Related papers: Neural Persistence: A Complexity Measure for Deep …

Persistent homology has become an important tool for extracting geometric and topological features from data, whose multi-scale features are summarized in a persistence diagram. From a statistical perspective, however, persistence diagrams…

We introduce a consistent estimator for the homology (an algebraic structure representing connected components and cycles) of level sets of both density and regression functions. Our method is based on kernel estimation. We apply this…

Training a deep neural network (DNN) often involves stochastic optimization, which means each run will produce a different model. Several works suggest this variability is negligible when models have the same performance, which in the case…

Deep learning models have proven to be successful in a wide range of machine learning tasks. Yet, they are often highly sensitive to perturbations on the input data which can lead to incorrect decisions with high confidence, hampering their…

Persistent homology is a technique recently developed in algebraic and computational topology well-suited to analysing structure in complex, high-dimensional data. In this paper, we exposit the theory of persistent homology from first…

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…

Neural networks have attracted a lot of attention due to its success in applications such as natural language processing and computer vision. For large scale data, due to the tremendous number of parameters in neural networks, overfitting…

Establishing associations between the structure and the generalisation ability of deep neural networks (DNNs) is a challenging task in modern machine learning. Producing solutions to this challenge will bring progress both in the…

Deep Learning's recent successes have mostly relied on Convolutional Networks, which exploit fundamental statistical properties of images, sounds and video data: the local stationarity and multi-scale compositional structure, that allows…

We introduce a unified theoretical framework for the rigorous analysis and systematic construction of deep neural networks (DNNs). This framework addresses a gap in existing theory by explicitly modeling the structure of tensor operations…

Deep neural networks (DNNs) are powerful machine learning models and have succeeded in various artificial intelligence tasks. Although various architectures and modules for the DNNs have been proposed, selecting and designing the…

Deep neural networks use multiple layers of functions to map an object represented by an input vector progressively to different representations, and with sufficient training, eventually to a single score for each class that is the output…

Document structure analysis, such as zone segmentation and table recognition, is a complex problem in document processing and is an active area of research. The recent success of deep learning in solving various computer vision and machine…

This paper presents a transformative framework for artificial neural networks over graded vector spaces, tailored to model hierarchical and structured data in fields like algebraic geometry and physics. By exploiting the algebraic…

Introduced the quantitative measure of the structural complexity of the graph (complex network, etc.) based on a procedure similar to the renormalization process, considering the difference between actual and averaged graph structures on…

Thresholding--the pruning of nodes or edges based on their properties or weights--is an essential preprocessing tool for extracting interpretable structure from complex network data, yet existing methods face several key limitations.…

A new design methodology for neural networks that is guided by traditional algorithm design is presented. To prove our point, we present two heuristics and demonstrate an algorithmic technique for incorporating additional weights in their…

Successful training of convolutional neural networks is often associated with sufficiently deep architectures composed of high amounts of features. These networks typically rely on a variety of regularization and pruning techniques to…

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…

We argue that the vulnerability of model parameters is of crucial value to the study of model robustness and generalization but little research has been devoted to understanding this matter. In this work, we propose an indicator to measure…