Symbolic Brittleness in Sequence Models: on Systematic Generalization in Symbolic Mathematics

TL;DR

This paper investigates the limitations of neural sequence models in symbolic mathematics, revealing challenges in systematic and out-of-distribution generalization despite strong in-distribution performance.

Contribution

It introduces a methodology for evaluating generalization in symbolic tasks and demonstrates the models' struggles with robustness, compositionality, and out-of-distribution scenarios.

Findings

Models perform well in-distribution but fail systematically out-of-distribution.

Manual test suites and genetic algorithms reveal numerous failure modes.

Highlighting the need for better evaluation methods and model robustness.

Abstract

Neural sequence models trained with maximum likelihood estimation have led to breakthroughs in many tasks, where success is defined by the gap between training and test performance. However, their ability to achieve stronger forms of generalization remains unclear. We consider the problem of symbolic mathematical integration, as it requires generalizing systematically beyond the test set. We develop a methodology for evaluating generalization that takes advantage of the problem domain's structure and access to a verifier. Despite promising in-distribution performance of sequence-to-sequence models in this domain, we demonstrate challenges in achieving robustness, compositionality, and out-of-distribution generalization, through both carefully constructed manual test suites and a genetic algorithm that automatically finds large collections of failures in a controllable manner. Our investigation highlights the difficulty of generalizing well with the predominant modeling and learning approach, and the importance of evaluating beyond the test set, across different aspects of generalization.