Natural Neural Networks

We introduce Natural Neural Networks, a novel family of algorithms that speed up convergence by adapting their internal representation during training to improve conditioning of the Fisher matrix. In particular, we show a specific example that employs a simple and efficient reparametrization of the neural network weights by implicitly whitening the representation obtained at each layer, while preserving the feed-forward computation of the network. Such networks can be trained efficiently via the proposed Projected Natural Gradient Descent algorithm (PRONG), which amortizes the cost of these reparametrizations over many parameter updates and is closely related to the Mirror Descent online learning algorithm. We highlight the benefits of our method on both unsupervised and supervised learning tasks, and showcase its scalability by training on the large-scale ImageNet Challenge dataset.

[1]  Yoshua Bengio,et al.  Gradient-based learning applied to document recognition , 1998, Proc. IEEE.

[2]  Nicol N. Schraudolph,et al.  Accelerated Gradient Descent by Factor-Centering Decomposition , 1998 .

[3]  Shun-ichi Amari,et al.  Natural Gradient Works Efficiently in Learning , 1998, Neural Computation.

[4]  Marc Teboulle,et al.  Mirror descent and nonlinear projected subgradient methods for convex optimization , 2003, Oper. Res. Lett..

[5]  Nicolas Le Roux,et al.  Topmoumoute Online Natural Gradient Algorithm , 2007, NIPS.

[6]  Alex Krizhevsky,et al.  Learning Multiple Layers of Features from Tiny Images , 2009 .

[7]  Yoram Singer,et al.  Adaptive Subgradient Methods for Online Learning and Stochastic Optimization , 2011, J. Mach. Learn. Res..

[8]  James Martens,et al.  Deep learning via Hessian-free optimization , 2010, ICML.

[9]  Yoshua Bengio,et al.  Understanding the difficulty of training deep feedforward neural networks , 2010, AISTATS.

[10]  Patrick L. Combettes,et al.  Proximal Splitting Methods in Signal Processing , 2009, Fixed-Point Algorithms for Inverse Problems in Science and Engineering.

[11]  Jascha Sohl-Dickstein,et al.  The Natural Gradient by Analogy to Signal Whitening, and Recipes and Tricks for its Use , 2012, ArXiv.

[12]  Klaus-Robert Müller,et al.  Deep Boltzmann Machines and the Centering Trick , 2012, Neural Networks: Tricks of the Trade.

[13]  Klaus-Robert Müller,et al.  Efficient BackProp , 2012, Neural Networks: Tricks of the Trade.

[14]  Tapani Raiko,et al.  Deep Learning Made Easier by Linear Transformations in Perceptrons , 2012, AISTATS.

[15]  Sridhar Mahadevan,et al.  Projected Natural Actor-Critic , 2013, NIPS.

[16]  Yann Ollivier,et al.  Riemannian metrics for neural networks , 2013, ArXiv.

[17]  Tapani Raiko,et al.  Pushing Stochastic Gradient towards Second-Order Methods -- Backpropagation Learning with Transformations in Nonlinearities , 2013, ICLR.

[18]  Nitish Srivastava,et al.  Dropout: a simple way to prevent neural networks from overfitting , 2014, J. Mach. Learn. Res..

[19]  Rich Caruana,et al.  Do Deep Nets Really Need to be Deep? , 2013, NIPS.

[20]  Razvan Pascanu,et al.  Revisiting Natural Gradient for Deep Networks , 2013, ICLR.

[21]  Xiaohui Zhang,et al.  Parallel training of Deep Neural Networks with Natural Gradient and Parameter Averaging , 2014, ICLR.

[22]  Sergey Ioffe,et al.  Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift , 2015, ICML.

[23]  Sayan Mukherjee,et al.  The Information Geometry of Mirror Descent , 2013, IEEE Transactions on Information Theory.

[24]  Ruslan Salakhutdinov,et al.  Scaling up Natural Gradient by Sparsely Factorizing the Inverse Fisher Matrix , 2015, ICML.

[25]  Roger B. Grosse,et al.  Optimizing Neural Networks with Kronecker-factored Approximate Curvature , 2015, ICML.

[26]  Dumitru Erhan,et al.  Going deeper with convolutions , 2014, 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[27]  Michael S. Bernstein,et al.  ImageNet Large Scale Visual Recognition Challenge , 2014, International Journal of Computer Vision.

[28]  Andrew Zisserman,et al.  Very Deep Convolutional Networks for Large-Scale Image Recognition , 2014, ICLR.