mlsanityData to 14 Oct 2026

Equilibrium Reasoners: Learning Attractors Enables Scalable Reasoning

arXiv 2605.21488 ↗First posted 20 May 2026cs.LGcited by 18

On the map: LLM reasoning → Test-time compute and efficient thinking

Abstract (arXiv)

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.

Key facts. Cited by 18 papers in the map (data through 14 Oct 2026). Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning. Builds on 47 of its 58 references that are in the map. First posted on arXiv 20 May 2026.

Builds on

47 of 58 references.

Closest ancestors · 13

Same direction, newest first

  1. 2026A Mechanistic Analysis of Looped Reasoning Language Models13 Apr
  2. 2026SPOT: Span-level Pause-of-Thought for Efficient and Interpretable Latent Reasoning in Large Language Models6 Mar
  3. 2026LoopFormer: Elastic-Depth Looped Transformers for Latent Reasoning via Shortcut Modulation11 Feb
  4. 2025Scaling Latent Reasoning via Looped Language Models29 Oct
  5. 2025Parallel Test-Time Scaling for Latent Reasoning Models9 Oct
  6. 2025Deep Think with Confidence21 Aug
  7. 2025Does Thinking More always Help? Mirage of Test-Time Scaling in Reasoning Models4 Jun
  8. 2025SoftCoT++: Test-Time Scaling with Soft Chain-of-Thought Reasoning16 May
  9. 2025Towards Thinking-Optimal Scaling of Test-Time Compute for LLM Reasoning25 Feb
  10. 2025Reasoning with Latent Thoughts: On the Power of Looped Transformers24 Feb
  11. 2025Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach7 Feb
  12. 2024Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters6 Aug
1 more
  1. 2023Think before you speak: Training Language Models With Pause Tokens3 Oct

Other references · 34

  1. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,459
  2. 2020Sharpness-Aware Minimization for Efficiently Improving Generalizationcited by 1,417
  3. 2024Training Large Language Models to Reason in a Continuous Latent Spacecited by 797
  4. 2018Universal Transformerscited by 647
  5. 2019Deep Equilibrium Modelscited by 615
  6. 2016Adaptive Computation Time for Recurrent Neural Networkscited by 506
  7. 2023Looped Transformers as Programmable Computerscited by 237
  8. 2023Looped Transformers are Better at Learning Learning Algorithmscited by 149
  9. 2025Mixture-of-Recursions: Learning Dynamic Recursive Depths for Adaptive Token-Level Computationcited by 133
  10. 2024InitNO: Boosting Text-to-Image Diffusion Models via Initial Noise Optimizationcited by 123
  11. 2021Can You Learn an Algorithm? Generalizing from Easy to Hard Problems with Recurrent Networkscited by 117
  12. 2025SoftCoT: Soft Chain-of-Thought for Efficient Reasoning with LLMscited by 116
22 more
  1. 2020Implicit Graph Neural Networkscited by 100
  2. 2023FreeInit: Bridging Initialization Gap in Video Diffusion Modelscited by 95
  3. 2024Beyond A*: Better Planning with Transformers via Search Dynamics Bootstrappingcited by 90
  4. 2021JFB: Jacobian-Free Backpropagation for Implicit Networkscited by 86
  5. 2021Is Attention Better Than Matrix Decomposition?cited by 77
  6. 2024Scaling Exponents Across Parameterizations and Optimizerscited by 76
  7. 2021On Training Implicit Modelscited by 75
  8. 2021Stabilizing Equilibrium Models by Jacobian Regularizationcited by 72
  9. 2025SIM-CoT: Supervised Implicit Chain-of-Thoughtcited by 70
  10. 2025PonderLM: Pretraining Language Models to Ponder in Continuous Spacecited by 44
  11. 2022Path Independent Equilibrium Models Can Better Exploit Test-Time Computationcited by 38
  12. 2024On Expressive Power of Looped Transformers: Theoretical Analysis and Enhancement via Timestep Encodingcited by 36
  13. 2025Latent Chain-of-Thought? Decoding the Depth-Recurrent Transformercited by 27
  14. 2026How Much Is One Recurrence Worth? Iso-Depth Scaling Laws for Looped Language Modelscited by 24
  15. 2026LoopViT: Scaling Visual ARC with Looped Transformerscited by 15
  16. 2025Two-Scale Latent Dynamics for Recurrent-Depth Transformerscited by 13
  17. 2026Stability and Generalization in Looped Transformerscited by 10
  18. 2026Inverse Depth Scaling From Most Layers Being Similarcited by 9
  19. 2025RingFormer: Rethinking Recurrent Transformer with Adaptive Level Signalscited by 6
  20. 2026Understanding Dynamic Compute Allocation in Recurrent Transformerscited by 6
  21. 2024Investigating Recurrent Transformers with Dynamic Haltcited by 5
  22. 2026Relational Preference Encoding in Looped Transformer Internal Statescited by 2

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  1. 2026Input-Conditioned Search for Efficient Test-Time Scaling of Recursive Reasoners
  2. 2026Reasoning as Attractor Dynamics: Latent Memory Retrieval via Gibbs-Weighted Energy Minimization
  3. 2026Solve the Loop: Attractor Models for Language and Reasoning
  4. 2026Interpreting Latent CoT Reasoning as Dynamical Systems
  5. 2026Port-Hamiltonian Latent Deliberation: Mitigating the Deliberation Drift Cliff in Test-Time Compute Scaling
  6. 2026Stabilizing Recurrent Dynamics for Test-Time Scalable Latent Reasoning in Looped Language Models
  7. 2025ReLaX: Reasoning with Latent Exploration for Large Reasoning Models
  8. 2026Boosting Inference with Guided Reasoning: Stochastic Exploration for Recursive Models