Extrapolatable Relational Reasoning With Comparators in Low-Dimensional Manifolds

TL;DR

This paper introduces a neuroscience-inspired module that projects high-dimensional object representations onto low-dimensional manifolds, significantly enhancing out-of-distribution generalisation in relational reasoning tasks.

Contribution

It proposes a novel inductive bias module that improves neural networks' ability to generalise out-of-distribution by focusing on low-dimensional manifold projections for relational reasoning.

Findings

Improved out-of-distribution generalisation on relational tasks

Better performance with the inductive bias module

Analysis of the importance of low-dimensional projections

Abstract

While modern deep neural architectures generalise well when test data is sampled from the same distribution as training data, they fail badly for cases when the test data distribution differs from the training distribution even along a few dimensions. This lack of out-of-distribution generalisation is increasingly manifested when the tasks become more abstract and complex, such as in relational reasoning. In this paper we propose a neuroscience-inspired inductive-biased module that can be readily amalgamated with current neural network architectures to improve out-of-distribution (o.o.d) generalisation performance on relational reasoning tasks. This module learns to project high-dimensional object representations to low-dimensional manifolds for more efficient and generalisable relational comparisons. We show that neural nets with this inductive bias achieve considerably better o.o.d generalisation performance for a range of relational reasoning tasks. We finally analyse the proposed inductive bias module to understand the importance of lower dimension projection, and propose an augmentation to the algorithmic alignment theory to better measure algorithmic alignment with generalisation.