mlsanityData to 14 Oct 2026

Calc-X and Calcformers: Empowering Arithmetical Chain-of-Thought through Interaction with Symbolic Systems

arXiv 2305.15017 ↗First posted 24 May 2023cs.LG cs.AI cs.CLcited by 13

On the map: LLM reasoning → Mathematical reasoning

Abstract (arXiv)

Despite outstanding performance in many tasks, language models are notoriously inclined to make factual errors in tasks requiring arithmetic computation. We address this deficiency by creating Calc-X, a collection of datasets that demonstrates the appropriate use of a calculator in reasoning chains. Calc-X is suitable for teaching language models to offload computations to a symbolic system. We survey and unify several existing chain-of-thought datasets into a proposed format, resulting in a standard collection of over 300,000 samples requiring arithmetic reasoning. Finally, we use the new Calc-X collection to train open-source calculator-using models we call Calcformers and show that these models approximately double the accuracy of generating correct results compared to vanilla language model baselines. We make all Calc-X datasets, source code and Calcformers models publicly available.

Key facts. Cited by 13 papers in the map (data through 14 Oct 2026). Placed in Mathematical reasoning, one of 17 directions in LLM reasoning. Builds on 13 of its 22 references that are in the map. First posted on arXiv 24 May 2023.

Builds on

13 of 22 references.

References · 13

  1. 2021Training Verifiers to Solve Math Word Problemscited by 10,109
  2. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,371
  3. 2014Neural Machine Translation by Jointly Learning to Align and Translatecited by 4,548
  4. 2023Toolformer: Language Models Can Teach Themselves to Use Toolscited by 4,182
  5. 2022Scaling Instruction-Finetuned Language Modelscited by 3,024
  6. 2021WebGPT: Browser-assisted question-answering with human feedbackcited by 1,745
  7. 2022LaMDA: Language Models for Dialog Applicationscited by 1,220
  8. 2019MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalismscited by 662
  9. 2022PAL: Program-aided Language Modelscited by 652
  10. 2017Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problemscited by 650
  11. 2019Analysing Mathematical Reasoning Abilities of Neural Modelscited by 335
  12. 2022TALM: Tool Augmented Language Modelscited by 197
1 more
  1. 2020Ape210K: A Large-Scale and Template-Rich Dataset of Math Word Problemscited by 60

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Citing papers per year: 2024: 6; 2025: 3; 2026: 4.

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  1. 2024Unraveling Arithmetic in Large Language Models: The Role of Algebraic Structures
  2. 2023Frugal LMs Trained to Invoke Symbolic Solvers Achieve Parameter-Efficient Arithmetic Reasoning
  3. 2024CoMAT: Chain of Mathematically Annotated Thought Improves Mathematical Reasoning
  4. 2026Arithmetic Pedagogy for Language Models
  5. 2025Chain-of-Reasoning: Towards Unified Mathematical Reasoning in Large Language Models via a Multi-Paradigm Perspective
  6. 2024MARIO: MAth Reasoning with code Interpreter Output -- A Reproducible Pipeline
  7. 2025Scaling Code-Assisted Chain-of-Thoughts and Instructions for Model Reasoning
  8. 2023Evaluating and Improving Tool-Augmented Computation-Intensive Math Reasoning