Large language models (LLMs) continue to face challenges in reliably solving reasoning tasks, particularly tasks that involve precise rule following, as often found in mathematical reasoning tasks. 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. Our 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), while not hindering the LLM’s performance on other tasks. We make our code available at https://github.com/vdhanraj/Neurosymbolic-LLM.

With the advancement of large pretrained language models (PLMs), many question answering (QA) benchmarks have been developed in order to evaluate the reasoning capabilities of these models. Augmenting PLMs with external knowledge in the form of Knowledge Graphs (KGs) has been a popular method to improve their reasoning capabilities, and a common method to reason over KGs is to use Graph Neural Networks (GNNs). As an alternative to GNNs to augment PLMs, we propose a novel graph reasoning module using Vector Symbolic Algebra (VSA) graph representations and a k-layer MLP. We demonstrate that our VSA-based model performs as well as QA-GNN, a model combining a PLM and a GNN-module, on 3 multiple-choice question answering (MCQA) datasets. Our model has a simpler architecture than QA-GNN and also converges 39% faster during training.