Fine-Tuning Fixes Mode Collapse and Over-Dispersion in LLMs

A new arXiv paper (2609.16454v1) finds that supervised fine-tuning (SFT) is not inherently biased toward mode collapse or its opposite, over-dispersion, in large language models. The authors derive a bias-variance decomposition showing finite-sample SFT can leave a model either under- or over-dispersed depending on the model and dataset, and prove the absolute gap between model and target collision probabilities is bounded by the square root of the Kullback-Leibler divergence from the target distribution to the model. Across three experiments — small transformers on synthetic languages, four LLMs fine-tuned on human surveys, and those LLMs fine-tuned on the CodeNet dataset of human code solutions — more target data moved model diversity toward the human or synthetic target level, consistent with the theoretical predictions.

arXiv:2609.16454v1 Announce Type: new Abstract: Recent work by Doshi and Hauser 2024 , Bisbee et al. 2024 , and Xie et al. 2026 raises concerns that outputs from large language models LLMs tend to be under-diverse: they repeat or resemble one another more often than responses from the population they are meant to represent, a phenomenon known as mode collapse. In this work, we show that whether mode-collapse, or its opposite, occurs depends on the specific model and dataset used. Further, with sufficient supervised fine-tuning SFT data, LLM output diversity converges toward that of the target distribution from which fine-tuning data are sampled. To quantify this comparison, we measure the probability that two responses sampled independently from the same fixed prompt coincide collide , or their expected similarity under a kernel. We derive a bias-variance decomposition of the expected gap between the model's and target's collision probabilities, showing that SFT is not inherently biased toward mode collapse or its opposite: finite-sample SFT can leave a model either under- or over-dispersed, depending on the model and dataset. Finally, we show that the absolute gap is bounded by the square root of the Kullback-Leibler KL divergence from the target distribution to the model. Consequently, a model sufficiently close to optimal under population cross-entropy cannot exhibit arbitrarily miscalibrated diversity. We test the decomposition and the bound in three experiments: small transformers on synthetic languages, four LLMs fine-tuned on human surveys, and these LLMs fine-tuned on CodeNet, a dataset of human code solutions. More target data moves model diversity toward the human or synthetic target level in all experiments, consistent with our theoretical predictions. These results show that diversity miscalibration can arise from finite-sample error and shrink as SFT better approximates the target distribution.