# Executable Functional Abstractions: Inferring Generative Programs for Advanced Math Problems

arXiv: https://arxiv.org/abs/2504.09763 · HTML: https://mlsanity.com/paper/2504.09763/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 41 references that are in the map.
- First posted on arXiv 14 Apr 2025.

## Builds on (most cited first, 28 of 28)

- [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)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [WizardLM: Empowering large pre-trained language models to follow complex instructions](https://mlsanity.com/paper/2304.12244/) (2023)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Large Language Models Can Be Easily Distracted by Irrelevant Context](https://mlsanity.com/paper/2302.00093/) (2023)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Models](https://mlsanity.com/paper/2312.06585/) (2023)
- [Holodeck: Language Guided Generation of 3D Embodied AI Environments](https://mlsanity.com/paper/2312.09067/) (2023)
- [BabyAI: A Platform to Study the Sample Efficiency of Grounded Language Learning](https://mlsanity.com/paper/1810.08272/) (2018)
- [Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process](https://mlsanity.com/paper/2407.20311/) (2024)
- [MATH-Perturb: Benchmarking LLMs' Math Reasoning Abilities against Hard Perturbations](https://mlsanity.com/paper/2502.06453/) (2025)
- [Functional Benchmarks for Robust Evaluation of Reasoning Performance, and the Reasoning Gap](https://mlsanity.com/paper/2402.19450/) (2024)
- [AceMath: Advancing Frontier Math Reasoning with Post-Training and Reward Modeling](https://mlsanity.com/paper/2412.15084/) (2024)
- [AI-Assisted Generation of Difficult Math Questions](https://mlsanity.com/paper/2407.21009/) (2024)
- [DARG: Dynamic Evaluation of Large Language Models via Adaptive Reasoning Graph](https://mlsanity.com/paper/2406.17271/) (2024)
- [DataEnvGym: Data Generation Agents in Teacher Environments with Student Feedback](https://mlsanity.com/paper/2410.06215/) (2024)
- [How to Get Your LLM to Generate Challenging Problems for Evaluation](https://mlsanity.com/paper/2502.14678/) (2025)

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

- [Evolving Programmatic Skill Networks](https://mlsanity.com/paper/2601.03509/) (2026)
- [Improving Language Agents through BREW: Bootstrapping expeRientially-learned Environmental knoWledge](https://mlsanity.com/paper/2511.20297/) (2025)
- [Question Begets Question: Self-Evolving Curriculum for Reinforcement Fine-Tuning on Competition Mathematics](https://mlsanity.com/paper/2608.01522/) (2026)
- [The Missing Primitive: Diagnosing and Repairing Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2610.02191/) (2026)

## Abstract (arXiv)

Scientists often infer abstract procedures from specific instances of problems and use the abstractions to generate new, related instances. For example, programs encoding the formal rules and properties of a system have been useful in fields ranging from reinforcement learning (procedural environments) to physics (simulation engines). These programs can be seen as functions which execute to different outputs based on their parameterizations (e.g., gridworld configuration or initial physical conditions). We introduce the term EFA (Executable Functional Abstraction) to denote such programs for math problems. EFA-like constructs have been shown to be useful for mathematical reasoning as problem generators for stress-testing models. However, prior work has been limited to automatically constructing abstractions for grade-school math (whose simple rules are easy to encode in programs), while generating EFAs for advanced math has thus far required human engineering. We explore the automatic construction of EFAs for advanced mathematics problems by developing EFAGen, which operationalizes the task of automatically inferring an EFA for a given seed problem and solution as a program synthesis task. We first formalize the properties of any valid EFA as executable unit tests. Using execution feedback from the unit tests, we search over candidate programs sampled from a LLM to find EFA programs that are faithful to the generalized problem and solution class underlying the seed problem. We then apply the tests as a reward signal, training LLMs to become better writers of EFAs. We show that EFAs inferred by EFAGen are faithful to the seed problems, produce learnable problem variations, and that EFAGen can infer EFAs across diverse sources of competition-level math problems. Finally, we show uses of model-written EFAs e.g., finding harder/easier problem variants, as well as data generation.