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Updated: Feb 28, 2026

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Enhancing progressive ensemble learning via normalized extra-Gradient initialization.

Zheshun Wu1, Yu Pan2, Dun Zeng3

  • 1State Key Laboratory of Smart Farm Technologies and Systems, Harbin,Heilongjiang, China; School of Computer Science and Technology, Harbin Institute of Technology (Shenzhen), Shenzhen, Guangdong, China.

Neural Networks : the Official Journal of the International Neural Network Society
|February 26, 2026
PubMed
Summary
This summary is machine-generated.

Progressive ensemble learning trains models in stages but faces stability issues. Normalized Extra-Gradient (NEG) Initialization, based on functional optimization, enhances training efficiency and stability for deep learning models.

Keywords:
Deep ensemble learningEfficient trainingInitializationProgressive training

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Area of Science:

  • Deep Learning
  • Machine Learning
  • Computer Vision

Background:

  • Deep learning models require substantial computational resources due to increasing scale.
  • Progressive training incrementally enlarges models, offering a solution to resource demands.
  • Progressive ensemble learning trains model ensembles stage-wise, but copy initialization methods compromise stability.

Purpose of the Study:

  • To address the training stability issues in progressive ensemble learning.
  • To develop a novel initialization method grounded in learning theory.
  • To improve the efficiency and stability of progressive ensemble learning.

Main Methods:

  • Formulated progressive ensemble learning as a functional optimization problem.
  • Introduced Normalized Extra-Gradient (NEG) Initialization.
  • Provided theoretical insights, including convergence guarantees and Edge-of-Stability analysis.

Main Results:

  • NEG Initialization enhances both training efficiency and stability.
  • Proof-of-concept experiments on synthetic data validated the method.
  • Application to Vision Transformer (ViT) models on ImageNet-200 and ImageNet-1K demonstrated superiority over baselines.

Conclusions:

  • NEG Initialization offers a theoretically grounded and empirically validated approach to improve progressive ensemble learning.
  • The method enhances computational efficiency and training stability.
  • Demonstrated broad applicability, particularly for Vision Transformer models in computer vision tasks.