An Information Theoretic Interpretation to Deep Neural Networks
This provides a theoretical interpretation for internal computations in DNNs, which is incremental as it builds on existing intuitions about feature extraction.
The paper tackles the problem of interpreting hidden layers in deep neural networks by formalizing feature extraction as a universal feature selection optimization problem, showing that trained weights project feature functions between spaces with operational meaning for inference tasks, supported by numerical experiments.
It is commonly believed that the hidden layers of deep neural networks (DNNs) attempt to extract informative features for learning tasks. In this paper, we formalize this intuition by showing that the features extracted by DNN coincide with the result of an optimization problem, which we call the `universal feature selection' problem, in a local analysis regime. We interpret the weights training in DNN as the projection of feature functions between feature spaces, specified by the network structure. Our formulation has direct operational meaning in terms of the performance for inference tasks, and gives interpretations to the internal computation results of DNNs. Results of numerical experiments are provided to support the analysis.