# Prediction Dynamics in Depth-Recurrent Language Models

arXiv: https://arxiv.org/abs/2609.21383 · HTML: https://mlsanity.com/paper/2609.21383/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 38 references that are in the map.
- First posted on arXiv 18 Sep 2026.

## Builds on (most cited first, 30 of 32)

- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [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)
- [Eliciting Latent Predictions from Transformers with the Tuned Lens](https://mlsanity.com/paper/2303.08112/) (2023)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Transformer Feed-Forward Layers Build Predictions by Promoting Concepts in the Vocabulary Space](https://mlsanity.com/paper/2203.14680/) (2022)
- [Adaptive Computation Time for Recurrent Neural Networks](https://mlsanity.com/paper/1603.08983/) (2016)
- [Large Language Models Are Not Robust Multiple Choice Selectors](https://mlsanity.com/paper/2309.03882/) (2023)
- [Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach](https://mlsanity.com/paper/2502.05171/) (2025)
- [DoLa: Decoding by Contrasting Layers Improves Factuality in Large Language Models](https://mlsanity.com/paper/2309.03883/) (2023)
- [DeeBERT: Dynamic Early Exiting for Accelerating BERT Inference](https://mlsanity.com/paper/2004.12993/) (2020)
- [Confident Adaptive Language Modeling](https://mlsanity.com/paper/2207.07061/) (2022)
- [LayerSkip: Enabling Early Exit Inference and Self-Speculative Decoding](https://mlsanity.com/paper/2404.16710/) (2024)
- [Think before you speak: Training Language Models With Pause Tokens](https://mlsanity.com/paper/2310.02226/) (2023)
- [Surface Form Competition: Why the Highest Probability Answer Isn't Always Right](https://mlsanity.com/paper/2104.08315/) (2021)
- [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)
- [Leveraging Large Language Models for Multiple Choice Question Answering](https://mlsanity.com/paper/2210.12353/) (2022)
- [Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networks](https://mlsanity.com/paper/1802.04034/) (2018)
- [Formal Guarantees on the Robustness of a Classifier against Adversarial Manipulation](https://mlsanity.com/paper/1705.08475/) (2017)
- [Lessons from the Trenches on Reproducible Evaluation of Language Models](https://mlsanity.com/paper/2405.14782/) (2024)
- [Scaling Latent Reasoning via Looped Language Models](https://mlsanity.com/paper/2510.25741/) (2025)
- [On the Properties of the Softmax Function with Application in Game Theory and Reinforcement Learning](https://mlsanity.com/paper/1704.00805/) (2017)
- [Mixture-of-Recursions: Learning Dynamic Recursive Depths for Adaptive Token-Level Computation](https://mlsanity.com/paper/2507.10524/) (2025)
- [Jump to Conclusions: Short-Cutting Transformers With Linear Transformations](https://mlsanity.com/paper/2303.09435/) (2023)
- [Relaxed Recursive Transformers: Effective Parameter Sharing with Layer-wise LoRA](https://mlsanity.com/paper/2410.20672/) (2024)
- [LoopFormer: Elastic-Depth Looped Transformers for Latent Reasoning via Shortcut Modulation](https://mlsanity.com/paper/2602.11451/) (2026)
- [Teaching Pretrained Language Models to Think Deeper with Retrofitted Recurrence](https://mlsanity.com/paper/2511.07384/) (2025)
- [Answer Convergence as a Signal for Early Stopping in Reasoning](https://mlsanity.com/paper/2506.02536/) (2025)

## Built on by (most cited first, 1 of 1)

- [Monitoring latent reasoning in looped language models](https://mlsanity.com/paper/2610.18127/) (2026)

## Abstract (arXiv)

Depth-recurrent language models refine predictions through repeated latent updates. Why can intermediate answers agree with the endpoint while their scores continue to change? We derive a sharp margin characterization that decomposes the conservatism of a magnitude bound into common translation, direction relative to the winner, and the pairing of each competitor's update with its score gap. Across Huginn-3.5B and Ouro-1.4B, accounting for update direction and competitor pairing reduces the mean earliest qualifying depth by a further 22.5-34.4% of the total depth beyond translation removal under full answer-text scoring. This retrospective comparison uses completed trajectories. Substantial contributions also occur under label scoring. For shared predictive distributions, we separate common and contrast motion orthogonally and express the common component through candidate-set mass and within-set concentration. Common and contrast energies can attenuate at different rates, allowing a growing preference-change share to coexist with shrinking absolute updates. These findings explain finite-depth answer preservation through the geometry and composition of observed score changes.