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The hessian-eigenthings module provides an efficient way to compute the eigendecomposition of the Hessian for an arbitrary PyTorch model. It uses PyTorch's Hessian-vector product and stochastic power iteration with deflation to compute the top eigenvalues and eigenvectors of the Hessian.


For now, you have to install from this repo. It's a tiny thing so why put it on pypi.

pip install --upgrade git+


The main function you're probably interested in is compute_hessian_eigenthings. Sample usage is like so:

import torch
from hessian_eigenthings import compute_hessian_eigenthings

model = ResNet18()
dataloader = ...
loss = torch.nn.functional.cross_entropy

num_eigenthings = 20  # compute top 20 eigenvalues/eigenvectors

eigenvals, eigenvecs = compute_hessian_eigenthings(model, dataloader,
                                                   loss, num_eigenthings)

This also includes a more general power iteration with deflation implementation in


This code was written in collaboration with Zhewei Yao, Amir Gholami, and Michael Mahoney in UC Berkeley's RISELab.

The deflated power iteration routine is based on code in the HessianFlow repository recently described in the following paper: Z. Yao, A. Gholami, Q. Lei, K. Keutzer, M. Mahoney. "Hessian-based Analysis of Large Batch Training and Robustness to Adversaries", NIPS'18 (arXiv:1802.08241)

Stochastic power iteration with acceleration is based on the following paper: C. De Sa, B. He, I. Mitliagkas, C. Ré, P. Xu. "Accelerated Stochastic Power Iteration", PMLR-21 (arXiv:1707.02670)