Lattice Deduction Transformers
Liam Davis, Leopold Haller, Alberto Alfarano, Mark Santolucito
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 approximation of the set of solution candidates based on abstract interpretation. An $800$K-parameter LDT outperforms prior small recurrent reasoners on Sudoku-Extreme with under $2\%$ of their estimated training FLOPs, solving $99.999\%$ of the $422{,}786$ test puzzles. 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. A $1.8$M-parameter LDT variant reaches $99.8\%$ accuracy on Maze-Hard. Our code is available at github.com/lcrh/lattice-deduction-transformers.
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