nice video!</p>\n","updatedAt":"2026-05-26T00:36:32.863Z","author":{"_id":"655601f1ae085c2ba7a22b95","avatarUrl":"https://cdn-avatars.huggingface.co/v1/production/uploads/noauth/4UmxFrc_TEiXcnm3RewZM.jpeg","fullname":"Xiaoji Zheng","name":"Student-Xiaoji","type":"user","isPro":false,"isHf":false,"isHfAdmin":false,"isMod":false,"followerCount":3,"isUserFollowing":false}},"numEdits":0,"identifiedLanguage":{"language":"it","probability":0.19524987041950226},"editors":["Student-Xiaoji"],"editorAvatarUrls":["https://cdn-avatars.huggingface.co/v1/production/uploads/noauth/4UmxFrc_TEiXcnm3RewZM.jpeg"],"reactions":[],"isReport":false}}],"primaryEmailConfirmed":false,"paper":{"id":"2605.21488","authors":[{"_id":"6a1278994d9e8d8602d2006d","name":"Benhao Huang","hidden":false},{"_id":"6a1278994d9e8d8602d2006e","name":"Zhengyang Geng","hidden":false},{"_id":"6a1278994d9e8d8602d2006f","name":"Zico Kolter","hidden":false}],"mediaUrls":["https://cdn-uploads.huggingface.co/production/uploads/64b22e6b0a54158d66f18688/4WRt9X-WHJTC2S7W0lDbq.mp4","https://cdn-uploads.huggingface.co/production/uploads/64b22e6b0a54158d66f18688/vuw9FTv6l5z88IQWBvMzv.gif","https://cdn-uploads.huggingface.co/production/uploads/64b22e6b0a54158d66f18688/G3MR3dIK94YvmkSbNOU8q.gif"],"publishedAt":"2026-05-20T00:00:00.000Z","submittedOnDailyAt":"2026-05-25T00:00:00.000Z","title":"Equilibrium Reasoners: Learning Attractors Enables Scalable Reasoning","submittedOnDailyBy":{"_id":"64b22e6b0a54158d66f18688","avatarUrl":"https://cdn-avatars.huggingface.co/v1/production/uploads/64b22e6b0a54158d66f18688/Cbl3oMMMANbnCMoSUYenI.png","isPro":true,"fullname":"Benhao Huang","user":"HuskyDoge","type":"user","name":"HuskyDoge"},"summary":"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.\n 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.\n 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.","upvotes":2,"discussionId":"6a1278994d9e8d8602d20070","projectPage":"https://x.com/huskydogewoof/status/2057641657580064941?s=20","githubRepo":"https://github.com/locuslab/eqr","githubRepoAddedBy":"user","ai_summary":"Equilibrium Reasoners enable scalable reasoning through task-conditioned attractors that guide latent dynamical systems toward valid solutions, achieving significant accuracy improvements through iterative test-time computation.","ai_keywords":["Equilibrium Reasoners","attractors","latent dynamical systems","test-time scaling","iterative models","task-conditioned attractors","stochastic trajectories","convergence","Sudoku-Extreme"],"githubStars":25,"organization":{"_id":"6553f32fd13e8d851dc9c064","name":"locuslab","fullname":"Locus Lab","avatar":"https://cdn-avatars.huggingface.co/v1/production/uploads/632c826d1d303f5f9acf5917/09Idg76Z9ZTI5MMm1svV8.png"}},"canReadDatabase":false,"canManagePapers":false,"canSubmit":false,"hasHfLevelAccess":false,"upvoted":false,"upvoters":[{"_id":"64b22e6b0a54158d66f18688","avatarUrl":"https://cdn-avatars.huggingface.co/v1/production/uploads/64b22e6b0a54158d66f18688/Cbl3oMMMANbnCMoSUYenI.png","isPro":true,"fullname":"Benhao Huang","user":"HuskyDoge","type":"user"},{"_id":"655601f1ae085c2ba7a22b95","avatarUrl":"https://cdn-avatars.huggingface.co/v1/production/uploads/noauth/4UmxFrc_TEiXcnm3RewZM.jpeg","isPro":false,"fullname":"Xiaoji Zheng","user":"Student-Xiaoji","type":"user"}],"acceptLanguages":["en"],"dailyPaperRank":0,"organization":{"_id":"6553f32fd13e8d851dc9c064","name":"locuslab","fullname":"Locus Lab","avatar":"https://cdn-avatars.huggingface.co/v1/production/uploads/632c826d1d303f5f9acf5917/09Idg76Z9ZTI5MMm1svV8.png"},"markdownContentUrl":"https://huggingface.co/buckets/huggingchat/papers-content/resolve/2605/2605.21488.md"}">
Equilibrium Reasoners: Learning Attractors Enables Scalable Reasoning
Abstract
Equilibrium Reasoners enable scalable reasoning through task-conditioned attractors that guide latent dynamical systems toward valid solutions, achieving significant accuracy improvements through iterative test-time computation.
AI-generated summary
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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