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

  • Eduardo Vera Sousa UFF
  • Leandro A. F. Fernandes UFF
  • Cristina Nader Vasconcelos UFF


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.
Palavras-chave: Graphics, Geometry, Costs, Convolution, Neural networks, Convolutional neural networks, Arithmetic, convolutional neural network, non linear activation, associativity
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SOUSA, Eduardo Vera; FERNANDES, Leandro A. F.; VASCONCELOS, Cristina Nader. ConformalLayers: A non-linear sequential neural network with associative layers. In: CONFERENCE ON GRAPHICS, PATTERNS AND IMAGES (SIBGRAPI), 34. , 2021, Online. Anais [...]. Porto Alegre: Sociedade Brasileira de Computação, 2021 .