# An Expression Tree Decoding Strategy for Mathematical Equation Generation

arXiv: https://arxiv.org/abs/2310.09619 · HTML: https://mlsanity.com/paper/2310.09619/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 65 references that are in the map.
- First posted on arXiv 14 Oct 2023.

## Builds on (most cited first, 30 of 44)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [BLIP-2: Bootstrapping Language-Image Pre-training with Frozen Image Encoders and Large Language Models](https://mlsanity.com/paper/2301.12597/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [HuggingGPT: Solving AI Tasks with ChatGPT and its Friends in Hugging Face](https://mlsanity.com/paper/2303.17580/) (2023)
- [Perceiver: General Perception with Iterative Attention](https://mlsanity.com/paper/2103.03206/) (2021)
- [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)
- [QANet: Combining Local Convolution with Global Self-Attention for Reading Comprehension](https://mlsanity.com/paper/1804.09541/) (2018)
- [Solving Math Word Problems by Combining Language Models With Symbolic Solvers](https://mlsanity.com/paper/2304.09102/) (2023)
- [Generate & Rank: A Multi-task Framework for Math Word Problems](https://mlsanity.com/paper/2109.03034/) (2021)
- [Data-Copilot: Bridging Billions of Data and Humans with Autonomous Workflow](https://mlsanity.com/paper/2306.07209/) (2023)
- [Rasa: Open Source Language Understanding and Dialogue Management](https://mlsanity.com/paper/1712.05181/) (2017)
- [Translating a Math Word Problem to an Expression Tree](https://mlsanity.com/paper/1811.05632/) (2018)
- [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)
- [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)
- [LogicSolver: Towards Interpretable Math Word Problem Solving with Logical Prompt-enhanced Learning](https://mlsanity.com/paper/2205.08232/) (2022)
- [Investigating Math Word Problems using Pretrained Multilingual Language Models](https://mlsanity.com/paper/2105.08928/) (2021)
- [Learning by Analogy: Diverse Questions Generation in Math Word Problem](https://mlsanity.com/paper/2306.09064/) (2023)
- [Interpretable Math Word Problem Solution Generation Via Step-by-step Planning](https://mlsanity.com/paper/2306.00784/) (2023)
- [ELASTIC: Numerical Reasoning with Adaptive Symbolic Compiler](https://mlsanity.com/paper/2210.10105/) (2022)

## Built on by (most cited first, 4 of 4)

- [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)
- [EvoEmpirBench: Dynamic Spatial Reasoning with Agent-ExpVer](https://mlsanity.com/paper/2509.12718/) (2025)
- [SciText2Eq: Assessing LLMs for Explainable Equation Generation for Scientific Creativity](https://mlsanity.com/paper/2606.16003/) (2026)

## Abstract (arXiv)

Generating mathematical equations from natural language requires an accurate understanding of the relations among math expressions. Existing approaches can be broadly categorized into token-level and expression-level generation. The former treats equations as a mathematical language, sequentially generating math tokens. Expression-level methods generate each expression one by one. However, each expression represents a solving step, and there naturally exist parallel or dependent relations between these steps, which are ignored by current sequential methods. Therefore, we integrate tree structure into the expression-level generation and advocate an expression tree decoding strategy. To generate a tree with expression as its node, we employ a layer-wise parallel decoding strategy: we decode multiple independent expressions (leaf nodes) in parallel at each layer and repeat parallel decoding layer by layer to sequentially generate these parent node expressions that depend on others. Besides, a bipartite matching algorithm is adopted to align multiple predictions with annotations for each layer. Experiments show our method outperforms other baselines, especially for these equations with complex structures.