Information-Theoretic Understanding of Population Risk Improvement with Model Compression
This provides a theoretical foundation for model compression as a regularization technique, potentially benefiting practitioners in machine learning by improving model performance beyond just efficiency gains.
The paper tackles the problem of whether model compression can improve a model's population risk by analyzing the trade-off between reduced generalization error and increased empirical risk. It proves that compression reduces a generalization bound and shows through linear regression and neural network experiments that population risk can indeed decrease if the generalization improvement outweighs the empirical risk increase.
We show that model compression can improve the population risk of a pre-trained model, by studying the tradeoff between the decrease in the generalization error and the increase in the empirical risk with model compression. We first prove that model compression reduces an information-theoretic bound on the generalization error; this allows for an interpretation of model compression as a regularization technique to avoid overfitting. We then characterize the increase in empirical risk with model compression using rate distortion theory. These results imply that the population risk could be improved by model compression if the decrease in generalization error exceeds the increase in empirical risk. We show through a linear regression example that such a decrease in population risk due to model compression is indeed possible. Our theoretical results further suggest that the Hessian-weighted $K$-means clustering compression approach can be improved by regularizing the distance between the clustering centers. We provide experiments with neural networks to support our theoretical assertions.