Related papers: Neural Persistence: A Complexity Measure for Deep …
Recent years have witnessed an increased interest in the application of persistent homology, a topological tool for data analysis, to machine learning problems. Persistent homology is known for its ability to numerically characterize the…
This paper presents a mathematically rigorous framework for brain-inspired representation learning founded on the interplay between persistent topological structures and cohomological flows. Neural computation is reformulated as the…
Topological data analysis (TDA) is an emerging mathematical concept for characterizing shapes in complex data. In TDA, persistence diagrams are widely recognized as a useful descriptor of data, and can distinguish robust and noisy…
The classical approach to measure the expressive power of deep neural networks with piecewise linear activations is based on counting their maximum number of linear regions. This complexity measure is quite relevant to understand general…
We investigate the robustness of sparse artificial neural networks trained with adaptive topology. We focus on a simple yet effective architecture consisting of three sparse layers with 99% sparsity followed by a dense layer, applied to…
Deep neural networks have achieved remarkable results across many language processing tasks, however these methods are highly sensitive to noise and adversarial attacks. We present a regularization based method for limiting network…
Large-scale recurrent networks have drawn increasing attention recently because of their capabilities in modeling a large variety of real-world phenomena and physical mechanisms. This paper studies how to identify all authentic connections…
As complex networks find applications in a growing range of disciplines, the diversity of naturally occurring and model networks being studied is exploding. The adoption of a well-developed collection of network taxonomies is a natural…
The influence of deep learning is continuously expanding across different domains, and its new applications are ubiquitous. The question of neural network design thus increases in importance, as traditional empirical approaches are reaching…
The inner representation of deep neural networks (DNNs) is indecipherable, which makes it difficult to tune DNN models, control their training process, and interpret their outputs. In this paper, we propose a novel approach to investigate…
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…
This paper is a cursory study on how topological features are preserved within the internal representations of neural network layers. Using techniques from topological data analysis, namely persistent homology, the topological features of a…
In this paper, we propose Graph Retention Networks (GRNs) as a unified architecture for deep learning on dynamic graphs. The GRN extends the concept of retention into dynamic graph data as graph retention, equipping the model with three key…
Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…
Existing generalization measures that aim to capture a model's simplicity based on parameter counts or norms fail to explain generalization in overparameterized deep neural networks. In this paper, we introduce a new, theoretically…
Topological methods for data analysis present opportunities for enforcing certain invariances of broad interest in computer vision, including view-point in activity analysis, articulation in shape analysis, and measurement invariance in…
We study how the topology of feature embedding space changes as it passes through the layers of a well-trained deep neural network (DNN) through Betti numbers. Motivated by existing studies using simplicial complexes on shallow fully…
Persistent topological properties of an image serve as an additional descriptor providing an insight that might not be discovered by traditional neural networks. The existing research in this area focuses primarily on efficiently…
Neural networks are very successful at detecting patterns in noisy data, and have become the technology of choice in many fields. However, their usefulness is hampered by their susceptibility to adversarial attacks. Recently, many methods…
Neural networks (NN)-based learning algorithms are strongly affected by the choices of initialization and data distribution. Different optimization strategies have been proposed for improving the learning trajectory and finding a better…