We introduce the Lattice Deduction Transformer (LDT), a recurrent transformer that approximates logically sound deduction by projecting its latent state through a lattice between forward passes. We train on-policy in a process that mirrors deduction in a search-based constraint solver and supervise training via a domain-agnostic, abstract-interpretation-based approximation of the set of solution candidates. An 800K-parameter LDT achieves 100% accuracy on Sudoku-Extreme and Snowflake Sudoku, at a fraction of the training cost of prior small recurrent reasoners, while remaining empirically sound: the model returns a correct answer or abstains. A 1.8M-parameter variant reaches 99.9% accuracy on Maze-Hard. Frontier LLMs score 0% on all three benchmarks.
@article{arxiv.2605.08605,
title = {Lattice Deduction Transformers},
author = {Liam Davis and Leopold Haller and Alberto Alfarano and Mark Santolucito},
journal= {arXiv preprint arXiv:2605.08605},
year = {2026}
}