# Investigating Symbolic Capabilities of Large Language Models

arXiv: https://arxiv.org/abs/2405.13209 · HTML: https://mlsanity.com/paper/2405.13209/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 26 references that are in the map.
- First posted on arXiv 21 May 2024.

## Builds on (most cited first, 16 of 16)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [Analysing Mathematical Reasoning Abilities of Neural Models](https://mlsanity.com/paper/1904.01557/) (2019)
- [Mathematical Capabilities of ChatGPT](https://mlsanity.com/paper/2301.13867/) (2023)
- [Neural Networks and the Chomsky Hierarchy](https://mlsanity.com/paper/2207.02098/) (2022)
- [Physics of Language Models: Part 3.3, Knowledge Capacity Scaling Laws](https://mlsanity.com/paper/2404.05405/) (2024)
- [Recognizing and Verifying Mathematical Equations using Multiplicative Differential Neural Units](https://mlsanity.com/paper/2104.02899/) (2021)
- [On the Computational Complexity and Formal Hierarchy of Second Order Recurrent Neural Networks](https://mlsanity.com/paper/2309.14691/) (2023)
- [A Primer for Neural Arithmetic Logic Modules](https://mlsanity.com/paper/2101.09530/) (2021)
- [Recognizing Long Grammatical Sequences Using Recurrent Networks Augmented With An External Differentiable Stack](https://mlsanity.com/paper/2004.07623/) (2020)
- [Stability Analysis of Various Symbolic Rule Extraction Methods from Recurrent Neural Network](https://mlsanity.com/paper/2402.02627/) (2024)

## Built on by (most cited first, 8 of 8)

- [Multilingual Mathematical Reasoning: Advancing Open-Source LLMs in Hindi and English](https://mlsanity.com/paper/2412.18415/) (2024)
- [Through the Thicket: A Study of Number-Oriented LLMs derived from Random Forest Models](https://mlsanity.com/paper/2406.04926/) (2024)
- [From Gameplay Traces to Game Mechanics: Causal Induction with Large Language Models](https://mlsanity.com/paper/2602.00190/) (2026)
- [Small Models, Smarter Learning: The Power of Joint Task Training](https://mlsanity.com/paper/2505.18369/) (2025)
- [Training Large Reasoning Models Efficiently via Progressive Thought Encoding](https://mlsanity.com/paper/2602.16839/) (2026)
- [Exploring Learnability in Memory-Augmented Recurrent Neural Networks: Precision, Stability, and Empirical Insights](https://mlsanity.com/paper/2410.03154/) (2024)
- [ReaLM: Reflection-Enhanced Autonomous Reasoning with Small Language Models](https://mlsanity.com/paper/2508.12387/) (2025)
- [Rethinking Reasoning in LLMs: Neuro-Symbolic Local RetoMaton Beyond ICL and CoT](https://mlsanity.com/paper/2508.19271/) (2025)

## Abstract (arXiv)

Prompting techniques have significantly enhanced the capabilities of Large Language Models (LLMs) across various complex tasks, including reasoning, planning, and solving math word problems. However, most research has predominantly focused on language-based reasoning and word problems, often overlooking the potential of LLMs in handling symbol-based calculations and reasoning. This study aims to bridge this gap by rigorously evaluating LLMs on a series of symbolic tasks, such as addition, multiplication, modulus arithmetic, numerical precision, and symbolic counting. Our analysis encompasses eight LLMs, including four enterprise-grade and four open-source models, of which three have been pre-trained on mathematical tasks. The assessment framework is anchored in Chomsky's Hierarchy, providing a robust measure of the computational abilities of these models. The evaluation employs minimally explained prompts alongside the zero-shot Chain of Thoughts technique, allowing models to navigate the solution process autonomously. The findings reveal a significant decline in LLMs' performance on context-free and context-sensitive symbolic tasks as the complexity, represented by the number of symbols, increases. Notably, even the fine-tuned GPT3.5 exhibits only marginal improvements, mirroring the performance trends observed in other models. Across the board, all models demonstrated a limited generalization ability on these symbol-intensive tasks. This research underscores LLMs' challenges with increasing symbolic complexity and highlights the need for specialized training, memory and architectural adjustments to enhance their proficiency in symbol-based reasoning tasks.