Reaching Nirvana: Maximizing the Margin in Both Euclidean and Angular Spaces for Deep Neural Network Classification.

Area of Science:

• Machine Learning
• Computer Vision
• Deep Learning

Background:

• Classification loss functions in deep neural networks typically optimize margins in either Euclidean or angular spaces.
• Existing methods use Euclidean distances or Cosine similarity separately, leading to potential inconsistencies.

Purpose of the Study:

• To introduce a novel classification loss function that simultaneously maximizes margins in both Euclidean and angular spaces.
• To improve classification accuracy and robustness by ensuring consistent distance metrics.

Main Methods:

• The proposed loss function clusters samples around class centers on a hypersphere.
• Class centers are positioned at the vertices of a regular simplex for equivalent pairwise distances.
• A single, easily configurable hyperparameter simplifies implementation.

Main Results:

• The novel loss function achieves consistent results between Euclidean and Cosine distances, enhancing accuracy.
• The method effectively clusters data, improving performance in classical classification.
• Demonstrated superior performance in open set recognition by effectively rejecting unfamiliar samples.

Conclusions:

• The proposed loss function offers a unified approach to margin maximization in both Euclidean and angular spaces.
• It provides significant improvements in both classical and open set recognition tasks.
• The method's simplicity and effectiveness make it highly suitable for practical applications.