Can LLMs Reason Abstractly Over Math Word Problems Without CoT? Disentangling Abstract Formulation From Arithmetic Computation
Bibliographic record
Abstract
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.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".