Convergence rates of deep ReLU networks for multiclass classification
This provides theoretical insights into the performance of deep networks in classification tasks, but it is incremental as it builds on existing convergence analysis.
The paper tackles the problem of analyzing convergence rates of deep ReLU networks for multiclass classification, deriving rates that depend on a margin-type condition related to near-zero class probabilities.
For classification problems, trained deep neural networks return probabilities of class memberships. In this work we study convergence of the learned probabilities to the true conditional class probabilities. More specifically we consider sparse deep ReLU network reconstructions minimizing cross-entropy loss in the multiclass classification setup. Interesting phenomena occur when the class membership probabilities are close to zero. Convergence rates are derived that depend on the near-zero behaviour via a margin-type condition.