# Can LLMs Reason Abstractly Over Math Word Problems Without CoT? Disentangling Abstract Formulation From Arithmetic Computation

arXiv: https://arxiv.org/abs/2505.23701 · HTML: https://mlsanity.com/paper/2505.23701/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 45 of its 64 references that are in the map.
- First posted on arXiv 29 May 2025.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 30 of 45)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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 Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Large Language Models Can Be Easily Distracted by Irrelevant Context](https://mlsanity.com/paper/2302.00093/) (2023)
- [AGIEval: A Human-Centric Benchmark for Evaluating Foundation Models](https://mlsanity.com/paper/2304.06364/) (2023)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [Eliciting Latent Predictions from Transformers with the Tuned Lens](https://mlsanity.com/paper/2303.08112/) (2023)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Towards Best Practices of Activation Patching in Language Models: Metrics and Methods](https://mlsanity.com/paper/2309.16042/) (2023)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [Think before you speak: Training Language Models With Pause Tokens](https://mlsanity.com/paper/2310.02226/) (2023)
- [To CoT or not to CoT? Chain-of-thought helps mainly on math and symbolic reasoning](https://mlsanity.com/paper/2409.12183/) (2024)
- [TokenSkip: Controllable Chain-of-Thought Compression in LLMs](https://mlsanity.com/paper/2502.12067/) (2025)
- [Patchscopes: A Unifying Framework for Inspecting Hidden Representations of Language Models](https://mlsanity.com/paper/2401.06102/) (2024)
- [Compressed Chain of Thought: Efficient Reasoning Through Dense Representations](https://mlsanity.com/paper/2412.13171/) (2024)
- [Localizing Model Behavior with Path Patching](https://mlsanity.com/paper/2304.05969/) (2023)
- [Let's Think Dot by Dot: Hidden Computation in Transformer Language Models](https://mlsanity.com/paper/2404.15758/) (2024)
- [A Careful Examination of Large Language Model Performance on Grade School Arithmetic](https://mlsanity.com/paper/2405.00332/) (2024)
- [Reasoning Models Can Be Effective Without Thinking](https://mlsanity.com/paper/2504.09858/) (2025)
- [Evaluating the Performance of Large Language Models on GAOKAO Benchmark](https://mlsanity.com/paper/2305.12474/) (2023)

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

- [Training Language Models via Neural Cellular Automata](https://mlsanity.com/paper/2603.10055/) (2026)
- [In-Context Algebra](https://mlsanity.com/paper/2512.16902/) (2025)
- [Are Arithmetic Heuristic Neurons Form-Invariant? A Mechanistic Analysis of Symbols, Text, and Code in LLMs](https://mlsanity.com/paper/2607.16693/) (2026)
- [Mechanistic Interpretability of Chain-of-Thought Reasoning via Sequential Activation Patching](https://mlsanity.com/paper/2608.22332/) (2026)
- [Value-Aware Numerical Representations for Transformer Language Models](https://mlsanity.com/paper/2601.09706/) (2026)
- [From Abstract to Contextual: What LLMs Still Cannot Do in Mathematics](https://mlsanity.com/paper/2601.23048/) (2026)
- [Semantic Bandits: In-Context Exploration-Exploitation is Biased by Semantic Priors](https://mlsanity.com/paper/2608.16707/) (2026)
- [When Tokenization is Secretly Output Supervision](https://mlsanity.com/paper/2609.01386/) (2026)

## Abstract (arXiv)

Final-answer-based metrics are commonly used for evaluating large language models (LLMs) on math word problems, often taken as proxies for reasoning ability. However, such metrics conflate two distinct sub-skills: abstract formulation (capturing mathematical relationships using expressions) and arithmetic computation (executing the calculations). Through a disentangled evaluation on GSM8K and SVAMP, we find that the final-answer accuracy of Llama-3 and Qwen2.5 (1B-32B) without CoT is overwhelmingly bottlenecked by the arithmetic computation step and not by the abstract formulation step. Contrary to the common belief, we show that CoT primarily aids in computation, with limited impact on abstract formulation. Mechanistically, we show that these two skills are composed conjunctively even in a single forward pass without any reasoning steps via an abstract-then-compute mechanism: models first capture problem abstractions, then handle computation. Causal patching confirms these abstractions are present, transferable, composable, and precede computation. These behavioural and mechanistic findings highlight the need for disentangled evaluation to accurately assess LLM reasoning and to guide future improvements.