Recognition: 1 theorem link
Are NLP Models really able to Solve Simple Math Word Problems?
Pith reviewed 2026-05-16 17:26 UTC · model grok-4.3
The pith
NLP solvers for simple math word problems achieve high benchmark scores by exploiting shallow patterns instead of actual reasoning.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
Existing MWP solvers rely on shallow heuristics rather than genuine arithmetic reasoning, as shown by their continued high accuracy when the question text is withheld or when problems are treated as unordered word collections, and by the sharp drop in performance on the SVAMP dataset that applies controlled variations to block those heuristics.
What carries the argument
The SVAMP dataset, constructed by applying carefully chosen variations to sampled examples from existing benchmarks to preserve the arithmetic requirement while removing reliance on surface patterns.
If this is right
- High accuracy on existing MWP benchmarks does not demonstrate that models perform true arithmetic reasoning.
- New evaluation sets must incorporate systematic variations to prevent exploitation of dataset-specific patterns.
- Research attention should prioritize models that maintain performance across rephrasings of the same underlying problem.
- Even for one-unknown elementary problems, current solvers have not reached reliable reasoning capability.
Where Pith is reading between the lines
- Similar pattern-based shortcuts may inflate reported progress in other structured NLP tasks that rely on narrow benchmarks.
- Training regimes could be redesigned to penalize solutions that ignore question wording or word order.
- Practitioners should routinely test deployed MWP systems on adversarial rephrasings before trusting their outputs.
Load-bearing premise
The specific variations used to build SVAMP are sufficient to block every shallow heuristic that current models might exploit.
What would settle it
State-of-the-art models achieving accuracy on SVAMP comparable to their scores on the original benchmarks would indicate that the variations failed to eliminate the relevant shortcuts.
read the original abstract
The problem of designing NLP solvers for math word problems (MWP) has seen sustained research activity and steady gains in the test accuracy. Since existing solvers achieve high performance on the benchmark datasets for elementary level MWPs containing one-unknown arithmetic word problems, such problems are often considered "solved" with the bulk of research attention moving to more complex MWPs. In this paper, we restrict our attention to English MWPs taught in grades four and lower. We provide strong evidence that the existing MWP solvers rely on shallow heuristics to achieve high performance on the benchmark datasets. To this end, we show that MWP solvers that do not have access to the question asked in the MWP can still solve a large fraction of MWPs. Similarly, models that treat MWPs as bag-of-words can also achieve surprisingly high accuracy. Further, we introduce a challenge dataset, SVAMP, created by applying carefully chosen variations over examples sampled from existing datasets. The best accuracy achieved by state-of-the-art models is substantially lower on SVAMP, thus showing that much remains to be done even for the simplest of the MWPs.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper claims that state-of-the-art NLP solvers for elementary math word problems (MWPs) achieve high benchmark accuracy by exploiting shallow heuristics rather than performing genuine arithmetic reasoning. This is evidenced by strong model performance when the question text is removed, when inputs are treated as bag-of-words, and by a substantial accuracy drop on the newly introduced SVAMP dataset created via targeted variations on existing examples.
Significance. If the results hold, the work is significant for exposing that reported high accuracies on simple MWPs do not reflect robust reasoning, thereby challenging the view that such problems are solved and motivating better evaluation practices. Credit is due for the direct empirical measurements (question ablation and bag-of-words baselines) against existing models plus the construction of the SVAMP dataset as a falsifiable challenge set that produces measurable performance degradation.
minor comments (2)
- [§4] §4 (SVAMP construction): provide a more explicit enumeration of the specific variations applied and the heuristics each is intended to block, to strengthen the claim that SVAMP isolates reasoning from shallow cues.
- [Table 1] Table 1 and §3.2: report the exact tokenization and feature extraction procedure for the bag-of-words baseline so that the high accuracy numbers can be reproduced without ambiguity.
Simulated Author's Rebuttal
We thank the referee for the positive summary and recommendation of minor revision. The assessment accurately captures the core contribution of our work in demonstrating that high benchmark accuracies on elementary MWPs do not necessarily indicate robust reasoning.
Circularity Check
No significant circularity detected
full rationale
The paper advances its claims through direct empirical measurements on existing MWP datasets and a newly constructed challenge set SVAMP. It reports accuracy of ablated models (no question text) and bag-of-words models on standard benchmarks, then shows performance drop under targeted variations. These are observational results from running existing solvers and constructing test examples; no derivation chain, equations, fitted parameters presented as predictions, or self-citation load-bearing steps exist. The argument is self-contained against external benchmarks and does not reduce any result to its inputs by construction.
Axiom & Free-Parameter Ledger
axioms (1)
- domain assumption Existing benchmark datasets for elementary MWPs contain shallow patterns that models can exploit without solving the arithmetic
invented entities (1)
-
SVAMP dataset
no independent evidence
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Reference graph
Works this paper leans on
-
[1]
Suchin Gururangan, Swabha Swayamdipta, Omer Levy, Roy Schwartz, Samuel Bowman, and Noah A
Evaluating models’ local decision boundaries via contrast sets. Suchin Gururangan, Swabha Swayamdipta, Omer Levy, Roy Schwartz, Samuel Bowman, and Noah A. Smith. 2018. Annotation artifacts in natural lan- guage inference data. In Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Linguistics: Human Langua...
work page 2018
-
[2]
A diverse corpus for evaluating and develop- ing English math word problem solvers. In Proceed- ings of the 58th Annual Meeting of the Association for Computational Linguistics, pages 975–984, On- line. Association for Computational Linguistics. Yixin Nie, Adina Williams, Emily Dinan, Mohit Bansal, Jason Weston, and Douwe Kiela. 2020. Ad- versarial NLI: A...
work page 2020
-
[3]
Exposing Shallow Heuristics of Relation Ex- traction Models with Challenge Data. In Proceed- ings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP) , pages 3702–3710, Online. Association for Computational Linguistics. Subhro Roy and Dan Roth. 2018. Mapping to declara- tive knowledge for word problem solving. Transac- tions...
work page 2020
-
[4]
IEEE Transac- tions on Pattern Analysis and Machine Intelligence , 42(9):2287–2305
The gap of semantic parsing: A survey on au- tomatic math word problem solvers. IEEE Transac- tions on Pattern Analysis and Machine Intelligence , 42(9):2287–2305. Jipeng Zhang, Lei Wang, Roy Ka-Wei Lee, Yi Bin, Yan Wang, Jie Shao, and Ee-Peng Lim. 2020. Graph-to- tree learning for solving math word problems. In Proceedings of the 58th Annual Meeting of t...
work page 2020
-
[5]
The scores on Question-removed datasets are provided in Table 17 and on SV AMP challenge set is provided in Table 18. B Implementation Details We use 8 NVIDIA Tesla P100 GPUs each with 16 GB memory to run our experiments. The hyperpa- rameters used for each model are shown in Table
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[6]
The best hyperparameters are highlighted in bold
The hyperparameters used in for the Trans- former model are provided in Table 20. The best hyperparameters are highlighted in bold. Follow- ing the setting of Zhang et al. (2020), the arithmetic word problems from MAWPS are divided into five folds, each of equal test size. For ASDiv-A, we consider the 5-fold split [238, 238, 238, 238, 266] provided by the ...
work page 2020
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[7]
Apply the Question Sensitivity variations on the Base Example
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[8]
Apply the Invert Operation variation on the Base Example and on all the variations ob- tained so far
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[9]
Then considering these variations as Base Examples, apply the Ques- tion Sensitivity variations
Apply the Add relevant information variation on the Base Example. Then considering these variations as Base Examples, apply the Ques- tion Sensitivity variations
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[10]
Apply the Add irrelevant information varia- tion on the Base Example and on all the vari- ations obtained so far
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[11]
Apply the Change information variation on the Base Example and on all the variations obtained so far
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[12]
Table 25 provides some variations for the exam- ple in Table 24
Apply the Change order of Objects and Change order of Events or Phrases variations on the Base Example and on all the variations obtained so far. Table 25 provides some variations for the exam- ple in Table 24. Note that two seperate examples were created through the ’Add irrelevant informa- tion’ variation. The first by applying the variation on the Origi...
work page 2020
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