相关论文: Projections of a learning space

We study properties of a category after quotienting out a suitable chosen group of isomorphisms on each object. Coproducts in the original category are described in its quotient by our new weaker notion of a 'phased coproduct'. We examine…

We show that any translate of a model set is a model set in some modified cut-and-project scheme. Restricting to Euclidean direct space, we show that any translate of an inter model set is a model set in some modified cut-and-project scheme…

The composition of objects and their parts, along with object-object positional relationships, provides a rich source of information for representation learning. Hence, spatial-aware pretext tasks have been actively explored in…

We offer an axiomatic presentation of three-dimensional projective space that adopts the line as its fundamental element and renders automatic the principle of duality.

In this paper, we propose Proq, a runtime assertion scheme for testing and debugging quantum programs on a quantum computer. The predicates in Proq are represented by projections (or equivalently, closed subspaces of the state space),…

Deep learning has recently been shown to be instrumental in the problem of domain adaptation, where the goal is to learn a model on a target domain using a similar --but not identical-- source domain. The rationale for coupling both…

Zero-shot Learning (ZSL) is a transfer learning technique which aims at transferring knowledge from seen classes to unseen classes. This knowledge transfer is possible because of underlying semantic space which is common to seen and unseen…

It is well known that perspective alignment plays a major role in the planning and interpretation of spatial language. In order to understand the role of perspective alignment and the cognitive processes involved, we have made precise…

Zero-shot learning (ZSL) aims to transfer knowledge from seen classes to unseen ones so that the latter can be recognised without any training samples. This is made possible by learning a projection function between a feature space and a…

Education is a goal-oriented field. But if we want to treat education scientifically so we can accumulate, evaluate, and refine what we learn, then we must develop a theoretical framework that is strongly rooted in objective observations…

We introduce CQnet, a neural network with origins in the CQ algorithm for solving convex split-feasibility problems and forward-backward splitting. CQnet's trajectories are interpretable as particles that are tracking a changing constraint…

There is a type of distance-regular graph, said to be $Q$-polynomial. In this paper we investigate a generalized $Q$-polynomial property involving a graph that is not necessarily distance-regular. We give a detailed description of an…

We study in some detail the structure of the projective quadric Q' obtained by taking the quotient of the isotropic cone in a standard pseudo-Hermitian space H_{p,q} with respect to the positive real numbers R^+ and, further, by taking the…

The purpose of this paper is to present a fresh idea on how symbolic learning might be realized via analogical reasoning. For this, we introduce directed analogical proportions between logic programs of the form "$P$ transforms into $Q$ as…

We define a class of L-convex-concave subsets of $\Bbb{R}P^n$, where L is a projective subspace of dimension l in $\Bbb{R}P^n$. These are sets whose sections by any (l+1)-dimensional space L' containing L are convex and concavely depend on…

Stability issues with reinforcement learning methods persist. To better understand some of these stability and convergence issues involving deep reinforcement learning methods, we examine a simple linear quadratic example. We interpret the…

Q-learning can be described as an all-purpose automaton that provides estimates (Q-values) of the continuation values associated with each available action and follows the naive policy of almost always choosing the action with highest…

Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…

We study the set of localizations of an integral domain from a topological point of view, showing that it is always a spectral space and characterizing when it is a proconstructible subspace of the space of all overrings. We then study the…

We study whether inputs from the same class can be connected by a continuous path, in original or latent representation space, such that all points on the path are mapped by the neural network model to the same class. Understanding how the…