Related papers: Projective characterization of higher-order quantu…
Dual to Koldobsky's notion of j-intersection bodies, the class of j-projection bodies is introduced, generalizing Minkowski's classical notion of projection bodies of convex bodies. A Fourier analytic characterization of j-projection bodies…
Quantum machine learning (QML) has attracted growing interest with the rapid parallel advances in large-scale classical machine learning and quantum technologies. Similar to classical machine learning, QML models also face challenges…
We characterize the class of quantum measurements that matches the applications of quantum theory to cognition (and decision making) - quantum-like modeling. Projective measurements describe the canonical measurements of the basic…
Transformers have become methods of choice in many applications thanks to their ability to represent complex interactions between elements. However, extending the Transformer architecture to non-sequential data such as molecules and…
Many real-world phenomena are naturally modeled by graphs and networks. However, classical graph models are often limited to pairwise interactions and may not adequately capture the richer structures that arise in practice. Higher-order…
A semi-projective representation is a homomorphism of a finite group into the group of semi-projective transformations of a finite dimensional vector space over a field. Schur's concept of a representation group for projective…
Bidirectional devices are devices for which the roles of the input and output ports can be exchanged. Mathematically, these devices are described by bistochastic quantum channels, namely completely positive linear maps that are both…
Feature attributions are post-training analysis methods that assess how various input features of a machine learning model contribute to an output prediction. Their interpretation is straightforward when features act independently, but it…
Semantic role labeling is primarily used to identify predicates, arguments, and their semantic relationships. Due to the limitations of modeling methods and the conditions of pre-identified predicates, previous work has focused on the…
The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schr\"odinger equation allows the derivation of an alternative…
This paper reports a novel method for supervised machine learning based on the mathematical formalism that supports quantum mechanics. The method uses projective quantum measurement as a way of building a prediction function. Specifically,…
P-algebras are a non-commutative, non-associative generalization of Boolean algebras that are for quantum logic what Boolean algebras are for classical logic. P-algebras have type <X, 0, ', .> where 0 is a constant, ' is unary and . is…
Transformer networks have revolutionized NLP representation learning since they were introduced. Though a great effort has been made to explain the representation in transformers, it is widely recognized that our understanding is not…
In a recent paper the notion of {\em quantum perceptron} has been introduced in connection with projection operators. Here we extend this idea, using these kind of operators to produce a {\em clustering machine}, i.e. a framework which…
Contrastive Learning (CL) has emerged as a powerful method for training feature extraction models using unlabeled data. Recent studies suggest that incorporating a linear projection head post-backbone significantly enhances model…
There are two approaches to projective representation theory of symmetric and alternating groups, which are powerful enough to work for modular representations. One is based on Sergeev duality, which connects projective representation…
We discuss the time-convolutionless (TCL) projection operator approach to transport in closed quantum systems. The projection onto local densities of quantities such as energy, magnetization, particle number, etc. yields the reduced…
We introduce so-called super/sub-martingale projections as a family of endomorphisms defined on unions of Polish spaces. Such projections allow us to identify martingales as collections of transformations that relate path-valued random…
Parameterization extends higher-order processes with the capability of abstraction (akin to that in lambda-calculus), and is known to be able to enhance the expressiveness. This paper focuses on the parameterization of names, i.e. a…
We provide a new characterisation of quantum supermaps in terms of an axiom that refers only to sequential and parallel composition. Consequently, we generalize quantum supermaps to arbitrary monoidal categories and operational…