Equilibrium Reasoners: Learning Attractors Enables Scalable Reasoning

Scaling test-time compute by iteratively updating a latent state has emerged as a powerful paradigm for reasoning. Yet, the internal mechanisms that enable these iterative models to generalize beyond memorized patterns remain fundamentally unclear. We hypothesize that such generalizable reasoning arises from learning task-conditioned attractors: a latent dynamical system where stable fixed points correspond to valid solutions. We formalize this process by introducing Equilibrium Reasoners (EqR). EqR enables test-time scaling without relying on external verifiers or task-specific priors. Instead, our models scale internal dynamics along two axes: depth by running more iterations and breadth by aggregating stochastic trajectories from multiple initializations. Empirically, performance gains from scaling test-time compute are tightly coupled with better convergence to attractors. This attractor perspective allows neural networks to adaptively allocate test-time compute based on task difficulty. While simple cases converge within 1 to 5 iteration steps, the hardest cases benefit from massive test-time scaling. By unrolling up to an equivalent of 40,000 layers, this scalable latent reasoning boosts accuracy from 2.6% for feedforward models to over 99% on Sudoku-Extreme. We hope our attractor perspective sheds light on scalable reasoning.