232 research outputs found
Synchronization and Noise: A Mechanism for Regularization in Neural Systems
To learn and reason in the presence of uncertainty, the brain must be capable
of imposing some form of regularization. Here we suggest, through theoretical
and computational arguments, that the combination of noise with synchronization
provides a plausible mechanism for regularization in the nervous system. The
functional role of regularization is considered in a general context in which
coupled computational systems receive inputs corrupted by correlated noise.
Noise on the inputs is shown to impose regularization, and when synchronization
upstream induces time-varying correlations across noise variables, the degree
of regularization can be calibrated over time. The proposed mechanism is
explored first in the context of a simple associative learning problem, and
then in the context of a hierarchical sensory coding task. The resulting
qualitative behavior coincides with experimental data from visual cortex.Comment: 32 pages, 7 figures. under revie
Audio Classification from Time-Frequency Texture
Time-frequency representations of audio signals often resemble texture
images. This paper derives a simple audio classification algorithm based on
treating sound spectrograms as texture images. The algorithm is inspired by an
earlier visual classification scheme particularly efficient at classifying
textures. While solely based on time-frequency texture features, the algorithm
achieves surprisingly good performance in musical instrument classification
experiments
Contraction analysis of nonlinear random dynamical systems
In order to bring contraction analysis into the very fruitful and topical
fields of stochastic and Bayesian systems, we extend here the theory describes
in \cite{Lohmiller98} to random differential equations. We propose new
definitions of contraction (almost sure contraction and contraction in mean
square) which allow to master the evolution of a stochastic system in two
manners. The first one guarantees eventual exponential convergence of the
system for almost all draws, whereas the other guarantees the exponential
convergence in of to a unique trajectory. We then illustrate the relative
simplicity of this extension by analyzing usual deterministic properties in the
presence of noise. Specifically, we analyze stochastic gradient descent, impact
of noise on oscillators synchronization and extensions of combination
properties of contracting systems to the stochastic case. This is a first step
towards combining the interesting and simplifying properties of contracting
systems with the probabilistic approach.Comment: No. RR-8368 (2013
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