Publication

Chaining Meets Chain Rule: Multilevel Entropic Regularization and\n Training of Neural Nets

2019

Abstract

We derive generalization and excess risk bounds for neural nets using a\nfamily of complexity measures based on a multilevel relative entropy. The\nbounds are obtained by introducing the notion of generated hierarchical\ncoverings of neural nets and by using the technique of chaining mutual\ninformation introduced in Asadi et al. NeurIPS'18. The resulting bounds are\nalgorithm-dependent and exploit the multilevel structure of neural nets. This,\nin turn, leads to an empirical risk minimization problem with a multilevel\nentropic regularization. The minimization problem is resolved by introducing a\nmulti-scale generalization of the celebrated Gibbs posterior distribution,\nproving that the derived distribution achieves the unique minimum. This leads\nto a new training procedure for neural nets with performance guarantees, which\nexploits the chain rule of relative entropy rather than the chain rule of\nderivatives (as in backpropagation). To obtain an efficient implementation of\nthe latter, we further develop a multilevel Metropolis algorithm simulating the\nmulti-scale Gibbs distribution, with an experiment for a two-layer neural net\non the MNIST data set.\n

Official source

https://infoscience.epfl.ch/entities/publication/6407a6dc-0f68-4461-bb4e-23401b5d4fc4

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2019

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/6407a6dc-0f68-4461-bb4e-23401b5d4fc4

About this result

Related concepts (32)

Convolutional neural network

Convolutional neural network (CNN) is a regularized type of feed-forward neural network that learns feature engineering by itself via filters (or kernel) optimization. Vanishing gradients and exploding gradients, seen during backpropagation in earlier neural networks, are prevented by using regularized weights over fewer connections. For example, for each neuron in the fully-connected layer 10,000 weights would be required for processing an image sized 100 × 100 pixels.

Artificial neural network

Artificial neural networks (ANNs, also shortened to neural networks (NNs) or neural nets) are a branch of machine learning models that are built using principles of neuronal organization discovered by connectionism in the biological neural networks constituting animal brains. An ANN is based on a collection of connected units or nodes called artificial neurons, which loosely model the neurons in a biological brain. Each connection, like the synapses in a biological brain, can transmit a signal to other neurons.

Feedforward neural network

A feedforward neural network (FNN) is one of the two broad types of artificial neural network, characterized by direction of the flow of information between its layers. Its flow is uni-directional, meaning that the information in the model flows in only one direction—forward—from the input nodes, through the hidden nodes (if any) and to the output nodes, without any cycles or loops, in contrast to recurrent neural networks, which have a bi-directional flow.

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