Feed-Forward Neural Networks Need Inductive Bias to Learn Equality Relations

TL;DR

This paper demonstrates that standard feed-forward neural networks struggle to learn equality relations and fail to generalize, but adding differential rectifier units introduces an inductive bias that enables successful learning and generalization.

Contribution

The study introduces differential rectifier units as a novel inductive bias to improve neural networks' ability to learn and generalize equality relations from limited data.

Findings

Standard networks fail to generalize equality relations.

DR units enable networks to learn equality with few examples.

Inductive bias benefits relational learning tasks.

Abstract

Basic binary relations such as equality and inequality are fundamental to relational data structures. Neural networks should learn such relations and generalise to new unseen data. We show in this study, however, that this generalisation fails with standard feed-forward networks on binary vectors. Even when trained with maximal training data, standard networks do not reliably detect equality.We introduce differential rectifier (DR) units that we add to the network in different configurations. The DR units create an inductive bias in the networks, so that they do learn to generalise, even from small numbers of examples and we have not found any negative effect of their inclusion in the network. Given the fundamental nature of these relations, we hypothesize that feed-forward neural network learning benefits from inductive bias in other relations as well. Consequently, the further development of suitable inductive biases will be beneficial to many tasks in relational learning with neural networks.