15,354 research outputs found
Intrinsic adaptation in autonomous recurrent neural networks
A massively recurrent neural network responds on one side to input stimuli
and is autonomously active, on the other side, in the absence of sensory
inputs. Stimuli and information processing depends crucially on the qualia of
the autonomous-state dynamics of the ongoing neural activity. This default
neural activity may be dynamically structured in time and space, showing
regular, synchronized, bursting or chaotic activity patterns.
We study the influence of non-synaptic plasticity on the default dynamical
state of recurrent neural networks. The non-synaptic adaption considered acts
on intrinsic neural parameters, such as the threshold and the gain, and is
driven by the optimization of the information entropy. We observe, in the
presence of the intrinsic adaptation processes, three distinct and globally
attracting dynamical regimes, a regular synchronized, an overall chaotic and an
intermittent bursting regime. The intermittent bursting regime is characterized
by intervals of regular flows, which are quite insensitive to external stimuli,
interseeded by chaotic bursts which respond sensitively to input signals. We
discuss these finding in the context of self-organized information processing
and critical brain dynamics.Comment: 24 pages, 8 figure
Intrinsically-generated fluctuating activity in excitatory-inhibitory networks
Recurrent networks of non-linear units display a variety of dynamical regimes
depending on the structure of their synaptic connectivity. A particularly
remarkable phenomenon is the appearance of strongly fluctuating, chaotic
activity in networks of deterministic, but randomly connected rate units. How
this type of intrinsi- cally generated fluctuations appears in more realistic
networks of spiking neurons has been a long standing question. To ease the
comparison between rate and spiking networks, recent works investigated the
dynami- cal regimes of randomly-connected rate networks with segregated
excitatory and inhibitory populations, and firing rates constrained to be
positive. These works derived general dynamical mean field (DMF) equations
describing the fluctuating dynamics, but solved these equations only in the
case of purely inhibitory networks. Using a simplified excitatory-inhibitory
architecture in which DMF equations are more easily tractable, here we show
that the presence of excitation qualitatively modifies the fluctuating activity
compared to purely inhibitory networks. In presence of excitation,
intrinsically generated fluctuations induce a strong increase in mean firing
rates, a phenomenon that is much weaker in purely inhibitory networks.
Excitation moreover induces two different fluctuating regimes: for moderate
overall coupling, recurrent inhibition is sufficient to stabilize fluctuations,
for strong coupling, firing rates are stabilized solely by the upper bound
imposed on activity, even if inhibition is stronger than excitation. These
results extend to more general network architectures, and to rate networks
receiving noisy inputs mimicking spiking activity. Finally, we show that
signatures of the second dynamical regime appear in networks of
integrate-and-fire neurons
Solving constraint-satisfaction problems with distributed neocortical-like neuronal networks
Finding actions that satisfy the constraints imposed by both external inputs
and internal representations is central to decision making. We demonstrate that
some important classes of constraint satisfaction problems (CSPs) can be solved
by networks composed of homogeneous cooperative-competitive modules that have
connectivity similar to motifs observed in the superficial layers of neocortex.
The winner-take-all modules are sparsely coupled by programming neurons that
embed the constraints onto the otherwise homogeneous modular computational
substrate. We show rules that embed any instance of the CSPs planar four-color
graph coloring, maximum independent set, and Sudoku on this substrate, and
provide mathematical proofs that guarantee these graph coloring problems will
convergence to a solution. The network is composed of non-saturating linear
threshold neurons. Their lack of right saturation allows the overall network to
explore the problem space driven through the unstable dynamics generated by
recurrent excitation. The direction of exploration is steered by the constraint
neurons. While many problems can be solved using only linear inhibitory
constraints, network performance on hard problems benefits significantly when
these negative constraints are implemented by non-linear multiplicative
inhibition. Overall, our results demonstrate the importance of instability
rather than stability in network computation, and also offer insight into the
computational role of dual inhibitory mechanisms in neural circuits.Comment: Accepted manuscript, in press, Neural Computation (2018
A mathematical analysis of the effects of Hebbian learning rules on the dynamics and structure of discrete-time random recurrent neural networks
We present a mathematical analysis of the effects of Hebbian learning in
random recurrent neural networks, with a generic Hebbian learning rule
including passive forgetting and different time scales for neuronal activity
and learning dynamics. Previous numerical works have reported that Hebbian
learning drives the system from chaos to a steady state through a sequence of
bifurcations. Here, we interpret these results mathematically and show that
these effects, involving a complex coupling between neuronal dynamics and
synaptic graph structure, can be analyzed using Jacobian matrices, which
introduce both a structural and a dynamical point of view on the neural network
evolution. Furthermore, we show that the sensitivity to a learned pattern is
maximal when the largest Lyapunov exponent is close to 0. We discuss how neural
networks may take advantage of this regime of high functional interest
Time-Delay Polaritonics
Non-linearity and finite signal propagation speeds are omnipresent in nature,
technologies, and real-world problems, where efficient ways of describing and
predicting the effects of these elements are in high demand. Advances in
engineering condensed matter systems, such as lattices of trapped condensates,
have enabled studies on non-linear effects in many-body systems where exchange
of particles between lattice nodes is effectively instantaneous. Here, we
demonstrate a regime of macroscopic matter-wave systems, in which ballistically
expanding condensates of microcavity exciton-polaritons act as picosecond,
microscale non-linear oscillators subject to time-delayed interaction. The ease
of optical control and readout of polariton condensates enables us to explore
the phase space of two interacting condensates up to macroscopic distances
highlighting its potential in extended configurations. We demonstrate
deterministic tuning of the coupled-condensate system between fixed point and
limit cycle regimes, which is fully reproduced by time-delayed coupled
equations of motion similar to the Lang-Kobayashi equation
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