arXiv Machine Learning By Edison V\'azquez, Yingdong Lu, Tomasz Nowicki

Convex Equilibrium Potentials for Monge--Amp\`ere: Curvature Bounds and A Posteriori Evaluation

Read the original on arXiv Machine Learning →

arXiv:2610. 31386v1 Announce Type: cross Abstract: Equilibrium neural networks define their hidden state as the fixed point of a contraction, so their effective depth is set at evaluation time rather than by the architecture.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

arXiv AI
Aug 6

The Hamilton-Jacobi Theory of Deep Learning

arXiv:2605. 28983v2 Announce Type: replace-cross Abstract: In this paper, training a neural network is identified, exactly, as a search through Hamilton--Jacobi initial-value problems: each gradient step selects the initial data of a viscous Hamilton--Jacobi equation whose Hopf--Cole propagator best fits the observations; at inference, the input is the spatial point at which that solution is evaluated and the initial condition is already encoded in the weights.

By Jose Marie Antonio Mi\~noza, Erika Fille T. Legara, Christopher P. Monterola
arXiv Machine Learning
Jul 22

Boundary-Adapted PINNs for Elliptic Dirichlet Problems: $H^2(\Omega)$ A Priori Error Bounds with Application to Mean Escape Time Computation

arXiv:2607. 19167v1 Announce Type: cross Abstract: Motivated by the numerical computation of the Mean Escape Time (MET) $\tau:\Omega\to\mathbb{R}$ of a stochastic process from a bounded domain $\Omega\subseteq\mathbb{R}^d$, we study elliptic Dirichlet boundary value problems (BVPs) using boundary-enforced Physics-Informed Neural Networks (PINNs), in which the Dirichlet condition is imposed exactly by multiplying the network output with a predefined distance-to-boundary approximation $\rho$.

By Nathanael Tepakbong, Jun Fan, Xiang Zhou, Ding-Xuan Zhou
arXiv Machine Learning
Oct 21

Low Residuals, Wrong Value: Learning the Viscosity Solution of Hamilton-Jacobi-Isaacs Equations with PINNs

arXiv:2610.27193v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) and other residual-trained solvers judge a candidate solution by the size of its sampled PDE residual. For f...

By Raul Jimenez, Pablo Tejerina-P\'erez, Leonid Sarieddine, Pedro Taranc\'on-\'Alvarez, Marisol Traforetti, Pau Sol\'e-Vilar\'o, Oleksii Ignatenko, Nazar Tkach, Pavlos Protopapas
arXiv Machine Learning
Sep 4

Residual neural networks overcome the curse of dimensionality for semilinear heat equations

arXiv:2609. 03626v1 Announce Type: cross Abstract: Rigorous results show that feedforward neural networks can overcome the curse of dimensionality in the numerical approximation of high-dimensional partial differential equations (PDEs), but comparatively little is known about residual neural networks (ResNets) in the nonlinear PDE setting.

By Ilkhom Mukhammadiev, Diyora Salimova
arXiv Machine Learning
Sep 16

Certified Inference and Training for Deep Equilibrium Networks: A Continuation Framework with Polynomial Complexity Guarantees

The paper introduces a certified continuation framework for computing and training deep equilibrium networks (DEQs). It uses compact input homotopy and a rounded Newton tracker for inference, and augments local-plus-low-rank recurrence with programmable dormant bilinear rank‑one channels for training. The approach guarantees polynomial‑time bit complexity, with certified bounds on inference and training error budgets.

By Alex Borisevich