12,584 research outputs found
Statistical physics of neural systems with non-additive dendritic coupling
How neurons process their inputs crucially determines the dynamics of
biological and artificial neural networks. In such neural and neural-like
systems, synaptic input is typically considered to be merely transmitted
linearly or sublinearly by the dendritic compartments. Yet, single-neuron
experiments report pronounced supralinear dendritic summation of sufficiently
synchronous and spatially close-by inputs. Here, we provide a statistical
physics approach to study the impact of such non-additive dendritic processing
on single neuron responses and the performance of associative memory tasks in
artificial neural networks. First, we compute the effect of random input to a
neuron incorporating nonlinear dendrites. This approach is independent of the
details of the neuronal dynamics. Second, we use those results to study the
impact of dendritic nonlinearities on the network dynamics in a paradigmatic
model for associative memory, both numerically and analytically. We find that
dendritic nonlinearities maintain network convergence and increase the
robustness of memory performance against noise. Interestingly, an intermediate
number of dendritic branches is optimal for memory functionality
From patterned response dependency to structured covariate dependency: categorical-pattern-matching
Data generated from a system of interest typically consists of measurements
from an ensemble of subjects across multiple response and covariate features,
and is naturally represented by one response-matrix against one
covariate-matrix. Likely each of these two matrices simultaneously embraces
heterogeneous data types: continuous, discrete and categorical. Here a matrix
is used as a practical platform to ideally keep hidden dependency among/between
subjects and features intact on its lattice. Response and covariate dependency
is individually computed and expressed through mutliscale blocks via a newly
developed computing paradigm named Data Mechanics. We propose a categorical
pattern matching approach to establish causal linkages in a form of information
flows from patterned response dependency to structured covariate dependency.
The strength of an information flow is evaluated by applying the combinatorial
information theory. This unified platform for system knowledge discovery is
illustrated through five data sets. In each illustrative case, an information
flow is demonstrated as an organization of discovered knowledge loci via
emergent visible and readable heterogeneity. This unified approach
fundamentally resolves many long standing issues, including statistical
modeling, multiple response, renormalization and feature selections, in data
analysis, but without involving man-made structures and distribution
assumptions. The results reported here enhance the idea that linking patterns
of response dependency to structures of covariate dependency is the true
philosophical foundation underlying data-driven computing and learning in
sciences.Comment: 32 pages, 10 figures, 3 box picture
Extensive load in multitasking associative networks
We use belief-propagation techniques to study the equilibrium behavior of a
bipartite spin-glass, with interactions between two sets of and spins. Each spin has a finite degree, i.e.\ number of interaction partners
in the opposite set; an equivalent view is then of a system of neurons
storing diluted patterns. We show that in a large part of the parameter
space of noise, dilution and storage load, delimited by a critical surface, the
network behaves as an extensive parallel processor, retrieving all patterns
{\it in parallel} without falling into spurious states due to pattern
cross-talk and typical of the structural glassiness built into the network. Our
approach allows us to consider effects beyond those studied in replica theory
so far, including pattern asymmetry and heterogeneous dilution. Parallel
extensive retrieval is more robust for homogeneous degree distributions, and is
not disrupted by biases in the distributions of the spin-glass links
A ferrofluid based neural network: design of an analogue associative memory
We analyse an associative memory based on a ferrofluid, consisting of a
system of magnetic nano-particles suspended in a carrier fluid of variable
viscosity subject to patterns of magnetic fields from an array of input and
output magnetic pads. The association relies on forming patterns in the
ferrofluid during a trainingdphase, in which the magnetic dipoles are free to
move and rotate to minimize the total energy of the system. Once equilibrated
in energy for a given input-output magnetic field pattern-pair the particles
are fully or partially immobilized by cooling the carrier liquid. Thus produced
particle distributions control the memory states, which are read out
magnetically using spin-valve sensors incorporated in the output pads. The
actual memory consists of spin distributions that is dynamic in nature,
realized only in response to the input patterns that the system has been
trained for. Two training algorithms for storing multiple patterns are
investigated. Using Monte Carlo simulations of the physical system we
demonstrate that the device is capable of storing and recalling two sets of
images, each with an accuracy approaching 100%.Comment: submitted to Neural Network
Quantum-implemented selective reconstruction of high-resolution images
This paper proposes quantum image reconstruction. Input-triggered selection
of an image among many stored ones, and its reconstruction if the input is
occluded or noisy, has been simulated by a computer program implementable in a
real quantum-physical system. It is based on the Hopfield associative net; the
quantum-wave implementation bases on holography. The main limitations of the
classical Hopfield net are much reduced with the new, original --
quantum-optical -- implementation. Image resolution can be almost arbitrarily
increased.Comment: 4 pages, 15 figures, essential
Schur Polynomials and the Yang-Baxter equation
We show that within the six-vertex model there is a parametrized Yang-Baxter
equation with nonabelian parameter group GL(2)xGL(1) at the center of the
disordered regime. As an application we rederive deformations of the Weyl
character formule of Tokuyama and of Hamel and King.Comment: Revised introduction; slightly changed reference
Neurogenesis Drives Stimulus Decorrelation in a Model of the Olfactory Bulb
The reshaping and decorrelation of similar activity patterns by neuronal
networks can enhance their discriminability, storage, and retrieval. How can
such networks learn to decorrelate new complex patterns, as they arise in the
olfactory system? Using a computational network model for the dominant neural
populations of the olfactory bulb we show that fundamental aspects of the adult
neurogenesis observed in the olfactory bulb -- the persistent addition of new
inhibitory granule cells to the network, their activity-dependent survival, and
the reciprocal character of their synapses with the principal mitral cells --
are sufficient to restructure the network and to alter its encoding of odor
stimuli adaptively so as to reduce the correlations between the bulbar
representations of similar stimuli. The decorrelation is quite robust with
respect to various types of perturbations of the reciprocity. The model
parsimoniously captures the experimentally observed role of neurogenesis in
perceptual learning and the enhanced response of young granule cells to novel
stimuli. Moreover, it makes specific predictions for the type of odor
enrichment that should be effective in enhancing the ability of animals to
discriminate similar odor mixtures
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