Related papers: Projections of a learning space

Algebraic operations are understood as topologiztion of algebra. They become an example of simplest convergence space. In our article the convergence is a arbitrary multivalued appointment. The continuity of some mapping between two…

Quantum deep learning (QDL) explores the use of both quantum and quantum-inspired resources to determine when deep learning's core capabilities, such as expressivity, generalization, and scalability, can be enhanced based on specific…

Explanations in Computer Vision are often desired, but most Deep Neural Networks can only provide saliency maps with questionable faithfulness. Self-Explaining Neural Networks (SENN) extract interpretable concepts with fidelity, diversity,…

A quantum physical projector is proposed for generally covariant theories which are derivable from a Lagrangian. The projector is the quantum analogue of the integral over the generators of finite one-parameter subgroups of the gauge…

A basis of the ideal of the complement of a linear subspace in a projective space over a finite field is given. As an application, the second largest number of points of plane curves of degree $d$ over the finite field of $q$ elements is…

We study the GIT-quotient of the Cartesian power of projective space modulo the projective orthogonal group. A classical isomorphism of this group with the Inversive group of birational transformations of the projective space of one…

Interpretable rationales for model predictions play a critical role in practical applications. In this study, we develop models possessing interpretable inference process for structured prediction. Specifically, we present a method of…

Zero-shot learning (ZSL) aims to recognize unseen object classes without any training samples, which can be regarded as a form of transfer learning from seen classes to unseen ones. This is made possible by learning a projection between a…

For a given poset, we consider its representations by systems of subspaces of a unitary space ordered by inclusion. We classify such systems for all posets for which an explicit classification is possible.

Most machine learning theory and practice is concerned with learning a single task. In this thesis it is argued that in general there is insufficient information in a single task for a learner to generalise well and that what is required…

We propose a constructive and dynamical redefinition of spatial structure, grounded in the interplay between mechanical evolution and observational acts. Rather than presupposing space as a static background, we interpret space as an…

Partitionings (or segmentations) divide a given domain into disjoint connected regions whose union forms again the entire domain. Multi-dimensional partitionings occur, for example, when analyzing parameter spaces of simulation models,…

In this paper, we consider a model of classical linear logic based on coherence spaces endowed with a notion of totality. If we restrict ourselves to total objects, each coherence space can be regarded as a uniform space and each linear map…

We study the projections in vector spaces over finite fields. We prove finite fields analogues of the bounds on the dimensions of the exceptional sets for Euclidean projection mapping. We provide examples which do not have exceptional…

Recent advances in big/foundation models reveal a promising path for deep learning, where the roadmap steadily moves from big data to big models to (the newly-introduced) big learning. Specifically, the big learning exhaustively exploits…

Deep reinforcement learning techniques have demonstrated superior performance in a wide variety of environments. As improvements in training algorithms continue at a brisk pace, theoretical or empirical studies on understanding what these…

In a recent article, Alon, Hanneke, Holzman, and Moran (FOCS '21) introduced a unifying framework to study the learnability of classes of partial concepts. One of the central questions studied in their work is whether the learnability of a…

A projection space is a collection of spaces interrelated by the combinatorics of projection onto tensor factors in a symmetric monoidal background category. Examples include classical configuration spaces, orbit configuration spaces, the…

Here we classify all topological spaces where all bijections to itself are homeomorphisms. As a consequence, we also classify all topological spaces where all maps to itself are continuous. Analogously, we classify all measurable spaces…

Using the concept of projective systems for linear codes and elementary linear algebra, we show that projective $[n,k]_q$ codes form a connected subgraph in the Grassmann graph consisting of $k$-dimensional subspaces of an $n$-dimensional…