# Knowledge transfer between simple discrete worlds

arXiv: https://arxiv.org/abs/2610.15081 · HTML: https://mlsanity.com/paper/2610.15081/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 21 references that are in the map.
- First posted on arXiv 10 Oct 2026.

## Builds on (most cited first, 13 of 13)

- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [COGS: A Compositional Generalization Challenge Based on Semantic Interpretation](https://mlsanity.com/paper/2010.05465/) (2020)
- [BabyAI: A Platform to Study the Sample Efficiency of Grounded Language Learning](https://mlsanity.com/paper/1810.08272/) (2018)
- [Hierarchical Reasoning Model](https://mlsanity.com/paper/2506.21734/) (2025)
- [Causal Language Modeling Can Elicit Search and Reasoning Capabilities on Logic Puzzles](https://mlsanity.com/paper/2409.10502/) (2024)
- [Discovering modular solutions that generalize compositionally](https://mlsanity.com/paper/2312.15001/) (2023)
- [AI Must Embrace Specialization via Superhuman Adaptable Intelligence](https://mlsanity.com/paper/2602.23643/) (2026)
- [Teaching Transformers to Solve Combinatorial Problems through Efficient Trial & Error](https://mlsanity.com/paper/2509.22023/) (2025)
- [Lattice Deduction Transformers](https://mlsanity.com/paper/2605.08605/) (2026)
- [DiG-bench: Discovery in Games](https://mlsanity.com/paper/2608.12593/) (2026)

## Abstract (arXiv)

Adapting to a new world and reasoning correctly about which outcomes are possible under rules one has not met before is a basic capacity underlying general intelligence. We study it in small discrete worlds: sets of grid configurations consistent with a shared set of rules, concretely Sudoku-like puzzles built from a common base and a handful of extra rules. We train a single depth-recurrent model on many combinations of rules and test it at four levels of novelty: a new puzzle, a new combination of known rules, a pairing of rules never seen together, and a rule instance not seen at all during training. The model receives the active rules either as a symbolic description or as two solved examples, and a model that gets no rule information is used as a baseline. At recombining rules it was trained on, the description matches or exceeds examples (99% against 95% on new combinations). On rule instances whose components never co-occurred in training, the description falls below the no-information baseline while examples stay above it. The framework allows us to test many such generalization regimes in more systematic way than benchmarks such as ARC-AGI and provides new ground for evaluating depth-recurrent reasoning models, which are typically tested on saturated Sudoku benchmarks.