Equilibrium Reasoners: A New Paradigm for Scalable Reasoning Through Learning Attractors

Research reveals that iterative models capable of scaling test-time computation achieve generalizable reasoning through learned task-conditioned attractors. These latent dynamical systems, corresponding to stable fixed points, formalize the reasoning process via Equilibrium Reasoners (EqR). The study demonstrates that scaling occurs along two dimensions: depth through increased iterations and breadth by aggregating stochastic trajectories from multiple initializations. Results indicate that effective test-time scaling enhances convergence toward solution-aligned attractors, enabling neural networks to adaptively allocate resources based on task difficulty. Notably, the approach significantly improves accuracy on complex tasks, such as Sudoku-Extreme, where performance jumps from 2.6% to over 99% by utilizing extensive test-time scaling techniques, thus providing insights into the mechanisms behind scalable reasoning in iterative models.