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.

This paper studies how AI systems can improve their reasoning by spending more time working on a problem before giving an answer. Instead of producing an answer in one pass, our model repeatedly updates its internal state until it settles on a stable answer. We call this approach Equilibrium Reasoners. The key idea is that good reasoning behavior can be viewed as learning a process whose stable outcomes correspond to correct solutions. We test this idea on structured reasoning problems such as Sudoku and mazes, where it is possible to measure whether the model truly generalizes beyond memorized patterns. Our results show that when the model learns better settling behavior, giving it more computation at test time reliably improves accuracy. Easy problems can be solved with only a few update steps, while harder problems benefit from many more steps and from combining multiple attempts. This provides a controlled way to study why test-time computation helps reasoning and how models can use extra computation more effectively.