  The timed position of documents retrieved by learning to rank models can be
seen as signals. Signals carry useful information such as drop or rise of
documents over time or user behaviors. In this work, we propose to use the
logic formalism called Signal Temporal Logic (STL) to characterize document
behaviors in ranking accordingly to the specified formulas. Our analysis shows
that interesting document behaviors can be easily formalized and detected
thanks to STL formulas. We validate our idea on a dataset of 100K product
signals. Through the presented framework, we uncover interesting patterns, such
as cold start, warm start, spikes, and inspect how they affect our learning to
ranks models.
