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    <titleInfo>
        <title>KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?</title>
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    <name type="personal">
        <namePart type="given">Soumadeep</namePart>
        <namePart type="family">Saha</namePart>
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        <namePart type="given">Akshay</namePart>
        <namePart type="family">Chaturvedi</namePart>
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        <namePart type="given">Saptarshi</namePart>
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    <name type="personal">
        <namePart type="given">Utpal</namePart>
        <namePart type="family">Garain</namePart>
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    <name type="personal">
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    <abstract>Chain-of-thought (CoT) traces have been shown to improve performance of large language models on a plethora of reasoning tasks, yet there is no consensus on the mechanism by which this boost is achieved. To shed more light on this, we introduce Causal CoT Graphs (CCGraphs), which are directed acyclic graphs automatically extracted from reasoning traces that model finegrained causal dependencies in language-model outputs. A collection of 1671 mathematical reasoning problems from MATH500, GSM8K, and AIME, together with their associated CCGraphs, has been compiled into our dataset—KisMATH. Our detailed empirical analysis with 15 open-weight LLMs shows that (i) reasoning nodes in the CCGraphs are causal contributors to the final answer, which we argue is constitutive of reasoning; and (ii) LLMs emphasize the reasoning paths captured by the CCGraphs, indicating that the models internally realize structures similar to our graphs. KisMATH enables controlled, graph-aligned interventions and opens avenues for further investigation into the role of CoT in LLM reasoning.</abstract>
    <identifier type="citekey">saha-etal-2026-kismath</identifier>
    <identifier type="doi">10.1162/tacl.a.729</identifier>
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        <date>2026</date>
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            <start>1308</start>
            <end>1328</end>
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%0 Journal Article
%T KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?
%A Saha, Soumadeep
%A Chaturvedi, Akshay
%A Saha, Saptarshi
%A Garain, Utpal
%A Asher, Nicholas
%J Transactions of the Association for Computational Linguistics
%D 2026
%V 14
%I MIT Press
%C Cambridge, MA
%F saha-etal-2026-kismath
%X Chain-of-thought (CoT) traces have been shown to improve performance of large language models on a plethora of reasoning tasks, yet there is no consensus on the mechanism by which this boost is achieved. To shed more light on this, we introduce Causal CoT Graphs (CCGraphs), which are directed acyclic graphs automatically extracted from reasoning traces that model finegrained causal dependencies in language-model outputs. A collection of 1671 mathematical reasoning problems from MATH500, GSM8K, and AIME, together with their associated CCGraphs, has been compiled into our dataset—KisMATH. Our detailed empirical analysis with 15 open-weight LLMs shows that (i) reasoning nodes in the CCGraphs are causal contributors to the final answer, which we argue is constitutive of reasoning; and (ii) LLMs emphasize the reasoning paths captured by the CCGraphs, indicating that the models internally realize structures similar to our graphs. KisMATH enables controlled, graph-aligned interventions and opens avenues for further investigation into the role of CoT in LLM reasoning.
%R 10.1162/tacl.a.729
%U https://aclanthology.org/2026.tacl-1.59/
%U https://doi.org/10.1162/tacl.a.729
%P 1308-1328

Markdown (Informal)

[KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?](https://aclanthology.org/2026.tacl-1.59/) (Saha et al., TACL 2026)

• KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? (Saha et al., TACL 2026)

ACL

• Soumadeep Saha, Akshay Chaturvedi, Saptarshi Saha, Utpal Garain, and Nicholas Asher. 2026. KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?. Transactions of the Association for Computational Linguistics, 14:1308–1328.