Convolutional Neural Networks (CNNs) are multi-layer deep structures that have been very successful in visual recognition tasks. These networks basically consist of the convolution, pooling, and the nonlinearity layers, each of which operates on the representation produced by the preceding layer and generates a new representation. Convolution layers naturally compute some inner product between a plane represented by the weight parameters and input patches. Recently, Generalized Convolutional Neural Networks (GCNN) have been introduced which justify the use of some kernels or distance functions in place of the inner product operator inside the convolution layers. Although GCNNs gained interesting results on the MNIST dataset, their application to more challenging datasets is hindered by lack of an efficient implementation. In this paper, we focus on a specific generalized convolution operator which is based on the weighted L2 norm distance (WL2Dist). By replacing the nonlinear part with three convolution operators and using effective matrix-matrix multiplications, we were able to efficiently compute the WL2Dist convolution layer both on CPU and GPU. Our experiments show that, on CPU (GPU), the proposed implementation of the WL2Dist layer achieves a 5.5x (21x) speed-up over the initial BLAS-based (CUDA-based) implementations.

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