Rethinking generalization of classifiers in separable classes scenarios and over-parameterized regimes

We investigate the learning dynamics of classifiers in scenarios where classes are separable or classifiers are over-parameterized. In both cases, Empirical Risk Minimization (ERM) results in zero training error. However, there are many global minima with a training error of zero, some of which generalize well and some of which do not. We show that in separable classes scenarios the proportion of "bad" global minima diminishes exponentially with the number of training data n. Our analysis provides bounds and learning curves dependent solely on the density distribution of the true error for the given classifier function set, irrespective of the set's size or complexity (e.g., number of parameters). This observation may shed light on the unexpectedly good generalization of over-parameterized Neural Networks. For the over-parameterized scenario, we propose a model for the density distribution of the true error, yielding learning curves that align with experiments on MNIST and CIFAR-10.

Enhancing Generalization in Convolutional Neural Networks through Regularization with Edge and Line Features

This paper proposes a novel regularization approach to bias Convolutional Neural Networks (CNNs) toward utilizing edge and line features in their hidden layers. Rather than learning arbitrary kernels, we constrain the convolution layers to edge and line detection kernels. This intentional bias regularizes the models, improving generalization performance, especially on small datasets. As a result, test accuracies improve by margins of 5-11 percentage points across four challenging fine-grained classification datasets with limited training data and an identical number of trainable parameters. Instead of traditional convolutional layers, we use Pre-defined Filter Modules, which convolve input data using a fixed set of 3x3 pre-defined edge and line filters. A subsequent ReLU erases information that did not trigger any positive response. Next, a 1x1 convolutional layer generates linear combinations. Notably, the pre-defined filters are a fixed component of the architecture, remaining unchanged during the training phase. Our findings reveal that the number of dimensions spanned by the set of pre-defined filters has a low impact on recognition performance. However, the size of the set of filters matters, with nine or more filters providing optimal results.

Leaky ReLUs That Differ in Forward and Backward Pass Facilitate Activation Maximization in Deep Neural Networks

Activation maximization (AM) strives to generate optimal input stimuli, revealing features that trigger high responses in trained deep neural networks. AM is an important method of explainable AI. We demonstrate that AM fails to produce optimal input stimuli for simple functions containing ReLUs or Leaky ReLUs, casting doubt on the practical usefulness of AM and the visual interpretation of the generated images. This paper proposes a solution based on using Leaky ReLUs with a high negative slope in the backward pass while keeping the original, usually zero, slope in the forward pass. The approach significantly increases the maxima found by AM. The resulting ProxyGrad algorithm implements a novel optimization technique for neural networks that employs a secondary network as a proxy for gradient computation. This proxy network is designed to have a simpler loss landscape with fewer local maxima than the original network. Our chosen proxy network is an identical copy of the original network, including its weights, with distinct negative slopes in the Leaky ReLUs. Moreover, we show that ProxyGrad can be used to train the weights of Convolutional Neural Networks for classification such that, on some of the tested benchmarks, they outperform traditional networks.

Large Neural Networks Learning from Scratch with Very Few Data and without Regularization

Recent findings have shown that Neural Networks generalize also in over-parametrized regimes with zero training error. This is surprising, since it is completely against traditional machine learning wisdom. In our empirical study we fortify these findings in the domain of fine-grained image classification. We show that very large Convolutional Neural Networks with millions of weights do learn with only a handful of training samples and without image augmentation, explicit regularization or pretraining. We train the architectures ResNet018, ResNet101 and VGG19 on subsets of the difficult benchmark datasets Caltech101, CUB_200_2011, FGVCAircraft, Flowers102 and StanfordCars with 100 classes and more, perform a comprehensive comparative study and draw implications for the practical application of CNNs. Finally, we show that VGG19 with 140 million weights learns to distinguish airplanes and motorbikes up to 95% accuracy with only 20 samples per class.

Explainable COVID-19 Detection Using Chest CT Scans and Deep Learning

This paper explores how well deep learning models trained on chest CT images can diagnose COVID-19 infected people in a fast and automated process. To this end, we adopt advanced deep network architectures and propose a transfer learning strategy using custom-sized input tailored for each deep architecture to achieve the best performance. We conduct extensive sets of experiments on two CT image datasets, namely the SARS-CoV-2 CT-scan and the COVID19-CT. The obtained results show superior performances for our models compared with previous studies, where our best models achieve average accuracy, precision, sensitivity, specificity and F1 score of 99.4%, 99.6%, 99.8%, 99.6% and 99.4% on the SARS-CoV-2 dataset; and 92.9%, 91.3%, 93.7%, 92.2% and 92.5% on the COVID19-CT dataset, respectively. Furthermore, we apply two visualization techniques to provide visual explanations for the models' predictions. The visualizations show well-separated clusters for CT images of COVID-19 from other lung diseases, and accurate localizations of the COVID-19 associated regions.