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1. Universal Approximation Property and Equivalence of Stochastic Computing-Based Neural Networks and Binary Neural Networks

   https://doi.org/10.1609/aaai.v33i01.33015369  

   Wang, Yanzhi; Zhan, Zheng; Zhao, Liang; Tang, Jian; Wang, Siyue; Li, Jiayu; Yuan, Bo; Wen, Wujie; Lin, Xue (February 2019, Proceedings of the AAAI Conference on Artificial Intelligence)

   Large-scale deep neural networks are both memory and computation-intensive, thereby posing stringent requirements on the computing platforms. Hardware accelerations of deep neural networks have been extensively investigated. Specific forms of binary neural networks (BNNs) and stochastic computing-based neural networks (SCNNs) are particularly appealing to hardware implementations since they can be implemented almost entirely with binary operations. Despite the obvious advantages in hardware implementation, these approximate computing techniques are questioned by researchers in terms of accuracy and universal applicability. Also it is important to understand the relative pros and cons of SCNNs and BNNs in theory and in actual hardware implementations. In order to address these concerns, in this paper, we prove that the ”ideal” SCNNs and BNNs satisfy the universal approximation property with probability 1 (due to the stochastic behavior), which is a new angle from the original approximation property. The proof is conducted by first proving the property for SCNNs from the strong law of large numbers, and then using SCNNs as a “bridge” to prove for BNNs. Besides the universal approximation property, we also derive an appropriate bound for bit length M in order to provide insights for the actual neural network implementations. Based on the universal approximation property, we further prove that SCNNs and BNNs exhibit the same energy complexity. In other words, they have the same asymptotic energy consumption with the growth of network size. We also provide a detailed analysis of the pros and cons of SCNNs and BNNs for hardware implementations and conclude that SCNNs are more suitable. 

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2. Grover's Implementation of Quantum Binary Neural Networks

   https://doi.org/10.1109/QCE57702.2023.00043  

   Wrighter, Brody; Alarcon, Sonia Lopez (September 2023, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE))

   Binary Neural Networks (BNNs) are the result of a simplification of network parameters in Artificial Neural Networks (ANNs). The computational complexity of training ANNs increases significantly as the size of the network increases. This complexity can be greatly reduced if the parameters of the network are binarized. Binarization, which is a one bit quantization, can also come with complications including error and information loss. The implementation of BNNs on quantum hardware could potentially provide a computational advantage over its classical counterpart. This is due to the fact that binarized parameters fit nicely to the nature of quantum hardware. Quantum superposition allows the network to be trained more efficiently, without using back propagation techniques, with the application of Grover’s Algorithm for the training process. This paper looks into two BNN designs that utilize only quantum hardware, as opposed to hybrid quantum-classical implementations. It also provides practical implementations for both of them. Looking into their scalability, improvements on the design are proposed to reduce complexity even further. 

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3. ULEEN: A Novel Architecture for Ultra-low-energy Edge Neural Networks

   https://doi.org/10.1145/3629522  

   Susskind, Zachary; Arora, Aman; Miranda, Igor_D S; Bacellar, Alan_T L; Villon, Luis_A Q; Katopodis, Rafael F; de_Araújo, Leandro S; Dutra, Diego_L C; Lima, Priscila_M V; França, Felipe_M G; et al (December 2023, ACM Transactions on Architecture and Code Optimization)

   ‘‘Extreme edge”¹devices, such as smart sensors, are a uniquely challenging environment for the deployment of machine learning. The tiny energy budgets of these devices lie beyond what is feasible for conventional deep neural networks, particularly in high-throughput scenarios, requiring us to rethink how we approach edge inference. In this work, we propose ULEEN, a model and FPGA-based accelerator architecture based on weightless neural networks (WNNs). WNNs eliminate energy-intensive arithmetic operations, instead using table lookups to perform computation, which makes them theoretically well-suited for edge inference. However, WNNs have historically suffered from poor accuracy and excessive memory usage. ULEEN incorporates algorithmic improvements and a novel training strategy inspired by binary neural networks (BNNs) to make significant strides in addressing these issues. We compare ULEEN against BNNs in software and hardware using the four MLPerf Tiny datasets and MNIST. Our FPGA implementations of ULEEN accomplish classification at 4.0–14.3 million inferences per second, improving area-normalized throughput by an average of 3.6× and steady-state energy efficiency by an average of 7.1× compared to the FPGA-based Xilinx FINN BNN inference platform. While ULEEN is not a universally applicable machine learning model, we demonstrate that it can be an excellent choice for certain applications in energy- and latency-critical edge environments. 

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4. BNN Pruning: Pruning Binary Neural Network Guided by Weight Flipping Frequency

   Li, Yixing; Ren, Fengbo (March 2020, International Symposium on Quality Electronic Design)

   A binary neural network (BNN) is a compact form of neural network. Both the weights and activations in BNNs can be binary values, which leads to a significant reduction in both parameter size and computational complexity compared to their full-precision counterparts. Such reductions can directly translate into reduced memory footprint and computation cost in hardware, making BNNs highly suitable for a wide range of hardware accelerators. However, it is unclear whether and how a BNN can be further pruned for ultimate compactness. As both 0s and 1s are non-trivial in BNNs, it is not proper to adopt any existing pruning method of full- precision networks that interprets 0s as trivial. In this paper, we present a pruning method tailored to BNNs and illustrate that BNNs can be further pruned by using weight flipping frequency as an indicator of sensitivity to accuracy. The experiments performed on the binary versions of a 9- layer Network-in-Network (NIN) and the AlexNet with the CIFAR-10 dataset show that the proposed BNN-pruning method can achieve 20-40% reduction in binary operations with 0.5-1.0% accuracy drop, which leads to a 15-40% run- time speedup on a TitanX GPU. 

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5. Verifying Binary Neural Networks on Continuous Input Space using Star Reachability

   https://doi.org/10.1109/FormaliSE58978.2023.00009  

   Ivashchenko, Mykhailo; Choi, Sung Woo; Nguyen, Luan Viet; Tran, Hoang-Dung (May 2023, 2023 IEEE/ACM 11th International Conference on Formal Methods in Software Engineering (FormaliSE))

   Deep Neural Networks (DNNs) have become a popular instrument for solving various real-world problems. DNNs’ sophisticated structure allows them to learn complex representations and features. For this reason, Binary Neural Networks (BNNs) are widely used on edge devices, such as microcomputers. However, architecture specifics and floating-point number usage result in an increased computational operations complexity. Like other DNNs, BNNs are vulnerable to adversarial attacks; even a small perturbation to the input set may lead to an errant output. Unfortunately, only a few approaches have been proposed for verifying BNNs.This paper proposes an approach to verify BNNs on continuous input space using star reachability analysis. Our approach can compute both exact and overapproximate reachable sets of BNNs with Sign activation functions and use them for verification. The proposed approach is also efficient in constructing a complete set of counterexamples in case a network is unsafe. We implemented our approach in NNV, a neural network verification tool for DNNs and learning-enabled Cyber-Physical Systems. The experimental results show that our star-based approach is less conservative, more efficient, and scalable than the recent SMT-based method implemented in Marabou. We also provide a comparison with a quantization-based tool EEVBNN. 

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