This is Part II of the two-part comprehensive survey devoted to a computing framework most commonly known under the names Hyperdimensional Computing and Vector Symbolic Architectures (HDC/VSA). Both ...names refer to a family of computational models that use high-dimensional distributed representations and rely on the algebraic properties of their key operations to incorporate the advantages of structured symbolic representations and vector distributed representations. Holographic Reduced Representations 321, 326 is an influential HDC/VSA model that is well known in the machine learning domain and often used to refer to the whole family. However, for the sake of consistency, we use HDC/VSA to refer to the field.Part I of this survey 222 covered foundational aspects of the field, such as the historical context leading to the development of HDC/VSA, key elements of any HDC/VSA model, known HDC/VSA models, and the transformation of input data of various types into high-dimensional vectors suitable for HDC/VSA. This second part surveys existing applications, the role of HDC/VSA in cognitive computing and architectures, as well as directions for future work. Most of the applications lie within the Machine Learning/Artificial Intelligence domain; however, we also cover other applications to provide a complete picture. The survey is written to be useful for both newcomers and practitioners.
Vorgestellt wird eine weitreichende Analogie als hilfreiche Verknüpfung von makroskopischer und mathematisch‐symbolischer Betrachtungsebene. Die modellhafte Darstellung der Bälleschlacht im ...Kinderzimmer ist mehrfach erfolgreich in Unterrichtsreihen zur Reaktionsgeschwindigkeit sowie zur Einstellung, Störung und Veränderung von Gleichgewichten eingesetzt worden, um den Lernenden ein vernetztes Verständnis über alle drei Betrachtungsebenen nach Johnstone zu ermöglichen. Gerne möchten wir eine Diskussion und Weiterentwicklung anregen und stellen alle Materialien dazu unter CC‐BY‐SA 4.0 zur Verfügung.
This two-part comprehensive survey is devoted to a computing framework most commonly known under the names Hyperdimensional Computing and Vector Symbolic Architectures (HDC/VSA). Both names refer to ...a family of computational models that use high-dimensional distributed representations and rely on the algebraic properties of their key operations to incorporate the advantages of structured symbolic representations and distributed vector representations. Notable models in the HDC/VSA family are Tensor Product Representations, Holographic Reduced Representations, Multiply-Add-Permute, Binary Spatter Codes, and Sparse Binary Distributed Representations but there are other models too. HDC/VSA is a highly interdisciplinary field with connections to computer science, electrical engineering, artificial intelligence, mathematics, and cognitive science. This fact makes it challenging to create a thorough overview of the field. However, due to a surge of new researchers joining the field in recent years, the necessity for a comprehensive survey of the field has become extremely important. Therefore, amongst other aspects of the field, this Part I surveys important aspects such as: known computational models of HDC/VSA and transformations of various input data types to high-dimensional distributed representations. Part II of this survey 84 is devoted to applications, cognitive computing and architectures, as well as directions for future work. The survey is written to be useful for both newcomers and practitioners.
A MINIMAL CONGRUENCE LATTICE REPRESENTATION FOR BUNN, ROGER; GROW, DAVID; INSALL, MATT ...
Journal of the Australian Mathematical Society (2001),
06/2020, Letnik:
108, Številka:
3
Journal Article
Recenzirano
Let
$p$
be an odd prime. The unary algebra consisting of the dihedral group of order
$2p$
, acting on itself by left translation, is a minimal congruence lattice representation of
$\mathbb{M}_{p+1}$
....
We determine the irreducible 2-modular representations of the group G=GLn+1(2) in which a Singer cycle has eigenvalue 1, and show that in these representations every element g∈G has eigenvalue 1.
Since Otto Frank first introduced the Windkessel (0D) model in 1899 to reproduce the arterial network, various versions were constructed which differ through their number of elements and their ...disposal. The purpose of this paper is to couple the left heart model given by M. Danielsen and J.T. Ottesen to a classic three-element 0D representation of the arterial network and compare the results with the output of a 13-elements arterial model coupled with the heart. This is done in order to proof that no great benefit is gained when increasing the number of elements of the Windkessel model if the input satisfies normal physiological conditions. After confirming that the model works properly, a simulation is performed with parameters specific for a hypertensive person. The output is assessed against results specific for a normal person and the differences are further analysed.
A positive representation for a set of complex densities is constructed. In particular, complex measures on a direct product of
U
(1) groups are studied. After identifying general conditions which ...such representations should satisfy, several concrete realizations are proposed. Their utility is illustrated in few concrete examples representing problems in abelian lattice gauge theories.
We investigate possible renormalization-group fixed points at nonzero coupling in ϕ3 theories in six spacetime dimensions, using beta functions calculated to the four-loop level. We analyze three ...theories of this type, with (a) a one-component scalar, (b) a scalar transforming as the fundamental representation of a global SU(N) symmetry group, and (c) a scalar transforming as a bi-adjoint representation of a global SU(N) ⊗ SU(N) symmetry. We do not find robust evidence for such fixed points in theories (a) or (b). Theory (c) has the special feature that the one-loop term in the beta function is zero; implications of this are discussed.
PDF
