Related papers: Classification regions of deep neural networks
Over the past decade, deep learning has proven to be a highly effective tool for learning meaningful features from raw data. However, it remains an open question how deep networks perform hierarchical feature learning across layers. In this…
We present a lightweight network that infers grouping and boundaries, including curves, corners and junctions. It operates in a bottom-up fashion, analogous to classical methods for sub-pixel edge localization and edge-linking, but with a…
This work develops the global equations of neural networks through stacked piecewise manifolds, fixed-point theory, and boundary-conditioned iteration. Once fixed coordinates and operators are removed, a neural network appears as a…
Deep convolutional neural networks have proven to be well suited for image classification applications. However, if there is distortion in the image, the classification accuracy can be significantly degraded, even with state-of-the-art…
The representations learned by deep neural networks are difficult to interpret in part due to their large parameter space and the complexities introduced by their multi-layer structure. We introduce a method for computing persistent…
Despite being effective in many application areas, Deep Neural Networks (DNNs) are vulnerable to being attacked. In object recognition, the attack takes the form of a small perturbation added to an image, that causes the DNN to misclassify,…
Inspired by a growing interest in analyzing network data, we study the problem of node classification on graphs, focusing on approaches based on kernel machines. Conventionally, kernel machines are linear classifiers in the implicit feature…
We investigate recurrent neural networks with asymmetric interactions and demonstrate that the inclusion of self-couplings or sparse excitatory inter-module connections leads to the emergence of a densely connected manifold of dynamically…
While a lot of progress has been made in recent years, the dynamics of learning in deep nonlinear neural networks remain to this day largely misunderstood. In this work, we study the case of binary classification and prove various…
Deep learning has arguably achieved tremendous success in recent years. In simple words, deep learning uses the composition of many nonlinear functions to model the complex dependency between input features and labels. While neural networks…
Many tasks require mapping continuous input data (e.g. images) to discrete task outputs (e.g. class labels). Yet, how neural networks learn to perform such discrete computations on continuous data manifolds remains poorly understood. Here,…
Datasets such as images, text, or movies are embedded in high-dimensional spaces. However, in important cases such as images of objects, the statistical structure in the data constrains samples to a manifold of dramatically lower…
The subject of deep learning has recently attracted users of machine learning from various disciplines, including: medical diagnosis and bioinformatics, financial market analysis and online advertisement, speech and handwriting recognition,…
Deep neural networks are widely used in various domains. However, the nature of computations at each layer of the deep networks is far from being well understood. Increasing the interpretability of deep neural networks is thus important.…
Deep convolutional neural networks have achieved great successes over recent years, particularly in the domain of computer vision. They are fast, convenient, and -- thanks to mature frameworks -- relatively easy to implement and deploy.…
Recent genomic and bioinformatic advances have motivated the development of numerous random network models purporting to describe graphs of biological, technological, and sociological origin. The success of a model has been evaluated by how…
While both shape and texture are fundamental to visual recognition, research on deep neural networks (DNNs) has predominantly focused on the latter, leaving their geometric understanding poorly probed. Here, we show: first, that optimized…
Deep neural networks have demonstrated superior performance in artificial intelligence applications, but the opaqueness of their inner working mechanism is one major drawback in their application. The prevailing unit-based interpretation is…
In this paper, we investigate the impact of neural networks (NNs) topology on adversarial robustness. Specifically, we study the graph produced when an input traverses all the layers of a NN, and show that such graphs are different for…
We propose a deep learning strategy to estimate the mean curvature of two-dimensional implicit interfaces in the level-set method. Our approach is based on fitting feed-forward neural networks to synthetic data sets constructed from…