Keith M. Chugg

William Chang, Hassan Hamad, Keith M. Chugg

Standard artificial neural networks (ANNs) use sum-product or multiply-accumulate node operations with a memoryless nonlinear activation. These neural networks are known to have universal function approximation capabilities. Previously proposed morphological perceptrons use max-sum, in place of sum-product, node processing and have promising properties for circuit implementations. In this paper we show that these max-sum ANNs do not have universal approximation capabilities. Furthermore, we consider proposed signed-max-sum and max-star-sum generalizations of morphological ANNs and show that these variants also do not have universal approximation capabilities. We contrast these variations to log-number system (LNS) implementations which also avoid multiplications, but do exhibit universal approximation capabilities.

Sourya Dey, Saikrishna C. Kanala, Keith M. Chugg et al.

We present Deep-n-Cheap -- an open-source AutoML framework to search for deep learning models. This search includes both architecture and training hyperparameters, and supports convolutional neural networks and multi-layer perceptrons. Our framework is targeted for deployment on both benchmark and custom datasets, and as a result, offers a greater degree of search space customizability as compared to a more limited search over only pre-existing models from literature. We also introduce the technique of 'search transfer', which demonstrates the generalization capabilities of the models found by our framework to multiple datasets. Deep-n-Cheap includes a user-customizable complexity penalty which trades off performance with training time or number of parameters. Specifically, our framework results in models offering performance comparable to state-of-the-art while taking 1-2 orders of magnitude less time to train than models from other AutoML and model search frameworks. Additionally, this work investigates and develops various insights regarding the search process. In particular, we show the superiority of a greedy strategy and justify our choice of Bayesian optimization as the primary search methodology over random / grid search.

Sourya Dey, Keith M. Chugg, Peter A. Beerel

We present an algorithm to generate synthetic datasets of tunable difficulty on classification of Morse code symbols for supervised machine learning problems, in particular, neural networks. The datasets are spatially one-dimensional and have a small number of input features, leading to high density of input information content. This makes them particularly challenging when implementing network complexity reduction methods. We explore how network performance is affected by deliberately adding various forms of noise and expanding the feature set and dataset size. Finally, we establish several metrics to indicate the difficulty of a dataset, and evaluate their merits. The algorithm and datasets are open-source.

Hassan Hamad, Yuou Qiu, Peter A. Beerel et al.

While advancements in quantization have significantly reduced the computational costs of inference in deep learning, training still predominantly relies on complex floating-point arithmetic. Low-precision fixed-point training presents a compelling alternative. This work introduces a novel enhancement in low-precision logarithmic fixed-point training, geared towards future hardware accelerator designs. We propose incorporating bitwidth in the design of approximations to arithmetic operations. To this end, we introduce a new hardware-friendly, piece-wise linear approximation for logarithmic addition. Using simulated annealing, we optimize this approximation at different precision levels. A C++ bit-true simulation demonstrates training of VGG-11 and VGG-16 models on CIFAR-100 and TinyImageNet, respectively, using 12-bit integer arithmetic with minimal accuracy degradation compared to 32-bit floating-point training. Our hardware study reveals up to 32.5% reduction in area and 53.5% reduction in energy consumption for the proposed LNS multiply-accumulate units compared to that of linear fixed-point equivalents.

Souvik Kundu, Mahdi Nazemi, Massoud Pedram et al.

The high energy cost of processing deep convolutional neural networks impedes their ubiquitous deployment in energy-constrained platforms such as embedded systems and IoT devices. This work introduces convolutional layers with pre-defined sparse 2D kernels that have support sets that repeat periodically within and across filters. Due to the efficient storage of our periodic sparse kernels, the parameter savings can translate into considerable improvements in energy efficiency due to reduced DRAM accesses, thus promising significant improvements in the trade-off between energy consumption and accuracy for both training and inference. To evaluate this approach, we performed experiments with two widely accepted datasets, CIFAR-10 and Tiny ImageNet in sparse variants of the ResNet18 and VGG16 architectures. Compared to baseline models, our proposed sparse variants require up to 82% fewer model parameters with 5.6times fewer FLOPs with negligible loss in accuracy for ResNet18 on CIFAR-10. For VGG16 trained on Tiny ImageNet, our approach requires 5.8times fewer FLOPs and up to 83.3% fewer model parameters with a drop in top-5 (top-1) accuracy of only 1.2% (2.1%). We also compared the performance of our proposed architectures with that of ShuffleNet andMobileNetV2. Using similar hyperparameters and FLOPs, our ResNet18 variants yield an average accuracy improvement of 2.8%.

Arnab Sanyal, Peter A. Beerel, Keith M. Chugg

The high computational complexity associated with training deep neural networks limits online and real-time training on edge devices. This paper proposed an end-to-end training and inference scheme that eliminates multiplications by approximate operations in the log-domain which has the potential to significantly reduce implementation complexity. We implement the entire training procedure in the log-domain, with fixed-point data representations. This training procedure is inspired by hardware-friendly approximations of log-domain addition which are based on look-up tables and bit-shifts. We show that our 16-bit log-based training can achieve classification accuracy within approximately 1% of the equivalent floating-point baselines for a number of commonly used datasets.

Souvik Kundu, Saurav Prakash, Haleh Akrami et al.

The high demand for computational and storage resources severely impede the deployment of deep convolutional neural networks (CNNs) in limited-resource devices. Recent CNN architectures have proposed reduced complexity versions (e.g. SuffleNet and MobileNet) but at the cost of modest decreases inaccuracy. This paper proposes pSConv, a pre-defined sparse 2D kernel-based convolution, which promises significant improvements in the trade-off between complexity and accuracy for both CNN training and inference. To explore the potential of this approach, we have experimented with two widely accepted datasets, CIFAR-10 and Tiny ImageNet, in sparse variants of both the ResNet18 and VGG16 architectures. Our approach shows a parameter count reduction of up to 4.24x with modest degradation in classification accuracy relative to that of standard CNNs. Our approach outperforms a popular variant of ShuffleNet using a variant of ResNet18 with pSConv having 3x3 kernels with only four of nine elements not fixed at zero. In particular, the parameter count is reduced by 1.7x for CIFAR-10 and 2.29x for Tiny ImageNet with an increased accuracy of ~4%.

Sourya Dey, Kuan-Wen Huang, Peter A. Beerel et al.

Neural networks have proven to be extremely powerful tools for modern artificial intelligence applications, but computational and storage complexity remain limiting factors. This paper presents two compatible contributions towards reducing the time, energy, computational, and storage complexities associated with multilayer perceptrons. Pre-defined sparsity is proposed to reduce the complexity during both training and inference, regardless of the implementation platform. Our results show that storage and computational complexity can be reduced by factors greater than 5X without significant performance loss. The second contribution is an architecture for hardware acceleration that is compatible with pre-defined sparsity. This architecture supports both training and inference modes and is flexible in the sense that it is not tied to a specific number of neurons. For example, this flexibility implies that various sized neural networks can be supported on various sized Field Programmable Gate Array (FPGA)s.

Sourya Dey, Diandian Chen, Zongyang Li et al.

We demonstrate an FPGA implementation of a parallel and reconfigurable architecture for sparse neural networks, capable of on-chip training and inference. The network connectivity uses pre-determined, structured sparsity to significantly reduce complexity by lowering memory and computational requirements. The architecture uses a notion of edge-processing, leading to efficient pipelining and parallelization. Moreover, the device can be reconfigured to trade off resource utilization with training time to fit networks and datasets of varying sizes. The combined effects of complexity reduction and easy reconfigurability enable significantly greater exploration of network hyperparameters and structures on-chip. As proof of concept, we show implementation results on an Artix-7 FPGA.

Sourya Dey, Peter A. Beerel, Keith M. Chugg

We propose a class of interleavers for a novel deep neural network (DNN) architecture that uses algorithmically pre-determined, structured sparsity to significantly lower memory and computational requirements, and speed up training. The interleavers guarantee clash-free memory accesses to eliminate idle operational cycles, optimize spread and dispersion to improve network performance, and are designed to ease the complexity of memory address computations in hardware. We present a design algorithm with mathematical proofs for these properties. We also explore interleaver variations and analyze the behavior of neural networks as a function of interleaver metrics.

Sourya Dey, Kuan-Wen Huang, Peter A. Beerel et al.

We propose a novel way of reducing the number of parameters in the storage-hungry fully connected layers of a neural network by using pre-defined sparsity, where the majority of connections are absent prior to starting training. Our results indicate that convolutional neural networks can operate without any loss of accuracy at less than half percent classification layer connection density, or less than 5 percent overall network connection density. We also investigate the effects of pre-defining the sparsity of networks with only fully connected layers. Based on our sparsifying technique, we introduce the `scatter' metric to characterize the quality of a particular connection pattern. As proof of concept, we show results on CIFAR, MNIST and a new dataset on classifying Morse code symbols, which highlights some interesting trends and limits of sparse connection patterns.

Sourya Dey, Yinan Shao, Keith M. Chugg et al.

We propose a reconfigurable hardware architecture for deep neural networks (DNNs) capable of online training and inference, which uses algorithmically pre-determined, structured sparsity to significantly lower memory and computational requirements. This novel architecture introduces the notion of edge-processing to provide flexibility and combines junction pipelining and operational parallelization to speed up training. The overall effect is to reduce network complexity by factors up to 30x and training time by up to 35x relative to GPUs, while maintaining high fidelity of inference results. This has the potential to enable extensive parameter searches and development of the largely unexplored theoretical foundation of DNNs. The architecture automatically adapts itself to different network sizes given available hardware resources. As proof of concept, we show results obtained for different bit widths.