Related papers: Flabby and injective objects in toposes
We define a new geometric object--the stack of local systems with restricted variation. We formulate a version of the categorical geometric Langlands conjecture that makes sense for any constructible sheaf theory (such as l-adic sheaves).…
Deep-learning and large scale language-image training have produced image object detectors that generalise well to diverse environments and semantic classes. However, single-image object detectors trained on internet data are not optimally…
This is the fourth in a series of papers extending Martin-L\"of's meaning explanation of dependent type theory to higher-dimensional types. In this installment, we show how to define cubical type systems supporting a general schema of…
We first elaborate on the theory of relative internality in stable theories, focusing on the notion of uniform relative internality (called collapse of the groupoid in an earlier work of the second author), and relating it to orthogonality,…
In this short note we would like to show how it is possible to use techniques introduced in the theory of local dynamics of holomorphic germs tangent to the identity to study global meromorphic self-maps of the complex projective space. In…
We introduce algorithms to visualize feature spaces used by object detectors. The tools in this paper allow a human to put on `HOG goggles' and perceive the visual world as a HOG based object detector sees it. We found that these…
We prove that $F$-injectivity localizes, descends under faithfully flat homomorphisms, and ascends under flat homomorphisms with Cohen-Macaulay and geometrically $F$-injective fibers, all for arbitrary Noetherian rings of prime…
We define the notion of mixed Frobenius structure which is a generalization of the structure of a Frobenius manifold. We construct a mixed Frobenius structure on the cohomology of weak Fano toric surfaces and that of the three dimensional…
This paper addresses the challenge of learning a local visual pattern of an object from one image, and generating images depicting objects with that pattern. Learning a localized concept and placing it on an object in a target image is a…
This paper presents a Fuzzy Cognitive Map model to quantify implicit bias in structured datasets where features can be numeric or discrete. In our proposal, problem features are mapped to neural concepts that are initially activated by…
Implicit functions provide a fundamental basis to model 3D objects, no matter they are rigid or deformable, in computer graphics and geometric modeling. This paper introduces a new constructive scheme of implicitly-defined 3D objects based…
The implicit convex feasibility problem attempts to find a point in the intersection of a finite family of convex sets, some of which are not explicitly determined but may vary. We develop simultaneous and sequential projection methods…
An image is not just a collection of objects, but rather a graph where each object is related to other objects through spatial and semantic relations. Using relational reasoning modules, such as the non-local module \cite{wang2017non}, can…
We develop a local-to-global formalism for constructing Calabi-Yau structures for global sections of constructible sheaves or cosheaves of categories. The required data - an isomorphism of the sheafified Hochschild homology with the…
While previous researches in eye fixation prediction typically rely on integrating low-level features (e.g. color, edge) to form a saliency map, recently it has been found that the structural organization of these features into a…
In this paper, we study superficial elements of an ideal with respect to a module from a geometrical point of view, using blowing-ups. The notion of weak transform is particularly relevant to this study. We use this viewpoint to get a…
We develop a general theory of extensions of flat functors along geometric morphisms of toposes, and apply it to the study of the class of theories whose classifying topos is equivalent to a presheaf topos. As a result, we obtain a…
While human infants exhibit knowledge about object permanence from two months of age onwards, deep-learning approaches still largely fail to recognize objects' continued existence. We introduce a slot-based autoregressive deep learning…
The purpose of this short article is to prove some potential estimates that naturally arise in the study of subelliptic Sobolev inequalites for functions. This will allow us to prove a local subelliptic Sobolev inequality with the optimal…
The notion of an existentially closed model is generalised to a property of geometric morphisms between toposes. We show that important properties of existentially closed models extend to existentially closed geometric morphisms, such as…