7,267 research outputs found
A three-threshold learning rule approaches the maximal capacity of recurrent neural networks
Understanding the theoretical foundations of how memories are encoded and
retrieved in neural populations is a central challenge in neuroscience. A
popular theoretical scenario for modeling memory function is the attractor
neural network scenario, whose prototype is the Hopfield model. The model has a
poor storage capacity, compared with the capacity achieved with perceptron
learning algorithms. Here, by transforming the perceptron learning rule, we
present an online learning rule for a recurrent neural network that achieves
near-maximal storage capacity without an explicit supervisory error signal,
relying only upon locally accessible information. The fully-connected network
consists of excitatory binary neurons with plastic recurrent connections and
non-plastic inhibitory feedback stabilizing the network dynamics; the memory
patterns are presented online as strong afferent currents, producing a bimodal
distribution for the neuron synaptic inputs. Synapses corresponding to active
inputs are modified as a function of the value of the local fields with respect
to three thresholds. Above the highest threshold, and below the lowest
threshold, no plasticity occurs. In between these two thresholds,
potentiation/depression occurs when the local field is above/below an
intermediate threshold. We simulated and analyzed a network of binary neurons
implementing this rule and measured its storage capacity for different sizes of
the basins of attraction. The storage capacity obtained through numerical
simulations is shown to be close to the value predicted by analytical
calculations. We also measured the dependence of capacity on the strength of
external inputs. Finally, we quantified the statistics of the resulting
synaptic connectivity matrix, and found that both the fraction of zero weight
synapses and the degree of symmetry of the weight matrix increase with the
number of stored patterns.Comment: 24 pages, 10 figures, to be published in PLOS Computational Biolog
Complexity without chaos: Plasticity within random recurrent networks generates robust timing and motor control
It is widely accepted that the complex dynamics characteristic of recurrent
neural circuits contributes in a fundamental manner to brain function. Progress
has been slow in understanding and exploiting the computational power of
recurrent dynamics for two main reasons: nonlinear recurrent networks often
exhibit chaotic behavior and most known learning rules do not work in robust
fashion in recurrent networks. Here we address both these problems by
demonstrating how random recurrent networks (RRN) that initially exhibit
chaotic dynamics can be tuned through a supervised learning rule to generate
locally stable neural patterns of activity that are both complex and robust to
noise. The outcome is a novel neural network regime that exhibits both
transiently stable and chaotic trajectories. We further show that the recurrent
learning rule dramatically increases the ability of RRNs to generate complex
spatiotemporal motor patterns, and accounts for recent experimental data
showing a decrease in neural variability in response to stimulus onset
Storage of phase-coded patterns via STDP in fully-connected and sparse network: a study of the network capacity
We study the storage and retrieval of phase-coded patterns as stable
dynamical attractors in recurrent neural networks, for both an analog and a
integrate-and-fire spiking model. The synaptic strength is determined by a
learning rule based on spike-time-dependent plasticity, with an asymmetric time
window depending on the relative timing between pre- and post-synaptic
activity. We store multiple patterns and study the network capacity.
For the analog model, we find that the network capacity scales linearly with
the network size, and that both capacity and the oscillation frequency of the
retrieval state depend on the asymmetry of the learning time window. In
addition to fully-connected networks, we study sparse networks, where each
neuron is connected only to a small number z << N of other neurons. Connections
can be short range, between neighboring neurons placed on a regular lattice, or
long range, between randomly chosen pairs of neurons. We find that a small
fraction of long range connections is able to amplify the capacity of the
network. This imply that a small-world-network topology is optimal, as a
compromise between the cost of long range connections and the capacity
increase.
Also in the spiking integrate and fire model the crucial result of storing
and retrieval of multiple phase-coded patterns is observed. The capacity of the
fully-connected spiking network is investigated, together with the relation
between oscillation frequency of retrieval state and window asymmetry
Integer Echo State Networks: Hyperdimensional Reservoir Computing
We propose an approximation of Echo State Networks (ESN) that can be
efficiently implemented on digital hardware based on the mathematics of
hyperdimensional computing. The reservoir of the proposed Integer Echo State
Network (intESN) is a vector containing only n-bits integers (where n<8 is
normally sufficient for a satisfactory performance). The recurrent matrix
multiplication is replaced with an efficient cyclic shift operation. The intESN
architecture is verified with typical tasks in reservoir computing: memorizing
of a sequence of inputs; classifying time-series; learning dynamic processes.
Such an architecture results in dramatic improvements in memory footprint and
computational efficiency, with minimal performance loss.Comment: 10 pages, 10 figures, 1 tabl
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