Derives exact Frobenius norm imbalance identity for deep nonlinear networks, classifies activations into four classes, and obtains critical-depth escape time law τ★ = Θ(ε^{-(r-2)}) from reduction to scalar ODE on permutation-symmetric submanifold.
A mean field view of the landscape of two-layer neural networks
5 Pith papers cite this work, alongside 519 external citations. Polarity classification is still indexing.
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In a sequential d,n→∞ then m→∞ limit with dm/n fixed, the spectrum of a deep linear Gaussian network's feature covariance converges to the free log-normal law, whose T-transform solves a Burgers equation.
Transformer residual layers are approximated as an explicit Euler scheme for a controlled hidden-state flow whose mean-field limit is a first-order transport control problem with Pontryagin terminal condition given by the softmax residual.
Maximum entropy connectivity constrained by task moments and weight scale reproduces the qualitative and quantitative structure of gradient-trained networks across learning regimes.
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A Theory of Saddle Escape in Deep Nonlinear Networks
Derives exact Frobenius norm imbalance identity for deep nonlinear networks, classifies activations into four classes, and obtains critical-depth escape time law τ★ = Θ(ε^{-(r-2)}) from reduction to scalar ODE on permutation-symmetric submanifold.
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Geometric Dyson Brownian Motions and the Free Log-Normal Limit for a Non-Square Gaussian Matrix Product
In a sequential d,n→∞ then m→∞ limit with dm/n fixed, the spectrum of a deep linear Gaussian network's feature covariance converges to the free log-normal law, whose T-transform solves a Burgers equation.
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A First-Order Mean Field Control Analysis of Transformer Layers under Cross-Entropy Training
Transformer residual layers are approximated as an explicit Euler scheme for a controlled hidden-state flow whose mean-field limit is a first-order transport control problem with Pontryagin terminal condition given by the softmax residual.
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Balancing structure and randomness: maximum entropy networks for context-dependent computations
Maximum entropy connectivity constrained by task moments and weight scale reproduces the qualitative and quantitative structure of gradient-trained networks across learning regimes.
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