Track papers across labs, topics, and trends.
Search papers, labs, and topics across Lattice.
This paper investigates the Lattice Deduction Transformer (LDT) in the context of solving clue-rich Sudoku puzzles, revealing that it operates as a one-shot predictor rather than an iterative solver due to a phenomenon termed "first-pass poisoning." The study finds that the LDT's initial pass eliminates critical values needed for solutions, leading to a significant reduction in computational redundancy, with a 1,497-fold decrease in invalid derivations. Notably, the introduction of digit-permutation augmentation dramatically improves accuracy from below 1% to 96.5% on challenging instances, underscoring the importance of calibration and symmetry in enhancing performance.
First-pass poisoning in neural solvers can drastically undermine solution accuracy, but clever data augmentation can flip the script, boosting performance from near-zero to nearly perfect.
Neural solvers are built to deduce, branch, and revise intermediate states. The Lattice Deduction Transformer (LDT) appears to do exactly that. In clue-rich Sudoku, it does not: one forward pass commits essentially the entire grid (every blank cell on standard 6x6, 94-96% on augmented 9x9), turning the iterative solver into a one-shot predictor wrapped in an exact verifier. All hard-slice failures are decided before search begins, when the first pass confidently deletes a value required by the true solution. We call this first-pass poisoning. Adding learned branching, MRV, backtracking, value exclusion, and shared nogoods (CoLT) does not change which Sudoku instances are solved; it cuts repeated invalid derivations 1,497-fold. At the frozen training budget, constraint-graph attention alone matches full-CoLT accuracy, while positional tables recover only under substantially longer training, indicating an optimization and sample-efficiency advantage rather than an absolute capacity difference. The diagnosis predicts two effective interventions. Digit-permutation augmentation raises 9x9 accuracy from below 1% to 96.5 +/- 0.3 across three training seeds on a symmetry-disjoint split. Test-time union over symmetry-transformed passes raises all three hard-slice checkpoints from 72.8-78.9% to 100% without retraining. On from-scratch graph coloring, one-shot behavior disappears and search changes accuracy. In clue-rich completion, LDT-like systems are one-shot amortized predictors rather than learned search procedures: accuracy is determined by calibration and symmetry, while search primarily removes computational waste.