This paper proposes to learn a set of high-level feature representations through deep learning, referred to as Deep hidden IDentity features (DeepID), for face verification. We argue that DeepID can be effectively learned through challenging multi-class face identification tasks, whilst they can be generalized to other tasks (such as verification) and new identities unseen in the training set. Moreover, the generalization capability of DeepID increases as more face classes are to be predicted at training. DeepID features are taken from the last hidden layer neuron activations of deep convolutional networks (ConvNets). When learned as classifiers to recognize about 10, 000 face identities in the training set and configured to keep reducing the neuron numbers along the feature extraction hierarchy, these deep ConvNets gradually form compact identity-related features in the top layers with only a small number of hidden neurons. The proposed features are extracted from various face regions to form complementary and over-complete representations. Any state-of-the-art classifiers can be learned based on these high-level representations for face verification. 97.45% verification accuracy on LFW is achieved with only weakly aligned faces.

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This paper designs a high-performance deep convolutional network (DeepID2+) for face recognition. It is learned with the identification-verification supervisory signal. By increasing the dimension of hidden representations and adding supervision to early convolutional layers, DeepID2+ achieves new state-of-the-art on LFW and YouTube Faces benchmarks.Through empirical studies, we have discovered three properties of its deep neural activations critical for the high performance: sparsity, selectiveness and robustness. (1) It is observed that neural activations are moderately sparse. Moderate sparsity maximizes the discriminative power of the deep net as well as the distance between images. It is surprising that DeepID2+ still can achieve high recognition accuracy even after the neural responses are binarized. (2) Its neurons in higher layers are highly selective to identities and identity-related attributes. We can identify different subsets of neurons which are either constantly excited or inhibited when different identities or attributes are present. Although DeepID2+ is not taught to distinguish attributes during training, it has implicitly learned such high-level concepts.(3) It is much more robust to occlusions, although occlusion patterns are not included in the training set.

Abstract. We study the attribution problem, that is, the problem of attributing a change in the value of a characteristic function f to its independent variables. We make three contributions. First, we propose a formalization of the problem based on a standard cost sharing model. Second, we show that there is a unique attribution method that satisfies Dummy, Additivity, Conditional Nonnegativity, Affine Scale Invariance, and Anonymity for all characteristic functions that are the sum of a multilinear function and an additive function. We term this the Aumann-Shapley-Shubik method. Conversely, we show that such a uniqueness result does not hold for characteristic functions outside this class. Third, we study multilinear characteristic functions in detail; we describe a computationally efficient implementation of the AumannShapley-Shubik method and discuss practical applications to pay-per-click advertising and portfolio analysis.