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REVIEW 3 major objections 4 minor 35 references

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

T0 review · 3 major / 4 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read In clue-rich Sudoku, a neural 'reasoner' is a one-shot predictor: one forward pass commits the whole grid, and every measured failure happens there, before search.

desk verdict A genuinely useful diagnostic result — first-pass poisoning explains clue-rich Sudoku failures — but the 'search inertness' claim is measured on a baseline stripped of LDT's augmentation, so the headline generalization is shakier than the abstract implies. read the letter →

arxiv 2607.19635 v1 pith:24IIVYUM submitted 2026-07-22 cs.LG cs.AI

Aleksey Komissarov This is my paper · ORCID
classification cs.LGcs.AI
keywords one-shotamortizationfirst-passpoisoninglatticedeductionverify-or-abstainsolverSudokuconstraintsatisfactiontest-timeaugmentationgraphcoloring
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish where a sound neural deduction system's accuracy actually comes from. In clue-rich Sudoku, the answer is the very first forward pass: one pass drives nearly every blank cell to a single candidate, so whether a puzzle is solved is already fixed before the iterative loop branches, backtracks, or checks anything. The mechanism of failure is first-pass poisoning—the pass confidently deleting a value the true solution needs—and since the lattice only ever removes candidates, no later search can restore it; every one of the 43 hard-slice failures, and none of the 137 successes, was poisoned. It follows that adding learned search (branching, backtracking, nogoods) cannot change which clue-rich puzzles get solved, only how much compute is wasted (about 1,500x less). The payoff is that the two fixes the diagnosis predicts work: train-time digit-permutation augmentation lifts 9x9 accuracy from below 1% to 96.5%, and test-time union over digit-permuted passes lifts three checkpoints to 100% with no retraining.

What carries the argument

The load-bearing machinery is the candidate-set lattice: each cell holds a multi-hot set of still-possible values, deduction only removes values, and conflict is an empty cell. Because removal is monotone, a true-solution value eliminated on the first forward pass can never be restored by any later branch, backtrack, or nogood—making first-pass poisoning sufficient for failure. The paper shows it is also necessary by running one clean forward pass per puzzle and finding that all failures, and only failures, are poisoned. Two named mechanisms carry the argument: the depth-0 'abstraction operator' target, which for a unique-solution puzzle is the complete solution, so a well-fit propagator is

What would settle it

Take the hard 14-clue 6x6 slice and, for each puzzle, run one clean forward pass and check whether a true-solution value was deleted. The paper predicts every failed puzzle is poisoned and every clean first pass is solved; a single failed-clean or poisoned-solved puzzle would falsify the contingency.

Watch

Extended reading notes

Core claim

The central discovery is that a sound lattice deduction transformer, despite appearing to run a deduce-branch-backtrack loop, acts as a one-shot amortized predictor in clue-rich regimes. Measured on the author's reimplementations, one forward pass drives all blank 6x6 test cells to exactly one candidate (singleton rate 1.0; 94–96% on augmented 9x9), turning the iterative solver into an exact verifier around a one-shot guesser. On a harder 14-clue 6x6 slice, the success/failure split is exactly explained by whether the first pass deletes a value the true solution needs: 43 failures were first-pass poisoned, 137 clean successes were not, and no late failures appeared—replicated across seeds an

Load-bearing premise

The diagnosis rests on the assumption that the author's own unaugmented reimplementation of the LDT recipe behaves like the original architecture; if the original's per-step digit shuffling changes the first-pass commit or poisoning profile, the one-shot/poisoning result may not transfer.

Editorial extensions

If this is right

  • On clue-rich 6x6 Sudoku at the frozen budget, adding MRV, learned branching, DFS backtracking, and a nogood ban set leaves the exact set of solved puzzles unchanged; it cuts repeated wrong completions by 1,497x.
  • The accuracy ceiling lives in propagator calibration, not search: lowering the elimination threshold does nothing, while digit-permutation augmentation raises 9x9/25-clue accuracy from 0.2% to 96.5% ± 0.3 over three seeds.
  • Test-time ensembling over K digit-permuted forward passes with union aggregation removes the failure mode without retraining: three hard-slice checkpoints go from 72.8–78.9% to 100% at K=8; mean aggregation does not, because false eliminations are one-sided.
  • The diagnosis is regime-bound: on from-scratch graph coloring near the 3-colorability threshold, singleton rate drops to 1.4%, DFS beats restart, and value symmetry makes the depth-0 elimination target all-ones—so there is no signal to amortize.
  • One multi-size checkpoint transfers the local elimination propagator zero-shot from 4x4/6x6 to 9x9 (precision 0.977 at recall 0.597), but the global conflict and policy heads do not transfer, leaving size-invariant global readouts as an open item.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same union-symmetry recipe should transfer to other clue-rich completion tasks with exact value symmetries (Latin squares, Kakuro, nonograms): the paper's frame-type factorial predicts geometry-only frames help less than value relabeling.
  • If one-shot amortization is the general behavior of verify-or-abstain recurrent reasoners, then benchmark accuracy comparisons among such systems will keep reporting noise unless they control for first-pass calibration rather than search strength.
  • A direct architectural continuation suggested by the paper: exact value-permutation equivariance in the network should make the V!-fold augmentation unnecessary; the poisoning data make that prediction testable.
  • The poisoning contingency offers a cheap diagnostic for any new reasoner: run one clean pass and check whether every failed instance had a true value deleted; if any failure survives a clean first pass, the system is doing something beyond amortization and the paper's negative result does not apply.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper reimplements the Lattice Deduction Transformer (LDT) and introduces CoLT, a CDCL-inspired variant with learned branching, DFS/backtracking, and verified leaf-level nogoods, to test whether search compute is what makes sound lattice reasoners accurate. On clue-rich Sudoku (6x6 standard and hard slices, 9x9 at 25 clues), the authors report that a single forward pass commits essentially all blank cells; all observed hard-slice failures are explained by first-pass poisoning (43/43 vs. 0/137, replicated across seeds and environments); and search-side components are accuracy-inert while cutting wasted wrong-completion derivations by roughly 1,500x. Two symmetry interventions predicted by the diagnosis both work: train-time digit-permutation augmentation raises 9x9 accuracy from at most 0.6% to 96.5 +/- 0.3% on a symmetry-disjoint split, and test-time union over symmetry frames raises hard-slice accuracy from about 76% to 100% without retraining. On from-scratch graph coloring, the one-shot behavior disappears and DFS changes accuracy, mapping the boundary of the claim.

Significance. If the central claim holds for the intended class of systems, this is a valuable mechanistic result: it separates amortized prediction from search in neural reasoners, locates the accuracy ceiling in calibration and symmetry rather than search policy, and gives falsifiable predictions that succeed. The paper is exemplary in reproducibility practice -- frozen protocol, pinned data and raw JSONs, clean-room verifier audit, three-seed replications, and an explicit claim audit. The perfect poisoning contingency and the two successful interventions are strong evidence within the experimental scope. The main significance risk is that the negative result is established on a deliberately stripped baseline (LDT without its published per-step augmentation), so the breadth of the 'LDT-like' conclusion is not yet supported; this is a scope/transfer issue rather than an internal inconsistency.

major comments (3)
  1. [§4, §5.3, §5.4 (H2)] The central negative result -- search is inert, and failures are decided in the first forward pass -- is measured on a baseline from which the published LDT recipe's per-step digit-permutation × dihedral augmentation has been removed (Table 2 footnote; §4 Baselines). The paper itself identifies that augmentation as a mechanism for de-correlating elimination errors across steps and chains (§5.3). Under per-step augmentation the first pass is not a single canonical state: a value removed in one random frame can be kept in another, so the monotone-lattice 'no restoration' argument does not bind across frames. The H2 test-time-union experiment demonstrates de-poisoning outside the search loop, but it does not show that the original augmented iterative solver is search-inert. The abstract's claim about 'LDT-like systems' therefore overreaches the experiments as reported. Please either run the
  2. [§6 and §4 (leakage audit)] The paper correctly states that class-level generalization can rest only on the 9x9 splits, since the 6x6 domain does not admit a symmetry-disjoint split. But the 9x9 head-to-head compares CoLT-aug (96.5%) against an unaugmented LDT reimplementation (0%); no LDT-with-augmentation arm is reported, even though the published LDT recipe includes exactly this augmentation. Consequently the headline 'digit-permutation augmentation raises 9x9 accuracy from below 1% to 96.5%' is a property of CoLT-aug, not of the LDT family. This is load-bearing because the only clean class-level evidence for the general claim is that 9x9 result. Adding the LDT-with-augmentation cell, or narrowing the generalization claim to the CoLT parameterization, is needed.
  3. [§5.4 (2×2 factorial)] The 2x2 factorial is used to support the claim that the CoLT parameterization is what makes augmentation affordable at the frozen budget and that the interaction is a convergence-speed effect rather than an absolute incompatibility. The decisive cell -- positional tables with augmentation at extended budget -- is not run; the paper states the augmented extended-budget arm 'remains in the revision protocol.' The unaugmented positional-table sweep (16.1% at 3x, 37.2% at 10x steps) does not test the augmented condition, where relabeling is expected to erase exactly the value-specific positional patterns the positional model relies on. Since this cell is one of the preconditions for the 'optimization and sample-efficiency, not capacity' interpretation, it should either be run or the claim should be reported as a hypothesis rather than as an established interaction.
minor comments (4)
  1. [Abstract and §1] The term 'LDT-like' is used in the abstract and throughout without a precise definition. Given the augmentation caveat, define it at first use, e.g., 'the lattice-deduction family as reimplemented here, including the variant without the originally published per-step augmentation.'
  2. [Table 4] Table 4 reports identical accuracy (76.1%) for all six arms. §4 says arm equalities are exact set equalities, but the table itself should state whether the solved sets are identical, since the 'search is inert' conclusion depends on this being true puzzle-by-puzzle, not only in aggregate.
  3. [§5.1] The GRAM comparison is clearly scoped by the 10-100x budget starvation, but the subsection heading 'Emission validity of a no-abstention baseline' could be even more explicit that the near-100% wrong-answer rate is a matched-budget artifact, not a property of GRAM as an architecture.
  4. [Throughout] Minor formatting: 'MR V' appears with a spurious space in several places (e.g., Table 1, §5.1). In Table 2, a footnote explaining that the LDT row is a reimplementation rather than the original checkpoint would help readers who do not read §4 first.

Circularity Check

1 steps flagged · score 4.0 of 10

One-shot amortization is partly engineered into the depth-0 training target (Eq. 1), but the poisoning contingency, the two symmetry cures, and the boundary study are independent empirical content; no claim reduces entirely to a fit.

  1. self definitional [§5.4 (H1); Eq. (1)]
    "For a unique-solution puzzle the depth-0 target of Eq. 1 is the complete solution (α of a singleton solution set keeps exactly the solution values), so a candidate head that fits the objective perfectly is, by construction, a one-shot solver; H1 measures how completely that optimum is reached."

    The abstract's first finding—that one forward pass commits essentially the whole grid, turning the iterative solver into a one-shot predictor—is not an independent anatomical discovery. Eq. (1) defines the depth-0 regression target as the complete solution whenever the puzzle has a unique solution, so any well-fit candidate head is forced to eliminate every non-solution candidate on the first pass. Thus the one-shot commit measured by H1 is the optimum of the training loss, not an emergent property of LDT-like search. The circularity is partial and explicitly disclosed: the paper itself says one-shot behavior is the optimum of unique-solution supervision, so the remaining independent content is how completely the model attains that optimum, the exact poisoning contingency, and the success

full rationale

The paper contains one disclosed definitional element: in clue-rich unique-solution Sudoku, the depth-0 target of Eq. (1) is the complete solution, so a perfectly fitting candidate head is a one-shot solver by construction. The paper does not hide this—its contribution list states that one-shot behavior 'is itself the optimum of unique-solution supervision' and reframes H1 as measuring how completely the optimum is reached. Because it is disclosed, this is a partial circularity rather than a deceptive derivation. The rest of the load-bearing chain is genuinely empirical and self-contained: the 43/43 vs 0/137 first-pass-poisoning contingency (replicated at 49/49 vs 0/131 and 38/38 vs 0/142), the monotonicity lemma, the θ_elim invariance, the 2×2 structure-by-augmentation interaction, the 9×9 augmentation jump from below 1% to 96.5±0.3%, the test-time union cure to 100%, and the from-scratch graph-coloring boundary where one-shot behavior disappears and search changes accuracy. None of these results reduces to Eq. (1) by construction; they are measured with committed artifacts, frozen protocols, and an independent clean-room verifier. The reliance on the author's own LDT reimplementation with the published augmentation deliberately omitted is a transferability caveat, not circularity: the paper marks it as an instrumented control and states the deviation explicitly. Proposition 1 is a mathematical proof, and Observation 1 is definitional in a logical, non-vicious sense. Overall, the central claim has substantial independent empirical content, marred only by the acknowledged definitional origin of the one-shot characterization, so the appropriate score is 4 rather than 0 or 8.

Assumptions & free parameters 3 free parameters · 5 assumptions · 1 invented entities

No constants are fitted to data; the model hyperparameters are fixed in a frozen protocol and the few hand-set thresholds are shown invariant where they matter. The main unpaid inputs are the verify-or-abstain gate, unique-solution generated puzzles, and the symmetry audit. First-pass poisoning is a mechanistic construct with direct empirical handles.

free parameters (3)
  • theta_elim (candidate elimination threshold) = 0.1
    Hand-set threshold used to define first-pass commitment and poisoning; the paper shows the poisoning count is invariant at 0.05 and 0.02, so it is not a tuned-to-result knob.
  • K union frames (test-time symmetry ensemble) = 8
    Test-time intervention uses K=8 digit-permutation frames; K=4 already reaches 100% on the hard slice, while K=1 and identity frames do not, so the value is not fit to the result.
  • Policy loss weight and branch temperature = lambda_pol=0.25, tau=1.5
    Training hyperparameters fixed in the frozen protocol; the policy head is accuracy-inert anyway, so the central claim does not depend on them.
assumptions (5)
  • domain assumption Verify-or-abstain emission: an answer is emitted only when it passes an exact external checker.
    Observation 1 in Section 1; the soundness guarantee and the conclusion that search is a free design space rest on this definitional gate.
  • domain assumption Unique-solution Sudoku generation with exact-uniqueness verification; the depth-0 target (Eq. 1) equals the complete solution.
    Sections 2 and 4; the one-shot target and the first-pass poisoning logic depend on uniqueness of solutions and the abstraction operator over the full solution set.
  • domain assumption Monotone lattice semantics: candidates are only removed, so a true-value deletion cannot be undone.
    Section 2 and Section 5.3; sufficiency of first-pass poisoning is a lemma of this monotonicity.
  • standard math Value-symmetry of graph coloring and the full-alphabet-at-every-variable condition in Proposition 1.
    Section 8; the no-depth-0-signal proposition is proved from these assumptions.
  • domain assumption Leakage audit enumerating the full Sudoku symmetry group exactly.
    Section 4; the claim that 9x9 splits are symmetry-disjoint and that 6x6 cannot be depends on the exactness of the audit implementation.
invented entities (1)
  • First-pass poisoning independent evidence
    purpose: Explanatory mechanism for why clue-rich completion failures are decided before search begins.
    Supported by a perfect contingency (43/43 vs 0/137, replicated) and by two interventions (augmentation, union ensemble) that remove the failure mode; it is a postulated mechanism, not a physical entity.

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Cite this review

Pith. "Pith review of Anatomy of a Sound Neural Reasoner: One-Shot Amortization, First-Pass Poisoning, and Search Inertness in Clue-Rich Completion." pith.science (2026). https://pith.science/paper/24IIVYUM

@misc{pith2026260719635,
  author       = {Pith},
  title        = {Pith review of: Anatomy of a Sound Neural Reasoner: One-Shot Amortization, First-Pass Poisoning, and Search Inertness in Clue-Rich Completion},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/24IIVYUM}},
  note         = {Machine review of arXiv:2607.19635}
}
read the original abstract

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.

Figures

Figures reproduced from arXiv: 2607.19635 by the authors.

Figure 1
Figure 1. The paper in one picture. (a) The architecture implements an iterative deduce–branch– [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗

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Reference graph

Works this paper leans on

35 extracted references · 6 linked inside Pith

  1. [1]

    Maria Chiara Angelini and Federico Ricci-Tersenghi. Modern graph neural networks do worse than classical greedy algorithms in solving combinatorial optimization problems like maximum independent set.Nature Machine Intelligence, 5:29–31, 2023

    2023

  2. [2]

    Gen- erative Recursive Reasoning.arXiv preprint arXiv:2605.19376, 2026

    Junyeob Baek, Mingyu Jo, Minsu Kim, Mengye Ren, Yoshua Bengio, and Sungjin Ahn. Gen- erative Recursive Reasoning.arXiv preprint arXiv:2605.19376, 2026

    arXiv 2026

  3. [3]

    End-to-end algorithm synthesis with recurrent networks: Logical extrapolation without overthinking

    Arpit Bansal, Avi Schwarzschild, Eitan Borgnia, Zeyad Emam, Furong Huang, Micah Gold- blum, and Tom Goldstein. End-to-end algorithm synthesis with recurrent networks: Logical extrapolation without overthinking. InAdvances in Neural Information Processing Systems, volume 35, 2022

    2022

  4. [4]

    Machine learning for combinatorial optimization: A methodological tour d’horizon.European Journal of Operational Research, 290(2):405–421, 2021

    Yoshua Bengio, Andrea Lodi, and Antoine Prouvost. Machine learning for combinatorial optimization: A methodological tour d’horizon.European Journal of Operational Research, 290(2):405–421, 2021

    2021

  5. [5]

    Peter Cheeseman, Bob Kanefsky, and William M. Taylor. Where the really hard problems are. InProceedings of the 12th International Joint Conference on Artificial Intelligence (IJCAI-91), pages 331–337, 1991

    1991

  6. [6]

    Lattice Deduction Transformers.arXiv preprint arXiv:2605.08605, 2026

    Liam Davis, Leopold Haller, Alberto Alfarano, and Mark Santolucito. Lattice Deduction Transformers.arXiv preprint arXiv:2605.08605, 2026

    arXiv 2026

  7. [7]

    Learning to rank the initial branching order of SAT solvers.arXiv preprint arXiv:2603.07176, 2026

    Arvid Eriksson, Gabriel Poesia, Roman Bresson, Karl Henrik Johansson, and David Broman. Learning to rank the initial branching order of SAT solvers.arXiv preprint arXiv:2603.07176, 2026

    arXiv 2026

  8. [8]

    Kanishk Gandhi, Denise Lee, Gabriel Grand, Muxin Liu, Winson Cheng, Archit Sharma, and Noah D. Goodman. Stream of search (SoS): Learning to search in language.arXiv preprint arXiv:2404.03683, 2024. 20

    arXiv 2024

Show all 35 references
  1. [9]

    Exact combinatorial optimization with graph convolutional neural networks

    Maxime Gasse, Didier Ch´ etelat, Nicola Ferroni, Laurent Charlin, and Andrea Lodi. Exact combinatorial optimization with graph convolutional neural networks. InAdvances in Neural Information Processing Systems 32, 2019

    2019

  2. [10]

    Gershman and Noah D

    Samuel J. Gershman and Noah D. Goodman. Amortized inference in probabilistic reasoning. InProceedings of the 36th Annual Conference of the Cognitive Science Society, 2014

    2014

  3. [11]

    Haralick and Gordon L

    Robert M. Haralick and Gordon L. Elliott. Increasing tree search efficiency for constraint satisfaction problems.Artificial Intelligence, 14(3):263–313, 1980

    1980

  4. [12]

    Less is more: Recursive reasoning with tiny networks.arXiv preprint arXiv:2510.04871, 2025

    Alexia Jolicoeur-Martineau. Less is more: Recursive reasoning with tiny networks.arXiv preprint arXiv:2510.04871, 2025

    2025 arXiv

  5. [13]

    Khalil, Pierre Le Bodic, Le Song, George Nemhauser, and Bistra Dilkina

    Elias B. Khalil, Pierre Le Bodic, Le Song, George Nemhauser, and Bistra Dilkina. Learning to branch in mixed integer programming. InProceedings of the 30th AAAI Conference on Artificial Intelligence, pages 724–731, 2016

    2016

  6. [14]

    GRAM — community reimplementation of Generative Recursive Rea- soning Models, 2026

    Aleksey Komissarov. GRAM — community reimplementation of Generative Recursive Rea- soning Models, 2026. URLhttps://github.com/ad3002/gram

    2026

  7. [15]

    LDT — community reimplementation of the Lattice Deduction Trans- former, 2026

    Aleksey Komissarov. LDT — community reimplementation of the Lattice Deduction Trans- former, 2026. URLhttps://github.com/ad3002/LTD

    2026

  8. [16]

    Beyond A*: Better planning with transformers via search dynamics bootstrapping.arXiv preprint arXiv:2402.14083, 2024

    Lucas Lehnert, Sainbayar Sukhbaatar, DiJia Su, Qinqing Zheng, Paul Mcvay, Michael Rabbat, and Yuandong Tian. Beyond A*: Better planning with transformers via search dynamics bootstrapping.arXiv preprint arXiv:2402.14083, 2024

    2024 arXiv

  9. [17]

    Marques-Silva and Karem A

    Jo˜ ao P. Marques-Silva and Karem A. Sakallah. GRASP: A search algorithm for propositional satisfiability.IEEE Transactions on Computers, 48(5):506–521, 1999

    1999

  10. [18]

    Analytic and algorithmic solution of random satisfiability problems.Science, 297:812–815, 2002

    Marc M´ ezard, Giorgio Parisi, and Riccardo Zecchina. Analytic and algorithmic solution of random satisfiability problems.Science, 297:812–815, 2002

    2002

  11. [19]

    Determining computational complexity from characteristic ‘phase transitions’.Nature, 400: 133–137, 1999

    R´ emi Monasson, Riccardo Zecchina, Scott Kirkpatrick, Bart Selman, and Lidror Troyansky. Determining computational complexity from characteristic ‘phase transitions’.Nature, 400: 133–137, 1999

    1999

  12. [20]

    Moskewicz, Conor F

    Matthew W. Moskewicz, Conor F. Madigan, Ying Zhao, Lintao Zhang, and Sharad Malik. Chaff: Engineering an efficient SAT solver. InProceedings of the 38th Design Automation Conference (DAC), pages 530–535, 2001

    2001

  13. [21]

    Coloring random graphs.Physical Review Letters, 89(26):268701, 2002

    Roberto Mulet, Andrea Pagnani, Martin Weigt, and Riccardo Zecchina. Coloring random graphs.Physical Review Letters, 89(26):268701, 2002

    2002

  14. [22]

    Stuckey, and Michael Codish

    Olga Ohrimenko, Peter J. Stuckey, and Michael Codish. Propagation via lazy clause generation. Constraints, 14(3):357–391, 2009

    2009

  15. [23]

    Recurrent relational networks

    Rasmus Berg Palm, Ulrich Paquet, and Ole Winther. Recurrent relational networks. In Advances in Neural Information Processing Systems 31, 2018

    2018

  16. [24]

    Martin J. A. Schuetz, J. Kyle Brubaker, and Helmut G. Katzgraber. Combinatorial optimiza- tion with physics-inspired graph neural networks.Nature Machine Intelligence, 4:367–377, 2022. 21

    2022

  17. [25]

    Can you learn an algorithm? Generalizing from easy to hard problems with recurrent networks

    Avi Schwarzschild, Eitan Borgnia, Arjun Gupta, Furong Huang, Uzi Vishkin, Micah Goldblum, and Tom Goldstein. Can you learn an algorithm? Generalizing from easy to hard problems with recurrent networks. InAdvances in Neural Information Processing Systems, volume 34, 2021

    2021

  18. [26]

    Guiding high-performance SAT solvers with unsat-core predictions

    Daniel Selsam and Nikolaj Bjørner. Guiding high-performance SAT solvers with unsat-core predictions. InTheory and Applications of Satisfiability Testing – SAT 2019, volume 11628 of Lecture Notes in Computer Science, pages 336–353, 2019

    2019

  19. [27]

    Daniel Selsam, Matthew Lamm, Benedikt B¨ unz, Percy Liang, Leonardo de Moura, and David L. Dill. Learning a SAT solver from single-bit supervision. InInternational Conference on Learning Representations (ICLR), 2019

    2019

  20. [28]

    Better aggregation in test-time augmentation

    Divya Shanmugam, Davis Blalock, Guha Balakrishnan, and John Guttag. Better aggregation in test-time augmentation. InProceedings of the IEEE/CVF International Conference on Computer Vision, pages 1214–1223, 2021

    2021

  21. [29]

    A general reinforcement learning algorithm that masters chess, shogi, and Go through self-play.Science, 362(6419):1140–1144, 2018

    David Silver, Thomas Hubert, Julian Schrittwieser, Ioannis Antonoglou, Matthew Lai, Arthur Guez, Marc Lanctot, Laurent Sifre, Dharshan Kumaran, Thore Graepel, Timothy Lillicrap, Karen Simonyan, and Demis Hassabis. A general reinforcement learning algorithm that masters chess, ...

    2018

  22. [30]

    Graph neural networks for maximum constraint satisfaction.Frontiers in Artificial Intelligence, 3:580607, 2021

    Jan T¨ onshoff, Martin Ritzert, Hinrikus Wolf, and Martin Grohe. Graph neural networks for maximum constraint satisfaction.Frontiers in Artificial Intelligence, 3:580607, 2021

    2021

  23. [31]

    Neural algorithmic reasoning.Patterns, 2(7):100273, 2021

    Petar Veliˇ ckovi´ c and Charles Blundell. Neural algorithmic reasoning.Patterns, 2(7):100273, 2021

    2021

  24. [32]

    Hierarchical reasoning model.arXiv preprint arXiv:2506.21734, 2025

    Guan Wang, Jin Li, Yuhao Sun, Xing Chen, Changling Liu, Yue Wu, Meng Lu, Sen Song, and Yasin Abbasi Yadkori. Hierarchical reasoning model.arXiv preprint arXiv:2506.21734, 2025

    2025 arXiv

  25. [33]

    Donti, Bryan Wilder, and J

    Po-Wei Wang, Priya L. Donti, Bryan Wilder, and J. Zico Kolter. SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver. InProceedings of the 36th International Conference on Machine Learning, volume 97 ofPMLR, pages 6545–6554, 2019

    2019

  26. [34]

    NeuroBack: Improving CDCL SAT solving using graph neural networks

    Wenxi Wang, Yang Hu, Mohit Tiwari, Sarfraz Khurshid, Kenneth McMillan, and Risto Mi- ikkulainen. NeuroBack: Improving CDCL SAT solving using graph neural networks. In International Conference on Learning Representations, 2024

    2024

  27. [35]

    Do transformers really perform badly for graph representation? InAdvances in Neural Information Processing Systems, volume 34, pages 28877–28888, 2021

    Chengxuan Ying, Tianle Cai, Shengjie Luo, Shuxin Zheng, Guolin Ke, Di He, Yanming Shen, and Tie-Yan Liu. Do transformers really perform badly for graph representation? InAdvances in Neural Information Processing Systems, volume 34, pages 28877–28888, 2021. A Claim audit: each ...

    2021

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