Related papers: On Machine Learning Knowledge Representation In Th…
Metrics and pseudometrics are defined on the group of unitary operators in a Hilbert space. Several explicit formulas are derived. A special feature of the work is investigation of pseudometrics in unitary groups. The rich classes of…
We demonstrate how Quantum Cognition Machine Learning (QCML) encodes data as quantum geometry. In QCML, features of the data are represented by learned Hermitian matrices, and data points are mapped to states in Hilbert space. The quantum…
We derive the Hilbert space formalism of quantum mechanics from epistemic principles. A key assumption is that a physical theory that relies on entities or distinctions that are unknowable in principle gives rise to wrong predictions. An…
The power of big data and machine learning has been drastically demonstrated in many fields during the past twenty years which somehow leads to the vague even false understanding that the huge amount of precious human knowledge accumulated…
We show that the unitary operator on a separable Hilbert space is a parametrization of any conditional probability measure in a standard measure space. We propose unitary inference, a generalization of Bayesian inference. We study…
A non-associative algebra of observables cannot be represented as operators on a Hilbert space, but it may appear in certain physical situations. This article employs algebraic methods in order to derive uncertainty relations and…
In this paper, a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, is presented and the guidelines to how to extend…
Latent space models are widely used for analyzing high-dimensional discrete data matrices, such as patient-feature matrices in electronic health records (EHRs), by capturing complex dependence structures through low-dimensional embeddings.…
Interpreting the representation and generalization powers has been a long-standing issue in the field of machine learning (ML) and artificial intelligence. This work contributes to uncovering the emergence of universal scaling laws in…
Quantum machine learning (QML) is a discipline that seeks to transfer the advantages of quantum computing to data-driven tasks. However, many studies rely on toy datasets or heavy feature reduction, raising concerns about their scalability.…
Consider a Machine Learning Service Provider (MLSP) designed to rapidly create highly accurate learners for a never-ending stream of new tasks. The challenge is to produce task-specific learners that can be trained from few labeled samples,…
The construction of a class of unitary operators generating linear superpositions of generalized coherent states from the ground state of a quantum harmonic oscillator is reported. Such a construction, based on the properties of a new ad…
The way Quantum Mechanics (QM) is introduced to people used to Classical Mechanics (CM) is by a complete change of the general methodology) despite QM historically stemming from CM as a means to explain experimental results. Therefore, it…
The kernel trick in supervised learning signifies transformations of an inner product by a feature map, which then restructures training data in a larger Hilbert space according to an endowed inner product. A quantum feature map corresponds…
The mechanism of describing quantum states by standard probability (tomographic one) instead of wave function or density matrix is elucidated. Quantum tomography is formulated in an abstract Hilbert space framework, by means of the identity…
Quantum machine learning is an emerging field that combines machine learning with advances in quantum technologies. Many works have suggested great possibilities of using near-term quantum hardware in supervised learning. Motivated by these…
Pre-trained language representation models, such as BERT, capture a general language representation from large-scale corpora, but lack domain-specific knowledge. When reading a domain text, experts make inferences with relevant knowledge.…
Symbolic and logic computation systems ranging from computer algebra systems to theorem provers are finding their way into science, technology, mathematics and engineering. But such systems rely on explicitly or implicitly represented…
As ultracold atom experiments become highly controlled and scalable quantum simulators, they require sophisticated control over high-dimensional parameter spaces and generate increasingly complex measurement data that need to be analyzed…
We introduce a class of bipartite operators acting on $\mathcal{H} \otimes \mathcal{H}$ ($\mathcal{H}$ being an $n$-dimensional Hilbert space) defined by a set of $n$ Completely Different Permutations CDP. Bipartite operators are of…