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Deep neural networks are widely used for nonlinear function approximation with applications ranging from computer vision to control. Although these networks involve the composition of simple arithmetic operations, it can be very challenging to verify whether a particular network satisfies certain input-output properties. This article surveys methods that have emerged recently for soundly verifying such properties. These methods borrow insights from reachability analysis, optimization, and search. We discuss fundamental differences and connections between existing algorithms. In addition, we provide pedagogical implementations of existing methods and compare them on a set of benchmark problems.
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Despite the functional success of deep neural networks (DNNs), their trustworthiness remains a crucial open challenge. To address this challenge, both testing and verification techniques have been proposed. But these existing techniques provide either scalability to large networks or formal guarantees, not both. In this paper, we propose a scalable quantitative verification framework for deep neural networks, i.e., a test-driven approach that comes with formal guarantees that a desired probabilistic property is satisfied. Our technique performs enough tests until soundness of a formal probabilistic property can be proven. It can be used to certify properties of both deterministic and randomized DNNs. We implement our approach in a tool called PROVERO and apply it in the context of certifying adversarial robustness of DNNs. In this context, we first show a new attack-agnostic measure of robustness which offers an alternative to purely attack-based methodology of evaluating robustness being reported today. Second, PROVERO provides certificates of robustness for large DNNs, where existing state-of-the-art verification tools fail to produce conclusive results. Our work paves the way forward for verifying properties of distributions captured by real-world deep neural networks, with provable guarantees, even where testers only have black-box access to the neural network.
Parameters in deep neural networks which are trained on large-scale databases can generalize across multiple domains, which is referred as transferability. Unfortunately, the transferability is usually defined as discrete states and it differs with domains and network architectures. Existing works usually heuristically apply parameter-sharing or fine-tuning, and there is no principled approach to learn a parameter transfer strategy. To address the gap, a parameter transfer unit (PTU) is proposed in this paper. The PTU learns a fine-grained nonlinear combination of activations from both the source and the target domain networks, and subsumes hand-crafted discrete transfer states. In the PTU, the transferability is controlled by two gates which are artificial neurons and can be learned from data. The PTU is a general and flexible module which can be used in both CNNs and RNNs. Experiments are conducted with various network architectures and multiple transfer domain pairs. Results demonstrate the effectiveness of the PTU as it outperforms heuristic parameter-sharing and fine-tuning in most settings.
With ever-increasing computational demand for deep learning, it is critical to investigate the implications of the numeric representation and precision of DNN model weights and activations on computational efficiency. In this work, we explore unconventional narrow-precision floating-point representations as it relates to inference accuracy and efficiency to steer the improved design of future DNN platforms. We show that inference using these custom numeric representations on production-grade DNNs, including GoogLeNet and VGG, achieves an average speedup of 7.6x with less than 1% degradation in inference accuracy relative to a state-of-the-art baseline platform representing the most sophisticated hardware using single-precision floating point. To facilitate the use of such customized precision, we also present a novel technique that drastically reduces the time required to derive the optimal precision configuration.
Conventional research attributes the improvements of generalization ability of deep neural networks either to powerful optimizers or the new network design. Different from them, in this paper, we aim to link the generalization ability of a deep network to optimizing a new objective function. To this end, we propose a textit{nonlinear collaborative scheme} for deep network training, with the key technique as combining different loss functions in a nonlinear manner. We find that after adaptively tuning the weights of different loss functions, the proposed objective function can efficiently guide the optimization process. What is more, we demonstrate that, from the mathematical perspective, the nonlinear collaborative scheme can lead to (i) smaller KL divergence with respect to optimal solutions; (ii) data-driven stochastic gradient descent; (iii) tighter PAC-Bayes bound. We also prove that its advantage can be strengthened by nonlinearity increasing. To some extent, we bridge the gap between learning (i.e., minimizing the new objective function) and generalization (i.e., minimizing a PAC-Bayes bound) in the new scheme. We also interpret our findings through the experiments on Residual Networks and DenseNet, showing that our new scheme performs superior to single-loss and multi-loss schemes no matter with randomization or not.
A deep neural network model is a powerful framework for learning representations. Usually, it is used to learn the relation $x to y$ by exploiting the regularities in the input $x$. In structured output prediction problems, $y$ is multi-dimensional and structural relations often exist between the dimensions. The motivation of this work is to learn the output dependencies that may lie in the output data in order to improve the prediction accuracy. Unfortunately, feedforward networks are unable to exploit the relations between the outputs. In order to overcome this issue, we propose in this paper a regularization scheme for training neural networks for these particular tasks using a multi-task framework. Our scheme aims at incorporating the learning of the output representation $y$ in the training process in an unsupervised fashion while learning the supervised mapping function $x to y$. We evaluate our framework on a facial landmark detection problem which is a typical structured output task. We show over two public challenging datasets (LFPW and HELEN) that our regularization scheme improves the generalization of deep neural networks and accelerates their training. The use of unlabeled data and label-only data is also explored, showing an additional improvement of the results. We provide an opensource implementation (https://github.com/sbelharbi/structured-output-ae) of our framework.
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