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

A central problem in machine learning is often formulated as follows: Given a dataset $\{(x_j, y_j)\}_{j=1}^M$, which is a sample drawn from an unknown probability distribution, the goal is to construct a functional model $f$ such that…

This paper focuses on the analysis of the application effectiveness of the integration of deep learning and computer vision technologies. Deep learning achieves a historic breakthrough by constructing hierarchical neural networks, enabling…

Developing deep learning techniques for geometric data is an active and fruitful research area. This paper tackles the problem of sphere-type surface learning by developing a novel surface-to-image representation. Using this representation…

Deep learning has enjoyed tremendous success in a variety of applications but its application to quantile regressions remains scarce. A major advantage of the deep learning approach is its flexibility to model complex data in a more…

Algorithmicists are well-aware that fast dynamic programming algorithms are very often the correct choice when computing on compositional (or even recursive) graphs. Here we initiate the study of how to generalize this folklore intuition to…

A theory of graded manifolds can be viewed as a generalization of differential geometry of smooth manifolds. It allows one to work with functions which locally depend not only on ordinary real variables, but also on $\mathbb{Z}$-graded…

These notes aim to give a first introduction to intersection cohomology and perverse sheaves with applications to representation theory or quantum groups in mind.

Despite significant advances in the field of deep learning in applications to various fields, explaining the inner processes of deep learning models remains an important and open question. The purpose of this article is to describe and…

Delicate cloth simulations have long been desired in computer graphics. Various methods were proposed to improve engaged force interactions, collision handling, and numerical integrations. Deep learning has the potential to achieve fast and…

In recent years, deep learning techniques revolutionized the way remote sensing data are processed. Classification of hyperspectral data is no exception to the rule, but has intrinsic specificities which make application of deep learning…

Posets are discrete mathematical structures which are ubiquitous in a broad range of data analysis and machine learning applications. Research connecting posets to the data science domain has been ongoing for many years. In this paper, a…

Deep neural networks ("deep learning") have emerged as a technology of choice to tackle problems in natural language processing, computer vision, speech recognition and gameplay, and in just a few years has led to superhuman level…

Deep learning based on deep neural networks of various structures and architectures has been powerful in many practical applications, but it lacks enough theoretical verifications. In this paper, we consider a family of deep convolutional…

Deep supervision, or known as 'intermediate supervision' or 'auxiliary supervision', is to add supervision at hidden layers of a neural network. This technique has been increasingly applied in deep neural network learning systems for…

Learning representations of data is an important problem in statistics and machine learning. While the origin of learning representations can be traced back to factor analysis and multidimensional scaling in statistics, it has become a…

Bayesian interpretations of neural network have a long history, dating back to early work in the 1990's and have recently regained attention because of their desirable properties like uncertainty estimation, model robustness and…

Input-output maps are prevalent throughout science and technology. They are empirically observed to be biased towards simple outputs, but we don't understand why. To address this puzzle, we study the archetypal input-output map: a…

This paper investigates the foundations of deep learning through insight of geometry, algebra and differential calculus. At is core, artificial intelligence relies on assumption that data and its intrinsic structure can be embedded into…

Deep learning has been widely used for supervised learning and classification/regression problems. Recently, a novel area of research has applied this paradigm to unsupervised tasks; indeed, a gradient-based approach extracts, efficiently…

In this article we review computational aspects of Deep Learning (DL). Deep learning uses network architectures consisting of hierarchical layers of latent variables to construct predictors for high-dimensional input-output models. Training…