Fixed-Point Reasoners: Stable and Adaptive Deep Looped Transformers

Fixed-Point Reasoning Model (FPRM): Stable looped Transformers with adaptive compute via fixed-point halting

Researchers introduce FPRM, a Transformer-based Fixed-Point Reasoning Model that uses fixed-point convergence as a halting mechanism in looped architectures, addressing signal propagation problems through pre-norm layers and residual scaling. Looped architectures provide inductive bias for compositional reasoning, but suffer from depth-induced signal degradation when halting is deferred; FPRM resolves this while enabling compute to scale with task difficulty. The model is evaluated on Sudoku, Maze, state-tracking, and ARC-AGI benchmarks. This contributes to the growing body of work on adaptive-compute and iterative-refinement architectures for reasoning.