Fisher-Rao metric clarifies data mix to prevent AI model collapse
Preventing Model Collapse: A Fisher-Rao Perspective on the Dynamics of Training with Synthetic Data
Machine Learning
Summary
Large language models often train on computer-generated (synthetic) data once human data runs out. But training too much on synthetic data can cause the model to forget real-world patterns, called model collapse. The authors show mathematically that mixing human with synthetic data keeps training stable, and they find the precise minimum amount of human data needed. They use a special math tool called the Fisher-Rao metric to make this finding accurate even when dealing with many categories of language. This new way of measuring improves on older methods that didn’t work well in complex settings.
What this means in practice
- •For machine learning engineers: Determine the minimum human data proportion required when combining synthetic and real data to avoid model performance degradation during training.
- •For data platform architects: Design training data pipelines that maintain model stability by ensuring adequate human data ratios informed by Fisher-Rao metric insights.
A theory result. No direct application yet.
Authors
Matteo Marchi, João Pedro Silvestre, Bahman Gharesifard, Paulo Tabuada
Abstract
Large Language Models (LLMs) are now routinely trained using synthetic data, since high-quality human data has been exhausted by the ever increasing needs of larger and larger models. However, recursive training on synthetic data frequently induces model collapse, a degenerative feedback loop where models progressively forget the true underlying data distribution. Training on a mixture of synthetic and fresh human data is a logical countermeasure and can prevent model collapse. However, it is an open question as to what is the exact minimum required ratio of human-to-synthetic data to maintain training stability. In this paper, we establish rigorous theoretical guarantees on the minimum rate of human data required to prevent model collapse. Although previous work established a formal lower bound for this ratio, such bound can be vacuous for very high dimensions, as the analysis relies on the usual Euclidean metric in R^n and is not adapted to the space of categorical probability distributions. Instead, in this paper we explicitly leverage the information-geometric structure of the probability simplex by analyzing the dynamics of the process under the Fisher-Rao metric. We derive quantitative contraction and invariance bounds that are stable and do not become trivial as the dimensions increase. Thus, we show that the effective required data ratio to prevent model collapse is different than previously implied.