22,006 research outputs found
The Knowledge: Its Presentation and Role in Recognition Systems
The concept of knowledge is the central one used when solving the various problems of data
mining and pattern recognition in finite spaces of Boolean or multi-valued attributes. A special form of
knowledge representation, called implicative regularities, is proposed for applying in two powerful tools of
modern logic: the inductive inference and the deductive inference. The first one is used for extracting the
knowledge from the data. The second is applied when the knowledge is used for calculation of the goal
attribute values. A set of efficient algorithms was developed for that, dealing with Boolean functions and finite
predicates represented by logical vectors and matrices
Contrastive Hebbian Learning with Random Feedback Weights
Neural networks are commonly trained to make predictions through learning
algorithms. Contrastive Hebbian learning, which is a powerful rule inspired by
gradient backpropagation, is based on Hebb's rule and the contrastive
divergence algorithm. It operates in two phases, the forward (or free) phase,
where the data are fed to the network, and a backward (or clamped) phase, where
the target signals are clamped to the output layer of the network and the
feedback signals are transformed through the transpose synaptic weight
matrices. This implies symmetries at the synaptic level, for which there is no
evidence in the brain. In this work, we propose a new variant of the algorithm,
called random contrastive Hebbian learning, which does not rely on any synaptic
weights symmetries. Instead, it uses random matrices to transform the feedback
signals during the clamped phase, and the neural dynamics are described by
first order non-linear differential equations. The algorithm is experimentally
verified by solving a Boolean logic task, classification tasks (handwritten
digits and letters), and an autoencoding task. This article also shows how the
parameters affect learning, especially the random matrices. We use the
pseudospectra analysis to investigate further how random matrices impact the
learning process. Finally, we discuss the biological plausibility of the
proposed algorithm, and how it can give rise to better computational models for
learning
Quantum theory as a relevant framework for the statement of probabilistic and many-valued logic
Based on ideas of quantum theory of open systems we propose the consistent
approach to the formulation of logic of plausible propositions. To this end we
associate with every plausible proposition diagonal matrix of its likelihood
and examine it as density matrix of relevant quantum system. We are showing
that all logical connectives between plausible propositions can be represented
as special positive valued transformations of these matrices. We demonstrate
also the above transformations can be realized in relevant composite quantum
systems by quantum engineering methods. The approach proposed allows one not
only to reproduce and generalize results of well-known logical systems
(Boolean, Lukasiewicz and so on) but also to classify and analyze from unified
point of view various actual problems in psychophysics and social sciences.Comment: 7 page
DDMF: An Efficient Decision Diagram Structure for Design Verification of Quantum Circuits under a Practical Restriction
Recently much attention has been paid to quantum circuit design to prepare
for the future "quantum computation era." Like the conventional logic
synthesis, it should be important to verify and analyze the functionalities of
generated quantum circuits. For that purpose, we propose an efficient
verification method for quantum circuits under a practical restriction. Thanks
to the restriction, we can introduce an efficient verification scheme based on
decision diagrams called
Decision Diagrams for Matrix Functions (DDMFs). Then, we show analytically
the advantages of our approach based on DDMFs over the previous verification
techniques. In order to introduce DDMFs, we also introduce new concepts,
quantum functions and matrix functions, which may also be interesting and
useful on their own for designing quantum circuits.Comment: 15 pages, 14 figures, to appear IEICE Trans. Fundamentals, Vol.
E91-A, No.1
Swap structures semantics for Ivlev-like modal logics
In 1988, J. Ivlev proposed some (non-normal) modal systems which are semantically characterized by four-valued non-deterministic matrices in the sense of A. Avron and I. Lev. Swap structures are multialgebras (a.k.a. hyperalgebras) of a special kind, which were introduced in 2016 by W. Carnielli and M. Coniglio in order to give a non-deterministic semantical account for several paraconsistent logics known as logics of formal inconsistency, which are not algebraizable by means of the standard techniques. Each swap structure induces naturally a non-deterministic matrix. The aim of this paper is to obtain a swap structures semantics for some Ivlev-like modal systems proposed in 2015 by M. Coniglio, L. Fariñas del Cerro and N. Peron. Completeness results will be stated by means of the notion of Lindenbaum–Tarski swap structures, which constitute a natural generalization to multialgebras of the concept of Lindenbaum–Tarski algebras
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