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Population Risk Improvement with Model Compression: An Information-Theoretic Approach.

Yuheng Bu1, Weihao Gao2, Shaofeng Zou3

  • 1Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61820, USA.

Entropy (Basel, Switzerland)
|October 23, 2021
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Summary
This summary is machine-generated.

Model compression can improve deep learning model performance by acting as a regularization technique. This study explains how reducing generalization error can outweigh increased empirical risk, leading to better population risk.

Keywords:
K-means clusteringempirical riskgeneralization errormodel compressionpopulation riskrate distortion theoryvector quantization

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Area of Science:

  • Machine Learning
  • Information Theory
  • Deep Learning

Background:

  • Deep model compression often results in improved population risk compared to original models.
  • Existing research highlights this phenomenon but lacks a unified theoretical explanation.

Purpose of the Study:

  • To provide an information-theoretic explanation for the population risk improvement observed in deep model compression.
  • To analyze the interplay between generalization error and empirical risk during model compression.

Main Methods:

  • Utilizing information-theoretic bounds to analyze generalization error reduction.
  • Applying rate distortion theory to characterize empirical risk increase.
  • Developing a regularized Hessian-weighted K-means clustering algorithm.

Main Results:

  • Model compression acts as a regularization technique, reducing generalization error and preventing overfitting.
  • Population risk improvement is possible when the decrease in generalization error surpasses the increase in empirical risk.
  • A modified K-means clustering algorithm shows improved performance in neural network compression experiments.

Conclusions:

  • The study offers a theoretical framework explaining how model compression can enhance population risk.
  • Theoretical insights guide improvements in model compression algorithms, such as regularized K-means clustering.
  • Empirical validation with neural networks confirms the theoretical assertions on population risk improvement.