  Deep models produce a number of features in each internal layer. A key
problem in applications such as feature compression for remote inference is
determining how important each feature is for the task(s) performed by the
model. The problem is especially challenging in the case of multi-task
inference, where the same feature may carry different importance for different
tasks. In this paper, we examine how effective is mutual information (MI)
between a feature and a model's task output as a measure of the feature's
importance for that task. Experiments involving hard selection and soft
selection (unequal compression) based on MI are carried out to compare the
MI-based method with alternative approaches. Multi-objective analysis is
provided to offer further insight.
