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Full-Text Articles in Physical Sciences and Mathematics
Improved Generalisation Bounds For Deep Learning Through L∞ Covering Numbers, Antoine Ledent, Yunwen Lei, Marius Kloft
Improved Generalisation Bounds For Deep Learning Through L∞ Covering Numbers, Antoine Ledent, Yunwen Lei, Marius Kloft
Research Collection School Of Computing and Information Systems
Using proof techniques involving L∞ covering numbers, we show generalisation error bounds for deep learning with two main improvements over the state of the art. First, our bounds have no explicit dependence on the number of classes except for logarithmic factors. This holds even when formulating the bounds in terms of the L 2 norm of the weight matrices, while previous bounds exhibit at least a square-root dependence on the number of classes in this case. Second, we adapt the Rademacher analysis of DNNs to incorporate weight sharing—a task of fundamental theoretical importance which was previously attempted only under very …
Deep Anomaly Detection With Deviation Networks, Guansong Pang, Chunhua Shen, Anton Van Den Hengel
Deep Anomaly Detection With Deviation Networks, Guansong Pang, Chunhua Shen, Anton Van Den Hengel
Research Collection School Of Computing and Information Systems
Although deep learning has been applied to successfully address many data mining problems, relatively limited work has been done on deep learning for anomaly detection. Existing deep anomaly detection methods, which focus on learning new feature representations to enable downstream anomaly detection methods, perform indirect optimization of anomaly scores, leading to data-inefficient learning and suboptimal anomaly scoring. Also, they are typically designed as unsupervised learning due to the lack of large-scale labeled anomaly data. As a result, they are difficult to leverage prior knowledge (e.g., a few labeled anomalies) when such information is available as in many real-world anomaly detection …
Sliced Wasserstein Generative Models, Jiqing Wu, Zhiwu Huang, Dinesh Acharya, Wen Li, Janine Thoma, Danda Pani Paudel, Luc Van Gool
Sliced Wasserstein Generative Models, Jiqing Wu, Zhiwu Huang, Dinesh Acharya, Wen Li, Janine Thoma, Danda Pani Paudel, Luc Van Gool
Research Collection School Of Computing and Information Systems
In generative modeling, the Wasserstein distance (WD) has emerged as a useful metric to measure the discrepancy between generated and real data distributions. Unfortunately, it is challenging to approximate the WD of high-dimensional distributions. In contrast, the sliced Wasserstein distance (SWD) factorizes high-dimensional distributions into their multiple one-dimensional marginal distributions and is thus easier to approximate. In this paper, we introduce novel approximations of the primal and dual SWD. Instead of using a large number of random projections, as it is done by conventional SWD approximation methods, we propose to approximate SWDs with a small number of parameterized orthogonal projections …