Exponentially Increasing the Capacity-to-Computation Ratio for Conditional Computation in Deep Learning

TL;DR

This paper introduces a novel neural network parametrization that exponentially increases the capacity-to-computation ratio by activating parameters based on specific activation patterns, enabling more efficient conditional computation.

Contribution

The authors propose a tree-structured parametrization that activates weight matrices based on hidden unit activation patterns, significantly boosting capacity without proportional computation increase.

Findings

Potential to exponentially increase capacity-to-computation ratio

Tree-structured parametrization controls overfitting

Activation based on hidden unit sign patterns

Abstract

Many state-of-the-art results obtained with deep networks are achieved with the largest models that could be trained, and if more computation power was available, we might be able to exploit much larger datasets in order to improve generalization ability. Whereas in learning algorithms such as decision trees the ratio of capacity (e.g., the number of parameters) to computation is very favorable (up to exponentially more parameters than computation), the ratio is essentially 1 for deep neural networks. Conditional computation has been proposed as a way to increase the capacity of a deep neural network without increasing the amount of computation required, by activating some parameters and computation "on-demand", on a per-example basis. In this note, we propose a novel parametrization of weight matrices in neural networks which has the potential to increase up to exponentially the ratio of the number of parameters to computation. The proposed approach is based on turning on some parameters (weight matrices) when specific bit patterns of hidden unit activations are obtained. In order to better control for the overfitting that might result, we propose a parametrization that is tree-structured, where each node of the tree corresponds to a prefix of a sequence of sign bits, or gating units, associated with hidden units.