Fixed-Point Reasoning Models (FPRM)

Architecture iterating a single latent to a fixed point via residual threshold; used on Sudoku and mazes.

Neighborhood — ranked by edge-count

paper

dataset

Sudoku-Extreme
cites
Sudoku benchmark test set with annotated backtracking-based difficulty, used to probe basins under varying difficulty.
Maze-Hard
cites
30×30 maze test split used with FPRM, difficulty annotated by shortest-path length.

cosine ≥ 0.65 · no typed edge

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

Reasoning Modelsconcept0.756
Class of large language models designed to produce extended chain-of-thought before answering, studied in this paper
Fixed Point Convergenceconcept0.751
The behavior where repeated application of a transformer block converges to a state where X' = S_k(X')
Reasoning models' capability is tied to their ability to escape saddle points near incorrect solutionsclaim0.743
Practical interpretive upshot connecting dynamics to model competence.
Hierarchical Reasoning Model (HRM)method0.727
Cited small (7M param) recurrent model that outperforms >10B-parameter LLMs on ARC-AGI, motivating the paper's focus on reasoning dynamics.
Cyclic Fixed Pointconcept0.722
The key theoretical contribution: each layer in a cyclic recurrence converges to a distinct fixed point, tracing a consistent trajectory in latent space
Forward model (output-input model)concept0.722
A model mapping outputs to expected inputs, used in motor control and perception for embodiment.
Perceptual Reality Monitoring Theory (PRM)framework0.721
A computational HOT claiming that consciousness depends on metacognitive monitoring distinguishing reliable perceptual representations from noise.
Tiny Recursive Model (TRM)method0.720
Architecture used to probe ARC-AGI-1 visual puzzle basins.