Neural Solvers Often Act as One-Shot Predictors

This research delves into the operational mechanics of neural solvers, specifically examining the Lattice Deduction Transformer (LDT) in clue-rich Sudoku puzzles. Contrary to the expectation that these solvers iteratively deduce and revise states, the study found that LDT primarily functions as a one-shot predictor. It commits to nearly the entire grid in a single forward pass, effectively turning the iterative solver into a verification wrapper around an initial prediction. The core issue, termed "first-pass poisoning," occurs when the initial pass confidently deletes a value essential for the true solution, predetermining failures before any search begins. Even adding sophisticated search components like learned branching or backtracking did not change which Sudoku instances were solved, only reducing computational waste. The study highlights that accuracy is largely driven by calibration and symmetry, not by the search process itself. Effective interventions included digit-permutation augmentation and test-time union over symmetry-transformed passes, drastically improving accuracy without retraining, further supporting the one-shot amortization hypothesis for clue-rich completion tasks.