Negotiated Recursive Reasoning

Small recursive networks solve structured problems by repeatedly refining a latent state with shared weights. Splitting a problem into overlapping local views exposes its constraints but creates a coordination problem: in Sudoku, a row, a column, and a box can propose different values for their shared cell. We introduce Negotiated Recursive Reasoning (NRR), which coordinates local recursion while it takes place. A shared local reasoner refines a proposal and a private reasoning state for each view, while an explicit negotiation step constructs targets that reduce overlap disagreement and carries unresolved disagreement into the next round. We use a normalized soft-consensus system with a bounded condition number and characterize the gradient path through which task supervision learns the coupling. In the benchmark setting, NRR reaches 95.2% exact solve on Sudoku-Extreme and 90.4% on Maze-Hard, 5.3 points above a learned-link replacement on both tasks, with larger gains on harder Sudoku puzzles. In controlled comparisons, NRR exceeds a native TRM rerun by 6.2 and 3.6 points, and disagreement memory improves both recursive and feed-forward local solvers, with larger mean gains for recursive updates. On larger mazes, sparse coordination gives a better accuracy–latency tradeoff than global attention recurrence. These results identify the organization of interaction among partial solutions as a useful design dimension for recursive reasoning, alongside model capacity and recursion depth.