# Exploring the Compositional Deficiency of Large Language Models in Mathematical Reasoning arXiv: https://arxiv.org/abs/2405.06680 ยท HTML: https://mlsanity.com/paper/2405.06680/ ## Key facts - Cited by 15 papers in the map (data through 14 Oct 2026). - Placed in Mathematical reasoning, one of 17 directions in LLM reasoning. - Builds on 18 of its 40 references that are in the map. - First posted on arXiv 5 May 2024. ## Placed in - LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/) ## Builds on (most cited first, 18 of 18) - [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) - [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023) - [DeepSeek-Coder: When the Large Language Model Meets Programming -- The Rise of Code Intelligence](https://mlsanity.com/paper/2401.14196/) (2024) - [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021) - [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (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) - [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021) - [Reasoning or Reciting? Exploring the Capabilities and Limitations of Language Models Through Counterfactual Tasks](https://mlsanity.com/paper/2307.02477/) (2023) - [The pitfalls of next-token prediction](https://mlsanity.com/paper/2403.06963/) (2024) - [OpenMathInstruct-1: A 1.8 Million Math Instruction Tuning Dataset](https://mlsanity.com/paper/2402.10176/) (2024) - [LAMBADA: Backward Chaining for Automated Reasoning in Natural Language](https://mlsanity.com/paper/2212.13894/) (2022) - [Training Large Language Models for Reasoning through Reverse Curriculum Reinforcement Learning](https://mlsanity.com/paper/2402.05808/) (2024) - [Self-Polish: Enhance Reasoning in Large Language Models via Problem Refinement](https://mlsanity.com/paper/2305.14497/) (2023) - [On the Compositional Generalization Gap of In-Context Learning](https://mlsanity.com/paper/2211.08473/) (2022) - [RobustLR: Evaluating Robustness to Logical Perturbation in Deductive Reasoning](https://mlsanity.com/paper/2205.12598/) (2022) - [Humans in Humans Out: On GPT Converging Toward Common Sense in both Success and Failure](https://mlsanity.com/paper/2303.17276/) (2023) ## Built on by (most cited first, 15 of 15) - [Large Language Model Reasoning Failures](https://mlsanity.com/paper/2602.06176/) (2026) - [Limits of Deep Learning: Sequence Modeling through the Lens of Complexity Theory](https://mlsanity.com/paper/2405.16674/) (2024) - [Recitation over Reasoning: How Cutting-Edge Language Models Can Fail on Elementary School-Level Reasoning Problems?](https://mlsanity.com/paper/2504.00509/) (2025) - [Unveiling the Compositional Ability Gap in Vision-Language Reasoning Model](https://mlsanity.com/paper/2505.19406/) (2025) - [AI Can Learn Scientific Taste](https://mlsanity.com/paper/2603.14473/) (2026) - [EvaLearn: Quantifying the Learning Capability and Efficiency of LLMs via Sequential Problem Solving](https://mlsanity.com/paper/2506.02672/) (2025) - [MathDebugger: Detecting and Diagnosing Errors in Synthetic Mathematical Data](https://mlsanity.com/paper/2502.19058/) (2025) - [The Thin Line Between Comprehension and Persuasion in LLMs](https://mlsanity.com/paper/2507.01936/) (2025) - [Barriers to Discrete Reasoning with Transformers: A Survey Across Depth, Exactness, and Bandwidth](https://mlsanity.com/paper/2602.11175/) (2026) - [CompoST: A Benchmark for Analyzing the Ability of LLMs To Compositionally Interpret Questions in a QALD Setting](https://mlsanity.com/paper/2507.21257/) (2025) - [Theme-Explanation Structure for Table Summarization using Large Language Models: A Case Study on Korean Tabular Data](https://mlsanity.com/paper/2501.10487/) (2025) - [Diagnosing Structural Failures in LLM-Based Evidence Extraction for Meta-Analysis](https://mlsanity.com/paper/2602.10881/) (2026) - [FlowEdit: Information-Theoretic Control of LLM Reasoning Flows for Ill-posed Problems Involving Conflicts](https://mlsanity.com/paper/2607.20500/) (2026) - [R2A: Learning Persona Policies Through Persona Representation Learning and Runtime Alignment](https://mlsanity.com/paper/2608.29798/) (2026) - [When Tokenization is Secretly Output Supervision](https://mlsanity.com/paper/2609.01386/) (2026) ## Abstract (arXiv) Human cognition exhibits systematic compositionality, the algebraic ability to generate infinite novel combinations from finite learned components, which is the key to understanding and reasoning about complex logic. In this work, we investigate the compositionality of large language models (LLMs) in mathematical reasoning. Specifically, we construct a new dataset textscMathTrap by introducing carefully designed logical traps into the problem descriptions of MATH and GSM8K. Since problems with logical flaws are quite rare in the real world, these represent "unseen" cases to LLMs. Solving these requires the models to systematically compose (1) the mathematical knowledge involved in the original problems with (2) knowledge related to the introduced traps. Our experiments show that while LLMs possess both components of requisite knowledge, they do not spontaneously combine them to handle these novel cases. We explore several methods to mitigate this deficiency, such as natural language prompts, few-shot demonstrations, and fine-tuning. Additionally, we test the recently released OpenAI o1 model and find that human-like `slow thinking' helps improve the compositionality of LLMs. Overall, systematic compositionality remains an open challenge for large language models.