Dynamic Sparse Training (DST) methods achieve state-of-the-art results in sparse neural network training, matching the generalization of dense models while enabling sparse training and inference. Although the resulting models are highly sparse and theoretically less computationally expensive, achieving speedups with unstructured sparsity on real-world hardware is challenging. In this work, we propose a sparse-to-sparse DST method, Structured RigL (SRigL), to learn a variant of fine-grained structured N:M sparsity by imposing a constant fan-in constraint. Using our empirical analysis of existing DST methods at high sparsity, we additionally employ a neuron ablation method which enables SRigL to achieve state-of-the-art sparse-to-sparse structured DST performance on a variety of Neural Network (NN) architectures. Using a 90% sparse linear layer, we demonstrate a real-world acceleration of 3.4×/2.5× on CPU for online inference and 1.7×/13.0× on GPU for inference with a batch size of 256 when compared to equivalent dense/unstructured (CSR) sparse layers, respectively.

Despite remarkable performance on a variety of tasks, many properties of deep neural networks are not yet theoretically understood. One such mystery is the depth degeneracy phenomenon: the deeper you make your network, the closer your network is to a constant function on initialization. In this paper, we examine the evolution of the angle between two inputs to a ReLU neural network as a function of the number of layers. By using combinatorial expansions, we find precise formulas for how fast this angle goes to zero as depth increases. These formulas capture microscopic fluctuations that are not visible in the popular framework of infinite width limits, and leads to qualitatively different predictions. We validate our theoretical results with Monte Carlo experiments and show that our results accurately approximate finite network behaviour. We also empirically investigate how the depth degeneracy phenomenon can negatively impact training of real networks. The formulas are given in terms of the mixed moments of correlated Gaussians passed through the ReLU function. We also find a surprising combinatorial connection between these mixed moments and the Bessel numbers that allows us to explicitly evaluate these moments.

Scenario-based approaches have been receiving a huge amount of attention in research and engineering of automated driving systems. Due to the complexity and uncertainty of the driving environment, and the complexity of the driving task itself, the number of possible driving scenarios that an Automated Driving System or Advanced Driving-Assistance System may encounter is virtually infinite. Therefore it is essential to be able to reason about the identification of scenarios and in particular critical ones that may impose unacceptable risk if not considered. Critical scenarios are particularly important to support design, verification and validation efforts, and as a basis for a safety case. In this paper, we present the results of a systematic mapping study in the context of autonomous driving. The main contributions are: (i) introducing a comprehensive taxonomy for critical scenario identification methods; (ii) giving an overview of the state-of-the-art research based on the taxonomy encompassing 86 papers between 2017 and 2020; and (iii) identifying open issues and directions for further research. The provided taxonomy comprises three main perspectives encompassing the problem definition (the why), the solution (the methods to derive scenarios), and the assessment of the established scenarios. In addition, we discuss open research issues considering the perspectives of coverage, practicability, and scenario space explosion.

The logit outputs of a feedforward neural network at initialization are conditionally Gaussian, given a random covariance matrix defined by the penultimate layer. In this work, we study the distribution of this random matrix. Recent work has shown that shaping the activation function as network depth grows large is necessary for this covariance matrix to be non-degenerate. However, the current infinite-width-style understanding of this shaping method is unsatisfactory for large depth: infinite-width analyses ignore the microscopic fluctuations from layer to layer, but these fluctuations accumulate over many layers. To overcome this shortcoming, we study the random covariance matrix in the shaped infinite-depth-and-width limit. We identify the precise scaling of the activation function necessary to arrive at a non-trivial limit, and show that the random covariance matrix is governed by a stochastic differential equation (SDE) that we call the Neural Covariance SDE. Using simulations, we show that the SDE closely matches the distribution of the random covariance matrix of finite networks. Additionally, we recover an if-and-only-if condition for exploding and vanishing norms of large shaped networks based on the activation function.

Theoretical results show that neural networks can be approximated by Gaussian processes in the infinite-width limit. However, for fully connected networks, it has been previously shown that for any fixed network width, $n$, the Gaussian approximation gets worse as the network depth, $d$, increases. Given that modern networks are deep, this raises the question of how well modern architectures, like ResNets, are captured by the infinite-width limit. To provide a better approximation, we study ReLU ResNets in the infinite-depth-and-width limit, where \emph{both} depth and width tend to infinity as their ratio, $d/n$, remains constant. In contrast to the Gaussian infinite-width limit, we show theoretically that the network exhibits log-Gaussian behaviour at initialization in the infinite-depth-and-width limit, with parameters depending on the ratio $d/n$. Using Monte Carlo simulations, we demonstrate that even basic properties of standard ResNet architectures are poorly captured by the Gaussian limit, but remarkably well captured by our log-Gaussian limit. Moreover, our analysis reveals that ReLU ResNets at initialization are hypoactivated: fewer than half of the ReLUs are activated. Additionally, we calculate the interlayer correlations, which have the effect of exponentially increasing the variance of the network output. Based on our analysis, we introduce \emph{Balanced ResNets}, a simple architecture modification, which eliminates hypoactivation and interlayer correlations and is more amenable to theoretical analysis.

In this paper, we outline the use of a genetic algorithm for test parameter optimization in the context of autonomous and automated driving. Our approach iteratively optimizes test parameters to aim at obtaining critical scenarios that form the basis for virtual verification and validation of Advanced Driver Assistant Systems (ADAS). We consider a test scenario to be critical if the underlying parameter set causes a malfunction of the system equipped with the ADAS function (i.e., near crash or crash of the vehicle). For evaluating the effectiveness of our approach, we set up an automated simulation framework, where we simulated the Euro NCAP car-to-car rear scenario. To assess the criticality of each test scenario we rely on time-to-collision (TTC), which is a well-known and often used time-based safety indicator for recognizing rear-end conflicts. Our genetic algorithm approach showed a higher chance to generate a critical scenario, compared to a random selection of test parameters.

SUMMARY Tools for automated fault localization usually generate too many bug candidates depending on the underlying technique. Hence, more information is required in order to further restrict the number of bug candidates. Approaches that rely on specific knowledge of the program to be debugged, such as variable values at specific positions in the source code, are not easily accessible for users especially in the case of software maintenance. In order to avoid this problem, we suggest integrating testing to restrict the number of bug candidates. In particular, we propose computing possible corrections of the program and from this distinguishing test cases. A distinguishing test case is a test that reveals different output values for two program variants given the same input values. Besides the formal definitions and algorithms, we extend the first empirical results of our approach in this paper. The obtained empirical results show that the use of mutations and distinguishing test cases reduces the number of bug candidates by more than 90% on average. Copyright © 2012 John Wiley & Sons, Ltd.