Related papers: Reverse Tangent Categories
This paper presents a new technique for learning category-level manipulation from raw RGB-D videos of task demonstrations, with no manual labels or annotations. Category-level learning aims to acquire skills that can be generalized to new…
We describe the framework for the notion of a restricted inverse limit of categories, with the main motivating example being the category of polynomial representations of the group $GL_{\infty}$. This category is also known as the category…
We study statistical inverse learning in the context of nonlinear inverse problems under random design. Specifically, we address a class of nonlinear problems by employing gradient descent (GD) and stochastic gradient descent (SGD) with…
Stratifolds are considered from a categorical point of view. We show among others that the category of stratifolds fully faithfully embeds into the category of ${\mathbb R}$-algebras as does the category of smooth manifolds. We prove that a…
Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects has recently been investigated…
We extend the theory of exterior differential systems from manifolds and their tangent bundles to Lie algebroids. In particular, we define the concept of an integral manifold of such an exterior differential system. We support our…
Gradient-based meta-learning methods leverage gradient descent to learn the commonalities among various tasks. While previous such methods have been successful in meta-learning tasks, they resort to simple gradient descent during…
We study the partially wrapped Fukaya category of a surface with boundary with an action of a group of order two. Inspired by skew-group algebras and categories, we define the notion of a skew-group $A_\infty$-category and let it play the…
We develop in full detail the formalism of tangent states to the manifold of matrix product states, and show how they naturally appear in studying time-evolution, excitations and spectral functions. We focus on the case of systems with…
This paper explores differential bundles in tangent categories, characterizing them as functors from a structure category. This is analogous to the actegory perspective of Garner and Leung, which we also use to describe the tangent…
Manifold hypotheses are typically used for tasks such as dimensionality reduction, interpolation, or improving classification performance. In the less common problem of manifold estimation, the task is to characterize the geometric…
Significant theoretical work has established that in specific regimes, neural networks trained by gradient descent behave like kernel methods. However, in practice, it is known that neural networks strongly outperform their associated…
Supervised dimensionality reduction has emerged as an important theme in the last decade. Despite the plethora of models and formulations, there is a lack of a simple model which aims to project the set of patterns into a space defined by…
We suggest a concept of generalized `angles' in arbitrary real normed vector spaces. We give for each real number a definition of an `angle' by means of the shape of the unit ball. They all yield the well known Euclidean angle in the…
We define a simplicial category called the category of derived manifolds. It contains the category of smooth manifolds as a full discrete subcategory, and it is closed under taking arbitrary intersections in a manifold. A derived manifold…
This paper concerns open-world classification, where the classifier not only needs to classify test examples into seen classes that have appeared in training but also reject examples from unseen or novel classes that have not appeared in…
Many different types of fractional calculus have been proposed, which can be organised into some general classes of operators. For a unified mathematical theory, results should be proved in the most general possible setting. Two important…
We present an approach to semantic scene analysis using deep convolutional networks. Our approach is based on tangent convolutions - a new construction for convolutional networks on 3D data. In contrast to volumetric approaches, our method…
We conservatively extend classical elementary differential calculus to the Cartesian closed category of convergence spaces. By specializing results about the convergence space representation of directed graphs, we use Cayley graphs to…
Understanding how the adult human brain learns novel categories is an important problem in neuroscience. Drift-diffusion models are popular in such contexts for their ability to mimic the underlying neural mechanisms. One such model for…