相关论文: On a realization of motion and similarity group eq…
We initiate the study of computable presentations of real and complex C*-algebras under the program of effective metric structure theory. With the group situation as a model, we develop corresponding notions of recursive presentations and…
Performance disparities of image recognition across demographic groups are known to exist in deep learning-based models, due to imbalanced group representations or spurious correlation between group and target labels. Previous work has…
We show that the theory of the partial order of computably enumerable equivalence relations (ceers) under computable reduction is 1-equivalent to true arithmetic. We show the same result for the structure comprised of the dark ceers and the…
We study unit disk visibility graphs, where the visibility relation between a pair of geometric entities is defined by not only obstacles, but also the distance between them. That is, two entities are not mutually visible if they are too…
The quantum equivalence principle says that, for any given point, it is possible to find a quantum coordinate system with respect to which we have definite causal structure in the vicinity of that point. It is conjectured that this…
Distance function is a main metrics of measuring the affinity between two data points in machine learning. Extant distance functions often provide unreachable distance values in real applications. This can lead to incorrect measure of the…
We address goal-based imitation learning, where the aim is to output the symbolic goal from a third-person video demonstration. This enables the robot to plan for execution and reproduce the same goal in a completely different environment.…
Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. We propose the systematic use of symmetric spaces in representation learning,…
We address several problems concerning the geometry of the space of Hermitian operators on a finite-dimensional Hilbert space, in particular the geometry of the space of density states and canonical group actions on it. For quantum…
By considering appropriate finite covering spaces of closed non-orientable surfaces, we construct linear representations of their mapping class group which have finite index image in certain big arithmetic groups.
As the request for deep learning solutions increases, the need for explainability is even more fundamental. In this setting, particular attention has been given to visualization techniques, that try to attribute the right relevance to each…
In this paper we introduce a homotopy theoretic technique for proving that the $K$-theoretic assembly map is an equivalence. It is an extension of the methods used to prove split injectivity of the assembly and applies to any geometrically…
This paper is about similarity between objects that can be represented as points in metric measure spaces. A metric measure space is a metric space that is also equipped with a measure. For example, a network with distances between its…
The class of metrizable spaces $M$ with the following approximation property is introduced and investigated: $M\in AP(n,0)$ if for every $\e>0$ and a map $g\colon\I^n\to M$ there exists a 0-dimensional map $g'\colon\I^n\to M$ which is…
We prove the existence of a quantum isometry groups for new classes of metric spaces: (i) geodesic metrics for compact connected Riemannian manifolds (possibly with boundary) and (ii) metric spaces admitting a uniformly distributed…
In this paper we introduce a new class of metric actions on separable (not necessarily connected) metric spaces called "Cauchy-indivisible" actions. This new class coincides with that of proper actions on locally compact metric spaces and,…
We study the problem of supervised learning a metric space under discriminative constraints. Given a universe $X$ and sets ${\cal S}, {\cal D}\subset {X \choose 2}$ of similar and dissimilar pairs, we seek to find a mapping $f:X\to Y$, into…
In this paper we study the existence and uniqueness of fixed points of a class of mappings defined on complete, (sequentially compact) cone metric spaces, without continuity conditions and depending on another function.
Quantum computers represent a new computational paradigm with steadily improving hardware capabilities. In this article, we present the first study exploring how current quantum computers can be used to classify different neutrino event…
In the field of object classification, identification based on object variations is a challenge in itself. Variations include shape, size, color, and texture, these can cause problems in recognizing and distinguishing objects accurately.…