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General purpose Hessian-free optimization in Theano
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I wrapped my Hessian-free code in a generic class, usable as a black-box to train your models if you can provide the cost function as a Theano expression. It includes all the details in Martens (ICML 2010) and Martens & Sutskever (ICML 2011) crucial to make it work: - Tikhonov damping with the Levenberg-Marquardt heuristics, - Gauss-Newton matrix products (you specify an Theano expression `s` to section your computational graph in 2), - Proper handling of batches and mini-batches (an example SequenceDataset class is provided for variable-length input) - Conjugate gradient (CG) with information sharing, backtracking, preconditioning and terminations conditions. - Structural damping for RNNs. It relies heavily on the Rop. In practice, I could make it work without hassle for a feed-forward network, an RNN with different objectives, NADE (Larochelle) and a more complex model (RNN-NADE) that ties two scans together, so it seems reasonably flexible. Only the gradients and Gauss-Newton matrix products (95% of the computation) are in Theano, CG and the training logic is in python. It runs on GPU, but for the models I tried, it was a bit slower. Hessian-free is slow, you need CG batch sizes of 1000+ (don't skimp on this), but you can get really better results than SGD from it with almost zero tweaking. There is an option to save and recover a checkpoint of training and do early stopping. I included an RNN example that can memorize an input for 100 time steps (example_RNN). Launch it on 4 cores, come back in 8 hours, and you should have at least one nice solution with 0 error on the validation set. In comparison, SGD can solve this problem about 0.0% of the time. It is available here: https://github.com/boulanni/theano-hf If you use this software for academic research, please cite the following paper:  N. Boulanger-Lewandowski, Y. Bengio and P. Vincent, "Modeling Temporal Dependencies in High-Dimensional Sequences: Application to Polyphonic Music Generation and Transcription", Proc. ICML 29, 2012. Author: Nicolas Boulanger-Lewandowski University of Montreal, 2012