Dimension-Corrected Hitting Times for Heavy-Tailed Spectral Emergence in Neural Optimizer Dynamics
Heavy-tailed empirical spectral densities of neural-network weight matrices are widely used as diagnostics of implicit self-regularization, but the step complexity of heavy-tail emergence remains poorly understood. We formulate spectral heavy-tail formation as a right-censored hitting-time problem: a run that does not reach a heavy-tail diagnostic within the observation horizon is treated as censored rather than discarded. In controlled full-batch teacher--student dynamics, we find that the first-step spike--bulk gap alone does not explain onset time. Instead, finite-onset regression supports a dimension-corrected spectral-gap law, (τ_{\mathrm{HT}}\approx CΔ_1^{-γ}d^ρ), with (R^2=0.683), ...
| Authors | Zongmin Liu |
|---|---|
| Primary category | cs.LG |
| Published | 10 July 2026 |
| Last updated at source | 10 July 2026 |
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