Accelerating Training Speed of Tiny Recursive Models via Curriculum Guided Adaptive Recursion

2025-11-11

AI Summary

Training small recursive reasoning models incurs high computational costs (e.g., 36 GPU-hours per dataset). Method: This work introduces curriculum learning along the recursive depth dimension—the first such approach—proposing a training paradigm based on progressive depth growth and hierarchical supervision weighting, augmented by exponentially decaying loss weights and dynamic recursive depth adjustment. Unlike prior methods, it avoids data reordering and instead systematically modulates the complexity of the model’s recursive structure. Contribution/Results: The method achieves Pareto-optimal improvements in training efficiency and performance. On Sudoku-Extreme, training time is reduced by 42% (from 10.93 to 6.38 GPU-hours), with only a marginal accuracy drop of 0.63%. Inference halting accuracy reaches 100%, and average inference steps decrease by 11%. This work establishes a novel, efficient training paradigm for small recursive models.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Search and Optimization: Learning to Search
• Cognitive Modeling & Cognitive Systems: Computational Creativity

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Recursive reasoning models achieve remarkable performance on complex reasoning tasks through iterative refinement, enabling tiny networks to match large language models thousands of times their size. However, training remains computationally expensive, prior work reporting approximately 36 GPU-hours per dataset, limiting broader adoption and research. We propose CGAR, a novel training methodology that applies curriculum learning to architectural depth rather than traditional data ordering. CGAR introduces two synergistic components: Progressive Depth Curriculum dynamically adjusts recursion depth from shallow to deep configurations during training, preventing early overfitting while reducing computational cost, and Hierarchical Supervision Weighting applies exponentially decaying importance to supervision steps, aligning loss weighting with observed gradient magnitude decay. On Sudoku-Extreme with 423,168 test puzzles, CGAR achieves 1.71x training speedup (10.93 to 6.38 hours, 42% cost reduction) with only 0.63% accuracy drop (86.65% to 86.02%). Systematic ablations reveal Progressive Depth Curriculum alone achieves 2.26x speedup with 85.47% accuracy, demonstrating a rare Pareto improvement where architectural curriculum simultaneously enhances training efficiency and solution quality. CGAR-trained models exhibit superior inference efficiency with 100% halting accuracy and 11% fewer reasoning steps. Our work demonstrates that principled curriculum on architectural depth enables efficient training of recursive reasoning models on modest hardware. Code and models: https://github.com/Kaleemullahqasim/CGAR and https://huggingface.co/Kaleemullah/trm-cgar-sudoku

Problem

• Accelerates training speed of recursive reasoning models
• Reduces computational costs while maintaining model accuracy
• Enables efficient training on modest hardware through curriculum learning

Innovation

• Curriculum learning applied to architectural depth
• Progressive Depth Curriculum adjusts recursion depth dynamically
• Hierarchical Supervision Weighting decays supervision step importance