# Multi-View Reasoning: Consistent Contrastive Learning for Math Word Problem

arXiv: https://arxiv.org/abs/2210.11694 · HTML: https://mlsanity.com/paper/2210.11694/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 51 references that are in the map.
- First posted on arXiv 21 Oct 2022.

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [Generate & Rank: A Multi-task Framework for Math Word Problems](https://mlsanity.com/paper/2109.03034/) (2021)
- [Semantically-Aligned Equation Generation for Solving and Reasoning Math Word Problems](https://mlsanity.com/paper/1811.00720/) (2018)
- [Learning to Reason Deductively: Math Word Problem Solving as Complex Relation Extraction](https://mlsanity.com/paper/2203.10316/) (2022)
- [MWPToolkit: An Open-Source Framework for Deep Learning-Based Math Word Problem Solvers](https://mlsanity.com/paper/2109.00799/) (2021)
- [Neural-Symbolic Solver for Math Word Problems with Auxiliary Tasks](https://mlsanity.com/paper/2107.01431/) (2021)
- [Mapping to Declarative Knowledge for Word Problem Solving](https://mlsanity.com/paper/1712.09391/) (2017)
- [Graph-to-Tree Neural Networks for Learning Structured Input-Output Translation with Applications to Semantic Parsing and Math Word Problem](https://mlsanity.com/paper/2004.13781/) (2020)
- [Seeking Patterns, Not just Memorizing Procedures: Contrastive Learning for Solving Math Word Problems](https://mlsanity.com/paper/2110.08464/) (2021)
- [A Trigger-Sense Memory Flow Framework for Joint Entity and Relation Extraction](https://mlsanity.com/paper/2101.10213/) (2021)
- [Investigating Math Word Problems using Pretrained Multilingual Language Models](https://mlsanity.com/paper/2105.08928/) (2021)
- [Towards Tractable Mathematical Reasoning: Challenges, Strategies, and Opportunities for Solving Math Word Problems](https://mlsanity.com/paper/2111.05364/) (2021)
- [A Closed-Loop Perception, Decision-Making and Reasoning Mechanism for Human-Like Navigation](https://mlsanity.com/paper/2207.11901/) (2022)
- [Learning to Navigate in a VUCA Environment: Hierarchical Multi-expert Approach](https://mlsanity.com/paper/2111.08364/) (2021)

## Built on by (most cited first, 13 of 13)

- [Agent-Pro: Learning to Evolve via Policy-Level Reflection and Optimization](https://mlsanity.com/paper/2402.17574/) (2024)
- [Self-Contrast: Better Reflection Through Inconsistent Solving Perspectives](https://mlsanity.com/paper/2401.02009/) (2024)
- [Heterogeneous Contrastive Learning for Foundation Models and Beyond](https://mlsanity.com/paper/2404.00225/) (2024)
- [FT-MDT: Extracting Decision Trees from Medical Texts via a Novel Low-rank Adaptation Method](https://mlsanity.com/paper/2510.04655/) (2025)
- [Text2MDT: Extracting Medical Decision Trees from Medical Texts](https://mlsanity.com/paper/2401.02034/) (2024)
- [EvoEmpirBench: Dynamic Spatial Reasoning with Agent-ExpVer](https://mlsanity.com/paper/2509.12718/) (2025)
- [An Expression Tree Decoding Strategy for Mathematical Equation Generation](https://mlsanity.com/paper/2310.09619/) (2023)
- [Survey of Natural Language Processing for Education: Taxonomy, Systematic Review, and Future Trends](https://mlsanity.com/paper/2401.07518/) (2024)
- [Teaching-Inspired Integrated Prompting Framework: A Novel Approach for Enhancing Reasoning in Large Language Models](https://mlsanity.com/paper/2410.08068/) (2024)
- [Foundation of Intelligence: Review of Math Word Problems from Human Cognition Perspective](https://mlsanity.com/paper/2510.21999/) (2025)
- [CogNarr Ecosystem: Facilitating Group Cognition at Scale](https://mlsanity.com/paper/2407.18945/) (2024)
- [A Diversity-Enhanced Knowledge Distillation Model for Practical Math Word Problem Solving](https://mlsanity.com/paper/2501.03670/) (2025)
- [Elementary Math Word Problem Generation using Large Language Models](https://mlsanity.com/paper/2506.05950/) (2025)

## Abstract (arXiv)

Math word problem solver requires both precise relation reasoning about quantities in the text and reliable generation for the diverse equation. Current sequence-to-tree or relation extraction methods regard this only from a fixed view, struggling to simultaneously handle complex semantics and diverse equations. However, human solving naturally involves two consistent reasoning views: top-down and bottom-up, just as math equations also can be expressed in multiple equivalent forms: pre-order and post-order. We propose a multi-view consistent contrastive learning for a more complete semantics-to-equation mapping. The entire process is decoupled into two independent but consistent views: top-down decomposition and bottom-up construction, and the two reasoning views are aligned in multi-granularity for consistency, enhancing global generation and precise reasoning. Experiments on multiple datasets across two languages show our approach significantly outperforms the existing baselines, especially on complex problems. We also show after consistent alignment, multi-view can absorb the merits of both views and generate more diverse results consistent with the mathematical laws.