeding the classical convergence threshold yet the loss decreases over long timescales, is ubiquitous in modern deep learning but remains poorly understood in realistic settings.
arXiv:2607. 08340v1 Announce Type: cross Abstract: Q-learning is a fundamental algorithm in reinforcement learning (RL) for solving discounted Markov decision processes (MDPs) when the transition kernel is unknown.
arXiv:2606. 04476v1 Announce Type: new Abstract: In this paper, we study the gradient descent dynamics for jointly training both layers of a one-hidden-layer ReLU network to fit a linear target function.
arXiv:2606. 18175v1 Announce Type: cross Abstract: We present a numerical method for the forward solution of nonlinear partial differential equations (PDEs) in which Bellman-Kalaba quasilinearization reduces the nonlinear problem to a sequence of linear subproblems, each discretized by collocation onto a trial space that is linear in its parameters and solved by a single direct linear least-squares QR factorization.