Traversing the Local Polytopes of ReLU Neural Networks: A Unified Approach for Network Verification

Although neural networks (NNs) with ReLU activation functions have found success in a wide range of applications, their adoption in risk-sensitive settings has been limited by the concerns on robustness and interpretability. Previous works to examine robustness and to improve interpretability partially exploited the piecewise linear function form of ReLU NNs. In this paper, we explore the unique topological structure that ReLU NNs create in the input space, identifying the adjacency among the partitioned local polytopes and developing a traversing algorithm based on this adjacency. Our polytope traversing algorithm can be adapted to verify a wide range of network properties related to robustness and interpretability, providing an unified approach to examine the network behavior. As the traversing algorithm explicitly visits all local polytopes, it returns a clear and full picture of the network behavior within the traversed region. The time and space complexity of the traversing algorithm is determined by the number of a ReLU NN's partitioning hyperplanes passing through the traversing region.

Distributed stochastic proximal algorithm with random reshuffling for non-smooth finite-sum optimization

The non-smooth finite-sum minimization is a fundamental problem in machine learning. This paper develops a distributed stochastic proximal-gradient algorithm with random reshuffling to solve the finite-sum minimization over time-varying multi-agent networks. The objective function is a sum of differentiable convex functions and non-smooth regularization. Each agent in the network updates local variables with a constant step-size by local information and cooperates to seek an optimal solution. We prove that local variable estimates generated by the proposed algorithm achieve consensus and are attracted to a neighborhood of the optimal solution in expectation with an $\mathcal{O}(\frac{1}{T}+\frac{1}{\sqrt{T}})$ convergence rate. In addition, this paper shows that the steady-state error of the objective function can be arbitrarily small by choosing small enough step-sizes. Finally, some comparative simulations are provided to verify the convergence performance of the proposed algorithm.

Data-driven Hedging of Stock Index Options via Deep Learning

We develop deep learning models to learn the hedge ratio for S&P500 index options directly from options data. We compare different combinations of features and show that a feedforward neural network model with time to maturity, Black-Scholes delta and a sentiment variable (VIX for calls and index return for puts) as input features performs the best in the out-of-sample test. This model significantly outperforms the standard hedging practice that uses the Black-Scholes delta and a recent data-driven model. Our results demonstrate the importance of market sentiment for hedging efficiency, a factor previously ignored in developing hedging strategies.

Vega: A 10-Core SoC for IoT End-Nodes with DNN Acceleration and Cognitive Wake-Up From MRAM-Based State-Retentive Sleep Mode

The Internet-of-Things requires end-nodes with ultra-low-power always-on capability for a long battery lifetime, as well as high performance, energy efficiency, and extreme flexibility to deal with complex and fast-evolving near-sensor analytics algorithms (NSAAs). We present Vega, an IoT end-node SoC capable of scaling from a 1.7 $\mathrm{\mu}$W fully retentive cognitive sleep mode up to 32.2 GOPS (@ 49.4 mW) peak performance on NSAAs, including mobile DNN inference, exploiting 1.6 MB of state-retentive SRAM, and 4 MB of non-volatile MRAM. To meet the performance and flexibility requirements of NSAAs, the SoC features 10 RISC-V cores: one core for SoC and IO management and a 9-cores cluster supporting multi-precision SIMD integer and floating-point computation. Vega achieves SoA-leading efficiency of 615 GOPS/W on 8-bit INT computation (boosted to 1.3TOPS/W for 8-bit DNN inference with hardware acceleration). On floating-point (FP) compuation, it achieves SoA-leading efficiency of 79 and 129 GFLOPS/W on 32- and 16-bit FP, respectively. Two programmable machine-learning (ML) accelerators boost energy efficiency in cognitive sleep and active states, respectively.

Accelerating Training and Inference of Graph Neural Networks with Fast Sampling and Pipelining

Improving the training and inference performance of graph neural networks (GNNs) is faced with a challenge uncommon in general neural networks: creating mini-batches requires a lot of computation and data movement due to the exponential growth of multi-hop graph neighborhoods along network layers. Such a unique challenge gives rise to a diverse set of system design choices. We argue in favor of performing mini-batch training with neighborhood sampling in a distributed multi-GPU environment, under which we identify major performance bottlenecks hitherto under-explored by developers: mini-batch preparation and transfer. We present a sequence of improvements to mitigate these bottlenecks, including a performance-engineered neighborhood sampler, a shared-memory parallelization strategy, and the pipelining of batch transfer with GPU computation. We also conduct an empirical analysis that supports the use of sampling for inference, showing that test accuracies are not materially compromised. Such an observation unifies training and inference, simplifying model implementation. We report comprehensive experimental results with several benchmark data sets and GNN architectures, including a demonstration that, for the ogbn-papers100M data set, our system SALIENT achieves a speedup of 3x over a standard PyTorch-Geometric implementation with a single GPU and a further 8x parallel speedup with 16 GPUs. Therein, training a 3-layer GraphSAGE model with sampling fanout (15, 10, 5) takes 2.0 seconds per epoch and inference with fanout (20, 20, 20) takes 2.4 seconds, attaining test accuracy 64.58%.

Transient Performance Analysis of the $\ell_1$-RLS

The recursive least-squares algorithm with $\ell_1$-norm regularization ($\ell_1$-RLS) exhibits excellent performance in terms of convergence rate and steady-state error in identification of sparse systems. Nevertheless few works have studied its stochastic behavior, in particular its transient performance. In this letter, we derive analytical models of the transient behavior of the $\ell_1$-RLS in the mean and mean-square sense. Simulation results illustrate the accuracy of these models.

Non-imaging real-time detection and tracking of fast-moving objects using a single-pixel detector

Detection and tracking of fast-moving objects have widespread utility in many fields. However, fulfilling this demand for fast and efficient detecting and tracking using image-based techniques is problematic, owing to the complex calculations and limited data processing capabilities. To tackle this problem, we propose an image-free method to achieve real-time detection and tracking of fast-moving objects. It employs the Hadamard pattern to illuminate the fast-moving object by a spatial light modulator, in which the resulting light signal is collected by a single-pixel detector. The single-pixel measurement values are directly used to reconstruct the position information without image reconstruction. Furthermore, a new sampling method is used to optimize the pattern projection way for achieving an ultra-low sampling rate. Compared with the state-of-the-art methods, our approach is not only capable of handling real-time detection and tracking, but also it has a small amount of calculation and high efficiency. We experimentally demonstrate that the proposed method, using a 22kHz digital micro-mirror device, can implement a 105fps frame rate at a 1.28% sampling rate when tracks. Our method breaks through the traditional tracking ways, which can implement the object real-time tracking without image reconstruction.

Supervised Linear Dimension-Reduction Methods: Review, Extensions, and Comparisons

Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input variable that contains maximal variation and preserves as much information as possible. PCA has also been used in prediction models where the original, high-dimensional space of predictors is reduced to a smaller, more manageable, set before conducting regression analysis. However, this approach does not incorporate information in the response during the dimension-reduction stage and hence can have poor predictive performance. To address this concern, several supervised linear dimension-reduction techniques have been proposed in the literature. This paper reviews selected techniques, extends some of them, and compares their performance through simulations. Two of these techniques, partial least squares (PLS) and least-squares PCA (LSPCA), consistently outperform the others in this study.

On Faster Convergence of Scaled Sign Gradient Descent

Communication has been seen as a significant bottleneck in industrial applications over large-scale networks. To alleviate the communication burden, sign-based optimization algorithms have gained popularity recently in both industrial and academic communities, which is shown to be closely related to adaptive gradient methods, such as Adam. Along this line, this paper investigates faster convergence for a variant of sign-based gradient descent, called scaled signGD, in three cases: 1) the objective function is strongly convex; 2) the objective function is nonconvex but satisfies the Polyak-Lojasiewicz (PL) inequality; 3) the gradient is stochastic, called scaled signGD in this case. For the first two cases, it can be shown that the scaled signGD converges at a linear rate. For case 3), the algorithm is shown to converge linearly to a neighborhood of the optimal value when a constant learning rate is employed, and the algorithm converges at a rate of $O(1/k)$ when using a diminishing learning rate, where $k$ is the iteration number. The results are also extended to the distributed setting by majority vote in a parameter-server framework. Finally, numerical experiments on logistic regression are performed to corroborate the theoretical findings.

An Information Theory-inspired Strategy for Automatic Network Pruning

Despite superior performance on many computer vision tasks, deep convolution neural networks are well known to be compressed on devices that have resource constraints. Most existing network pruning methods require laborious human efforts and prohibitive computation resources, especially when the constraints are changed. This practically limits the application of model compression when the model needs to be deployed on a wide range of devices. Besides, existing methods are still challenged by the missing theoretical guidance. In this paper we propose an information theory-inspired strategy for automatic model compression. The principle behind our method is the information bottleneck theory, i.e., the hidden representation should compress information with each other. We thus introduce the normalized Hilbert-Schmidt Independence Criterion (nHSIC) on network activations as a stable and generalized indicator of layer importance. When a certain resource constraint is given, we integrate the HSIC indicator with the constraint to transform the architecture search problem into a linear programming problem with quadratic constraints. Such a problem is easily solved by a convex optimization method with a few seconds. We also provide a rigorous proof to reveal that optimizing the normalized HSIC simultaneously minimizes the mutual information between different layers. Without any search process, our method achieves better compression tradeoffs comparing to the state-of-the-art compression algorithms. For instance, with ResNet-50, we achieve a 45.3%-FLOPs reduction, with a 75.75 top-1 accuracy on ImageNet. Codes are avaliable at https://github.com/MAC-AutoML/ITPruner/tree/master.