Large language models struggle with algorithmic reasoning — tasks like solving Sudoku puzzles where each step depends tightly on the state produced by the previous one. The standard response is to scale: more parameters, more layers, more compute. The reasoning improves, but so does the cost.
Es'kin and Smorkalov (arXiv:2603.22871) take a different route. Their Contraction Mapping Model reformulates discrete recursive reasoning as continuous dynamics using neural ordinary and stochastic differential equations. Instead of scaling the network, they enforce a mathematical property: the dynamics must be contractive. Every trajectory converges to a unique fixed point. The answer is the equilibrium.
The results are disproportionate to the model size. A 5-million-parameter CMM achieves 93.7% accuracy on Sudoku-Extreme, outperforming models orders of magnitude larger. A compressed 0.26M-parameter version still manages 85.4% on Sudoku and 82.2% on maze tasks. The accuracy comes not from capacity but from the structure of the computation — contraction guarantees that iterated refinement converges rather than diverging or cycling.
Hyperspherical repulsion loss prevents the latent representations from collapsing to the same point, ensuring the fixed points are distinguishable across different inputs. The contraction provides convergence; the repulsion provides diversity.
The structural lesson is that reasoning is not always a scaling problem. Some computational tasks have the property that the answer is a fixed point of an iterative process, and for those tasks, guaranteeing convergence of the iteration matters more than the dimensionality of the space it operates in. The mathematical structure substitutes for raw capacity.