Improving Rule-based Reasoning in LLMs using Neurosymbolic Representations

TL;DR

This paper presents a neurosymbolic approach that enhances large language models' reasoning capabilities by encoding hidden states into neurosymbolic vectors, significantly improving performance on mathematical reasoning tasks while maintaining efficiency and interpretability.

Contribution

The paper introduces a novel neurosymbolic method that encodes LLM hidden states into vectors, boosting reasoning performance and efficiency without degrading other task performances.

Findings

88.6% lower cross-entropy loss

15.4 times more problems solved correctly

Improved reliability and interpretability

Abstract

Large language models (LLMs) continue to face challenges in reliably solving reasoning tasks, particularly those that require precise rule following, as often found in mathematical reasoning. This paper introduces a novel neurosymbolic method that improves LLM reasoning by encoding hidden states into neurosymbolic vectors, enabling problem-solving within a neurosymbolic vector space. The results are decoded and merged with the original hidden state, significantly boosting the model's performance on numerical reasoning tasks. By offloading computation through neurosymbolic representations, this method enhances efficiency, reliability, and interpretability. Experimental results demonstrate an average of 88.6% lower cross-entropy loss and 15.4 times more problems correctly solved on a suite of mathematical reasoning tasks compared to chain-of-thought prompting and supervised fine-tuning (LoRA), without degrading performance on other tasks. We make our code available at: https://github.com/vdhanraj/Neurosymbolic-LLM.