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Two-sample testing is a fundamental problem in statistics. Despite its long history, there has been renewed interest in this problem with the advent of high-dimensional and complex data. Specifically, in the machine learning literature,…
The duality between color and kinematics was originally observed for purely adjoint massless gauge theories, and later found to hold even after introducing massive fermionic and scalar matter in arbitrary gauge-group representations. Such a…
Graph-level contrastive learning, aiming to learn the representations for each graph by contrasting two augmented graphs, has attracted considerable attention. Previous studies usually simply assume that a graph and its augmented graph as a…
Global constraints proved themselves to be an efficient tool for modelling and solving large-scale real-life combinatorial problems. They encapsulate a set of binary constraints and using global reasoning about this set they filter the…
We introduce a new method for two-sample testing of high-dimensional linear regression coefficients without assuming that those coefficients are individually estimable. The procedure works by first projecting the matrices of covariates and…
The statistics of local measurements of joint quantum systems can sometimes be used to distinguish the spatiotemporal structure in which they were measured. We first prove that every bipartite separable density matrix is temporally…
The criteria for determining graph isomorphism are crucial for solving graph isomorphism problems. The necessary condition is that two isomorphic graphs possess invariants, but their function can only be used to filtrate and subdivide…
Bi-adjoint scalars are helpful in studying properties of color/kinematics duality and the double copy, which relates scattering amplitudes of gauge and gravity theories. Here we study bi-adjoint scalars from a worldline perspective. We show…
Graph Representation Learning (GRL) has emerged as a cornerstone technique for analysing complex, networked data across diverse domains, including biological systems, social networks, and data analysis. Traditional GRL methods often…
The quantum lens spaces form a natural and well-studied class of noncommutative spaces which can be subjected to classification using algebraic invariants by drawing on the fully developed classification theory of unital graph…
What can we say about the spectra of a collection of microscopic variables when only their coarse-grained sums are experimentally accessible? In this paper, using the tools and methodology from the study of quantum nonlocality, we develop a…
We propose a graded classification of the entire field of multivector physics, including all alternative points of view. The (often tacit) postulates of different types of formulations are contrasted, summarizing their consequences.…
The double-slit experiment has become a classic thought experiment, for its clarity in expressing the central puzzle of quantum mechanics -- wave-particle complementarity. Such wave-particle duality continues to be challenged and…
This paper investigates visual analogical reasoning in large multimodal models (LMMs) compared to human adults and children. A "visual analogy" is an abstract rule inferred from one image and applied to another. While benchmarks exist for…
We present a grapical way to describe invariants and covariants in the (4 dim) general relativity. This makes us free from the complexity of suffixes . Two new off-shell relations between (mass)$\ast\ast 6$\ invariants are obtained. These…
We consider the problem of distinguishing two vectors (visualized as images or barcodes) and learning if they are related to one another. For this, we develop a geometric quantum machine learning (GQML) approach with embedded symmetries…
Metaphoric glyphs enhance the readability and learnability of abstract glyphs used for the visualization of quantitative multidimensional data by building upon graphical entities that are intuitively related to the underlying problem…
This paper reviews recent results on hybrid inverse problems, which are also called coupled-physics inverse problems of multi-wave inverse problems. Inverse problems tend to be most useful in, e.g., medical and geophysical imaging, when…
To investigate the effect of a classical environment on a quantum mechanical system we consider two two-level atoms in a free radiation field in the presence of a screen. By assuming that the screen causes continuous ideal measurements on…
The diversity of patterns that emerge from complex systems motivates their use for scientific or artistic purposes. When exploring these systems, the challenges faced are the size of the parameter space and the strongly non-linear mapping…