# Stability as a Liability:Systematic Breakdown of Linguistic Structure in LLMs

arXiv: https://arxiv.org/abs/2601.18588 · HTML: https://mlsanity.com/paper/2601.18588/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 39 references that are in the map.
- First posted on arXiv 26 Jan 2026.

## Builds on (most cited first, 21 of 21)

- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Understanding the Difficulty of Training Transformers](https://mlsanity.com/paper/2004.08249/) (2020)
- [The Unreasonable Effectiveness of Entropy Minimization in LLM Reasoning](https://mlsanity.com/paper/2505.15134/) (2025)
- [Improving the Robustness of Deep Neural Networks via Stability Training](https://mlsanity.com/paper/1604.04326/) (2016)
- [Understanding Gradient Clipping in Private SGD: A Geometric Perspective](https://mlsanity.com/paper/2006.15429/) (2020)
- [Where LLM Agents Fail and How They can Learn From Failures](https://mlsanity.com/paper/2509.25370/) (2025)
- [Revisiting Gradient Clipping: Stochastic bias and tight convergence guarantees](https://mlsanity.com/paper/2305.01588/) (2023)
- [R1-Reward: Training Multimodal Reward Model Through Stable Reinforcement Learning](https://mlsanity.com/paper/2505.02835/) (2025)
- [Entropy Law: The Story Behind Data Compression and LLM Performance](https://mlsanity.com/paper/2407.06645/) (2024)
- [Understanding Adversarial Training: Increasing Local Stability of Neural Nets through Robust Optimization](https://mlsanity.com/paper/1511.05432/) (2015)
- [Edge of Stochastic Stability: Revisiting the Edge of Stability for SGD](https://mlsanity.com/paper/2412.20553/) (2024)
- [In-the-loop Hyper-Parameter Optimization for LLM-Based Automated Design of Heuristics](https://mlsanity.com/paper/2410.16309/) (2024)
- [Under the Surface: Tracking the Artifactuality of LLM-Generated Data](https://mlsanity.com/paper/2401.14698/) (2024)
- [A Survey on LLM Mid-Training](https://mlsanity.com/paper/2510.23081/) (2025)
- [RoBoSS: A Robust, Bounded, Sparse, and Smooth Loss Function for Supervised Learning](https://mlsanity.com/paper/2309.02250/) (2023)
- [Evaluating Uncertainty-based Failure Detection for Closed-Loop LLM Planners](https://mlsanity.com/paper/2406.00430/) (2024)
- [Methods of improving LLM training stability](https://mlsanity.com/paper/2410.16682/) (2024)
- [Characterizing and addressing the issue of oversmoothing in neural autoregressive sequence modeling](https://mlsanity.com/paper/2112.08914/) (2021)
- [Can LLMs Leverage Observational Data? Towards Data-Driven Causal Discovery with LLMs](https://mlsanity.com/paper/2504.10936/) (2025)
- [Control LLM: Controlled Evolution for Intelligence Retention in LLM](https://mlsanity.com/paper/2501.10979/) (2025)

## Abstract (arXiv)

Training stability is typically regarded as a prerequisite for reliable optimization in large language models. In this work, we analyze how stabilizing training dynamics affects the induced generation distribution. We show that under standard maximum likelihood training, stable parameter trajectories lead stationary solutions to approximately minimize the forward KL divergence to the empirical distribution, while implicitly reducing generative entropy. As a consequence, the learned model can concentrate probability mass on a limited subset of empirical modes, exhibiting systematic degeneration despite smooth loss convergence. We empirically validate this effect using a controlled feedback-based training framework that stabilizes internal generation statistics, observing consistent low-entropy outputs and repetitive behavior across architectures and random seeds. It indicates that optimization stability and generative expressivity are not inherently aligned, and that stability alone is an insufficient indicator of generative quality.