Non-normal spectral signatures of instability in neural network training dynamics
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 these operators, we derive a conservative pseudospectral precursor bound in which κ(V) serves as an early-warning indicator of transient amplifi...
| Authors | Souvik Ghosh |
|---|---|
| Primary category | cs.LG |
| Published | 22 May 2026 |
| Last updated at source | 22 May 2026 |
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