Analyzing surgical workflow is crucial for surgical assistance robots to understand surgeries. With the understanding of the complete surgical workflow, the robots are able to assist the surgeons in intra-operative events, such as by giving a warning when the surgeon is entering specific keys or high-risk phases. Deep learning techniques have recently been widely applied to recognizing surgical workflows. Many of the existing temporal neural network models are limited in their capability to handle long-term dependencies in the data, instead, relying upon the strong performance of the underlying per-frame visual models. We propose a new temporal network structure that leverages task-specific network representation to collect long-term sufficient statistics that are propagated by a sufficient statistics model (SSM). We implement our approach within an LSTM backbone for the task of surgical phase recognition and explore several choices for propagated statistics. We demonstrate superior results over existing and novel state-of-the-art segmentation techniques on two laparoscopic cholecystectomy datasets: the publicly available Cholec80 dataset and MGH100, a novel dataset with more challenging and clinically meaningful segment labels.