27,053 research outputs found
Generating functionals for autonomous latching dynamics in attractor relict networks
Coupling local, slowly adapting variables to an attractor network allows to destabilize all attractors, turning them into attractor ruins. The resulting attractor relict network may show ongoing autonomous latching dynamics. We propose to use two generating functionals for the construction of attractor relict networks, a Hopfield energy functional generating a neural attractor network and a functional based on information-theoretical principles, encoding the information content of the neural firing statistics, which induces latching transition from one transiently stable attractor ruin to the next. We investigate the influence of stress, in terms of conflicting optimization targets, on the resulting dynamics. Objective function stress is absent when the target level for the mean of neural activities is identical for the two generating functionals and the resulting latching dynamics is then found to be regular. Objective function stress is present when the respective target activity levels differ, inducing intermittent bursting latching dynamics
Cortical free association dynamics: distinct phases of a latching network
A Potts associative memory network has been proposed as a simplified model of
macroscopic cortical dynamics, in which each Potts unit stands for a patch of
cortex, which can be activated in one of S local attractor states. The internal
neuronal dynamics of the patch is not described by the model, rather it is
subsumed into an effective description in terms of graded Potts units, with
adaptation effects both specific to each attractor state and generic to the
patch. If each unit, or patch, receives effective (tensor) connections from C
other units, the network has been shown to be able to store a large number p of
global patterns, or network attractors, each with a fraction a of the units
active, where the critical load p_c scales roughly like p_c ~ (C S^2)/(a
ln(1/a)) (if the patterns are randomly correlated). Interestingly, after
retrieving an externally cued attractor, the network can continue jumping, or
latching, from attractor to attractor, driven by adaptation effects. The
occurrence and duration of latching dynamics is found through simulations to
depend critically on the strength of local attractor states, expressed in the
Potts model by a parameter w. Here we describe with simulations and then
analytically the boundaries between distinct phases of no latching, of
transient and sustained latching, deriving a phase diagram in the plane w-T,
where T parametrizes thermal noise effects. Implications for real cortical
dynamics are briefly reviewed in the conclusions
The effect of Hebbian plasticity on the attractors of a dynamical system
Poster presentation A central problem in neuroscience is to bridge local synaptic plasticity and the global behavior of a system. It has been shown that Hebbian learning of connections in a feedforward network performs PCA on its inputs [1]. In recurrent Hopfield network with binary units, the Hebbian-learnt patterns form the attractors of the network [2]. Starting from a random recurrent network, Hebbian learning reduces system complexity from chaotic to fixed point [3]. In this paper, we investigate the effect of Hebbian plasticity on the attractors of a continuous dynamical system. In a Hopfield network with binary units, it can be shown that Hebbian learning of an attractor stabilizes it with deepened energy landscape and larger basin of attraction. We are interested in how these properties carry over to continuous dynamical systems. Consider system of the form Math(1) where xi is a real variable, and fi a nondecreasing nonlinear function with range [-1,1]. T is the synaptic matrix, which is assumed to have been learned from orthogonal binary ({1,-1}) patterns ξμ, by the Hebbian rule: Math. Similar to the continuous Hopfield network [4], ξμ are no longer attractors, unless the gains gi are big. Assume that the system settles down to an attractor X*, and undergoes Hebbian plasticity: T´ = T + εX*X*T, where ε > 0 is the learning rate. We study how the attractor dynamics change following this plasticity. We show that, in system (1) under certain general conditions, Hebbian plasticity makes the attractor move towards its corner of the hypercube. Linear stability analysis around the attractor shows that the maximum eigenvalue becomes more negative with learning, indicating a deeper landscape. This in a way improves the system´s ability to retrieve the corresponding stored binary pattern, although the attractor itself is no longer stabilized the way it does in binary Hopfield networks
Real time unsupervised learning of visual stimuli in neuromorphic VLSI systems
Neuromorphic chips embody computational principles operating in the nervous
system, into microelectronic devices. In this domain it is important to
identify computational primitives that theory and experiments suggest as
generic and reusable cognitive elements. One such element is provided by
attractor dynamics in recurrent networks. Point attractors are equilibrium
states of the dynamics (up to fluctuations), determined by the synaptic
structure of the network; a `basin' of attraction comprises all initial states
leading to a given attractor upon relaxation, hence making attractor dynamics
suitable to implement robust associative memory. The initial network state is
dictated by the stimulus, and relaxation to the attractor state implements the
retrieval of the corresponding memorized prototypical pattern. In a previous
work we demonstrated that a neuromorphic recurrent network of spiking neurons
and suitably chosen, fixed synapses supports attractor dynamics. Here we focus
on learning: activating on-chip synaptic plasticity and using a theory-driven
strategy for choosing network parameters, we show that autonomous learning,
following repeated presentation of simple visual stimuli, shapes a synaptic
connectivity supporting stimulus-selective attractors. Associative memory
develops on chip as the result of the coupled stimulus-driven neural activity
and ensuing synaptic dynamics, with no artificial separation between learning
and retrieval phases.Comment: submitted to Scientific Repor
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
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