# Synthesis of Mathematical programs from Natural Language Specifications

arXiv: https://arxiv.org/abs/2304.03287 · HTML: https://mlsanity.com/paper/2304.03287/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 41 references that are in the map.
- First posted on arXiv 30 Mar 2023.

## Builds on (most cited first, 27 of 27)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [CodeBERT: A Pre-Trained Model for Programming and Natural Languages](https://mlsanity.com/paper/2002.08155/) (2020)
- [CodeT5: Identifier-aware Unified Pre-trained Encoder-Decoder Models for Code Understanding and Generation](https://mlsanity.com/paper/2109.00859/) (2021)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [CodeXGLUE: A Machine Learning Benchmark Dataset for Code Understanding and Generation](https://mlsanity.com/paper/2102.04664/) (2021)
- [Seq2SQL: Generating Structured Queries from Natural Language using Reinforcement Learning](https://mlsanity.com/paper/1709.00103/) (2017)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [PICARD: Parsing Incrementally for Constrained Auto-Regressive Decoding from Language Models](https://mlsanity.com/paper/2109.05093/) (2021)
- [Unified Pre-training for Program Understanding and Generation](https://mlsanity.com/paper/2103.06333/) (2021)
- [Unsupervised Translation of Programming Languages](https://mlsanity.com/paper/2006.03511/) (2020)
- [Lexically Constrained Decoding for Sequence Generation Using Grid Beam Search](https://mlsanity.com/paper/1704.07138/) (2017)
- [GPT3Mix: Leveraging Large-scale Language Models for Text Augmentation](https://mlsanity.com/paper/2104.08826/) (2021)
- [Synchromesh: Reliable code generation from pre-trained language models](https://mlsanity.com/paper/2201.11227/) (2022)
- [RobustFill: Neural Program Learning under Noisy I/O](https://mlsanity.com/paper/1703.07469/) (2017)
- [Jigsaw: Large Language Models meet Program Synthesis](https://mlsanity.com/paper/2112.02969/) (2021)
- [Write, Execute, Assess: Program Synthesis with a REPL](https://mlsanity.com/paper/1906.04604/) (2019)
- [Augmenting Operations Research with Auto-Formulation of Optimization Models from Problem Descriptions](https://mlsanity.com/paper/2209.15565/) (2022)
- [Data Augmentation for Intent Classification with Off-the-shelf Large Language Models](https://mlsanity.com/paper/2204.01959/) (2022)
- [Neural Program Meta-Induction](https://mlsanity.com/paper/1710.04157/) (2017)
- [MathOptInterface: a data structure for mathematical optimization problems](https://mlsanity.com/paper/2002.03447/) (2020)
- [Highlighting Named Entities in Input for Auto-Formulation of Optimization Problems](https://mlsanity.com/paper/2212.13201/) (2022)
- [Learning structured approximations of combinatorial optimization problems](https://mlsanity.com/paper/2107.04323/) (2021)
- [A Case for Business Process-Specific Foundation Models](https://mlsanity.com/paper/2210.14739/) (2022)
- [Mathematical Knowledge Representation: Semantic Models and Formalisms](https://mlsanity.com/paper/1408.6806/) (2014)
- [A Knowledge Representation Approach to Automated Mathematical Modelling](https://mlsanity.com/paper/2011.06300/) (2020)

## Built on by (most cited first, 8 of 8)

- [Text2Zinc: A Cross-Domain Dataset for Modeling Optimization and Satisfaction Problems in MiniZinc](https://mlsanity.com/paper/2503.10642/) (2025)
- [Abstract Operations Research Modeling Using Natural Language Inputs](https://mlsanity.com/paper/2408.07272/) (2024)
- [DualSchool: How Reliable are LLMs for Optimization Education?](https://mlsanity.com/paper/2505.21775/) (2025)
- [DCP-Bench-Open: Evaluating LLMs for Constraint Modelling of Discrete Combinatorial Problems](https://mlsanity.com/paper/2506.06052/) (2025)
- [Large Language Model-Based Automatic Formulation for Stochastic Optimization Models](https://mlsanity.com/paper/2508.17200/) (2025)
- [PEARL: Solver-in-the-Loop Interactive Optimization Modeling from Natural Language](https://mlsanity.com/paper/2607.18256/) (2026)
- [Reinforcement Learning Enhanced LLM Agents for Complex Vehicle Routing Problems](https://mlsanity.com/paper/2609.00859/) (2026)
- [Step-Opt: Boosting Optimization Modeling in LLMs through Iterative Data Synthesis and Structured Validation](https://mlsanity.com/paper/2506.17637/) (2025)

## Abstract (arXiv)

Several decision problems that are encountered in various business domains can be modeled as mathematical programs, i.e. optimization problems. The process of conducting such modeling often requires the involvement of experts trained in operations research and advanced algorithms. Surprisingly, despite the significant advances in the methods for program and code synthesis, AutoML, learning to optimize etc., there has been little or no attention paid to automating the task of synthesizing mathematical programs. We imagine a scenario where the specifications for modeling, i.e. the objective and constraints are expressed in an unstructured form in natural language (NL) and the mathematical program has to be synthesized from such an NL specification. In this work we evaluate the efficacy of employing CodeT5 with data augmentation and post-processing of beams. We utilize GPT-3 with back translation for generation of synthetic examples. Further we apply rules of linear programming to score beams and correct beams based on common error patterns. We observe that with these enhancements CodeT5 base gives an execution accuracy of 0.73 which is significantly better than zero-shot execution accuracy of 0.41 by ChatGPT and 0.36 by Codex.