Efficient learning of Scale-Adaptive Nearly Affine Invariant Networks

Area of Science:

• Computer Science
• Artificial Intelligence
• Machine Learning

Background:

• Incorporating invariance into neural networks is crucial for robust performance.
• Existing methods for affine invariance are computationally expensive due to direct sampling over large transformation groups.

Purpose of the Study:

• To develop a computationally efficient method for achieving nearly exact affine invariance in neural networks.
• To address the limitations of existing methods that require extensive sampling.

Main Methods:

• Decomposing affine invariance into the Euclidean group E(n) and uni-axial scaling group US(n).
• Employing an E(n)-invariant model for E(n)-invariance and data augmentation for US(n)-invariance.
• Implementing adaptive scale augmentation during training to prevent excessive scale invariance.

Main Results:

• Achieved significantly lower computational complexity (O(N^2) in 2D, O(N^4) in 3D) compared to existing methods (O(N^6) in 2D, O(N^12) in 3D).
• Obtained new state-of-the-art results on affNIST and SIM2MNIST classification tasks.
• Reduced inference time to less than 15% and decreased computational resources and model parameters.

Conclusions:

• The proposed subgroup decomposition method effectively incorporates affine invariance into neural networks efficiently.
• This novel approach offers a practical and superior alternative to existing computationally intensive methods for achieving affine invariance.
• The method demonstrates strong performance and efficiency, setting a new standard for affine-invariant neural networks.