Abstract
Neural solvers are designed to deduce, branch, and revise intermediate states. The Lattice Deduction Transformer (LDT) appears to do just that. However, in clue-rich Sudoku, it falls short: one forward pass essentially commits the entire grid (94-96% for every blank cell in standard 6x6, and similar for augmented 9x9), turning the iterative solver into a one-shot predictor wrapped in an exact verifier.
All hard-slice failures are decided before the search begins, when the first pass confidently deletes a value required by the true solution, which we term first-pass poisoning. Adding learned branching, MRV, backtracking, value exclusion, and shared nogoods (CoLT) does not change which Sudoku instances are solved; it reduces repeated invalid derivations by 1,497-fold.
At the fixed training budget, constraint-graph attention alone matches full-CoLT accuracy, while positional tables only recover under substantially longer training, indicating an advantage in optimization and sample efficiency 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.
In from-scratch graph coloring, one-shot behavior disappears and search accuracy changes. In clue-rich completion, LDT-like systems act as one-shot amortized predictors rather than learned search procedures: accuracy is determined by calibration and symmetry, while search primarily removes computational waste.
Blogger's Review: This paper delves into the performance of LDT in Sudoku reasoning, revealing its limitations in one-shot prediction and search processes. Through optimization and augmentation measures, the authors propose effective improvement strategies, showcasing the potential and challenges of neural networks in constraint reasoning tasks. Overall, the article provides valuable insights into the operational mechanisms of neural reasoners.