We investigate the $\ell_\infty$-constrained representation which demonstrates robustness to quantization errors, utilizing the tool of deep learning. Based on the Alternating Direction Method of Multipliers (ADMM), we formulate the original convex minimization problem as a feed-forward neural network, named \textit{Deep $\ell_\infty$ Encoder}, by introducing the novel Bounded Linear Unit (BLU) neuron and modeling the Lagrange multipliers as network biases. Such a structural prior acts as an effective network regularization, and facilitates the model initialization. We then investigate the effective use of the proposed model in the application of hashing, by coupling the proposed encoders under a supervised pairwise loss, to develop a \textit{Deep Siamese $\ell_\infty$ Network}, which can be optimized from end to end. Extensive experiments demonstrate the impressive performances of the proposed model. We also provide an in-depth analysis of its behaviors against the competitors.
Tsinghua Shenzhen International Graduate School, Tsinghua University（清华大学深圳国际研究生院）；PCL Research Center of Networks and Communications, Peng Cheng Laboratory（鹏城实验室网络通信研究中心）；vivo AI Lab（vivo AI研究院）；Department of Electrical and Computer Engineering, University of Waterloo（滑铁卢大学电气与计算机工程系）
Attribute-Aware Deep Hashing with Self-Consistency for Large-Scale Fine-Grained Image Retrieval
Southeast University（东南大学）；Nanjing University of Science and Technology（南京理工大学）；University of Electronic Science and Technology of China（电子科技大学）；Peking University（北京大学）
National Key Laboratory for Novel Software Technology（计算机软件新技术国家重点实验室）；Department of Computer Science and Technology（计算机科学与技术学院）；Nanjing University（南京大学）
HashTran-DNN: A Framework for Enhancing Robustness of Deep Neural Networks against Adversarial Malware Samples
Nanjing University of Science and Technology（南京理工大学）；Florida International University（佛罗里达国际大学）；Nanjing University of Posts and Telecommunications（南京邮电大学）；University of Texas at San Antonio（德克萨斯大学圣安东尼奥分校）
Near-Linear Time Projection onto the $\ell_{1,\infty}$ Ball; Application to Sparse Autoencoders
Université Côte d’Azur（蔚蓝海岸大学）；CNRS（法国国家科学研究中心）；King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学）；SDAIA-KAUST AI（SDAIA-KAUST人工智能中心）
