Related papers: Reverse Tangent Categories
This paper provides a bundle perspective to contextuality by introducing new categories of contextuality scenarios based on bundles of simplicial complexes and simplicial sets. The former approach generalizes earlier work on the…
We construct a topological space to study contextuality in quantum mechanics. The resulting space is a classifying space in the sense of algebraic topology. Cohomological invariants of our space correspond to physical quantities relevant to…
This paper studies the homotopy theory of parameterized spectrum objects in a model category from a global point of view. More precisely, for a model category $\mathcal{M}$ satisfying suitable conditions, we construct a relative model…
We develop a theory of descent and forms of tensor categories over arbitrary fields. We describe the general scheme of classification of such forms using algebraic and homotopical language, and give examples of explicit classification of…
Machine learning can greatly benefit from providing learning algorithms with pairs of contrastive training examples -- typically pairs of instances that differ only slightly, yet have different class labels. Intuitively, the difference in…
In this note, we describe the backward shift invariant subspaces for a large class of reproducing kernel Hilbert spaces. This class includes in particular de Branges-Rovnyak spaces (the non-extreme case) and the range space of co-analytic…
Deep neural networks (DNNs) have shown remarkable performance improvements on vision-related tasks such as object detection or image segmentation. Despite their success, they generally lack the understanding of 3D objects which form the…
We introduce a new technique for gradient normalization during neural network training. The gradients are rescaled during the backward pass using normalization layers introduced at certain points within the network architecture. These…
Tangent categories were introduced by Rosicky as a categorical setting for differential structures in algebra and geometry; in recent work of Cockett, Crutwell and others, they have also been applied to the study of differential structure…
Fractional derivatives are a well-studied generalization of integer order derivatives. Naturally, for optimization, it is of interest to understand the convergence properties of gradient descent using fractional derivatives. Convergence…
A stratified space is a kind of topological space together with a partition into smooth manifolds. These kinds of spaces naturally arise in the study of singular algebraic varieties, symplectic reduction, and differentiable stacks. In this…
Differential categories provide an axiomatization of the basics of differentiation and categorical models of differential linear logic. As differentiation is an important tool throughout quantum mechanics and quantum information, it makes…
This paper studies interpretability of convolutional networks by means of saliency maps. Most approaches based on Class Activation Maps (CAM) combine information from fully connected layers and gradient through variants of backpropagation.…
In this work, we investigated the application of score-based gradient learning in discriminative and generative classification settings. Score function can be used to characterize data distribution as an alternative to density. It can be…
Neural fields offer continuous, learnable representations that extend beyond traditional discrete formats in visual computing. We study the problem of learning neural representations of repeated antiderivatives directly from a function, a…
Non-Euclidean constraints are inherent in many kinds of data in computer vision and machine learning, typically as a result of specific invariance requirements that need to be respected during high-level inference. Often, these geometric…
Although multi-task learning (MTL) has been a preferred approach and successfully applied in many real-world scenarios, MTL models are not guaranteed to outperform single-task models on all tasks mainly due to the negative effects of…
We study generalized regular bent functions using a representation by bent rectangles, that is, special matrices with restrictions on rows and columns. We describe affine transformations of bent rectangles, propose new biaffine and bilinear…
We introduce an alternative formalization of curved spaces in which the concept of a pointwise affine space, as defined here, replaces that of a manifold. New or modified definitions of familiar notions from differential geometry such as…
A common belief in high-dimensional data analysis is that data are concentrated on a low-dimensional manifold. This motivates simultaneous dimension reduction and regression on manifolds. We provide an algorithm for learning gradients on…