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Hessian-free optimization for deep networks


Quick start

Install the package via:

pip install hessianfree

To make sure things are working, open a python interpreter and enter:

import hessianfree as hf

A simple xor training example will run, at the end of which it will display the target and actual outputs from the network.

Developer install

Use this if you want to track the latest changes from the repository:

git clone
cd hessianfree
python develop --user


  • python 2.7 or 3.5
  • numpy 1.9.2
  • matplotlib 1.3.1
  • optional: scipy 0.15.1, pycuda 2015.1.3, scikit-cuda 0.5.1, pytest 2.7.0

(older versions may work, but are untested)


All the standard features of Hessian-free optimization from Martens (2010) and Martens and Sutskever (2011) are implemented (Gauss-Newton approximation, early termination, CG backtracking, Tikhonov damping, structural damping, etc.). In addition, the code has been designed to make it easy to customize the network you want to train, without having to modify the internal computations of the optimization process.

  • Works for feedforward and recurrent deep networks (or mixtures of the two)
  • Standard nonlinearities built in (e.g., logistic, tanh, ReLU, softmax), and support for custom nonlinearities
  • Standard loss functions (squared error, cross entropy, sparsity constraints), and support for custom loss functions
  • Various weight initialization methods (although Hessian-free optimization doesn't usually require much tweaking)
  • Customizable connectivity between layers (e.g., skip connections)
  • Efficient implementation, taking advantage of things like activity caching
  • Optional GPU acceleration if PyCUDA and scikit-cuda are installed
  • Gradient checking (and Gauss-Newton matrix checking) implemented to help with debugging
  • Inputs can be predefined or generated dynamically by some other system (like an environmental simulation)
  • Different optimizers can be swapped out for comparison (e.g., Hessian-free versus SGD)


View the documentation at

In addition, examples illustrating the main features of the code can be found in


Hessian-free optimization for deep networks




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