Extrapolatable Relational Reasoning With Comparators in Low-Dimensional Manifolds

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 outof-distribution (o.o.d) generalisation performance on relational reasoning tasks. This module learns to project high-dimensional object representations to lowdimensional 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.

A Memory-Augmented Neural Network Model of Abstract Rule Learning

“…However, these models typically require very large training sets (on the order of 10 6 training examples), and generally fail to generalize outside of the very specific conditions under which they are trained. For example, state-of-the-art performance on the extrapolation regime of the PGM dataset, in which test problems contain feature values outside the range of those observed in the training set, is currently 25.9% [38], and state-of-the-art performance on other out-of-distribution generalization regimes (held-out shape-color, held-out line-type, etc.) is comparably poor [2,37].…”