# Learning Dynamics in RL Post-Training for Language Models

arXiv: https://arxiv.org/abs/2601.04670 · HTML: https://mlsanity.com/paper/2601.04670/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 44 of its 53 references that are in the map.
- First posted on arXiv 8 Jan 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 30 of 44)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [AlpacaFarm: A Simulation Framework for Methods that Learn from Human Feedback](https://mlsanity.com/paper/2305.14387/) (2023)
- [Fine-Tuning can Distort Pretrained Features and Underperform Out-of-Distribution](https://mlsanity.com/paper/2202.10054/) (2022)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [On Exact Computation with an Infinitely Wide Neural Net](https://mlsanity.com/paper/1904.11955/) (2019)
- [Attention is Not All You Need: Pure Attention Loses Rank Doubly Exponentially with Depth](https://mlsanity.com/paper/2103.03404/) (2021)
- [UltraFeedback: Boosting Language Models with Scaled AI Feedback](https://mlsanity.com/paper/2310.01377/) (2023)
- [Understanding the Effects of RLHF on LLM Generalisation and Diversity](https://mlsanity.com/paper/2310.06452/) (2023)
- [Interpretable Preferences via Multi-Objective Reward Modeling and Mixture-of-Experts](https://mlsanity.com/paper/2406.12845/) (2024)
- [Signal Propagation in Transformers: Theoretical Perspectives and the Role of Rank Collapse](https://mlsanity.com/paper/2206.03126/) (2022)
- [Echo Chamber: RL Post-training Amplifies Behaviors Learned in Pretraining](https://mlsanity.com/paper/2504.07912/) (2025)
- [A Kernel-Based View of Language Model Fine-Tuning](https://mlsanity.com/paper/2210.05643/) (2022)
- [Inducing Neural Collapse in Imbalanced Learning: Do We Really Need a Learnable Classifier at the End of Deep Neural Network?](https://mlsanity.com/paper/2203.09081/) (2022)
- [Is RLHF More Difficult than Standard RL?](https://mlsanity.com/paper/2306.14111/) (2023)
- [Learning Dynamics of LLM Finetuning](https://mlsanity.com/paper/2407.10490/) (2024)
- [More Than a Toy: Random Matrix Models Predict How Real-World Neural Representations Generalize](https://mlsanity.com/paper/2203.06176/) (2022)
- [What Makes a Reward Model a Good Teacher? An Optimization Perspective](https://mlsanity.com/paper/2503.15477/) (2025)
- [Unintentional Unalignment: Likelihood Displacement in Direct Preference Optimization](https://mlsanity.com/paper/2410.08847/) (2024)

## Built on by (most cited first, 2 of 2)

- [Train at Moving Edge: Online-Verified Prompt Selection for Efficient RL Training of Large Reasoning Model](https://mlsanity.com/paper/2603.25184/) (2026)
- [Gradients Know What Outcomes Don't: Unlocking Reinforcement Learning for LLM Reasoning with Gradient-Aligned Rewards](https://mlsanity.com/paper/2609.03342/) (2026)

## Abstract (arXiv)

Reinforcement learning (RL) post-training is a critical stage in modern language model development, playing a key role in improving alignment and reasoning ability. However, several phenomena remain poorly understood, including the reduction in output diversity. To gain a broader understanding of RL post-training, we analyze the learning dynamics of RL post-training from a perspective that has been studied in supervised learning but remains underexplored in RL. We adopt an empirical neural tangent kernel (NTK) framework and decompose the NTK into two components to characterize how RL updates propagate across training samples. Our analysis reveals that limited variability in feature representations can cause RL updates to systematically increase model confidence, providing an explanation for the commonly observed reduction in output diversity after RL post-training. Furthermore, we show that effective learning in this regime depends on rapidly shaping the classifier, which directly affects the gradient component of the NTK. Motivated by these insights, we propose classifier-first reinforcement learning (CF-RL), a simple two-stage training strategy that prioritizes classifier updates before standard RL optimization. Experimental results validate our theoretical analysis by demonstrating increased model confidence and accelerated optimization under CF-RL. Additional analysis shows that the mechanism underlying CF-RL differs from that of linear-probing-then-fine-tuning in supervised learning. Overall, our study formalizes the learning dynamics of RL post-training and motivates further analysis and improvement.