Pretrained Language Models are Symbolic Mathematics Solvers too!

TL;DR

This paper demonstrates that pretrained language models can efficiently solve symbolic mathematics problems, achieving high accuracy with significantly less training data by leveraging language translation pretraining.

Contribution

The authors introduce a sample-efficient pretraining approach for transformer models using language translation, improving symbolic mathematics solving with less data and analyzing language bias and robustness.

Findings

Achieves comparable integration accuracy with 1.5 orders of magnitude less data.

Lower accuracy on differential equations due to higher-order recursions.

Pretraining with language translation enhances generalization and robustness.

Abstract

Solving symbolic mathematics has always been of in the arena of human ingenuity that needs compositional reasoning and recurrence. However, recent studies have shown that large-scale language models such as transformers are universal and surprisingly can be trained as a sequence-to-sequence task to solve complex mathematical equations. These large transformer models need humongous amounts of training data to generalize to unseen symbolic mathematics problems. In this paper, we present a sample efficient way of solving the symbolic tasks by first pretraining the transformer model with language translation and then fine-tuning the pretrained transformer model to solve the downstream task of symbolic mathematics. We achieve comparable accuracy on the integration task with our pretrained model while using around $1.5$ orders of magnitude less number of training samples with respect to the state-of-the-art deep learning for symbolic mathematics. The test accuracy on differential equation tasks is considerably lower comparing with integration as they need higher order recursions that are not present in language translations. We propose the generalizability of our pretrained language model from Anna Karenina Principle (AKP). We pretrain our model with different pairs of language translations. Our results show language bias in solving symbolic mathematics tasks. Finally, we study the robustness of the fine-tuned model on symbolic math tasks against distribution shift, and our approach generalizes better in distribution shift scenarios for the function integration.