mlsanityData to 7 Oct 2026

Chaining Simultaneous Thoughts for Numerical Reasoning

arXiv 2211.16482 ↗First posted 29 Nov 2022cs.CL cs.AIcited by 14

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Abstract (arXiv)

Given that rich information is hidden behind ubiquitous numbers in text, numerical reasoning over text should be an essential skill of AI systems. To derive precise equations to solve numerical reasoning problems, previous work focused on modeling the structures of equations, and has proposed various structured decoders. Though structure modeling proves to be effective, these structured decoders construct a single equation in a pre-defined autoregressive order, potentially placing an unnecessary restriction on how a model should grasp the reasoning process. Intuitively, humans may have numerous pieces of thoughts popping up in no pre-defined order; thoughts are not limited to the problem at hand, and can even be concerned with other related problems. By comparing diverse thoughts and chaining relevant pieces, humans are less prone to errors. In this paper, we take this inspiration and propose CANTOR, a numerical reasoner that models reasoning steps using a directed acyclic graph where we produce diverse reasoning steps simultaneously without pre-defined decoding dependencies, and compare and chain relevant ones to reach a solution. Extensive experiments demonstrated the effectiveness of CANTOR under both fully-supervised and weakly-supervised settings.

Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). Builds on 26 of its 42 references that are in the map. First posted on arXiv 29 Nov 2022.

Builds on

26 of 42 references.

References · 26

  1. 2017Attention Is All You Needcited by 59,932
  2. 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,204
  3. 2019RoBERTa: A Robustly Optimized BERT Pretraining Approachcited by 13,266
  4. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,302
  5. 2021Training Verifiers to Solve Math Word Problemscited by 9,743
  6. 2022PaLM: Scaling Language Modeling with Pathwayscited by 5,304
  7. 2019DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphscited by 883
  8. 2021Are NLP Models really able to Solve Simple Math Word Problems?cited by 861
  9. 2019MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalismscited by 653
  10. 2021FinQA: A Dataset of Numerical Reasoning over Financial Datacited by 552
  11. 2017Non-Autoregressive Neural Machine Translationcited by 457
  12. 2021A Diverse Corpus for Evaluating and Developing English Math Word Problem Solverscited by 314
14 more
  1. 2022NumGLUE: A Suite of Fundamental yet Challenging Mathematical Reasoning Taskscited by 110
  2. 2021Generate & Rank: A Multi-task Framework for Math Word Problemscited by 82
  3. 2019A Discrete Hard EM Approach for Weakly Supervised Question Answeringcited by 78
  4. 2020Aligned Cross Entropy for Non-Autoregressive Machine Translationcited by 65
  5. 2021Order-Agnostic Cross Entropy for Non-Autoregressive Machine Translationcited by 57
  6. 2022Learning to Reason Deductively: Math Word Problem Solving as Complex Relation Extractioncited by 44
  7. 2022Directed Acyclic Transformer for Non-Autoregressive Machine Translationcited by 44
  8. 2019EQUATE: A Benchmark Evaluation Framework for Quantitative Reasoning in Natural Language Inferencecited by 39
  9. 2021MWPToolkit: An Open-Source Framework for Deep Learning-Based Math Word Problem Solverscited by 39
  10. 2021Seeking Patterns, Not just Memorizing Procedures: Contrastive Learning for Solving Math Word Problemscited by 30
  11. 2021Investigating Math Word Problems using Pretrained Multilingual Language Modelscited by 21
  12. 2021Span Pointer Networks for Non-Autoregressive Task-Oriented Semantic Parsingcited by 18
  13. 2021Non-Autoregressive Semantic Parsing for Compositional Task-Oriented Dialogcited by 17
  14. 2021A Mutual Information Maximization Approach for the Spurious Solution Problem in Weakly Supervised Question Answeringcited by 2

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Citing papers per year: 2023: 5; 2024: 5; 2025: 4.

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  1. 2023ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solvingcited by 276
  2. 2024Tool Learning with Large Language Models: A Surveycited by 221
  3. 2024MARIO: MAth Reasoning with code Interpreter Output -- A Reproducible Pipelinecited by 81
  4. 2025Self-rewarding correction for mathematical reasoningcited by 67
  5. 2024Building Math Agents with Multi-Turn Iterative Preference Learningcited by 66
  6. 2025ACEBench: Who Wins the Match Point in Tool Usage?cited by 66
  7. 2023Interpretable Math Word Problem Solution Generation Via Step-by-step Planningcited by 17
  8. 2023Leveraging Training Data in Few-Shot Prompting for Numerical Reasoningcited by 11
  9. 2024A Theory for Length Generalization in Learning to Reasoncited by 11
  10. 2023Math Word Problem Solving by Generating Linguistic Variants of Problem Statementscited by 7
  11. 2023Conditions for Length Generalization in Learning Reasoning Skillscited by 7
  12. 2025Local Look-Ahead Guidance via Verifier-in-the-Loop for Automated Theorem Provingcited by 2
2 more
  1. 2024Data Augmentation with In-Context Learning and Comparative Evaluation in Math Word Problem Solvingcited by 0
  2. 2025A Diversity-Enhanced Knowledge Distillation Model for Practical Math Word Problem Solvingcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024CoMAT: Chain of Mathematically Annotated Thought Improves Mathematical Reasoning
  2. 2022Learning to Reason With Relational Abstractions
  3. 2026Cognitive Loop of Thought: Reversible Hierarchical Markov Chain for Efficient Mathematical Reasoning
  4. 2022Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks
  5. 2024Diffusion of Thoughts: Chain-of-Thought Reasoning in Diffusion Language Models
  6. 2025A Formal Comparison Between Chain of Thought and Latent Thought
  7. 2025A Survey on Large Language Models for Mathematical Reasoning
  8. 2023Implicit Chain of Thought Reasoning via Knowledge Distillation