Deep Networks Learn Features From Local Discontinuities in the Label Function
Prithaj Banerjee Harish Guruprasad Ramaswamy Mahesh Lorik Yadav Chandra Shekar Lakshminarayanan
Deep neural networks outperform kernel machines on several datasets due to feature learning that happens during gradient descent training. In this paper, we analyze the mechanism through which feature learning happens and use a notion of features that corresponds to discontinuities in the true label function. We hypothesize that the core feature learning mechanism is label function discontinuities attracting model function discontinuities during training. To test this hypothesis, we perform experiments on classification data where the true label function is given by an oblique decision tree. This setup allows easy enumeration of label function discontinuities, while still remaining intractable for static kernel/linear methods. We then design/construct a novel deep architecture called a Deep Linearly Gated Network (DLGN), whose discontinuities in the input space can be easily enumerated.  In this setup, we provide supporting evidence demonstrating the movement of model function discontinuities towards the label function discontinuities during training. The easy enumerability of discontinuities in the DLGN also enables greater mechanistic interpretability. We demonstrate this by extracting the parameters of a high-accuracy decision tree from the parameters of a DLGN. We also show that the DLGN is competitive with ReLU networks and other tree-learning algorithms on several real-world tabular datasets.
Deep Learning, Feature learning, Interpretable, Local Discontinuities, Deep learning theory, Deep neural architectures, Supervised learning
Deep neural networks outperform kernel machines by learning features through discontinuities in label functions during gradient descent training, showing better performance and offering greater interpretability compared to ReLU networks.