Related papers: Projections of a learning space

It is well known that real points of the Study quadric (sliced along a 3-dimensional generator space) correspond to displacements of the Euclidean 3-space. But we still lack of a kinematic meaning for the points of the ambient 7-dimensional…

We consider graph drawing algorithms for learning spaces, a type of st-oriented partial cube derived from antimatroids and used to model states of knowledge of students. We show how to draw any st-planar learning space so all internal faces…

Predictive learning has emerged as a central paradigm for training models across diverse data domains and is increasingly viewed as a foundation for modern artificial intelligence. A common intuition for this success is that accurate…

We investigate an `assumption of projectivity' that is appropriate to the self-dual axiomatic formulation of three-dimensional projective space.

We present projective descriptions of classical spaces of functions and distributions. More precisely, we provide descriptions of these spaces by semi-norms which are defined by a combination of classical norms and multiplication or…

Unsupervised point cloud completion aims at estimating the corresponding complete point cloud of a partial point cloud in an unpaired manner. It is a crucial but challenging problem since there is no paired partial-complete supervision that…

The common-sense view of reality is expressed logically in Boolean subset logic (each element is either definitely in or not in a subset, i.e., either definitely has or does not have a property). But quantum mechanics does not agree with…

The quantum cohomology algebra of a projective manifold X is the cohomology H(X,Q) endowed with a different algebra structure, which takes into account the geometry of rational curves in X. We show that this algebra takes a remarkably…

Can simple algorithms with a good representation solve challenging reinforcement learning problems? In this work, we answer this question in the affirmative, where we take "simple learning algorithm" to be tabular Q-Learning, the "good…

It is known that the theory of any class of normed spaces over the reals that includes all spaces of a given dimension d > 1 is undecidable, and indeed, admits a relative interpretation of second-order arithmetic. The notion of a normed…

We generalize categories of spatial partitions in the sense of C\'ebron-Weber by introducing new base partitions. This allows us to construct additional examples of free orthogonal quantum groups but yields the same class of spatial…

This paper focuses on the relation between computational learning theory and resource-bounded dimension. We intend to establish close connections between the learnability/nonlearnability of a concept class and its corresponding size in…

Modern categorical logic as well as the Kripke and topological models of intuitionistic logic suggest that the interpretation of ordinary "propositional" logic should in general be the logic of subsets of a given universe set. Partitions on…

We study a cut-off function lemma in projective spaces. We believe that this is well-known. We provide the details of the computation for later uses.

In this paper we describe projective curves and surfaces such that almost all their hyperplane sections are projectively equivalent. Our description is complete for curves and close to being complete for smooth surfaces. In the appendix we…

What is a good vector representation of an object? We believe that it should be generative in 3D, in the sense that it can produce new 3D objects; as well as be predictable from 2D, in the sense that it can be perceived from 2D images. We…

Learning informative representations of data is one of the primary goals of deep learning, but there is still little understanding as to what representations a neural network actually learns. To better understand this, subspace match was…

Single-shot diffraction imaging of isolated nanosized particles has seen remarkable success in recent years, yielding in-situ measurements with ultra-high spatial and temporal resolution. The progress of high-repetition-rate sources for…

A plausible definition of "reasoning" could be "algebraically manipulating previously acquired knowledge in order to answer a new question". This definition covers first-order logical inference or probabilistic inference. It also includes…

We introduce the notion of an orthocomplemented subspace of a Hilbert space H, that is, a pair of orthogonal closed subspaces of H, as a two-dimensional counterpart to the one-dimensional notion of a closed subspace of H. Orthocomplemented…