Related papers: A rank decomposition for the topological classific…

Data samples collected for training machine learning models are typically assumed to be independent and identically distributed (iid). Recent research has demonstrated that this assumption can be problematic as it simplifies the manifold of…

A recent line of work has established intriguing connections between the generalization/compression properties of a deep neural network (DNN) model and the so-called layer weights' stable ranks. Intuitively, the latter are indicators of the…

Unified understanding of neuro networks (NNs) gets the users into great trouble because they have been puzzled by what kind of rules should be obeyed to optimize the internal structure of NNs. Considering the potential capability of random…

Neural networks encode inputs as high-dimensional vectors, known as representations, that capture how models process data by encoding task-relevant structure and semantics. Representation alignment refers to the degree to which different…

We study the multiple manifold problem, a binary classification task modeled on applications in machine vision, in which a deep fully-connected neural network is trained to separate two low-dimensional submanifolds of the unit sphere. We…

Networks are a useful representation for data on connections between units of interests, but the observed connections are often noisy and/or include missing values. One common approach to network analysis is to treat the network as a…

Although the convolutional neural networks (CNNs) have become popular for various image processing and computer vision task recently, it remains a challenging problem to reduce the storage cost of the parameters for resource-limited…

Deep neural networks can be effective means to automatically classify aerial images but is easy to overfit to the training data. It is critical for trained neural networks to be robust to variations that exist between training and test…

Deep neural networks have proved very successful in domains where large training sets are available, but when the number of training samples is small, their performance suffers from overfitting. Prior methods of reducing overfitting such as…

Over the past decade, deep neural networks have proven to be adept in image classification tasks, often surpassing humans in terms of accuracy. However, standard neural networks often fail to understand the concept of hierarchical…

Graph Neural Networks (GNNs) have gained popularity in various learning tasks, with successful applications in fields like molecular biology, transportation systems, and electrical grids. These fields naturally use graph data, benefiting…

The homological scaffold leverages persistent homology to construct a topologically sound summary of a weighted network. However, its crucial dependency on the choice of representative cycles hinders the ability to trace back global…

Training deep neural networks results in strong learned representations that show good generalization capabilities. In most cases, training involves iterative modification of all weights inside the network via back-propagation. In Extreme…

We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively…

A ReLU neural network leads to a finite polyhedral decomposition of input space and a corresponding finite dual graph. We show that while this dual graph is a coarse quantization of input space, it is sufficiently robust that it can be…

Social network analysis is an important problem in data mining. A fundamental step for analyzing social networks is to encode network data into low-dimensional representations, i.e., network embeddings, so that the network topology…

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…

Functional complex networks have meant a pivotal change in the way we understand complex systems, being the most outstanding one the human brain. These networks have classically been reconstructed using a frequentist approach that, while…

Understanding the operation of biological and artificial networks remains a difficult and important challenge. To identify general principles, researchers are increasingly interested in surveying large collections of networks that are…

Understanding how neural systems efficiently process information through distributed representations is a fundamental challenge at the interface of neuroscience and machine learning. Recent approaches analyze the statistical and geometrical…