Stochastic Estimation of the Layer-wise Hessian Trace for Monitoring Neural-network Training
The loss and the norm of its gradient separate the healthy and the pathological regimes of neural-network training only weakly, whilst the curvature of the empirical risk differs qualitatively between them but is inaccessible explicitly at parameter counts $P\sim 10^{6}-10^{8}$. We present a stochastic estimator of the trace of the diagonal blocks of the Hessian matrix of the empirical risk of a neural network. The procedure combines the Hutchinson stochastic trace estimator with a single Hessian-vector product over the whole parameter vector and recovers unbiased estimates of every per-layer trace in one backward pass through the computational graph. We show that correctness under weight...
| Authors | Maxim Bolshim, Alexander Kugaevskikh |
|---|---|
| Primary category | cs.LG |
| Published | 25 May 2026 |
| Last updated at source | 25 May 2026 |
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