Non-normal spectral signatures of instability in neural network training dynamics

arXiv:2605.23476v1 Announce Type: new Abstract: Training instabilities in deep networks - loss spikes, oscillatory convergence, and gradient pathologies - are empirically prevalent but lack a rigorous operator-theoretic explanation. We show that the linearized update operators for practically used optimizers are generically non-normal: for Adam, non-normality is controlled by the commutator [H, M] between the Hessian and the diagonal adaptive preconditioner, while for SGD with momentum it arises from the augmented state-space structure of the update map. Applying non-normal stability theory to

Source: arXiv cs.LG — read the full report at the original publisher.

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