Related papers: Topological Learning in Multi-Class Data Sets
Deep learning (DL) enables deep neural networks (DNNs) to automatically learn complex tasks or rules from given examples without instructions or guiding principles. As we do not engineer DNNs' functions, it is extremely difficult to…
Learning the topology of higher-order networks from data is a fundamental challenge in many signal processing and machine learning applications. Simplicial complexes provide a principled framework for modeling multi-way interactions, yet…
The intrinsically infinite-dimensional features of the functional observations over multidimensional domains render the standard classification methods effectively inapplicable. To address this problem, we introduce a novel multiclass…
The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is…
Recurrent neural networks are deep learning topologies that can be trained to classify long documents. However, in our recent work, we found a critical problem with these cells: they can use the length differences between texts of different…
Systematic relations between multiple objects that occur in various fields can be represented as networks. Real-world networks typically exhibit complex topologies whose structural properties are key factors in characterizing and further…
This chapter explores neural networks, topological data analysis, and topological deep learning techniques, alongside statistical Bayesian methods, for processing images, time series, and graphs to maximize the potential of artificial…
Deep Neural Networks (DNNs) are analyzed via the theoretical framework of the information bottleneck (IB) principle. We first show that any DNN can be quantified by the mutual information between the layers and the input and output…
Identifying the structural priors that enable Deep Neural Networks (DNNs) to overcome the curse of dimensionality is a fundamental challenge in machine learning theory. Existing literature suggests that effective high-dimensional learning…
Neural Networks sequentially build high-level features through their successive layers. We propose here a new neural network model where each layer is associated with a set of candidate mappings. When an input is processed, at each layer,…
Several recent works have shown separation results between deep neural networks, and hypothesis classes with inferior approximation capacity such as shallow networks or kernel classes. On the other hand, the fact that deep networks can…
The high degrees of freedom and complex structure of garments present significant challenges for clothing manipulation. In this paper, we propose a general topological dynamics model to fold complex clothing. By utilizing the visible…
Deep learning is a machine learning methodology using multi-layer neural network. A multi-layer neural network can be regarded as a chain of complete bipartite graphs. The nodes of the first partita is the input layer and the last is the…
Deep neural networks have achieved remarkable success, yet our understanding of how they learn remains limited. These models can learn high-dimensional tasks, which is generally statistically intractable due to the curse of dimensionality.…
We introduce a flexible setup allowing for a neural network to learn both its size and topology during the course of a standard gradient-based training. The resulting network has the structure of a graph tailored to the particular learning…
Graph neural networks (GNNs) have attracted much attention due to their ability to leverage the intrinsic geometries of the underlying data. Although many different types of GNN models have been developed, with many benchmarking procedures…
Thanks to the availability of large scale digital datasets and massive amounts of computational power, deep learning algorithms can learn representations of data by exploiting multiple levels of abstraction. These machine learning methods…
Deep networks have shown great performance in classification tasks. However, the parameters learned by the classifier networks usually discard stylistic information of the input, in favour of information strictly relevant to classification.…
Many classification problems consider classes that form a hierarchy. Classifiers that are aware of this hierarchy may be able to make confident predictions at a coarse level despite being uncertain at the fine-grained level. While it is…
Classification with a large number of classes is a key problem in machine learning and corresponds to many real-world applications like tagging of images or textual documents in social networks. If one-vs-all methods usually reach top…