# Anatomy of a Sound Neural Reasoner: One-Shot Amortization, First-Pass Poisoning, and Search Inertness in Clue-Rich Completion

arXiv: https://arxiv.org/abs/2607.19635 · HTML: https://mlsanity.com/paper/2607.19635/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 34 references that are in the map.
- First posted on arXiv 22 Jul 2026.

## Builds on (most cited first, 20 of 20)

- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Learning a SAT Solver from Single-Bit Supervision](https://mlsanity.com/paper/1802.03685/) (2018)
- [Hierarchical Reasoning Model](https://mlsanity.com/paper/2506.21734/) (2025)
- [SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver](https://mlsanity.com/paper/1905.12149/) (2019)
- [Stream of Search (SoS): Learning to Search in Language](https://mlsanity.com/paper/2404.03683/) (2024)
- [Better Aggregation in Test-Time Augmentation](https://mlsanity.com/paper/2011.11156/) (2020)
- [Can You Learn an Algorithm? Generalizing from Easy to Hard Problems with Recurrent Networks](https://mlsanity.com/paper/2106.04537/) (2021)
- [Combinatorial Optimization with Physics-Inspired Graph Neural Networks](https://mlsanity.com/paper/2107.01188/) (2021)
- [Neural Algorithmic Reasoning](https://mlsanity.com/paper/2105.02761/) (2021)
- [Beyond A*: Better Planning with Transformers via Search Dynamics Bootstrapping](https://mlsanity.com/paper/2402.14083/) (2024)
- [Recurrent Relational Networks](https://mlsanity.com/paper/1711.08028/) (2017)
- [Guiding High-Performance SAT Solvers with Unsat-Core Predictions](https://mlsanity.com/paper/1903.04671/) (2019)
- [Graph Neural Networks for Maximum Constraint Satisfaction](https://mlsanity.com/paper/1909.08387/) (2019)
- [End-to-end Algorithm Synthesis with Recurrent Networks: Logical Extrapolation Without Overthinking](https://mlsanity.com/paper/2202.05826/) (2022)
- [Modern graph neural networks do worse than classical greedy algorithms in solving combinatorial optimization problems like maximum independent set](https://mlsanity.com/paper/2206.13211/) (2022)
- [Generative Recursive Reasoning](https://mlsanity.com/paper/2605.19376/) (2026)
- [NeuroBack: Improving CDCL SAT Solving using Graph Neural Networks](https://mlsanity.com/paper/2110.14053/) (2021)
- [Lattice Deduction Transformers](https://mlsanity.com/paper/2605.08605/) (2026)
- [Learning to Rank the Initial Branching Order of SAT Solvers](https://mlsanity.com/paper/2603.07176/) (2026)

## Abstract (arXiv)

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.