Distance metric learning is a key field of machine learning, which aims at improving the performance of pattern classification and data discrimination by optimizing features to make samples of the same category closer in the feature space and samples of different classes farther apart. Most existing metric learning methods work in Euclidean space with zero curvature due to its simple and convenient characteristics. The latest studies show that non-zero curvature geometric spaces can better capture discriminative information. In this paper, to explore and form a more generalized feature space that is capable of matching complex data structure of samples, we look into metric learning problem in the mixed curvature space and present a new method called mixed-curvature metric learning (MCML). By simulating dimensionality reduction operations in different curvature spaces and conducting sample mining in mixed curvature space, our metric learning method is extended to feature spaces with a mixture of positive curvature, zero curvature, and negative curvature. Extensive experimental results show that our MCML approach achieves the superior performance in image retrieval task on multiples benchmark datasets, demonstrating the effectiveness of the proposed MCML method.

Anomaly detection is a challenging computer vision task in industrial scenario. Advancements in deep learning constantly revolutionize vision-based anomaly detection methods, and considerable progress has been made in both supervised and self-supervised anomaly detection. The commonly-used pipeline is to optimize the model by constraining the feature embeddings using a distance-based loss function. However, these methods work in Euclidean space, and they cannot well exploit the data lied in non-Euclidean space. In this paper, we are the first to explore anomaly detection task in hyperbolic space that is a representative of non-Euclidean space, and propose a hyperbolic anomaly detection (HypAD) method. Specifically, we first extract image features and then map them from Euclidean space to hyperbolic space, where the hyperbolic distance metric is employed to optimize the proposed HypAD. Extensive experiments on the benchmarking datasets including MVTec AD and VisA show that our HypAD approach obtains the state-of-the-art performance, demonstrating the effectiveness of our HypAD and the promise of investigating anomaly detection in hyperbolic space.

Physical unclonable function (PUF) is a technique to produce secret keys or complete authentication in integrated circuits (ICs) by exploiting the uncontrollable randomness due to manufacturing process variations. For better PUF applications, efficient analysis of different designs is important. In this article, a mathematical model to analyze the performance of typical strong PUF designs is proposed and applied to arbiter PUF, ring oscillator (RO) PUF, and duty cycle (DC) PUF. For better reliability, a new PUF design, DC multiplexer (DC MUX) PUF proposed in our previous work is analyzed. The proposed model indicates that DC MUX PUF achieves 2% higher reliability than arbiter PUF under environment influences. It also shows that DC PUF achieves 10% higher reliability than RO PUF. For verification, the aforementioned four PUF designs are testified using HSPICE. As our model analysis indicates, for reliability DC MUX PUF outperforms arbiter PUF, and DC PUF outperforms RO PUF. For randomness, DC MUX PUF and DC PUF outperform arbiter PUF and RO PUF, respectively. For security, LR attacks on DC MUX PUF and arbiter PUF are performed. The training time for DC MUX PUF is 40 000 times of arbiter PUF.