Input Prioritization for Testing Neural Networks

Deep neural networks (DNNs) are increasingly being adopted for sensing and control functions in a variety of safety and mission-critical systems such as self-driving cars, autonomous air vehicles, medical diagnostics, and industrial robotics. Failures of such systems can lead to loss of life or property, which necessitates stringent verification and validation for providing high assurance. Though formal verification approaches are being investigated, testing remains the primary technique for assessing the dependability of such systems. Due to the nature of the tasks handled by DNNs, the cost of obtaining test oracle data---the expected output, a.k.a. label, for a given input---is high, which significantly impacts the amount and quality of testing that can be performed. Thus, prioritizing input data for testing DNNs in meaningful ways to reduce the cost of labeling can go a long way in increasing testing efficacy. This paper proposes using gauges of the DNN's sentiment derived from the computation performed by the model, as a means to identify inputs that are likely to reveal weaknesses. We empirically assessed the efficacy of three such sentiment measures for prioritization---confidence, uncertainty, and surprise---and compare their effectiveness in terms of their fault-revealing capability and retraining effectiveness. The results indicate that sentiment measures can effectively flag inputs that expose unacceptable DNN behavior. For MNIST models, the average percentage of inputs correctly flagged ranged from 88% to 94.8%

Efficient Deep Feature Learning and Extraction via StochasticNets

Deep neural networks are a powerful tool for feature learning and extraction given their ability to model high-level abstractions in highly complex data. One area worth exploring in feature learning and extraction using deep neural networks is efficient neural connectivity formation for faster feature learning and extraction. Motivated by findings of stochastic synaptic connectivity formation in the brain as well as the brain's uncanny ability to efficiently represent information, we propose the efficient learning and extraction of features via StochasticNets, where sparsely-connected deep neural networks can be formed via stochastic connectivity between neurons. To evaluate the feasibility of such a deep neural network architecture for feature learning and extraction, we train deep convolutional StochasticNets to learn abstract features using the CIFAR-10 dataset, and extract the learned features from images to perform classification on the SVHN and STL-10 datasets. Experimental results show that features learned using deep convolutional StochasticNets, with fewer neural connections than conventional deep convolutional neural networks, can allow for better or comparable classification accuracy than conventional deep neural networks: relative test error decrease of ~4.5% for classification on the STL-10 dataset and ~1% for classification on the SVHN dataset. Furthermore, it was shown that the deep features extracted using deep convolutional StochasticNets can provide comparable classification accuracy even when only 10% of the training data is used for feature learning. Finally, it was also shown that significant gains in feature extraction speed can be achieved in embedded applications using StochasticNets. As such, StochasticNets allow for faster feature learning and extraction performance while facilitate for better or comparable accuracy performances.Comment: 10 pages. arXiv admin note: substantial text overlap with arXiv:1508.0546

SINVAD: Search-based Image Space Navigation for DNN Image Classifier Test Input Generation

The testing of Deep Neural Networks (DNNs) has become increasingly important as DNNs are widely adopted by safety critical systems. While many test adequacy criteria have been suggested, automated test input generation for many types of DNNs remains a challenge because the raw input space is too large to randomly sample or to navigate and search for plausible inputs. Consequently, current testing techniques for DNNs depend on small local perturbations to existing inputs, based on the metamorphic testing principle. We propose new ways to search not over the entire image space, but rather over a plausible input space that resembles the true training distribution. This space is constructed using Variational Autoencoders (VAEs), and navigated through their latent vector space. We show that this space helps efficiently produce test inputs that can reveal information about the robustness of DNNs when dealing with realistic tests, opening the field to meaningful exploration through the space of highly structured images

Stochastic gradient descent performs variational inference, converges to limit cycles for deep networks

Stochastic gradient descent (SGD) is widely believed to perform implicit regularization when used to train deep neural networks, but the precise manner in which this occurs has thus far been elusive. We prove that SGD minimizes an average potential over the posterior distribution of weights along with an entropic regularization term. This potential is however not the original loss function in general. So SGD does perform variational inference, but for a different loss than the one used to compute the gradients. Even more surprisingly, SGD does not even converge in the classical sense: we show that the most likely trajectories of SGD for deep networks do not behave like Brownian motion around critical points. Instead, they resemble closed loops with deterministic components. We prove that such "out-of-equilibrium" behavior is a consequence of highly non-isotropic gradient noise in SGD; the covariance matrix of mini-batch gradients for deep networks has a rank as small as 1% of its dimension. We provide extensive empirical validation of these claims, proven in the appendix