Inter-Layer Hessian Analysis of Neural Networks with DAG Architectures
Modern automatic differentiation frameworks (JAX, PyTorch) return the Hessian of the loss function as a monolithic tensor, without exposing the internal structure of inter-layer interactions. This paper presents an analytical formalism that explicitly decomposes the full Hessian into blocks indexed by the DAG of an arbitrary architecture. The canonical decomposition $H = H^{GN} + H^T$ separates the Gauss--Newton component (convex part) from the tensor component (residual curvature responsible for saddle points). For piecewise-linear activations (ReLU), the tensor component of the input Hessian vanishes ($H^{T}_{v,w}\!\equiv\!0$ a.e., $H^f_{v,w}\!=\!H^{GN}_{v,w}\!\succeq\!0$); the full par...
| Authors | Maxim Bolshim, Alexander Kugaevskikh |
|---|---|
| Primary category | cs.LG |
| Published | 13 April 2026 |
| Last updated at source | 13 April 2026 |
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