While many approaches to make neural networks more fathomable have been proposed, they are restricted to interrogating the network with input data. Measures for characterizing and monitoring structural properties, however, have not been developed. In this work, we propose neural persistence, a complexity measure for neural network architectures based on topological data analysis on weighted stratified graphs. To demonstrate the usefulness of our approach, we show that neural persistence reflects best practices developed in the deep learning community such as dropout and batch normalization. Moreover, we derive a neural persistence-based stopping criterion that shortens the training process while achieving comparable accuracies as early stopping based on validation loss.

Motivation: Sepsis is a life-threatening host response to infection associated with high mortality, morbidity and health costs. Its management is highly time-sensitive since each hour of delayed treatment increases mortality due to irreversible organ damage. Meanwhile, despite decades of clinical research robust biomarkers for sepsis are missing. Therefore, detecting sepsis early by utilizing the affluence of high-resolution intensive care records has become a challenging machine learning problem. Recent advances in deep learning and data mining promise a powerful set of tools to efficiently address this task. Results: This paper proposes two approaches for the early detection of sepsis: a new deep learning model (MGP-TCN) and a data mining model (DTW-KNN). MGP-TCN employs a temporal convolutional network as embedded in a Multitask Gaussian Process Adapter framework, making it directly applicable to irregularly spaced time series data. Our DTW-KNN is an ensemble approach that employs dynamic time warping. We then frame the timely detection of sepsis as a supervised time series classification task. For this, we derive the most recent sepsis definition in an hourly resolution to provide the first fully accessible early sepsis detection environment. Seven hours before sepsis onset, our methods MGP-TCN/DTW-KNN improve area under the precision--recall curve from 0.25 to 0.35/0.40 over the state of the art. This demonstrates that they are well-suited for detecting sepsis in the crucial earlier stages when management is most effective.