André Ferreira Leite

R. J. Cintra, S. Duffner, C. Garcia et al.

In this paper, we present an approach for minimizing the computational complexity of trained Convolutional Neural Networks (ConvNet). The idea is to approximate all elements of a given ConvNet and replace the original convolutional filters and parameters (pooling and bias coefficients; and activation function) with efficient approximations capable of extreme reductions in computational complexity. Low-complexity convolution filters are obtained through a binary (zero-one) linear programming scheme based on the Frobenius norm over sets of dyadic rationals. The resulting matrices allow for multiplication-free computations requiring only addition and bit-shifting operations. Such low-complexity structures pave the way for low-power, efficient hardware designs. We applied our approach on three use cases of different complexity: (i) a "light" but efficient ConvNet for face detection (with around 1000 parameters); (ii) another one for hand-written digit classification (with more than 180000 parameters); and (iii) a significantly larger ConvNet: AlexNet with $\approx$1.2 million matrices. We evaluated the overall performance on the respective tasks for different levels of approximations. In all considered applications, very low-complexity approximations have been derived maintaining an almost equal classification performance.

R. J. Cintra, F. M. Bayer, V. A. Coutinho et al.

Due to its remarkable energy compaction properties, the discrete cosine transform (DCT) is employed in a multitude of compression standards, such as JPEG and H.265/HEVC. Several low-complexity integer approximations for the DCT have been proposed for both 1-D and 2-D signal analysis. The increasing demand for low-complexity, energy efficient methods require algorithms with even lower computational costs. In this paper, new 8-point DCT approximations with very low arithmetic complexity are presented. The new transforms are proposed based on pruning state-of-the-art DCT approximations. The proposed algorithms were assessed in terms of arithmetic complexity, energy retention capability, and image compression performance. In addition, a metric combining performance and computational complexity measures was proposed. Results showed good performance and extremely low computational complexity. Introduced algorithms were mapped into systolic-array digital architectures and physically realized as digital prototype circuits using FPGA technology and mapped to 45nm CMOS technology. All hardware-related metrics showed low resource consumption of the proposed pruned approximate transforms. The best proposed transform according to the introduced metric presents a reduction in power consumption of 21--25%.