11,672 research outputs found
Entanglement-guided architectures of machine learning by quantum tensor network
It is a fundamental, but still elusive question whether the schemes based on
quantum mechanics, in particular on quantum entanglement, can be used for
classical information processing and machine learning. Even partial answer to
this question would bring important insights to both fields of machine learning
and quantum mechanics. In this work, we implement simple numerical experiments,
related to pattern/images classification, in which we represent the classifiers
by many-qubit quantum states written in the matrix product states (MPS).
Classical machine learning algorithm is applied to these quantum states to
learn the classical data. We explicitly show how quantum entanglement (i.e.,
single-site and bipartite entanglement) can emerge in such represented images.
Entanglement characterizes here the importance of data, and such information
are practically used to guide the architecture of MPS, and improve the
efficiency. The number of needed qubits can be reduced to less than 1/10 of the
original number, which is within the access of the state-of-the-art quantum
computers. We expect such numerical experiments could open new paths in
charactering classical machine learning algorithms, and at the same time shed
lights on the generic quantum simulations/computations of machine learning
tasks.Comment: 10 pages, 5 figure
Maximum Entropy and Bayesian Data Analysis: Entropic Priors
The problem of assigning probability distributions which objectively reflect
the prior information available about experiments is one of the major stumbling
blocks in the use of Bayesian methods of data analysis. In this paper the
method of Maximum (relative) Entropy (ME) is used to translate the information
contained in the known form of the likelihood into a prior distribution for
Bayesian inference. The argument is inspired and guided by intuition gained
from the successful use of ME methods in statistical mechanics. For experiments
that cannot be repeated the resulting "entropic prior" is formally identical
with the Einstein fluctuation formula. For repeatable experiments, however, the
expected value of the entropy of the likelihood turns out to be relevant
information that must be included in the analysis. The important case of a
Gaussian likelihood is treated in detail.Comment: 23 pages, 2 figure
Anatomy of a Spin: The Information-Theoretic Structure of Classical Spin Systems
Collective organization in matter plays a significant role in its expressed
physical properties. Typically, it is detected via an order parameter,
appropriately defined for each given system's observed emergent patterns.
Recent developments in information theory, however, suggest quantifying
collective organization in a system- and phenomenon-agnostic way: decompose the
system's thermodynamic entropy density into a localized entropy, that solely
contained in the dynamics at a single location, and a bound entropy, that
stored in space as domains, clusters, excitations, or other emergent
structures. We compute this decomposition and related quantities explicitly for
the nearest-neighbor Ising model on the 1D chain, the Bethe lattice with
coordination number k=3, and the 2D square lattice, illustrating its generality
and the functional insights it gives near and away from phase transitions. In
particular, we consider the roles that different spin motifs play (in cluster
bulk, cluster edges, and the like) and how these affect the dependencies
between spins.Comment: 12 pages, 8 figures;
http://csc.ucdavis.edu/~cmg/compmech/pubs/ising_bmu.ht
Realism about the Wave Function
A century after the discovery of quantum mechanics, the meaning of quantum
mechanics still remains elusive. This is largely due to the puzzling nature of
the wave function, the central object in quantum mechanics. If we are realists
about quantum mechanics, how should we understand the wave function? What does
it represent? What is its physical meaning? Answering these questions would
improve our understanding of what it means to be a realist about quantum
mechanics. In this survey article, I review and compare several realist
interpretations of the wave function. They fall into three categories:
ontological interpretations, nomological interpretations, and the \emph{sui
generis} interpretation. For simplicity, I will focus on non-relativistic
quantum mechanics.Comment: Penultimate version for Philosophy Compas
Editorial Comment on the Special Issue of "Information in Dynamical Systems and Complex Systems"
This special issue collects contributions from the participants of the
"Information in Dynamical Systems and Complex Systems" workshop, which cover a
wide range of important problems and new approaches that lie in the
intersection of information theory and dynamical systems. The contributions
include theoretical characterization and understanding of the different types
of information flow and causality in general stochastic processes, inference
and identification of coupling structure and parameters of system dynamics,
rigorous coarse-grain modeling of network dynamical systems, and exact
statistical testing of fundamental information-theoretic quantities such as the
mutual information. The collective efforts reported herein reflect a modern
perspective of the intimate connection between dynamical systems and
information flow, leading to the promise of better understanding and modeling
of natural complex systems and better/optimal design of engineering systems
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