5,659 research outputs found
Correlating matched-filter model for analysis and optimisation of neural networks
A new formalism is described for modelling neural networks by means of which a clear physical understanding of the network behaviour can be gained. In essence, the neural net is represented by an equivalent network of matched filters which is then analysed by standard correlation techniques. The procedure is demonstrated on the synchronous Little-Hopfield network. It is shown how the ability of this network to discriminate between stored binary, bipolar codes is optimised if the stored codes are chosen to be orthogonal. However, such a choice will not often be possible and so a new neural network architecture is proposed which enables the same discrimination to be obtained for arbitrary stored codes. The most efficient convergence of the synchronous Little-Hopfield net is obtained when the neurons are connected to themselves with a weight equal to the number of stored codes. The processing gain is presented for this case. The paper goes on to show how this modelling technique can be extended to analyse the behaviour of both hard and soft neural threshold responses and a novel time-dependent threshold response is described
The meanfield limit of a network of Hopfield neurons with correlated synaptic weights
We study the asymptotic behaviour for asymmetric neuronal dynamics in a
network of Hopfield neurons. The randomness in the network is modelled by
random couplings which are centered Gaussian correlated random variables. We
prove that the annealed law of the empirical measure satisfies a large
deviation principle without any condition on time. We prove that the good rate
function of this large deviation principle achieves its minimum value at a
unique Gaussian measure which is not Markovian. This implies almost sure
convergence of the empirical measure under the quenched law. We prove that the
limit equations are expressed as an infinite countable set of linear non
Markovian SDEs.Comment: 102 page
Correlating matched-filter model for analysis and optimisation of neural networks
A new formalism is described for modelling neural networks by means of which a clear physical understanding of the network behaviour can be gained. In essence, the neural net is represented by an equivalent network of matched filters which is then analysed by standard correlation techniques. The procedure is demonstrated on the synchronous Little-Hopfield network. It is shown how the ability of this network to discriminate between stored binary, bipolar codes is optimised if the stored codes are chosen to be orthogonal. However, such a choice will not often be possible and so a new neural network architecture is proposed which enables the same discrimination to be obtained for arbitrary stored codes. The most efficient convergence of the synchronous Little-Hopfield net is obtained when the neurons are connected to themselves with a weight equal to the number of stored codes. The processing gain is presented for this case. The paper goes on to show how this modelling technique can be extended to analyse the behaviour of both hard and soft neural threshold responses and a novel time-dependent threshold response is described
On the Dynamics of a Recurrent Hopfield Network
In this research paper novel real/complex valued recurrent Hopfield Neural
Network (RHNN) is proposed. The method of synthesizing the energy landscape of
such a network and the experimental investigation of dynamics of Recurrent
Hopfield Network is discussed. Parallel modes of operation (other than fully
parallel mode) in layered RHNN is proposed. Also, certain potential
applications are proposed.Comment: 6 pages, 6 figures, 1 table, submitted to IJCNN-201
Statistical physics of neural systems with non-additive dendritic coupling
How neurons process their inputs crucially determines the dynamics of
biological and artificial neural networks. In such neural and neural-like
systems, synaptic input is typically considered to be merely transmitted
linearly or sublinearly by the dendritic compartments. Yet, single-neuron
experiments report pronounced supralinear dendritic summation of sufficiently
synchronous and spatially close-by inputs. Here, we provide a statistical
physics approach to study the impact of such non-additive dendritic processing
on single neuron responses and the performance of associative memory tasks in
artificial neural networks. First, we compute the effect of random input to a
neuron incorporating nonlinear dendrites. This approach is independent of the
details of the neuronal dynamics. Second, we use those results to study the
impact of dendritic nonlinearities on the network dynamics in a paradigmatic
model for associative memory, both numerically and analytically. We find that
dendritic nonlinearities maintain network convergence and increase the
robustness of memory performance against noise. Interestingly, an intermediate
number of dendritic branches is optimal for memory functionality
Dreaming neural networks: forgetting spurious memories and reinforcing pure ones
The standard Hopfield model for associative neural networks accounts for
biological Hebbian learning and acts as the harmonic oscillator for pattern
recognition, however its maximal storage capacity is , far
from the theoretical bound for symmetric networks, i.e. . Inspired
by sleeping and dreaming mechanisms in mammal brains, we propose an extension
of this model displaying the standard on-line (awake) learning mechanism (that
allows the storage of external information in terms of patterns) and an
off-line (sleep) unlearningconsolidating mechanism (that allows
spurious-pattern removal and pure-pattern reinforcement): this obtained daily
prescription is able to saturate the theoretical bound , remaining
also extremely robust against thermal noise. Both neural and synaptic features
are analyzed both analytically and numerically. In particular, beyond obtaining
a phase diagram for neural dynamics, we focus on synaptic plasticity and we
give explicit prescriptions on the temporal evolution of the synaptic matrix.
We analytically prove that our algorithm makes the Hebbian kernel converge with
high probability to the projection matrix built over the pure stored patterns.
Furthermore, we obtain a sharp and explicit estimate for the "sleep rate" in
order to ensure such a convergence. Finally, we run extensive numerical
simulations (mainly Monte Carlo sampling) to check the approximations
underlying the analytical investigations (e.g., we developed the whole theory
at the so called replica-symmetric level, as standard in the
Amit-Gutfreund-Sompolinsky reference framework) and possible finite-size
effects, finding overall full agreement with the theory.Comment: 31 pages, 12 figure
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