Abstract: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 $800$K-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 $1.8$M-parameter variant reaches $99.9\%$ accuracy on Maze-Hard. Frontier LLMs score $0\%$ on all three benchmarks.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Logic in Computer Science (cs.LO) |
| Cite as: | arXiv:2605.08605 [cs.LG] |
| (or arXiv:2605.08605v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.08605 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Liam Davis [view email]
[v1]
Sat, 9 May 2026 01:55:45 UTC (123 KB)