Related papers: Flabby and injective objects in toposes
Object recognition for the most part has been approached as a one-hot problem that treats classes to be discrete and unrelated. Each image region has to be assigned to one member of a set of objects, including a background class,…
We introduce an original notion of extra-fine sheaf on a topological space, and a variant (hyper-extra-fine) for which \v{C}ech cohomology in strictly positive degree vanishes. We provide a characterization of such sheaves when the…
We present a way of constructing a Quillen model structure on a full subcategory of an elementary topos, starting with an interval object with connections and a certain dominance. The advantage of this method is that it does not require the…
This paper introduces self-taught object localization, a novel approach that leverages deep convolutional networks trained for whole-image recognition to localize objects in images without additional human supervision, i.e., without using…
We give characterizations, for various fragments of geometric logic, of the class of theories classified by a locally connected (resp. connected and locally connected, atomic, compact, presheaf) topos, and exploit the existence of multiple…
Sheaves are objects of a local nature: a global section is determined by how it looks locally. Hence, a sheaf cannot describe mathematical structures which contain global or nonlocal geometric information. To fill this gap, we introduce the…
We develop a homotopy theory of categories enriched in a monoidal model category V. In particular, we deal with homotopy weighted limits and colimits, and homotopy local presentability. The main result, which was known for…
Objects we interact with and manipulate often share similar parts, such as handles, that allow us to transfer our actions flexibly due to their shared functionality. This work addresses the problem of transferring a grasp experience or a…
The goal of this paper is to put the theory of approximate fibrations into the framework of higher topos theory. We define the notion of an approximate fibration for a general geometric morphism of $\infty$-topoi, give several…
The isometry class of the intersection form of a compact complex surface can be easily determined from complex-analytic invariants. For projective surfaces the primitive lattice is another naturally occurring lattice. The goal of this note…
Learning 3D shape representation with dense correspondence for deformable objects is a fundamental problem in computer vision. Existing approaches often need additional annotations of specific semantic domain, e.g., skeleton poses for human…
Interactive exploration of the unknown physical properties of objects such as stiffness, mass, center of mass, friction coefficient, and shape is crucial for autonomous robotic systems operating continuously in unstructured environments.…
We study the problem of concept induction in visual reasoning, i.e., identifying concepts and their hierarchical relationships from question-answer pairs associated with images; and achieve an interpretable model via working on the induced…
We describe what it means for an algebra to be internally d-Calabi-Yau with respect to an idempotent. This definition abstracts properties of endomorphism algebras of (d-1)-cluster-tilting objects in certain stably (d-1)-Calabi-Yau…
Learning how to interact with objects is an important step towards embodied visual intelligence, but existing techniques suffer from heavy supervision or sensing requirements. We propose an approach to learn human-object interaction…
The human visual system processes images with varied degrees of resolution, with the fovea, a small portion of the retina, capturing the highest acuity region, which gradually declines toward the field of view's periphery. However, the…
Common-sense physical reasoning in the real world requires learning about the interactions of objects and their dynamics. The notion of an abstract object, however, encompasses a wide variety of physical objects that differ greatly in terms…
We establish how a higher local field can be described as a locally convex vector space once an embedding of a local field into it has been fixed. This extends previous results that had been obtained in the two-dimensional case. In…
We introduce a generalized notion of inference system to support more flexible interpretations of recursive definitions. Besides axioms and inference rules with the usual meaning, we allow also coaxioms, which are, intuitively, axioms which…
This is an announcement of a long paper in progress. On a locally compact space, we introduce the stack of ind-sheaves (ind-objects of the category of sheaves with compact support) and construct the analogous of the usual six operations on…