Equilibrium Reasoners: Learning Attractors Enables Scalable Reasoning
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
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- 2025Towards Thinking-Optimal Scaling of Test-Time Compute for LLM Reasoning25 Feb
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- 2025Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach7 Feb
- 2024Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters6 Aug
Other references · 34
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- 2018Universal Transformerscited by 647
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- 2016Adaptive Computation Time for Recurrent Neural Networkscited by 506
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- 2021On Training Implicit Modelscited by 75
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- 2025SIM-CoT: Supervised Implicit Chain-of-Thoughtcited by 70
- 2025PonderLM: Pretraining Language Models to Ponder in Continuous Spacecited by 44
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- 2024On Expressive Power of Looped Transformers: Theoretical Analysis and Enhancement via Timestep Encodingcited by 36
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- 2026LoopViT: Scaling Visual ARC with Looped Transformerscited by 15
- 2025Two-Scale Latent Dynamics for Recurrent-Depth Transformerscited by 13
- 2026Stability and Generalization in Looped Transformerscited by 10
- 2026Inverse Depth Scaling From Most Layers Being Similarcited by 9
- 2025RingFormer: Rethinking Recurrent Transformer with Adaptive Level Signalscited by 6
- 2026Understanding Dynamic Compute Allocation in Recurrent Transformerscited by 6
- 2024Investigating Recurrent Transformers with Dynamic Haltcited by 5
- 2026Relational Preference Encoding in Looped Transformer Internal Statescited by 2
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Citing papers per year: 2026: 18.
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- 2026Fixed-Point Reasoners: Stable and Adaptive Deep Looped Transformerscited by 28
- 2026Think Shallow, Solve Deep: Controlling Recurrent Dynamics for Reliable Test-Time Depthcited by 9
- 2026Thinking with Looped Flowscited by 9
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- 2026Rotate the Loop: Blockwise Conformality for Looped Transformers30 Sep 2026
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- 2026Looped Actor: Depth-Recurrent Reasoning Models for Reinforcement Learning29 Sep 2026
- 2026When Recursive Models Finish Computing22 Sep 2026
- 2026Thinking with Looped Flows10 Sep 2026
- 2026Diffusion as a Training Curriculum for Timestep-Free Iterative Reasoning1 Sep 2026
6 more
- 2026Latent Recurrent Thoughts: Recurrent Refinement of Proposed Latents for Reasoning with Frozen LLMs1 Sep 2026
- 2026Think Shallow, Solve Deep: Controlling Recurrent Dynamics for Reliable Test-Time Depth18 Aug 2026
- 2026Loop the Loopies!17 Jul 2026
- 2026Energy-guided Recursive Model11 Jul 2026
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- 2026Fixed-Point Reasoners: Stable and Adaptive Deep Looped Transformers16 Jun 2026
- 2026Energy-guided Recursive Modelcited by 2
- 2026Quantizing Recursive Reasoning Modelscited by 2
- 2026Latent Recurrent Thoughts: Recurrent Refinement of Proposed Latents for Reasoning with Frozen LLMscited by 0
- 2026Looped Actor: Depth-Recurrent Reasoning Models for Reinforcement Learningcited by 0
- 2026Towards Better Exploration in Sequential Test-Time Scalingcited by 0
- 2026Towards Looped Models Done Right, Part II: Rethinking at Fixed Pointscited by 0
- 2026Unrolled Flow Models for Reasoningcited by 0
- 2026Resample the Answer: Where to Spend Test-Time Compute in Recursive Reasoningcited by 0
- 2026Resample the Answer: Where to Spend Test-Time Compute in Recursive Reasoning12 Oct 2026
- 2026Unrolled Flow Models for Reasoning7 Oct 2026
- 2026Towards Looped Models Done Right, Part II: Rethinking at Fixed Points5 Oct 2026
- 2026Towards Better Exploration in Sequential Test-Time Scaling30 Sep 2026
- 2026Looped Actor: Depth-Recurrent Reasoning Models for Reinforcement Learning29 Sep 2026
- 2026Latent Recurrent Thoughts: Recurrent Refinement of Proposed Latents for Reasoning with Frozen LLMs1 Sep 2026
- 2026Energy-guided Recursive Model11 Jul 2026
- 2026Quantizing Recursive Reasoning Models25 Jun 2026
- 2026Loop the Loopies!cited by 8
- 2026Loop the Loopies!17 Jul 2026
- 2026Fixed-Point Reasoners: Stable and Adaptive Deep Looped Transformerscited by 28
- 2026Think Shallow, Solve Deep: Controlling Recurrent Dynamics for Reliable Test-Time Depthcited by 9
- 2026Thinking with Looped Flowscited by 9
- 2026When Recursive Models Finish Computingcited by 1
- 2026Rotate the Loop: Blockwise Conformality for Looped Transformerscited by 0
- 2026Looped Reasoning Finishes Earlier Than You Thinkcited by 0
- 2026Tiny Recursive Message Passingcited by 0
- 2026Tiny Recursive Message Passing13 Oct 2026
- 2026Looped Reasoning Finishes Earlier Than You Think13 Oct 2026
- 2026Rotate the Loop: Blockwise Conformality for Looped Transformers30 Sep 2026
- 2026When Recursive Models Finish Computing22 Sep 2026
- 2026Thinking with Looped Flows10 Sep 2026
- 2026Think Shallow, Solve Deep: Controlling Recurrent Dynamics for Reliable Test-Time Depth18 Aug 2026
- 2026Fixed-Point Reasoners: Stable and Adaptive Deep Looped Transformers16 Jun 2026
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