Why and When Deep is Better than Shallow: Implementation-Agnostic State-Transition Model of Deep Learning

ArXi:2505.15064v4 Announce Type: replace Why and when does depth improve generalization? We study this question in an implementation-agnostic state-transition model, where a depth-$k$ predictor is a readout class $H$ composed with the word ball $B(k,F)$ generated by hidden state transitions. Generalization bounds separate implementation error, approximation error, and statistical complexity, and upper bound the depth-dependent variance term by a Dudley entropy integral over $B(k,F)$, with a conditional lower-bound diagnostic under readout separation.