Topological Deep Learning
Topological deep learning (TDL) is a research field that extends deep learning to handle complex, Non-Euclidean geometry, non-Euclidean data structures. Traditional deep learning models, such as Convolutional neural network, convolutional neural networks (CNNs) and Recurrent neural network, recurrent neural networks (RNNs), excel in processing data on regular grids and sequences. However, scientific and real-world data often exhibit more intricate data domains encountered in scientific computations , including point clouds, Polygon mesh, meshes, time series, scalar fields Graph theory, graphs, or general topological spaces like simplicial complexes and CW complexes. TDL addresses this by incorporating topological concepts to process data with higher-order relationships, such as interactions among multiple entities and complex hierarchies. This approach leverages structures like Simplicial complex, simplicial complexes and Hypergraph, hypergraphs to capture global dependencies and qu ...
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Deep Learning
Deep learning is a subset of machine learning that focuses on utilizing multilayered neural networks to perform tasks such as classification, regression, and representation learning. The field takes inspiration from biological neuroscience and is centered around stacking artificial neurons into layers and "training" them to process data. The adjective "deep" refers to the use of multiple layers (ranging from three to several hundred or thousands) in the network. Methods used can be either supervised, semi-supervised or unsupervised. Some common deep learning network architectures include fully connected networks, deep belief networks, recurrent neural networks, convolutional neural networks, generative adversarial networks, transformers, and neural radiance fields. These architectures have been applied to fields including computer vision, speech recognition, natural language processing, machine translation, bioinformatics, drug design, medical image analysis, c ...
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