Optimal depth-wise learning-rate scaling in deep scalar linear networks is data-dependent, so data-agnostic rules fail to transfer while the data-aware rule yields depth-independent linear convergence.
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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.
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Optimal Learning Rate Scaling Depends on Data in Deep Scalar Linear Networks
Optimal depth-wise learning-rate scaling in deep scalar linear networks is data-dependent, so data-agnostic rules fail to transfer while the data-aware rule yields depth-independent linear convergence.
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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.