# The Hessian of tall-skinny networks is easy to invert

arXiv: https://arxiv.org/abs/2601.06096 · HTML: https://mlsanity.com/paper/2601.06096/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 15 references that are in the map.
- First posted on arXiv 1 Jan 2026.

## Builds on (most cited first, 1 of 1)

- [An Investigation into Neural Net Optimization via Hessian Eigenvalue Density](https://mlsanity.com/paper/1901.10159/) (2019)

## Abstract (arXiv)

We describe an exact algorithm to solve linear systems of the form Hx=b where H is the Hessian of a deep net. The method computes Hessian-inverse-vector products without storing the Hessian or its inverse. It requires time and storage that scale linearly in the number of layers. This is in contrast to the naive approach of first computing the Hessian, then solving the linear system, which takes storage and time that are respectively quadratic and cubic in the number of layers. The Hessian-inverse-vector product method scales roughly like Pearlmutter's algorithm for computing Hessian-vector products.