4,325 research outputs found
Information Storage in the Stochastic Ising Model
Most information systems store data by modifying the local state of matter,
in the hope that atomic (or sub-atomic) local interactions would stabilize the
state for a sufficiently long time, thereby allowing later recovery. In this
work we initiate the study of information retention in locally-interacting
systems. The evolution in time of the interacting particles is modeled via the
stochastic Ising model (SIM). The initial spin configuration serves as
the user-controlled input. The output configuration is produced by
running steps of the Glauber chain. Our main goal is to evaluate the
information capacity when the time
scales with the size of the system . For the zero-temperature SIM on the
two-dimensional grid and free boundary conditions, it
is easy to show that for . In addition, we show
that on the order of bits can be stored for infinite time in striped
configurations. The achievability is optimal when and
is fixed.
One of the main results of this work is an achievability scheme that stores
more than bits (in orders of magnitude) for superlinear (in )
times. The analysis of the scheme decomposes the system into
independent Z-channels whose crossover probability is found via the (recently
rigorously established) Lifshitz law of phase boundary movement. We also
provide results for the positive but small temperature regime. We show that an
initial configuration drawn according to the Gibbs measure cannot retain more
than a single bit for . On the other hand,
when scaling time with , the stripe-based coding scheme (that stores for
infinite time at zero temperature) is shown to retain its bits for time that is
exponential in
Sparse cross-products of metadata in scientific simulation management
Managing scientific data is by no means a trivial task even in a single site environment
with a small number of researchers involved. We discuss some issues concerned with posing
well-specified experiments in terms of parameters or instrument settings and the metadata
framework that arises from doing so. We are particularly interested in parallel computer
simulation experiments, where very large quantities of warehouse-able data are involved. We
consider SQL databases and other framework technologies for manipulating experimental data.
Our framework manages the the outputs from parallel runs that arise from large cross-products
of parameter combinations. Considerable useful experiment planning and analysis can be done
with the sparse metadata without fully expanding the parameter cross-products. Extra value
can be obtained from simulation output that can subsequently be data-mined. We have
particular interests in running large scale Monte-Carlo physics model simulations. Finding
ourselves overwhelmed by the problems of managing data and compute ¿resources, we have
built a prototype tool using Java and MySQL that addresses these issues. We use this example
to discuss type-space management and other fundamental ideas for implementing a laboratory
information management system
Retrieval behavior and thermodynamic properties of symmetrically diluted Q-Ising neural networks
The retrieval behavior and thermodynamic properties of symmetrically diluted
Q-Ising neural networks are derived and studied in replica-symmetric mean-field
theory generalizing earlier works on either the fully connected or the
symmetrical extremely diluted network. Capacity-gain parameter phase diagrams
are obtained for the Q=3, Q=4 and state networks with uniformly
distributed patterns of low activity in order to search for the effects of a
gradual dilution of the synapses. It is shown that enlarged regions of
continuous changeover into a region of optimal performance are obtained for
finite stochastic noise and small but finite connectivity. The de
Almeida-Thouless lines of stability are obtained for arbitrary connectivity,
and the resulting phase diagrams are used to draw conclusions on the behavior
of symmetrically diluted networks with other pattern distributions of either
high or low activity.Comment: 21 pages, revte
Neural Networks retrieving Boolean patterns in a sea of Gaussian ones
Restricted Boltzmann Machines are key tools in Machine Learning and are
described by the energy function of bipartite spin-glasses. From a statistical
mechanical perspective, they share the same Gibbs measure of Hopfield networks
for associative memory. In this equivalence, weights in the former play as
patterns in the latter. As Boltzmann machines usually require real weights to
be trained with gradient descent like methods, while Hopfield networks
typically store binary patterns to be able to retrieve, the investigation of a
mixed Hebbian network, equipped with both real (e.g., Gaussian) and discrete
(e.g., Boolean) patterns naturally arises. We prove that, in the challenging
regime of a high storage of real patterns, where retrieval is forbidden, an
extra load of Boolean patterns can still be retrieved, as long as the ratio
among the overall load and the network size does not exceed a critical
threshold, that turns out to be the same of the standard
Amit-Gutfreund-Sompolinsky theory. Assuming replica symmetry, we study the case
of a low load of Boolean patterns combining the stochastic stability and
Hamilton-Jacobi interpolating techniques. The result can be extended to the
high load by a non rigorous but standard replica computation argument.Comment: 16 pages, 1 figur
Thouless-Anderson-Palmer equation for analog neural network with temporally fluctuating white synaptic noise
Effects of synaptic noise on the retrieval process of associative memory
neural networks are studied from the viewpoint of neurobiological and
biophysical understanding of information processing in the brain. We
investigate the statistical mechanical properties of stochastic analog neural
networks with temporally fluctuating synaptic noise, which is assumed to be
white noise. Such networks, in general, defy the use of the replica method,
since they have no energy concept. The self-consistent signal-to-noise analysis
(SCSNA), which is an alternative to the replica method for deriving a set of
order parameter equations, requires no energy concept and thus becomes
available in studying networks without energy functions. Applying the SCSNA to
stochastic network requires the knowledge of the Thouless-Anderson-Palmer (TAP)
equation which defines the deterministic networks equivalent to the original
stochastic ones. The study of the TAP equation which is of particular interest
for the case without energy concept is very few, while it is closely related to
the SCSNA in the case with energy concept. This paper aims to derive the TAP
equation for networks with synaptic noise together with a set of order
parameter equations by a hybrid use of the cavity method and the SCSNA.Comment: 13 pages, 3 figure
How Quantum Computers Fail: Quantum Codes, Correlations in Physical Systems, and Noise Accumulation
The feasibility of computationally superior quantum computers is one of the
most exciting and clear-cut scientific questions of our time. The question
touches on fundamental issues regarding probability, physics, and
computability, as well as on exciting problems in experimental physics,
engineering, computer science, and mathematics. We propose three related
directions towards a negative answer. The first is a conjecture about physical
realizations of quantum codes, the second has to do with correlations in
stochastic physical systems, and the third proposes a model for quantum
evolutions when noise accumulates. The paper is dedicated to the memory of
Itamar Pitowsky.Comment: 16 page
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