Abnormal event detection with the lowest latency is an indispensable function for safety-critical systems, such as cyber defense systems. However, as systems become increasingly complicated, conventional sequential event detection methods become less effective, especially when we need to define indicator metrics from complicated data manually. Although Deep Neural Networks (DNNs) have been used to handle heterogeneous data, the theoretic assurability and explainability are still insufficient. This paper provides a holistic framework for the quickest and sequential detection of abnormalities and time-dependent abnormal events. We explore the latent space characteristics of zero-bias neural networks considering the classification boundaries and abnormalities. We then provide a novel method to convert zero-bias DNN classifiers into performance-assured binary abnormality detectors. Finally, we provide a sequential Quickest Detection (QD) scheme that provides the theoretically assured lowest abnormal event detection delay under false alarm constraints using the converted abnormality detector. We verify the effectiveness of the framework using real massive signal records in aviation communication systems and simulation. Codes and data are available at.