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Stabilizing Recurrent Dynamics for Test-Time Scalable Latent Reasoning in Looped Language Models

ICML 2026 · Large language models › Reasoning and chain of thought · approach: Efficient and adaptive thinking · 0 citations (OpenAlex)

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Proposes STARS, which combines Jacobian spectral radius regularization (single-step power iteration with JVPs) and random loop sampling to stabilize latent recurrent dynamics in looped language models, enabling reliable test-time scaling of recurrence depth.

Problem

Looped language models (LoopLMs) show unreliable test-time scaling: performance peaks at some recurrence depth and then collapses as iterations increase beyond training depth.

Approach

Views recurrent latent reasoning as a dynamical system and regularizes the spectral radius of the Jacobian of the recurrent map (estimated cheaply via one-step power iteration with JVPs) at sampled loop depths, so latent states converge to asymptotically stable fixed points while retaining effectiveness.

Key results

• On GSM8K, Ouro-1.4B drops 20.47% from peak after 8 recurrences while Ouro-1.4B-STARS degrades only 8.26%, and STARS improves peak GSM8K accuracy by 4.01%.
• Ouro-1.4B-STARS reaches average accuracy 74.18% at 4 recurrent steps vs 70.46% for the SFT baseline, and retains 65.55% at 8 steps vs 52.97% for SFT.
• On multi-digit addition, STARS keeps accuracy at 100% across recurrent steps in the randomly initialized looped Transformer setting.

Surprising findings

• Post-norm (external normalization) systems converge to stable attractors but fail to perform deep reasoning, while pre-norm maintains effectiveness but diverges, showing a stability-effectiveness trade-off.
• L2 regularization on adjacent hidden states gives negligible benefit and underperforms pure random loop sampling when combined with it.

Limitations

• Evaluation concentrated on mathematical reasoning; generalization to other reasoning domains untested.
• Performance does not always improve monotonically with more recurrent steps on harder problems.
• Only single-step power iteration estimate, which may be noisy per sample.

Experimental setup

Datasets: NuminaMath-1.5 synthetic 4-digit addition

Benchmarks: GSM8K MATH500 ASDiv SVAMP AMC23

Metrics: accuracy

Baselines: Ouro-1.4B Ouro-1.4B-SFT Recurrent-Llama-3.2 Recurrent-OLMo-2-0425 Gemma3-1b-it Llama-3.2-3B-Instruct Qwen2.5-3B-Instruct Qwen3-1.7B Qwen3-4B

Builds on: Ouro Huginn Deep Equilibrium Models Lyapunov linearization theorem random loop sampling

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