Adaptive Aggregation of Monte Carlo Augmented Decomposed Filters for Efficient Group-Equivariant Convolutional Neural...

Area of Science:

• Artificial Intelligence
• Computer Vision
• Machine Learning

Background:

• Group-equivariant convolutional neural networks (G-CNNs) utilize parameter sharing for improved data efficiency and performance.
• However, parameter sharing in G-CNNs leads to significant computational burdens, limiting their scalability in deep learning.

Purpose of the Study:

• To propose a non-parameter-sharing approach for group equivariant neural networks.
• To address the computational challenges associated with traditional parameter-sharing G-CNNs.
• To enhance the efficiency and performance of G-CNNs and standard CNNs.

Main Methods:

• Developed an adaptive filter aggregation method using a weighted sum of stochastically augmented decomposed filters.
• Provided theoretical proof for achieving group equivariance with the proposed methods.
• Applied augmentation using Monte Carlo sampling for continuous groups and bootstrap resampling for discrete groups.

Main Results:

• The proposed non-parameter-sharing G-CNNs outperformed parameter-sharing G-CNNs.
• The method demonstrated enhanced performance in image classification and denoising tasks compared to standard CNNs.
• The approach facilitates the creation of efficient, lightweight networks.

Conclusions:

• The novel non-parameter-sharing strategy effectively achieves group equivariance while reducing computational load.
• This method offers a viable and efficient extension to standard Convolutional Neural Networks (CNNs).
• The proposed approach presents a promising direction for developing more scalable and efficient equivariant deep learning models.