The analysis of high-intensity runs (or sprints) in soccer has long been a topic of interest for sports science researchers and practitioners. In particular, recent studies suggested contextualizing sprints based on their tactical purposes to better understand the physical-tactical requirements of modern match-play. However, they have a limitation in scalability, as human experts have to manually classify hundreds of sprints for every match. To address this challenge, this paper proposes a deep learning framework for automatically classifying sprints in soccer into contextual categories. The proposed model covers the permutation-invariant and sequential nature of multi-agent trajectories in soccer by deploying Set Transformers and a bidirectional GRU. We train the model with category labels made through the collaboration of human annotators and a rule-based classifier. Experimental results show that our model classifies sprints in the test dataset into 15 categories with the accuracy of 77.65%, implying the potential of the proposed framework for facilitating the integrated analysis of soccer sprints at scale.