Deep Polynomial Neural Networks.

Area of Science:

• Machine Learning
• Computer Vision
• Artificial Intelligence

Background:

• Deep Convolutional Neural Networks (DCNNs) dominate computer vision and machine learning for generative and discriminative tasks.
• DCNNs' success relies on carefully chosen building blocks like residual blocks and normalization schemes.

Purpose of the Study:

• Introduce Π-Nets, a new class of function approximators based on polynomial expansions.
• Explore the potential of polynomial neural networks as an alternative to DCNNs.

Main Methods:

• Π-Nets represent outputs as high-order polynomials of the input.
• Utilize collective tensor factorization with shared factors to estimate network parameters.
• Implement tensor decompositions via hierarchical neural networks to reduce parameter count.

Main Results:

• Π-Nets demonstrate high expressiveness across diverse data types including images, graphs, and audio.
• Achieve good performance without non-linear activation functions.
• Attain state-of-the-art results in image generation, face verification, and 3D mesh representation learning when combined with activation functions.

Conclusions:

• Π-Nets present a powerful and versatile function approximator.
• Offer competitive or superior performance compared to existing methods in various machine learning tasks.
• Provide an efficient and effective alternative for deep learning applications.