Recurrent Convolutional Neural Networks Learn Succinct Learning Algorithms

TL;DR

This paper introduces a recurrent convolutional neural network architecture that can efficiently learn and implement succinct algorithms like Gaussian elimination for parity problems, highlighting the potential of RCNNs to discover discrete algorithms.

Contribution

The authors propose a novel RCNN architecture combining recurrent and convolutional weight sharing, enabling polynomial-time learning of efficient algorithms with constant-sized descriptions.

Findings

RCNNs can learn algorithms like Gaussian elimination for parity problems

The architecture reduces parameters to a constant size despite large network scale

RCNNs may naturally and powerfully parameterize discrete algorithms

Abstract

Neural networks (NNs) struggle to efficiently solve certain problems, such as learning parities, even when there are simple learning algorithms for those problems. Can NNs discover learning algorithms on their own? We exhibit a NN architecture that, in polynomial time, learns as well as any efficient learning algorithm describable by a constant-sized program. For example, on parity problems, the NN learns as well as Gaussian elimination, an efficient algorithm that can be succinctly described. Our architecture combines both recurrent weight sharing between layers and convolutional weight sharing to reduce the number of parameters down to a constant, even though the network itself may have trillions of nodes. While in practice the constants in our analysis are too large to be directly meaningful, our work suggests that the synergy of Recurrent and Convolutional NNs (RCNNs) may be more natural and powerful than either alone, particularly for concisely parameterizing discrete algorithms.