Related papers: Sheaf theory: from deep geometry to deep learning

Machine learning algorithms learn a desired input-output relation from examples in order to interpret new inputs. This is important for tasks such as image and speech recognition or strategy optimisation, with growing applications in the IT…

A brief synopsis of recent conceptions and results, the current status and future outlook of our research program of applying sheaf and topos-theoretic ideas to quantum gravity and quantum logic is presented.

Clustering is a fundamental machine learning task which has been widely studied in the literature. Classic clustering methods follow the assumption that data are represented as features in a vectorized form through various representation…

We show that every sheaf on the site of smooth manifolds with values in a stable (infinity,1)-category (like spectra or chain complexes) gives rise to a differential cohomology diagram and a homotopy formula, which are common features of…

Deep learning research aims at discovering learning algorithms that discover multiple levels of distributed representations, with higher levels representing more abstract concepts. Although the study of deep learning has already led to…

Deep learning, which is especially formidable in handling big data, has achieved great success in various fields, including bioinformatics. With the advances of the big data era in biology, it is foreseeable that deep learning will become…

Deep learning continues to re-shape numerous fields, from natural language processing and imaging to data analytics and recommendation systems. This report studies two research papers that represent recent progress on deep learning from two…

This focused review explores a range of neural operator architectures for approximating solutions to parametric partial differential equations (PDEs), emphasizing high-level concepts and practical implementation strategies. The study covers…

Researchers have been highly active to investigate the classical machine learning workflow and integrate best practices from the software engineering lifecycle. However, deep learning exhibits deviations that are not yet covered in this…

Graph neural networks face two fundamental challenges rooted in the linear structure of Euclidean vector spaces: (1) Current architectures represent geometry through vectors (directions, gradients), yet many tasks require matrix-valued…

The growing demand for sustainable development brings a series of information technologies to help agriculture production. Especially, the emergence of machine learning applications, a branch of artificial intelligence, has shown multiple…

Neural network models can now recognise images, understand text, translate languages, and play many human games at human or superhuman levels. These systems are highly abstracted, but are inspired by biological brains and use only…

An in-depth exploration of object detection and semantic segmentation is provided, combining theoretical foundations with practical applications. State-of-the-art advancements in machine learning and deep learning are reviewed, focusing on…

In this paper, we make the case that a scientific theory of deep learning is emerging. By this we mean a theory which characterizes important properties and statistics of the training process, hidden representations, final weights, and…

In this paper, we present a novel deep learning approach, deeply-fused nets. The central idea of our approach is deep fusion, i.e., combine the intermediate representations of base networks, where the fused output serves as the input of the…

Graphs have a superior ability to represent relational data, like chemical compounds, proteins, and social networks. Hence, graph-level learning, which takes a set of graphs as input, has been applied to many tasks including comparison,…

Recent times are witnessing rapid development in machine learning algorithm systems, especially in reinforcement learning, natural language processing, computer and robot vision, image processing, speech, and emotional processing and…

Heterogeneous graphs, whose nodes and edges can belong to different types and feature spaces, arise in many real-world domains, including biology, recommendation, social networks, and computer systems. Existing heterogeneous graph neural…

Deep learning is currently the subject of intensive study. However, fundamental concepts such as representations are not formally defined -- researchers "know them when they see them" -- and there is no common language for describing and…

Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and non-linearities.…