Flow Reasoning Models: recurrent flow architecture hits 99.5% on Sudoku-Extreme with 44x fewer FLOPs
alec_helbling · x · 2026-09-03
A new arXiv paper introduces Flow Reasoning Models (FRMs), a framework for structured reasoning that applies continuous flows to discrete structured outputs with recurrent self-conditioning refinement.
- How it works: self-conditioning a flow model on its own past outputs turns one-shot denoising into iterative solution refinement, letting the model make and revise interdependent decisions in parallel.
- Key fix: conventional self-conditioning breaks down at greater recurrent depth due to exposure bias; Fixed-Point Forcing (FPF) trains on states produced by the model's own inference dynamics while preserving the flow-matching objective. Multiple recurrent passes lift Sudoku-Extreme from 30% to 99%.
- Results: 99.5% / 100.0% / 99.9% solve rates on Sudoku-Extreme, Zebra, and Maze-Unique; on Sudoku-Extreme FRMs match EqR's 98.7% with 44x fewer FLOPs and reach a higher 99.5% peak accuracy, outperforming HRM, TRM, and masked diffusion on inference efficiency.
- Perspective: correct answers are fixed-point attractors of the self-conditioned flow's dynamics.
Related event: Flow Reasoning Models Turn Flows Into Efficient Recurrent Reasoners(6 posts)→
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