Biblio

As an emerging paradigm for energy-efficiency design, approximate computing can reduce power consumption through simplification of logic circuits. Although calculation errors are caused by approximate computing, their impacts on the final results can be negligible in some error resilient applications, such as Convolutional Neural Networks (CNNs). Therefore, approximate computing has been applied to CNNs to reduce the high demand for computing resources and energy. Compared with the traditional method such as reducing data precision, this paper investigates the effect of approximate computing on the accuracy and power consumption of CNNs. To optimize the approximate computing technology applied to CNNs, we propose a method for quantifying the error resilience of each neuron by theoretical analysis and observe that error resilience varies widely across different neurons. On the basic of quantitative error resilience, dynamic adaptation of approximate bit-width and the corresponding configurable adder are proposed to fully exploit the error resilience of CNNs. Experimental results show that the proposed method further improves the performance of power consumption while maintaining high accuracy. By adopting the optimal approximate bit-width for each layer found by our proposed algorithm, dynamic adaptation of approximate bit-width reduces power consumption by more than 30% and causes less than 1% loss of the accuracy for LeNet-5.

We consider the distributed statistical learning problem over decentralized systems that are prone to adversarial attacks. This setup arises in many practical applications, including Google's Federated Learning. Formally, we focus on a decentralized system that consists of a parameter server and m working machines; each working machine keeps N/m data samples, where N is the total number of samples. In each iteration, up to q of the m working machines suffer Byzantine faults – a faulty machine in the given iteration behaves arbitrarily badly against the system and has complete knowledge of the system. Additionally, the sets of faulty machines may be different across iterations. Our goal is to design robust algorithms such that the system can learn the underlying true parameter, which is of dimension d, despite the interruption of the Byzantine attacks. In this paper, based on the geometric median of means of the gradients, we propose a simple variant of the classical gradient descent method. We show that our method can tolerate q Byzantine failures up to 2(1+$ε$)q łe m for an arbitrarily small but fixed constant $ε$0. The parameter estimate converges in O(łog N) rounds with an estimation error on the order of max $\surd$dq/N, \textasciitilde$\surd$d/N , which is larger than the minimax-optimal error rate $\surd$d/N in the centralized and failure-free setting by at most a factor of $\surd$q . The total computational complexity of our algorithm is of O((Nd/m) log N) at each working machine and O(md + kd log 3 N) at the central server, and the total communication cost is of O(m d log N). We further provide an application of our general results to the linear regression problem. A key challenge arises in the above problem is that Byzantine failures create arbitrary and unspecified dependency among the iterations and the aggregated gradients. To handle this issue in the analysis, we prove that the aggregated gradient, as a function of model parameter, converges uniformly to the true gradient function.