{"@context":"https://schema.org","@type":"CreativeWork","@id":"https://forgecascade.org/public/capsules/f589a564-4cc3-4b29-9169-a4569b86b6bc","identifier":"f589a564-4cc3-4b29-9169-a4569b86b6bc","url":"https://forgecascade.org/public/capsules/f589a564-4cc3-4b29-9169-a4569b86b6bc","name":"Equilibrium Reasoners: Learning Attractors Enables Scalable Reasoning","text":"# Equilibrium Reasoners: Learning Attractors Enables Scalable Reasoning\n\n**Authors:** Benhao Huang, Zhengyang Geng, Zico Kolter\n**arXiv:** https://arxiv.org/abs/2605.21488v1\n**Published:** 2026-05-20T17:59:48Z\n\n## Abstract\nScaling 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.","keywords":["cs.LG"],"about":[{"@type":"Thing","name":"lactoferrin transmembrane transporter activity"},{"@type":"Thing","name":"chronic atrial and intestinal dysrhythmia"},{"@type":"Thing","name":"Scaling skin"},{"@type":"Thing","name":"Extreme axis deviation"},{"@type":"Thing","name":"SVG Smuggling"},{"@type":"Thing","name":"Compute Hijacking"},{"@type":"Thing","name":"vSphere Installation Bundles"},{"@type":"Thing","name":"extreme capsule"}],"citation":[],"isPartOf":{"@type":"Dataset","name":"Forge Cascade Knowledge Graph","url":"https://forgecascade.org"},"publisher":{"@type":"Organization","name":"Forge Cascade","url":"https://forgecascade.org"},"dateCreated":"2026-05-21T06:00:06.175000Z","dateModified":"2026-05-21T06:00:06.175000Z","isBasedOn":"https://arxiv.org/abs/2605.21488v1","additionalProperty":[{"@type":"PropertyValue","name":"trust_level","value":65},{"@type":"PropertyValue","name":"verification_status","value":"source_linked"},{"@type":"PropertyValue","name":"evidence_level","value":"primary_source"}]}