# Equilibrium Reasoners: Learning Attractors Enables Scalable Reasoning

arXiv: https://arxiv.org/abs/2605.21488 · HTML: https://mlsanity.com/paper/2605.21488/

## 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.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 47)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Adaptive Computation Time for Recurrent Neural Networks](https://mlsanity.com/paper/1603.08983/) (2016)
- [Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach](https://mlsanity.com/paper/2502.05171/) (2025)
- [Think before you speak: Training Language Models With Pause Tokens](https://mlsanity.com/paper/2310.02226/) (2023)
- [Reasoning with Latent Thoughts: On the Power of Looped Transformers](https://mlsanity.com/paper/2502.17416/) (2025)
- [Looped Transformers as Programmable Computers](https://mlsanity.com/paper/2301.13196/) (2023)
- [Deep Think with Confidence](https://mlsanity.com/paper/2508.15260/) (2025)
- [Scaling Latent Reasoning via Looped Language Models](https://mlsanity.com/paper/2510.25741/) (2025)
- [Looped Transformers are Better at Learning Learning Algorithms](https://mlsanity.com/paper/2311.12424/) (2023)
- [Mixture-of-Recursions: Learning Dynamic Recursive Depths for Adaptive Token-Level Computation](https://mlsanity.com/paper/2507.10524/) (2025)
- [InitNO: Boosting Text-to-Image Diffusion Models via Initial Noise Optimization](https://mlsanity.com/paper/2404.04650/) (2024)
- [Towards Thinking-Optimal Scaling of Test-Time Compute for LLM Reasoning](https://mlsanity.com/paper/2502.18080/) (2025)
- [Can You Learn an Algorithm? Generalizing from Easy to Hard Problems with Recurrent Networks](https://mlsanity.com/paper/2106.04537/) (2021)
- [SoftCoT: Soft Chain-of-Thought for Efficient Reasoning with LLMs](https://mlsanity.com/paper/2502.12134/) (2025)
- [Implicit Graph Neural Networks](https://mlsanity.com/paper/2009.06211/) (2020)
- [FreeInit: Bridging Initialization Gap in Video Diffusion Models](https://mlsanity.com/paper/2312.07537/) (2023)
- [Beyond A*: Better Planning with Transformers via Search Dynamics Bootstrapping](https://mlsanity.com/paper/2402.14083/) (2024)
- [JFB: Jacobian-Free Backpropagation for Implicit Networks](https://mlsanity.com/paper/2103.12803/) (2021)
- [Is Attention Better Than Matrix Decomposition?](https://mlsanity.com/paper/2109.04553/) (2021)
- [Scaling Exponents Across Parameterizations and Optimizers](https://mlsanity.com/paper/2407.05872/) (2024)
- [On Training Implicit Models](https://mlsanity.com/paper/2111.05177/) (2021)
- [Stabilizing Equilibrium Models by Jacobian Regularization](https://mlsanity.com/paper/2106.14342/) (2021)
- [SIM-CoT: Supervised Implicit Chain-of-Thought](https://mlsanity.com/paper/2509.20317/) (2025)
- [LoopFormer: Elastic-Depth Looped Transformers for Latent Reasoning via Shortcut Modulation](https://mlsanity.com/paper/2602.11451/) (2026)
- [Does Thinking More always Help? Mirage of Test-Time Scaling in Reasoning Models](https://mlsanity.com/paper/2506.04210/) (2025)

## Built on by (most cited first, 18 of 18)

- [Fixed-Point Reasoners: Stable and Adaptive Deep Looped Transformers](https://mlsanity.com/paper/2606.18206/) (2026)
- [Think Shallow, Solve Deep: Controlling Recurrent Dynamics for Reliable Test-Time Depth](https://mlsanity.com/paper/2608.18222/) (2026)
- [Thinking with Looped Flows](https://mlsanity.com/paper/2609.11801/) (2026)
- [Loop the Loopies!](https://mlsanity.com/paper/2607.16051/) (2026)
- [Energy-guided Recursive Model](https://mlsanity.com/paper/2607.10128/) (2026)
- [Quantizing Recursive Reasoning Models](https://mlsanity.com/paper/2607.16237/) (2026)
- [Diffusion as a Training Curriculum for Timestep-Free Iterative Reasoning](https://mlsanity.com/paper/2609.01449/) (2026)
- [When Recursive Models Finish Computing](https://mlsanity.com/paper/2609.26487/) (2026)
- [Latent Recurrent Thoughts: Recurrent Refinement of Proposed Latents for Reasoning with Frozen LLMs](https://mlsanity.com/paper/2609.01117/) (2026)
- [Looped Actor: Depth-Recurrent Reasoning Models for Reinforcement Learning](https://mlsanity.com/paper/2609.37432/) (2026)
- [Towards Better Exploration in Sequential Test-Time Scaling](https://mlsanity.com/paper/2609.39632/) (2026)
- [ALoDLM: Adaptively Looped Diffusion Language Models](https://mlsanity.com/paper/2610.04198/) (2026)
- [Towards Looped Models Done Right, Part II: Rethinking at Fixed Points](https://mlsanity.com/paper/2610.06833/) (2026)
- [Unrolled Flow Models for Reasoning](https://mlsanity.com/paper/2610.09759/) (2026)
- [Rotate the Loop: Blockwise Conformality for Looped Transformers](https://mlsanity.com/paper/2610.14030/) (2026)
- [Resample the Answer: Where to Spend Test-Time Compute in Recursive Reasoning](https://mlsanity.com/paper/2610.16427/) (2026)
- [Looped Reasoning Finishes Earlier Than You Think](https://mlsanity.com/paper/2610.18174/) (2026)
- [Tiny Recursive Message Passing](https://mlsanity.com/paper/2610.18649/) (2026)

## 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.