125 research outputs found
Search for uncharged faster than light particles
Searching for uncharged particles with spacelike four momentum traveling faster than ligh
A perturbative approach to non-linearities in the information carried by a two layer neural network
We evaluate the mutual information between the input and the output of a two
layer network in the case of a noisy and non-linear analogue channel. In the
case where the non-linearity is small with respect to the variability in the
noise, we derive an exact expression for the contribution to the mutual
information given by the non-linear term in first order of perturbation theory.
Finally we show how the calculation can be simplified by means of a
diagrammatic expansion. Our results suggest that the use of perturbation
theories applied to neural systems might give an insight on the contribution of
non-linearities to the information transmission and in general to the neuronal
dynamics.Comment: Accepted as a preprint of ICTP, Triest
Asymptotic Level Density of the Elastic Net Self-Organizing Feature Map
Whileas the Kohonen Self Organizing Map shows an asymptotic level density
following a power law with a magnification exponent 2/3, it would be desired to
have an exponent 1 in order to provide optimal mapping in the sense of
information theory. In this paper, we study analytically and numerically the
magnification behaviour of the Elastic Net algorithm as a model for
self-organizing feature maps. In contrast to the Kohonen map the Elastic Net
shows no power law, but for onedimensional maps nevertheless the density
follows an universal magnification law, i.e. depends on the local stimulus
density only and is independent on position and decouples from the stimulus
density at other positions.Comment: 8 pages, 10 figures. Link to publisher under
http://link.springer.de/link/service/series/0558/bibs/2415/24150939.ht
Investigation of topographical stability of the concave and convex Self-Organizing Map variant
We investigate, by a systematic numerical study, the parameter dependence of
the stability of the Kohonen Self-Organizing Map and the Zheng and Greenleaf
concave and convex learning with respect to different input distributions,
input and output dimensions
The mutual information of a stochastic binary channel: validity of the Replica Symmetry Ansatz
We calculate the mutual information (MI) of a two-layered neural network with
noiseless, continuous inputs and binary, stochastic outputs under several
assumptions on the synaptic efficiencies. The interesting regime corresponds to
the limit where the number of both input and output units is large but their
ratio is kept fixed at a value . We first present a solution for the MI
using the replica technique with a replica symmetric (RS) ansatz. Then we find
an exact solution for this quantity valid in a neighborhood of . An
analysis of this solution shows that the system must have a phase transition at
some finite value of . This transition shows a singularity in the third
derivative of the MI. As the RS solution turns out to be infinitely
differentiable, it could be regarded as a smooth approximation to the MI. This
is checked numerically in the validity domain of the exact solution.Comment: Latex, 29 pages, 2 Encapsulated Post Script figures. To appear in
Journal of Physics
Subbarrel patterns in somatosensory cortical barrels can emerge from local dynamic instabilities
Complex spatial patterning, common in the brain as well as in other biological systems, can emerge as a result of dynamic interactions that occur locally within developing structures. In the rodent somatosensory cortex, groups of neurons called "barrels" correspond to individual whiskers on the contralateral face. Barrels themselves often contain subbarrels organized into one of a few characteristic patterns. Here we demonstrate that similar patterns can be simulated by means of local growth-promoting and growth-retarding interactions within the circular domains of single barrels. The model correctly predicts that larger barrels contain more spatially complex subbarrel patterns, suggesting that the development of barrels and of the patterns within them may be understood in terms of some relatively simple dynamic processes. We also simulate the full nonlinear equations to demonstrate the predictive value of our linear analysis. Finally, we show that the pattern formation is robust with respect to the geometry of the barrel by simulating patterns on a realistically shaped barrel domain. This work shows how simple pattern forming mechanisms can explain neural wiring both qualitatively and quantitatively even in complex and irregular domains. © 2009 Ermentrout et al
Neural Decision Boundaries for Maximal Information Transmission
We consider here how to separate multidimensional signals into two
categories, such that the binary decision transmits the maximum possible
information transmitted about those signals. Our motivation comes from the
nervous system, where neurons process multidimensional signals into a binary
sequence of responses (spikes). In a small noise limit, we derive a general
equation for the decision boundary that locally relates its curvature to the
probability distribution of inputs. We show that for Gaussian inputs the
optimal boundaries are planar, but for non-Gaussian inputs the curvature is
nonzero. As an example, we consider exponentially distributed inputs, which are
known to approximate a variety of signals from natural environment.Comment: 5 pages, 3 figure
Reinforcement learning or active inference?
This paper questions the need for reinforcement learning or control theory when optimising behaviour. We show that it is fairly simple to teach an agent complicated and adaptive behaviours using a free-energy formulation of perception. In this formulation, agents adjust their internal states and sampling of the environment to minimize their free-energy. Such agents learn causal structure in the environment and sample it in an adaptive and self-supervised fashion. This results in behavioural policies that reproduce those optimised by reinforcement learning and dynamic programming. Critically, we do not need to invoke the notion of reward, value or utility. We illustrate these points by solving a benchmark problem in dynamic programming; namely the mountain-car problem, using active perception or inference under the free-energy principle. The ensuing proof-of-concept may be important because the free-energy formulation furnishes a unified account of both action and perception and may speak to a reappraisal of the role of dopamine in the brain
Coverage, Continuity and Visual Cortical Architecture
The primary visual cortex of many mammals contains a continuous
representation of visual space, with a roughly repetitive aperiodic map of
orientation preferences superimposed. It was recently found that orientation
preference maps (OPMs) obey statistical laws which are apparently invariant
among species widely separated in eutherian evolution. Here, we examine whether
one of the most prominent models for the optimization of cortical maps, the
elastic net (EN) model, can reproduce this common design. The EN model
generates representations which optimally trade of stimulus space coverage and
map continuity. While this model has been used in numerous studies, no
analytical results about the precise layout of the predicted OPMs have been
obtained so far. We present a mathematical approach to analytically calculate
the cortical representations predicted by the EN model for the joint mapping of
stimulus position and orientation. We find that in all previously studied
regimes, predicted OPM layouts are perfectly periodic. An unbiased search
through the EN parameter space identifies a novel regime of aperiodic OPMs with
pinwheel densities lower than found in experiments. In an extreme limit,
aperiodic OPMs quantitatively resembling experimental observations emerge.
Stabilization of these layouts results from strong nonlocal interactions rather
than from a coverage-continuity-compromise. Our results demonstrate that
optimization models for stimulus representations dominated by nonlocal
suppressive interactions are in principle capable of correctly predicting the
common OPM design. They question that visual cortical feature representations
can be explained by a coverage-continuity-compromise.Comment: 100 pages, including an Appendix, 21 + 7 figure
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