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…