# Teaching a Minimalist Machine to Discover Recursive Programs for Arithmetic

arXiv: https://arxiv.org/abs/2610.06304 · HTML: https://mlsanity.com/paper/2610.06304/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 22 references that are in the map.
- First posted on arXiv 5 Oct 2026.

## Builds on (most cited first, 4 of 4)

- [A Wholistic View of Continual Learning with Deep Neural Networks: Forgotten Lessons and the Bridge to Active and Open World Learning](https://mlsanity.com/paper/2009.01797/) (2020)
- [Inductive logic programming at 30: a new introduction](https://mlsanity.com/paper/2008.07912/) (2020)
- [Why AI systems don't learn and what to do about it: Lessons on autonomous learning from cognitive science](https://mlsanity.com/paper/2603.15381/) (2026)
- [Can humans teach machines to code?](https://mlsanity.com/paper/2404.19397/) (2024)

## Built on by (most cited first, 1 of 1)

- [Recursive Formation and First-Class Reuse of Compositional Capabilities](https://mlsanity.com/paper/2610.19414/) (2026)

## Abstract (arXiv)

Humans can often acquire and synthesize complex, recursive concepts from minimal experience. Leveraging cognitive insights, we propose the Minimalist Machine, a framework for inductive program synthesis designed to model such conceptual learning. The system uses a compact relational subset of Prolog: Programs are searched within a fixed schema of body-free facts and two-body conjunctive Horn clauses. Recursion is not defined by a dedicated metarule. Instead, it emerges when a target predicate is reused inside the body of a learned clause. Inspired by a primary school curriculum, the model is taught through a human-curated, sequential introduction of new concepts in arithmetic. Starting from initially empty knowledge base, it first acquires simple structural predicates, then successor-based state transformations, and finally recursive programs for addition, subtraction, multiplication, and division. Ultimately, this approach yields the fully transparent, inductive reasoning trace necessary for human-like conceptual learning.