Sepsis, a dysregulated immune system response to infection, is among the leading causes of morbidity, mortality, and cost overruns in the Intensive Care Unit (ICU). Early prediction of sepsis can improve situational awareness among clinicians and facilitate timely, protective interventions. While the application of predictive analytics in ICU patients has shown early promising results, much of the work has been encumbered by high false-alarm rates and lack of trust by the end-users due to the 'black box' nature of these models. Here, we present DeepAISE (Deep Artificial Intelligence Sepsis Expert), a recurrent neural survival model for the early prediction of sepsis. DeepAISE automatically learns predictive features related to higher-order interactions and temporal patterns among clinical risk factors that maximize the data likelihood of observed time to septic events. A comparative study of four baseline models on data from hospitalized patients at three different healthcare systems indicates that DeepAISE produces the most accurate predictions (AUCs between 0.87 and 0.90) at the lowest false alarm rates (FARs between 0.20 and 0.25) while simultaneously producing interpretable representations of the clinical time series and risk factors.