Lattice Deduction Transformer solves extreme logic puzzles with 800k parameters

Smaller models with hard structural constraints can outperform frontier language models on formal reasoning, according to a new preprint introducing the Lattice Deduction Transformer.

The architecture, described by Liam Davis, Leopold Haller, Alberto Alfarano, and Mark Santolucito, projects internal neural states onto a mathematically defined lattice—a rigid coordinate system that enforces logical consistency at each step. The model solves extreme Sudoku variants and other logic puzzles with perfect accuracy, while Claude 4.6 and GPT-5.4 score zero percent on the same tasks. The 800,000-parameter model achieves this despite being roughly 10,000 times smaller than frontier LLMs and requiring a fraction of their training compute.

The lattice acts as a hard constraint on the network's hidden states, preventing the drift and hallucination that plague larger models on formal reasoning. Rather than pattern-matching across token sequences, the architecture treats reasoning as navigation through a structured space, building proofs step-by-step instead of guessing answers. The recurrent design processes inputs sequentially, maintaining a state vector that must remain algebraically consistent with the lattice's rules at every iteration.

Ablation studies in the paper show that removing the lattice constraint causes accuracy to collapse even when parameter count and training time are held constant, confirming that the structural constraint—not scale—drives performance on these tasks. The authors argue the approach demonstrates that specialized architectures with formal guarantees can solve classes of problems where general-purpose scaling fails.

The preprint is available at arxiv.org/abs/2605.08605. No code or trained weights have been released.