# A Small-Scale System for Autoregressive Program Synthesis Enabling Controlled Experimentation

arXiv: https://arxiv.org/abs/2602.09112 · HTML: https://mlsanity.com/paper/2602.09112/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 16 references that are in the map.
- First posted on arXiv 9 Feb 2026.

## Builds on (most cited first, 12 of 12)

- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Analysing Mathematical Reasoning Abilities of Neural Models](https://mlsanity.com/paper/1904.01557/) (2019)
- [Looped Transformers as Programmable Computers](https://mlsanity.com/paper/2301.13196/) (2023)
- [Neural GPUs Learn Algorithms](https://mlsanity.com/paper/1511.08228/) (2015)
- [Learning to Execute](https://mlsanity.com/paper/1410.4615/) (2014)
- [Tracr: Compiled Transformers as a Laboratory for Interpretability](https://mlsanity.com/paper/2301.05062/) (2023)
- [Neural Arithmetic Logic Units](https://mlsanity.com/paper/1808.00508/) (2018)
- [Learning to Infer Program Sketches](https://mlsanity.com/paper/1902.06349/) (2019)
- [ExeDec: Execution Decomposition for Compositional Generalization in Neural Program Synthesis](https://mlsanity.com/paper/2307.13883/) (2023)
- [Algorithmic Capabilities of Random Transformers](https://mlsanity.com/paper/2410.04368/) (2024)
- [Nova: Generative Language Models for Assembly Code with Hierarchical Attention and Contrastive Learning](https://mlsanity.com/paper/2311.13721/) (2023)
- [Beyond Either-Or Reasoning: Transduction and Induction as Cooperative Problem-Solving Paradigms](https://mlsanity.com/paper/2505.14744/) (2025)

## Abstract (arXiv)

What research can be pursued with small models trained to complete true programs? Typically, researchers study program synthesis via large language models (LLMs) which introduce issues such as knowing what is in or out of distribution, understanding fine-tuning effects, understanding the effects of tokenization, and higher demand on compute and storage to carry out experiments. We present a system called Cadmus which includes an integer virtual machine (VM), a dataset composed of true programs of diverse tasks, and an autoregressive transformer model that is trained for under 200 of compute cost. The system can be used to study program completion, out-of-distribution representations, inductive reasoning, and instruction following in a setting where researchers have effective and affordable fine-grained control of the training distribution and the ability to inspect and instrument models. Smaller models working on complex reasoning tasks enable instrumentation and investigations that may be prohibitively expensive on larger models. To demonstrate that these tasks are complex enough to be of interest, we show that these Cadmus models outperform GPT-5 (by achieving 100% accuracy while GPT-5 has 95% accuracy) even on a simple task of completing correct, integer arithmetic programs in our domain-specific language (DSL) while providing transparency into the dataset's relationship to the problem. We also show that GPT-5 brings unknown priors into its reasoning process when solving the same tasks, demonstrating a confounding factor that prevents the use of large-scale LLMs for some investigations where the training set relationship to the task needs to be fully understood.