ConformalLayers: A non-linear sequential neural network with associative layers

TL;DR

This paper introduces ConformalLayers, a novel neural network architecture with an activation function that enables associativity, allowing for constant inference cost regardless of network depth by combining layers efficiently.

Contribution

The paper proposes a new non-linear activation function that ensures associativity in CNN layers, enabling layer combination and reducing inference complexity.

Findings

Enables layer combination for constant inference cost

Maintains linearity of key operations in conformal geometry

Reduces computational complexity in deep CNNs

Abstract

Convolutional Neural Networks (CNNs) have been widely applied. But as the CNNs grow, the number of arithmetic operations and memory footprint also increase. Furthermore, typical non-linear activation functions do not allow associativity of the operations encoded by consecutive layers, preventing the simplification of intermediate steps by combining them. We present a new activation function that allows associativity between sequential layers of CNNs. Even though our activation function is non-linear, it can be represented by a sequence of linear operations in the conformal model for Euclidean geometry. In this domain, operations like, but not limited to, convolution, average pooling, and dropout remain linear. We take advantage of associativity to combine all the "conformal layers" and make the cost of inference constant regardless of the depth of the network.