A lattice-guided transformer takes on deduction in puzzle benchmarks

A lattice-guided transformer takes on deduction in puzzle benchmarks

Liam Davis, Leopold Haller, Alberto Alfarano and Mark Santolucito introduce the Lattice Deduction Transformer (LDT), a recurrent transformer designed to approximate logically sound deduction. Between forward passes, it projects its latent state through a lattice; training follows a process modeled on deduction in a search-based constraint solver. The authors report that an 800K-parameter LDT solved 99.999% of 422,786 Sudoku-Extreme test puzzles, using under 2% of the estimated training FLOPs of prior small recurrent reasoners. They describe it as “nearly always sound”: across 1.27M puzzle evaluations, it gave a wrong answer four times, and otherwise returned a correct answer or abstained. A 1.8M-parameter variant reached 99.8% accuracy on Maze-Hard. These results make the paper’s case for a specific approach: combining recurrent transformers with lattice projections and a deduction-oriented training process can perform strongly on the reported puzzle tasks with a small model. The abstract reports results on Sudoku-Extreme and Maze-Hard; it does not establish performance on other kinds of problems.

Publication: eeb9f142-324c-465d-8174-1b696e3acf8d

attribution — pass: The draft correctly credits the four listed authors and keeps the results attributed to them as reported outcomes ("The authors report", "They describe it as").

Authors:Liam Davis, Leopold Haller, Alberto Alfarano, Mark Santolucito

summary — pass: The draft leads with the actor and the method, then gives the key results and the paper's own scope limits. It keeps the technical terms (recurrent transformer, latent state, lattice, forward passes, FLOPs) exactly, which suits tooltip explanation. It conveys soundness concretely: wrong answers versus correct answers or abstentions. The significance is framed as the paper's case for a small, efficient approach and is bounded to the reported puzzles. The title and question are fair, and the question is a genuine open issue rather than a leading claim.

The model is nearly always sound, in that it gives a wrong answer for $4$ of $1.27$M puzzle evaluations, and otherwise returns a correct answer or abstains.

date — pass: originalPublished is 2026-05-09, which matches the v1 submission date. It is not the 3 Nov 2026 revision or the November feed date.

Submitted on 9 May 2026 (v1), last revised 3 Nov 2026 (this version, v2)

support — pass: All the figures match the abstract: 800K parameters, 99.999% of 422,786 puzzles, under 2% of estimated training FLOPs, 4 wrong answers in 1.27M evaluations, and 1.8M parameters at 99.8% on Maze-Hard. The quoted phrase "nearly always sound" is exact. The draft does not stretch the benchmark results into real-world reliability, and its limitations stay within the abstract's scope.

An $800$K-parameter LDT outperforms prior small recurrent reasoners on Sudoku-Extreme with under $2\%$ of their estimated training FLOPs

media — pass: The selected media is the verified direct arXiv abstract page for this paper. It is the most direct way to reach the source.