502 research outputs found
Statistical Mechanics of Dictionary Learning
Finding a basis matrix (dictionary) by which objective signals are
represented sparsely is of major relevance in various scientific and
technological fields. We consider a problem to learn a dictionary from a set of
training signals. We employ techniques of statistical mechanics of disordered
systems to evaluate the size of the training set necessary to typically succeed
in the dictionary learning. The results indicate that the necessary size is
much smaller than previously estimated, which theoretically supports and/or
encourages the use of dictionary learning in practical situations.Comment: 6 pages, 4 figure
Statistical mechanics of typical set decoding
The performance of ``typical set (pairs) decoding'' for ensembles of
Gallager's linear code is investigated using statistical physics. In this
decoding, error happens when the information transmission is corrupted by an
untypical noise or two or more typical sequences satisfy the parity check
equation provided by the received codeword for which a typical noise is added.
We show that the average error rate for the latter case over a given code
ensemble can be tightly evaluated using the replica method, including the
sensitivity to the message length. Our approach generally improves the existing
analysis known in information theory community, which was reintroduced by
MacKay (1999) and believed as most accurate to date.Comment: 7 page
Numerical Study of TAP Metastable States in 3-body Ising Spin Glasses
The distribution of solutions of the Thouless-Anderson-Palmer equation is
studied by extensive numerical experiments for fully connected 3-body
interaction Ising spin glass models in a level of annealed calculation. A
recent study predicted that when the equilibrium state of the system is
characterized by one-step replica symmetry breaking, the distribution is
described by a Becchi-Rouet-Stora-Tyutin (BRST) supersymmetric solution in the
relatively low free energy region, whereas the BRST supersymmetry is broken for
higher values of free energy (Crisanti et al., Phys. Rev. B 71 (2005) 094202).
Our experiments qualitatively reproduce the discriminative behavior of
macroscopic variables predicted by the theoretical assessment.Comment: 13 pages, 4 figure
Analysis of CDMA systems that are characterized by eigenvalue spectrum
An approach by which to analyze the performance of the code division multiple
access (CDMA) scheme, which is a core technology used in modern wireless
communication systems, is provided. The approach characterizes the objective
system by the eigenvalue spectrum of a cross-correlation matrix composed of
signature sequences used in CDMA communication, which enables us to handle a
wider class of CDMA systems beyond the basic model reported by Tanaka. The
utility of the novel scheme is shown by analyzing a system in which the
generation of signature sequences is designed for enhancing the orthogonality.Comment: 7 pages, 2 figure
Parallel dynamics of continuous Hopfield model revisited
We have applied the generating functional analysis (GFA) to the continuous
Hopfield model. We have also confirmed that the GFA predictions in some typical
cases exhibit good consistency with computer simulation results. When a
retarded self-interaction term is omitted, the GFA result becomes identical to
that obtained using the statistical neurodynamics as well as the case of the
sequential binary Hopfield model.Comment: 4 pages, 2 figure
Analysis of common attacks in LDPCC-based public-key cryptosystems
We analyze the security and reliability of a recently proposed class of
public-key cryptosystems against attacks by unauthorized parties who have
acquired partial knowledge of one or more of the private key components and/or
of the plaintext. Phase diagrams are presented, showing critical partial
knowledge levels required for unauthorized decryptionComment: 14 pages, 6 figure
Typical Performance of Gallager-type Error-Correcting Codes
The performance of Gallager's error-correcting code is investigated via
methods of statistical physics. In this approach, the transmitted codeword
comprises products of the original message bits selected by two
randomly-constructed sparse matrices; the number of non-zero row/column
elements in these matrices constitutes a family of codes. We show that
Shannon's channel capacity is saturated for many of the codes while slightly
lower performance is obtained for others which may be of higher practical
relevance. Decoding aspects are considered by employing the TAP approach which
is identical to the commonly used belief-propagation-based decoding.Comment: 6 pages, latex, 1 figur
On-line learning of non-monotonic rules by simple perceptron
We study the generalization ability of a simple perceptron which learns
unlearnable rules. The rules are presented by a teacher perceptron with a
non-monotonic transfer function. The student is trained in the on-line mode.
The asymptotic behaviour of the generalization error is estimated under various
conditions. Several learning strategies are proposed and improved to obtain the
theoretical lower bound of the generalization error.Comment: LaTeX 20 pages using IOP LaTeX preprint style file, 14 figure
The Statistical Physics of Regular Low-Density Parity-Check Error-Correcting Codes
A variation of Gallager error-correcting codes is investigated using
statistical mechanics. In codes of this type, a given message is encoded into a
codeword which comprises Boolean sums of message bits selected by two randomly
constructed sparse matrices. The similarity of these codes to Ising spin
systems with random interaction makes it possible to assess their typical
performance by analytical methods developed in the study of disordered systems.
The typical case solutions obtained via the replica method are consistent with
those obtained in simulations using belief propagation (BP) decoding. We
discuss the practical implications of the results obtained and suggest a
computationally efficient construction for one of the more practical
configurations.Comment: 35 pages, 4 figure
Cryptographical Properties of Ising Spin Systems
The relation between Ising spin systems and public-key cryptography is
investigated using methods of statistical physics. The insight gained from the
analysis is used for devising a matrix-based cryptosystem whereby the
ciphertext comprises products of the original message bits; these are selected
by employing two predetermined randomly-constructed sparse matrices. The
ciphertext is decrypted using methods of belief-propagation. The analyzed
properties of the suggested cryptosystem show robustness against various
attacks and competitive performance to modern cyptographical methods.Comment: 4 pages, 2 figure
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