Tootfinder

When Diffusion Models Memorize: Inductive Biases in Probability Flow of Minimum-Norm Shallow Neural Nets
Chen Zeno, Hila Manor, Greg Ongie, Nir Weinberger, Tomer Michaeli, Daniel Soudry
https://arxiv.org/abs/2506.19031

When Diffusion Models Memorize: Inductive Biases in Probability Flow of Minimum-Norm Shallow Neural Nets
While diffusion models generate high-quality images via probability flow, the theoretical understanding of this process remains incomplete. A key question is when probability flow converges to training samples or more general points on the data manifold. We analyze this by studying the probability flow of shallow ReLU neural network denoisers trained with minimal $\ell^2$ norm. For intuition, we introduce a simpler score flow and show that for orthogonal datasets, both flows follow similar traj…

Physics-Informed Neural Networks for Control of Single-Phase Flow Systems Governed by Partial Differential Equations
Luis Kin Miyatake, Eduardo Camponogara, Eric Aislan Antonelo, Alexey Pavlov
https://arxiv.org/abs/2506.06188

Physics-Informed Neural Networks for Control of Single-Phase Flow Systems Governed by Partial Differential Equations
The modeling and control of single-phase flow systems governed by Partial Differential Equations (PDEs) present challenges, especially under transient conditions. In this work, we extend the Physics-Informed Neural Nets for Control (PINC) framework, originally proposed to modeling and control of Ordinary Differential Equations (ODE) without the need of any labeled data, to the PDE case, particularly to single-phase incompressible and compressible flows, integrating neural networks with physical…

This https://arxiv.org/abs/2407.19353 has been replaced.
initial toot: https://mastoxiv.page/@arX…

A spring-block theory of feature learning in deep neural networks
Feature-learning deep nets progressively collapse data to a regular low-dimensional geometry. How this emerges from the collective action of nonlinearity, noise, learning rate, and other factors, has eluded first-principles theories built from microscopic neuronal dynamics. We exhibit a noise-nonlinearity phase diagram that identifies regimes where shallow or deep layers learn more effectively and propose a macroscopic mechanical theory that reproduces the diagram and links feature learning acr…