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Efficient PyTorch Hessian eigendecomposition tools!

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module provides an efficient (and scalable!) way to compute the eigendecomposition of the Hessian for an arbitrary PyTorch model. It uses PyTorch's Hessian-vector product and your choice of (a) the Lanczos method or (b) stochastic power iteration with deflation in order 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+[email protected]#egg=hessian-eigenthings


The main function you're probably interested in is

. 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
calls a
to a battle-tested ARPACK implementation.

Example file

The example file in

for experiment orchestration, which can be installed via
pip install skeletor-ml
, but the rest of this library does not depend on it. You can execute the example via a command like
python example/  --mode=power_iter 
, where
 is a useful name like 
. But it may just be easier to use a simpler codebase to instantiate PyTorch models and dataloaders (such as

Citing this work

If you find this repo useful and would like to cite it in a publication (as others have done, thank you!), here is a BibTeX entry:

    author       = {Noah Golmant, Zhewei Yao, Amir Gholami, Michael Mahoney, Joseph Gonzalez},
    title        = {pytorch-hessian-eigenthings: efficient PyTorch Hessian eigendecomposition},
    month        = oct,
    year         = 2018,
    version      = {1.0},
    url          = {}


This code was written in collaboration with Zhewei Yao, Amir Gholami, Michael Mahoney, and Joseph Gonzalez 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)

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