Equilibrium Reasoners: Learning Attractors Enables Scalable Reasoning (May 2026)

Title: Equilibrium Reasoners: Learning Attractors Enables Scalable Reasoning (May 2026)
Link: http://arxiv.org/abs/2605.21488v1
Date: May 2026

Summary:
This paper introduces Equilibrium Reasoners (EqR), a framework that formalizes scalable reasoning as a process of converging toward task-conditioned attractors within a latent dynamical system. By scaling internal dynamics along depth (iterations) and breadth (stochastic trajectories), EqR achieves massive performance gains on complex benchmarks like Sudoku-Extreme and Maze-Unique. The study highlights that shaping the internal attractor landscape through randomized initialization and noise injection is crucial for enabling test-time compute to generalize beyond memorized patterns.

Key Topics:
- Test-time Scaling
- Neural Attractors
- Iterative Reasoning Models
- Fixed-point Dynamics
- Adaptive Computation Time
- Landscape Shaping
- Algorithmic Reasoning

Chapters:
00:00 - Intro To Equilibrium Reasoners
01:12 - Scaling Test Time Compute
02:26 - Weight Tied Iterative Models
03:41 - Shaping Geometric Valleys
04:52 - Reasoning Failure Modes
06:04 - Mode 4: Broad Attractors
07:08 - Detached Carry Constraints
08:25 - Segmented Online Training
09:33 - Randomized State Initialization
11:48 - Noise Injection Techniques
13:13 - Balancing Depth And Breadth
14:43 - Internal Self Verification Signals
16:23 - Adaptive Halting Budgets
17:26 - Benchmark Results And Conclusion

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