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

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.