# Improving Rule-based Reasoning in LLMs using Neurosymbolic Representations

arXiv: https://arxiv.org/abs/2502.01657 · HTML: https://mlsanity.com/paper/2502.01657/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 19 of its 39 references that are in the map.
- First posted on arXiv 31 Jan 2025.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 19 of 19)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [Fast Transformer Decoding: One Write-Head is All You Need](https://mlsanity.com/paper/1911.02150/) (2019)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [Delta Tuning: A Comprehensive Study of Parameter Efficient Methods for Pre-trained Language Models](https://mlsanity.com/paper/2203.06904/) (2022)
- [LINC: A Neurosymbolic Approach for Logical Reasoning by Combining Language Models with First-Order Logic Provers](https://mlsanity.com/paper/2310.15164/) (2023)
- [ARC Prize 2024: Technical Report](https://mlsanity.com/paper/2412.04604/) (2024)
- [Scaling Laws for Forgetting When Fine-Tuning Large Language Models](https://mlsanity.com/paper/2401.05605/) (2024)
- [Top-N: Equivariant set and graph generation without exchangeability](https://mlsanity.com/paper/2110.02096/) (2021)
- [SymbolicAI: A framework for logic-based approaches combining generative models and solvers](https://mlsanity.com/paper/2402.00854/) (2024)
- [ChatLogic: Integrating Logic Programming with Large Language Models for Multi-Step Reasoning](https://mlsanity.com/paper/2407.10162/) (2024)
- [PerfSAGE: Generalized Inference Performance Predictor for Arbitrary Deep Learning Models on Edge Devices](https://mlsanity.com/paper/2301.10999/) (2023)
- [Frauds Bargain Attack: Generating Adversarial Text Samples via Word Manipulation Process](https://mlsanity.com/paper/2303.01234/) (2023)
- [Fairness-Aware Data Valuation for Supervised Learning](https://mlsanity.com/paper/2303.16963/) (2023)
- [Assessing the Emergent Symbolic Reasoning Abilities of Llama Large Language Models](https://mlsanity.com/paper/2406.06588/) (2024)

## Built on by (most cited first, 3 of 3)

- [The Bicameral Model: Bidirectional Hidden-State Coupling Between Parallel Language Models](https://mlsanity.com/paper/2605.11167/) (2026)
- [Shaping Schema via Language Representation as the Next Frontier for LLM Intelligence Expanding](https://mlsanity.com/paper/2605.09271/) (2026)
- [SafeMath: Safe Solutions for Unsafe Math Word Problems](https://mlsanity.com/paper/2603.25201/) (2026)

## Abstract (arXiv)

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.