DrMAD

Source code for the paper: Distilling Reverse-Mode Automatic Differentiation for Optimizing Hyperparameters of Deep Neural Networks.

What's DrMAD?

DrMAD is a hyperparameter tuning method based on automatic differentiation, which is a most criminally underused tool for machine learning.

DrMAD can tune thousands of continuous hyperparameters (e.g. L1 norms for every single neuron) for deep models on GPUs.

AD vs Bayesian optimization (BO)

BO, as a global optimization approach, can hardly support tuning more than 20 hyperparameters, because it treats the learning algorithm being tuned as a black-box and can only get feedback signals after convergence. Also, the learning rate tuned by BO is fixed for all iterations.

AD is different from symbolic differentiation (used by Mathematica), and numerical differentiation. AD, as a local optimization method based on gradient information, can make use of the feedback signals after every iteration and can tune thounsands of hyperparameters by using (hyper-)gradients with respect to hyperparameters. Checkout this paper if you want to understand AD techniques deeply.

Therefore, AD can tune hundreds of thousands of constant (e.g. L1 norm for every neuron) or dynamic (e.g. learning rates for every neuron at every iteration) hyperparameters.

The standard way of computing these (hyper-)gradients involves a forward and backward pass of computations. However, the backward pass usually needs to consume unaffordable memory (e.g. TBs of RAM for MNIST dataset) to store all the intermediate variables to exactly reverse the forward training procedure.

Hypergradient with an approximate backward pass

We propose a simple but effective method, DrMAD, to distill the knowledge of the forward pass into a shortcut path, through which we approximately reverse the training trajectory. When run on CPUs, DrMAD is at least 45 times faster and consumes 100 times less memory compared to state-of-the-art methods for optimizing hyperparameters with almost no compromise to its effectiveness on small-scale problems as used in the previous studies.

CPU code for reproducing

For reproducing the original result in the paper, please refer to CPU version

In the original paper, we set the momentum to a small value (0.1). Now we found that setting this value to 0.9 or even 0.95 will give better performance.

GPU code

We've implemented GPU version with Theano, which is not included in the original paper. This GPU implementation does NOT mean it is practical for large-scale models.

Citation

@article{drmad2016,
  title={DrMAD: Distilling Reverse-Mode Automatic Differentiation for Optimizing Hyperparameters of Deep Neural Networks},
  author={Fu, Jie and Luo, Hongyin and Feng, Jiashi and Low, Kian Hsiang and Chua, Tat-Seng},
  journal={IJCAI},
  year={2016}
}

Contact

If you have any problems or suggestions, please contact: jie.fu A_T u.nus.education