Explicitly Bayesian Regularizations in Deep Learning
This provides a theoretical explanation for generalization in CNNs, addressing inconsistencies in traditional theories, but it is incremental as it builds on existing Bayesian regularization concepts.
The authors tackled the problem of generalization in deep learning by demonstrating that Convolutional Neural Networks (CNNs) have explicitly Bayesian regularizations, showing they correspond to Bayesian networks with prior distributions in hidden layers, and validated this on a synthetic dataset.
Generalization is essential for deep learning. In contrast to previous works claiming that Deep Neural Networks (DNNs) have an implicit regularization implemented by the stochastic gradient descent, we demonstrate explicitly Bayesian regularizations in a specific category of DNNs, i.e., Convolutional Neural Networks (CNNs). First, we introduce a novel probabilistic representation for the hidden layers of CNNs and demonstrate that CNNs correspond to Bayesian networks with the serial connection. Furthermore, we show that the hidden layers close to the input formulate prior distributions, thus CNNs have explicitly Bayesian regularizations based on the Bayesian regularization theory. In addition, we clarify two recently observed empirical phenomena that are inconsistent with traditional theories of generalization. Finally, we validate the proposed theory on a synthetic dataset