Calc-X and Calcformers: Empowering Arithmetical Chain-of-Thought through Interaction with Symbolic Systems
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
- 2021Training Verifiers to Solve Math Word Problemscited by 10,109
- 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,371
- 2014Neural Machine Translation by Jointly Learning to Align and Translatecited by 4,548
- 2023Toolformer: Language Models Can Teach Themselves to Use Toolscited by 4,182
- 2022Scaling Instruction-Finetuned Language Modelscited by 3,024
- 2021WebGPT: Browser-assisted question-answering with human feedbackcited by 1,745
- 2022LaMDA: Language Models for Dialog Applicationscited by 1,220
- 2019MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalismscited by 662
- 2022PAL: Program-aided Language Modelscited by 652
- 2017Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problemscited by 650
- 2019Analysing Mathematical Reasoning Abilities of Neural Modelscited by 335
- 2022TALM: Tool Augmented Language Modelscited by 197
1 more
Built on by
Citing papers per year: 2024: 6; 2025: 3; 2026: 4.
13 papers.
Sort:
By area:
- 2024Tool Learning with Large Language Models: A Surveycited by 223
- 2025Agent Lightning: Train ANY AI Agents with Reinforcement Learningcited by 109
- 2024Self-Training with Direct Preference Optimization Improves Chain-of-Thought Reasoningcited by 26
- 2026Skip a Layer or Loop It? Learning Program-of-Layers in LLMscited by 9
- 2024Learning by Analogy: Enhancing Few-Shot Prompting for Math Word Problem Solving with Computational Graph-Based Retrievalcited by 5
- 2024Improving Arithmetic Reasoning Ability of Large Language Models through Relation Tuples, Verification and Dynamic Feedbackcited by 4
- 2025Improving the OOD Performance of Closed-Source LLMs on NLI Through Strategic Data Selectioncited by 4
- 2025Pre-trained Language Models Learn Remarkably Accurate Representations of Numberscited by 4
- 2024Concept-aware Data Construction Improves In-context Learning of Language Modelscited by 2
- 2026Programs-of-Layers in LLMs through the Lens of Cortical Areascited by 1
- 2024Pre-Calc: Learning to Use the Calculator Improves Numeracy in Language Modelscited by 0
- 2026When Efficiency Backfires: Cascading LLMs Trigger Cascade Failure under Adversarial Attackcited by 0
1 more
- 2026Programs-of-Layers in LLMs through the Lens of Cortical Areas25 Sep 2026
- 2026Fusion Training for Mathematical Generalization in Large Language Models10 Aug 2026
- 2026Skip a Layer or Loop It? Learning Program-of-Layers in LLMs4 Jun 2026
- 2026When Efficiency Backfires: Cascading LLMs Trigger Cascade Failure under Adversarial Attack17 May 2026
- 2025Agent Lightning: Train ANY AI Agents with Reinforcement Learning5 Aug 2025
- 2025Pre-trained Language Models Learn Remarkably Accurate Representations of Numbers10 Jun 2025
- 2025Improving the OOD Performance of Closed-Source LLMs on NLI Through Strategic Data Selection26 May 2025
- 2024Learning by Analogy: Enhancing Few-Shot Prompting for Math Word Problem Solving with Computational Graph-Based Retrieval25 Nov 2024
- 2024Self-Training with Direct Preference Optimization Improves Chain-of-Thought Reasoning25 Jul 2024
- 2024Improving Arithmetic Reasoning Ability of Large Language Models through Relation Tuples, Verification and Dynamic Feedback25 Jun 2024
- 2024Tool Learning with Large Language Models: A Survey28 May 2024
- 2024Pre-Calc: Learning to Use the Calculator Improves Numeracy in Language Models22 Apr 2024
1 more
- 2024Self-Training with Direct Preference Optimization Improves Chain-of-Thought Reasoningcited by 26
- 2024Improving Arithmetic Reasoning Ability of Large Language Models through Relation Tuples, Verification and Dynamic Feedbackcited by 4
- 2026Fusion Training for Mathematical Generalization in Large Language Modelscited by 0
- 2026Fusion Training for Mathematical Generalization in Large Language Models10 Aug 2026
- 2024Self-Training with Direct Preference Optimization Improves Chain-of-Thought Reasoning25 Jul 2024
- 2024Improving Arithmetic Reasoning Ability of Large Language Models through Relation Tuples, Verification and Dynamic Feedback25 Jun 2024
- 2024Tool Learning with Large Language Models: A Surveycited by 223
- 2025Agent Lightning: Train ANY AI Agents with Reinforcement Learningcited by 109
- 2025Agent Lightning: Train ANY AI Agents with Reinforcement Learning5 Aug 2025
- 2024Tool Learning with Large Language Models: A Survey28 May 2024
- 2026Skip a Layer or Loop It? Learning Program-of-Layers in LLMscited by 9
- 2024Learning by Analogy: Enhancing Few-Shot Prompting for Math Word Problem Solving with Computational Graph-Based Retrievalcited by 5
- 2025Improving the OOD Performance of Closed-Source LLMs on NLI Through Strategic Data Selectioncited by 4
- 2025Pre-trained Language Models Learn Remarkably Accurate Representations of Numberscited by 4
- 2024Concept-aware Data Construction Improves In-context Learning of Language Modelscited by 2
- 2026Programs-of-Layers in LLMs through the Lens of Cortical Areascited by 1
- 2024Pre-Calc: Learning to Use the Calculator Improves Numeracy in Language Modelscited by 0
- 2026When Efficiency Backfires: Cascading LLMs Trigger Cascade Failure under Adversarial Attackcited by 0
- 2026Programs-of-Layers in LLMs through the Lens of Cortical Areas25 Sep 2026
- 2026Skip a Layer or Loop It? Learning Program-of-Layers in LLMs4 Jun 2026
- 2026When Efficiency Backfires: Cascading LLMs Trigger Cascade Failure under Adversarial Attack17 May 2026
- 2025Pre-trained Language Models Learn Remarkably Accurate Representations of Numbers10 Jun 2025
- 2025Improving the OOD Performance of Closed-Source LLMs on NLI Through Strategic Data Selection26 May 2025
- 2024Learning by Analogy: Enhancing Few-Shot Prompting for Math Word Problem Solving with Computational Graph-Based Retrieval25 Nov 2024
- 2024Pre-Calc: Learning to Use the Calculator Improves Numeracy in Language Models22 Apr 2024
- 2024Concept-aware Data Construction Improves In-context Learning of Language Models8 Mar 2024
Similar, not cited
Close in wording, no citation either way
- 2024Unraveling Arithmetic in Large Language Models: The Role of Algebraic Structures
- 2023Frugal LMs Trained to Invoke Symbolic Solvers Achieve Parameter-Efficient Arithmetic Reasoning
- 2024CoMAT: Chain of Mathematically Annotated Thought Improves Mathematical Reasoning
- 2026Arithmetic Pedagogy for Language Models
- 2025Chain-of-Reasoning: Towards Unified Mathematical Reasoning in Large Language Models via a Multi-Paradigm Perspective
- 2024MARIO: MAth Reasoning with code Interpreter Output -- A Reproducible Pipeline
- 2025Scaling Code-Assisted Chain-of-Thoughts and Instructions for Model Reasoning
- 2023Evaluating and Improving Tool-Augmented Computation-Intensive Math Reasoning