Authors
Kaleem Ullah Qasim, Jiashu Zhang, Razan Alharith, Muhammad Kafeel Shaheen
Published in
Neural networks : the official journal of the International Neural Network Society. Volume 206. Issue Pt A. Pages 109720. Oct 08, 2026. Epub Oct 08, 2026.
Abstract
Recursive reasoning models solve complex reasoning tasks through iterative refinement, enabling tiny networks to rival far larger language models. However, training remains expensive: prior work reports 36 GPU-hours for Sudoku-Extreme. We propose CGAR, a training methodology that applies curriculum learning to architectural depth rather than data ordering. CGAR combines Progressive Depth Curriculum (PDC), which adjusts recursion depth from shallow to deep configurations during training, and Hierarchical Supervision Weighting (HSW), which applies exponentially decaying importance to supervision steps to align loss weighting with observed gradient magnitude decay. On Sudoku-Extreme (423,168 test puzzles), CGAR achieves 1.71 × training speedup (10.93 to 6.38 hours, 42% cost reduction) with only 0.63% accuracy drop (86.65% to 86.02%), while preventing late-stage overfitting that degrades baseline to 86.31%. Ablations reveal PDC alone achieves 2.26 × speedup at 85.47% accuracy, improving training efficiency and accuracy at once. The speedup reproduces on Maze-Hard and ARC-AGI-1 (1.25-1.71 × over three tasks), with the fixed-depth baseline failing to learn ARC-AGI-1 under matched budget. CGAR-trained models exhibit near-perfect halting accuracy (99.5% for full CGAR; 100% for the PDC-only configuration) and 6% fewer reasoning steps. Curriculum on architectural depth enables efficient training of recursive reasoners on modest hardware. Code: https://github.com/Kaleemullahqasim/CGAR.
PMID:
42858689
Bibliographic data and abstract were imported from PubMed on 11 Oct 2026.
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