Vamshi C. Madala

Vamshi C. Madala, Shivkumar Chandrasekaran, Jason Bunk

Despite the success of convolutional neural networks (CNNs) in numerous computer vision tasks and their extraordinary generalization performances, several attempts to predict the generalization errors of CNNs have only been limited to a posteriori analyses thus far. A priori theories explaining the generalization performances of deep neural networks have mostly ignored the convolutionality aspect and do not specify why CNNs are able to seemingly overcome curse of dimensionality on computer vision tasks like image classification where the image dimensions are in thousands. Our work attempts to explain the generalization performance of CNNs on image classification under the hypothesis that CNNs operate on the domain of image patches. Ours is the first work we are aware of to derive an a priori error bound for the generalization error of CNNs and we present both quantitative and qualitative evidences in the support of our theory. Our patch-based theory also offers explanation for why data augmentation techniques like Cutout, CutMix and random cropping are effective in improving the generalization error of CNNs.

Abhejit Rajagopal, Vamshi C. Madala, Shivkumar Chandrasekaran et al.

We study generalization in deep learning by appealing to complexity measures originally developed in approximation and information theory. While these concepts are challenged by the high-dimensional and data-defined nature of deep learning, we show that simple vector quantization approaches such as PCA, GMMs, and SVMs capture their spirit when applied layer-wise to deep extracted features giving rise to relatively inexpensive complexity measures that correlate well with generalization performance. We discuss our results in 2020 NeurIPS PGDL challenge.