1,381 research outputs found
Transient dynamics for sequence processing neural networks
An exact solution of the transient dynamics for a sequential associative
memory model is discussed through both the path-integral method and the
statistical neurodynamics. Although the path-integral method has the ability to
give an exact solution of the transient dynamics, only stationary properties
have been discussed for the sequential associative memory. We have succeeded in
deriving an exact macroscopic description of the transient dynamics by
analyzing the correlation of crosstalk noise. Surprisingly, the order parameter
equations of this exact solution are completely equivalent to those of the
statistical neurodynamics, which is an approximation theory that assumes
crosstalk noise to obey the Gaussian distribution. In order to examine our
theoretical findings, we numerically obtain cumulants of the crosstalk noise.
We verify that the third- and fourth-order cumulants are equal to zero, and
that the crosstalk noise is normally distributed even in the non-retrieval
case. We show that the results obtained by our theory agree with those obtained
by computer simulations. We have also found that the macroscopic unstable state
completely coincides with the separatrix.Comment: 21 pages, 4 figure
Attractor Metadynamics in Adapting Neural Networks
Slow adaption processes, like synaptic and intrinsic plasticity, abound in
the brain and shape the landscape for the neural dynamics occurring on
substantially faster timescales. At any given time the network is characterized
by a set of internal parameters, which are adapting continuously, albeit
slowly. This set of parameters defines the number and the location of the
respective adiabatic attractors. The slow evolution of network parameters hence
induces an evolving attractor landscape, a process which we term attractor
metadynamics. We study the nature of the metadynamics of the attractor
landscape for several continuous-time autonomous model networks. We find both
first- and second-order changes in the location of adiabatic attractors and
argue that the study of the continuously evolving attractor landscape
constitutes a powerful tool for understanding the overall development of the
neural dynamics
A Survey on Continuous Time Computations
We provide an overview of theories of continuous time computation. These
theories allow us to understand both the hardness of questions related to
continuous time dynamical systems and the computational power of continuous
time analog models. We survey the existing models, summarizing results, and
point to relevant references in the literature
Sentient Networks
In this paper we consider the question whether a distributed network of
sensors and data processors can form "perceptions" based on the sensory data.
Because sensory data can have exponentially many explanations, the use of a
central data processor to analyze the outputs from a large ensemble of sensors
will in general introduce unacceptable latencies for responding to dangerous
situations. A better idea is to use a distributed "Helmholtz machine"
architecture in which the collective state of the network as a whole provides
an explanation for the sensory data.Comment: PostScript, 14 page
Short term synaptic depression improves information transfer in perceptual multistability
Competitive neural networks are often used to model the dynamics of
perceptual bistability. Switching between percepts can occur through
fluctuations and/or a slow adaptive process. Here, we analyze switching
statistics in competitive networks with short term synaptic depression and
noise. We start by analyzing a ring model that yields spatially structured
solutions and complement this with a study of a space-free network whose
populations are coupled with mutual inhibition. Dominance times arising from
depression driven switching can be approximated using a separation of
timescales in the ring and space-free model. For purely noise-driven switching,
we use energy arguments to justify how dominance times are exponentially
related to input strength. We also show that a combination of depression and
noise generates realistic distributions of dominance times. Unimodal functions
of dominance times are more easily differentiated from one another using
Bayesian sampling, suggesting synaptic depression induced switching transfers
more information about stimuli than noise-driven switching. Finally, we analyze
a competitive network model of perceptual tristability, showing depression
generates a memory of previous percepts based on the ordering of percepts.Comment: 26 pages, 15 figure
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