Structural Grid Descriptors Predict Within-Task Solver Success on ARC-AGI

• URL: http://arxiv.org/abs/2606.09026v2
• Date: Tue, 09 Jun 2026 17:11:01 GMT
• Title: Structural Grid Descriptors Predict Within-Task Solver Success on ARC-AGI
• Abstract summary: We ask whether structural properties of intermediate grid states predict whether a symbolic ARC-AGI solver will succeed, framed as a test of conditional mutual information I(X;Ytask) > 0.<n>Across 44,800 runs spanning two architecturally distinct search and DFS solvers, we find most content lies along a single grid-complexity axis.<n>The signal is not explained by solver capacity (-residualized AUC = 0.927 and 0.896 for beam search and SDFS, p 95) and is only weakly coupled to score trajectories (R2 approximately 0)
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We ask whether structural properties of intermediate grid states predict whether a symbolic ARC-AGI solver will succeed, framed as a test of conditional mutual information I(X;Y|task) > 0. Across 44,800 runs spanning two architecturally distinct solvers (beam search and Stochastic DFS), 400 ARC tasks, 28 configurations per solver, and both training and evaluation splits, hand-crafted grid descriptors measured at 50% trajectory completion discriminate successful from failed runs within the same task (mean within-task best-feature AUC = 0.885, p < 0.001 under within-task label permutation). Most predictive content lies along a single grid-complexity axis. The result generalizes across solver architectures: a feature selected on one solver predicts success on the other with AUC 0.747-0.762 in all four transfer directions (p < 0.001, leakage controlled). On a pre-registered held-out set of 41 reliable tasks, the frozen feature n_components_final achieves AUC = 0.765 (95% CI [0.717, 0.810], p < 0.001), robust under task-clustered bootstrap resampling and cross-solver task collapsing. The signal is not explained by solver capacity (configuration-residualized AUC = 0.927 and 0.896 for beam search and SDFS, p < 0.001) and is only weakly coupled to score trajectories (R^2 approximately 0). Early stopping at 50% completion reduces beam-search compute by 33.6% while retaining 98.9% of solves; degenerate-trajectory detection reduces SDFS compute by 65.3% with no solve loss. Finally, on 229 of 400 evaluation tasks the DSL primitive library produces no valid transition from the input grid. This 0-step collapse is invariant to search budget and universally failed by beam search, indicating a DSL coverage limitation rather than a search-budget effect.

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