Equilibrium Reasoners: Learning Attractors Enables Scalable Reasoning

• URL: http://arxiv.org/abs/2605.21488v1
• Date: Wed, 20 May 2026 17:59:48 GMT
• Title: Equilibrium Reasoners: Learning Attractors Enables Scalable Reasoning
• Abstract summary: We show that scalable latent reasoning boosts accuracy from 2.6% for feedforward models to over 99% on Sudoku-Extreme.<n>By unrolling up to the equivalent of 40,000 layers, scalable latent reasoning boosts accuracy from 2.6% for feedforward models to over 99% on Sudoku-Extreme.
• Score: 15.355823330309724
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 unclear. We hypothesize that generalizable reasoning arises from learning task-conditioned attractors: latent dynamical systems whose stable fixed points correspond to valid solutions. We formalize this process through Equilibrium Reasoners (EqR), which enable test-time scaling without external verifiers or task-specific priors. EqR scales internal dynamics along two axes: depth, by running more iterations, and breadth, by aggregating stochastic trajectories from multiple initializations. Empirically, gains from test-time scaling are tightly coupled with stronger convergence toward solution-aligned 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, harder cases benefit from massive test-time scaling. By unrolling up to the equivalent of 40,000 layers, scalable latent reasoning boosts accuracy from 2.6% for feedforward models to over 99% on Sudoku-Extreme. These results suggest that learned attractor landscapes provide a useful mechanistic lens for understanding scalable reasoning in iterative latent models.

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