In linear recurrent models, infinite-width signal propagation remains accurate only for depths t much smaller than sqrt(width n), with a critical regime at t ~ c sqrt(n) where finite-width effects emerge and dominate for larger t.
Finite depth and width corrections to the neural tangent kernel
3 Pith papers cite this work. Polarity classification is still indexing.
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Establishes Riemannian gradient flow equivalence for neural MMS steps, linear convergence under convexity conditions, and O(δ) tracking bounds for inexact iterates.
A mechanics of the learning process is emerging in deep learning theory, characterized by dynamics, coarse statistics, and falsifiable predictions across idealized settings, limits, laws, hyperparameters, and universal behaviors.
citing papers explorer
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How Long Does Infinite Width Last? Signal Propagation in Long-Range Linear Recurrences
In linear recurrent models, infinite-width signal propagation remains accurate only for depths t much smaller than sqrt(width n), with a critical regime at t ~ c sqrt(n) where finite-width effects emerge and dominate for larger t.
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Global Convergence and Error Propagation in Neural Gradient Flows: A Riemannian Optimization Framework
Establishes Riemannian gradient flow equivalence for neural MMS steps, linear convergence under convexity conditions, and O(δ) tracking bounds for inexact iterates.
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There Will Be a Scientific Theory of Deep Learning
A mechanics of the learning process is emerging in deep learning theory, characterized by dynamics, coarse statistics, and falsifiable predictions across idealized settings, limits, laws, hyperparameters, and universal behaviors.