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The natural world is full of complex systems characterized by intricate relations between their components: from social interactions between individuals in a social network to electrostatic interactions between atoms in a protein.…

Deep learning (DL) is a high dimensional data reduction technique for constructing high-dimensional predictors in input-output models. DL is a form of machine learning that uses hierarchical layers of latent features. In this article, we…

Topological deep learning is a formalism that is aimed at introducing topological language to deep learning for the purpose of utilizing the minimal mathematical structures to formalize problems that arise in a generic deep learning…

Graph machine learning has led to a significant increase in the capabilities of models that learn on arbitrary graph-structured data and has been applied to molecules, social networks, recommendation systems, and transportation, among other…

Computer networks are the foundation of modern digital infrastructure, facilitating global communication and data exchange. As demand for reliable high-bandwidth connectivity grows, advanced network modeling techniques become increasingly…

Topological data analysis (TDA) provides insight into data shape. The summaries obtained by these methods are principled global descriptions of multi-dimensional data whilst exhibiting stable properties such as robustness to deformation and…

Deep learning (DL) allows computer models to learn, visualize, optimize, refine, and predict data. To understand its present state, examining the most recent advancements and applications of deep learning across various domains is…

Deep learning (DL), a new-generation of artificial neural network research, has transformed industries, daily lives and various scientific disciplines in recent years. DL represents significant progress in the ability of neural networks to…

Deep learning (DL) is one of the fastest growing topics in materials data science, with rapidly emerging applications spanning atomistic, image-based, spectral, and textual data modalities. DL allows analysis of unstructured data and…

Empirically, Deep Learning (DL) has demonstrated unprecedented success in practical applications. However, DL remains by and large a mysterious "black-box", spurring recent theoretical research to build its mathematical foundations. In this…

With the growing adoption of AI-based systems across everyday life, the need to understand their decision-making mechanisms is correspondingly increasing. The level at which we can trust the statistical inferences made from AI-based…

Deep Learning (DL) techniques are now widespread and being integrated into many important systems. Their classification and recognition abilities ensure their relevance for multiple application domains. As machine-learning that relies on…

In the current landscape of deep learning research, there is a predominant emphasis on achieving high predictive accuracy in supervised tasks involving large image and language datasets. However, a broader perspective reveals a multitude of…

Geometric deep learning (GDL), which is based on neural network architectures that incorporate and process symmetry information, has emerged as a recent paradigm in artificial intelligence. GDL bears particular promise in molecular modeling…

Accurate and efficient prediction of polymer properties is of key importance for polymer design. Traditional experimental tools and density function theory (DFT)-based simulations for polymer property evaluation, are both expensive and…

Deep learning (DL) is becoming increasingly popular in several application domains and has made several new application features involving computer vision, speech recognition and synthesis, self-driving automobiles, drug design, etc.…

Topological deep learning (TDL) has emerged as a powerful tool for modeling higher-order interactions in relational data. However, phenomena such as oversquashing in topological message-passing remain understudied and lack theoretical…

Recently, topological deep learning (TDL), which integrates algebraic topology with deep neural networks, has achieved tremendous success in processing point-cloud data, emerging as a promising paradigm in data science. However, TDL has not…

Much of the world's most valued data is stored in relational databases and data warehouses, where the data is organized into many tables connected by primary-foreign key relations. However, building machine learning models using this data…

Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topology layer that computes persistent homology based on level set…