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.
Directional convergence near small initializations and saddles in two-homogeneous neural networks
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Neural networks exhibit condensation of neurons into clusters with similar outputs whose number increases monotonically during training, facilitated by small initializations or dropout, providing insights into generalization and reasoning.
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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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An overview of condensation phenomenon in deep learning
Neural networks exhibit condensation of neurons into clusters with similar outputs whose number increases monotonically during training, facilitated by small initializations or dropout, providing insights into generalization and reasoning.