Learned Correction Dynamics in Recursive Reasoning Models

Recursive reasoning models achieve strong performance on certain reasoning tasks by repeatedly applying a small neural network to an evolving latent state. Yet how recursion contributes to reasoning, what successive iterations accomplish, and when additional computation improves performance remain incompletely understood. We address these questions through trajectory measurements and controlled interventions on Sudoku-Extreme, studying released models alongside our compact solvers. We develop an empirical account of learned correction dynamics. Recursion can revise many cells while making little net progress before abrupt completion. Model-produced and randomly corrupted grids can differ in repairability at equal error counts. Continued communication and retained state support correction. Our controls separate solving capability from access through initialization, and finding correct answers from selecting them. Training comparisons show that useful generation and reliable selection need not be learned together. The repair and state findings also hold in our compact attention models, which achieve 99.48 % with 0.62M parameters and 99.62 % with 1.06M and 1.97M on all 422,786 test puzzles. Using 1,000 training puzzles and one fixed-start trajectory of 64 iterations, all exceed, to our knowledge, the best comparable published score of 98.22 % with less matrix multiplication work. Extending the analysis to ARC-AGI reveals a complementary limit: a released model's fit to training demonstrations does not ensure held-out query success, and tested pools lack correct candidates for most queries. The Sudoku findings motivate a conjecture of learned relaxation with memory: retained or reconstructed context could support coordinated revision of mutually supporting errors; on ARC, revising task representations alongside answers could generate new solutions.