arXiv:2511. 21466v3 Announce Type: replace Abstract: We study Consensus-Based Optimization (CBO) for two-layer neural network training.
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:2210. 16286v2 Announce Type: replace Abstract: To understand the training dynamics of neural networks, prior studies have considered the mean-field limit of two-layer neural networks as the width tends to infinity, establishing theoretical guarantees for its convergence under gradient flow training as well as approximation and generalization capabilities.
arXiv:2501.14993v4 Announce Type: replace-cross Abstract: The proximal algorithm is a powerful tool to minimize nonlinear and nonsmooth functionals in a general metric space. Motivated by the recent...
arXiv:2605. 10775v2 Announce Type: replace-cross Abstract: A surprising phenomenon in the training of neural networks is the ability of gradient descent to find global minimizers of the training loss despite its non-convexity.
The paper investigates gradient descent dynamics in the Edge of Stability regime, where a large learning rate causes persistent oscillations linked to improved generalization. It introduces a tractable continuous‑time mean–fluctuation model that couples the window‑averaged trajectory with its fluctuation covariance, derives this model rigorously from a sharp‑valley framework, and analyzes its stationary states and linear stability. The authors also extend the model to wide two‑layer networks, deriving a Wasserstein‑2 gradient flow for weights and fluctuations, proving well‑posedness, a mean‑field limit, and conditional convergence results, with numerical experiments illustrating the predictions and finite‑time limitations.
arXiv:2608. 02844v1 Announce Type: cross Abstract: We develop a class of diffusion-based stochastic particle optimisation methods for loss functions with intractable gradients.
arXiv:2505. 06589v2 Announce Type: replace-cross Abstract: Modern machine learning repeatedly manipulates probability measures: empirical datasets, generated samples, latent distributions, class-conditional laws, particle systems, weights of wide networks and attention patterns.