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Although the recent progress in the deep neural network has led to the development of learnable local feature descriptors, there is no explicit answer for estimation of the necessary size of a neural network. Specifically, the local feature…
One of the most important steps toward interpretability and explainability of neural network models is feature selection, which aims to identify the subset of relevant features. Theoretical results in the field have mostly focused on the…
Deep neural networks are widely used for nonlinear function approximation with applications ranging from computer vision to control. Although these networks involve the composition of simple arithmetic operations, it can be very challenging…
Deep neural networks (DNNs) offer significant flexibility and robust performance. This makes them ideal for building not only system models but also advanced neural network controllers (NNCs). However, their high complexity and…
In this work we demonstrate a novel separation between symmetric neural network architectures. Specifically, we consider the Relational Network~\parencite{santoro2017simple} architecture as a natural generalization of the…
We study the problem of attributing the prediction of a deep network to its input features, a problem previously studied by several other works. We identify two fundamental axioms---Sensitivity and Implementation Invariance that attribution…
Deep generative networks can simulate from a complex target distribution, by minimizing a loss with respect to samples from that distribution. However, often we do not have direct access to our target distribution - our data may be subject…
Activation functions play a decisive role in determining the capacity of Deep Neural Networks as they enable neural networks to capture inherent nonlinearities present in data fed to them. The prior research on activation functions…
The degree distribution is an important characteristic of complex networks. In many data analysis applications, the networks should be represented as fixed-length feature vectors and therefore the feature extraction from the degree…
We present a novel, domain-agnostic, model-independent, unsupervised, and universally applicable Machine Learning approach for dimensionality reduction based on the principles of algorithmic complexity. Specifically, but without loss of…
As machine learning is applied to an increasing variety of complex problems, which are defined by high dimensional and complex data sets, the necessity for task oriented feature learning grows in importance. With the advancement of Deep…
Finding the important nodes in complex networks by topological structure is of great significance to network invulnerability. Several centrality measures have been proposed recently to evaluate the performance of nodes based on their…
While much of the work in the design of convolutional networks over the last five years has revolved around the empirical investigation of the importance of depth, filter sizes, and number of feature channels, recent studies have shown that…
Network pruning reduces the computation costs of an over-parameterized network without performance damage. Prevailing pruning algorithms pre-define the width and depth of the pruned networks, and then transfer parameters from the unpruned…
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…
Recent works have suggested that finite Bayesian neural networks may sometimes outperform their infinite cousins because finite networks can flexibly adapt their internal representations. However, our theoretical understanding of how the…
Graph Nerual Networks (GNNs) are effective models in graph embedding. It extracts shallow features and neighborhood information by aggregating neighbor information to learn the embedding representation of different nodes. However, the local…
Three important properties of a classification machinery are: (i) the system preserves the core information of the input data; (ii) the training examples convey information about unseen data; and (iii) the system is able to treat…
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…
Deep neural networks are highly expressive models that have recently achieved state of the art performance on speech and visual recognition tasks. While their expressiveness is the reason they succeed, it also causes them to learn…