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

Deep learning models have gained great popularity in statistical modeling because they lead to very competitive regression models, often outperforming classical statistical models such as generalized linear models. The disadvantage of deep…

In this paper, we introduce a novel way to use geometric deep learning for knot data by constructing a functor that takes knots to graphs and using graph neural networks. We will attempt to predict several knot invariants with this…

Stock market prediction has been a classical yet challenging problem, with the attention from both economists and computer scientists. With the purpose of building an effective prediction model, both linear and machine learning tools have…

This paper tries to give a gentle introduction to deep learning in medical image processing, proceeding from theoretical foundations to applications. We first discuss general reasons for the popularity of deep learning, including several…

Continuation of algebraic structures in families of dynamical systems is described using category theory, sheaves, and lattice algebras. Well-known concepts in dynamics, such as attractors or invariant sets, are formulated as functors on…

Artificial intelligence has made remarkable progress in handling complex tasks, thanks to advances in hardware acceleration and machine learning algorithms. However, to acquire more accurate outcomes and solve more complex issues,…

This paper introduces the concept of supermanifolds, viewed as the super-analogues of classical manifolds. Instead of treating supermanifolds as sets of points, we adopt an algebraic-geometric perspective, emphasizing the algebra of…

Scientists often use observational time series data to study complex natural processes, but regression analyses often assume simplistic dynamics. Recent advances in deep learning have yielded startling improvements to the performance of…

Optimization theory serves as a pivotal scientific instrument for achieving optimal system performance, with its origins in economic applications to identify the best investment strategies for maximizing benefits. Over the centuries, from…

The field of speech processing has undergone a transformative shift with the advent of deep learning. The use of multiple processing layers has enabled the creation of models capable of extracting intricate features from speech data. This…

Applying deep-learning models to geophysical applications has attracted special attentions during the past a couple of years. There are several papers published in this domain involving with different topics primarily focusing on synthetic…

Deep learning has revolutionized many industries by enabling models to automatically learn complex patterns from raw data, reducing dependence on manual feature engineering. However, deep learning algorithms are sensitive to input data, and…

We define the notion of sheaf in the context of doctrines. We prove the associate sheaf functor theorem. We show that grothendieck toposes and toposes obtained by the tripos to topos construction are instances of categories of sheaves for a…

The widespread adoption of whole slide imaging has increased the demand for effective and efficient gigapixel image analysis. Deep learning is at the forefront of computer vision, showcasing significant improvements over previous…

We explore the use of deep learning hierarchical models for problems in financial prediction and classification. Financial prediction problems -- such as those presented in designing and pricing securities, constructing portfolios, and risk…

An evolving area of research in deep learning is the study of architectures and inductive biases that support the learning of relational feature representations. In this paper, we address the challenge of learning representations of…

Image semantic segmentation is more and more being of interest for computer vision and machine learning researchers. Many applications on the rise need accurate and efficient segmentation mechanisms: autonomous driving, indoor navigation,…

Sheaves are mathematical objects consisting of a base which constitutes a topological space and the data associated with each open set thereof, e.g. continuous functions defined on the open sets. Sheaves have originally been used in…

Computers and algorithms play an ever-increasing role in obtaining new results in graph theory. In this survey, we present a broad range of techniques used in computer-assisted graph theory, including the exhaustive generation of all…

Recent advances in deep learning have allowed Artificial Intelligence (AI) to reach near human-level performance in many sensory, perceptual, linguistic or cognitive tasks. There is a growing need, however, for novel, brain-inspired…