Optimizing the Simplicial-Map Neural Network Architecture.

Area of Science:

• Computational topology
• Machine learning
• Neural network architectures

Background:

• Simplicial-map neural networks are a recent architecture based on simplicial maps.
• These networks are proven universal approximators and can be refined for robustness against adversarial attacks.

Purpose of the Study:

• To optimize the refinement process for simplicial-map neural networks toward robustness.
• To reduce the number of simplices (nodes) required in the refined network.

Main Methods:

• Investigated the relationship between network size and robustness in simplicial-map neural networks.
• Experimental evaluation of a refined network with a reduced number of simplices.

Main Results:

• The refined simplicial-map neural network demonstrates equivalent classification performance to the original network.
• The optimized network requires substantially less storage capacity.

Conclusions:

• Reducing the number of simplices in simplicial-map neural networks is an effective optimization strategy.
• This refinement maintains network utility while improving storage efficiency.