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.
Simon, Maksis Knutins, Liu Ziyin, Daniel Geisz, Abraham J
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Low-rank graphs induce latents that form causal abstractions, with identifiability results and a practical objective enabling unsupervised learning of high-level SCMs from low-level measurements.
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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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Unsupervised Causal Abstractions Discovery
Low-rank graphs induce latents that form causal abstractions, with identifiability results and a practical objective enabling unsupervised learning of high-level SCMs from low-level measurements.