33,889 research outputs found
Non-orthogonal eigenvectors, fluctuation-dissipation relations and entropy production
Celebrated fluctuation-dissipation theorem (FDT) linking the response
function to time dependent correlations of observables measured in the
reference unperturbed state is one of the central results in equilibrium
statistical mechanics. In this letter we discuss an extension of the standard
FDT to the case when multidimensional matrix representing transition
probabilities is strictly non-normal. This feature dramatically modifies the
dynamics, by incorporating the effect of eigenvector non-orthogonality via the
associated overlap matrix of Chalker-Mehlig type. In particular, the rate of
entropy production per unit time is strongly enhanced by that matrix. We
suggest, that this mechanism has an impact on the studies of collective
phenomena in neural matrix models, leading, via transient behavior, to such
phenomena as synchronisation and emergence of the memory. We also expect, that
the described mechanism generating the entropy production is generic for wide
class of phenomena, where dynamics is driven by non-normal operators. For the
case of driving by a large Ginibre matrix the entropy production rate is
evaluated analytically, as well as for the Rajan-Abbott model for neural
networks.Comment: 3 figures, 8 pages. Important references added, calculation of
entropy production rates for Rajan-Abbott model of neural networks and for
Ginibre ensemble completed, title change
Dynamical Entropy Production in Spiking Neuron Networks in the Balanced State
We demonstrate deterministic extensive chaos in the dynamics of large sparse
networks of theta neurons in the balanced state. The analysis is based on
numerically exact calculations of the full spectrum of Lyapunov exponents, the
entropy production rate and the attractor dimension. Extensive chaos is found
in inhibitory networks and becomes more intense when an excitatory population
is included. We find a strikingly high rate of entropy production that would
limit information representation in cortical spike patterns to the immediate
stimulus response.Comment: 4 pages, 4 figure
Structured chaos shapes spike-response noise entropy in balanced neural networks
Large networks of sparsely coupled, excitatory and inhibitory cells occur
throughout the brain. A striking feature of these networks is that they are
chaotic. How does this chaos manifest in the neural code? Specifically, how
variable are the spike patterns that such a network produces in response to an
input signal? To answer this, we derive a bound for the entropy of multi-cell
spike pattern distributions in large recurrent networks of spiking neurons
responding to fluctuating inputs. The analysis is based on results from random
dynamical systems theory and is complimented by detailed numerical simulations.
We find that the spike pattern entropy is an order of magnitude lower than what
would be extrapolated from single cells. This holds despite the fact that
network coupling becomes vanishingly sparse as network size grows -- a
phenomenon that depends on ``extensive chaos," as previously discovered for
balanced networks without stimulus drive. Moreover, we show how spike pattern
entropy is controlled by temporal features of the inputs. Our findings provide
insight into how neural networks may encode stimuli in the presence of
inherently chaotic dynamics.Comment: 9 pages, 5 figure
Max-Pooling Loss Training of Long Short-Term Memory Networks for Small-Footprint Keyword Spotting
We propose a max-pooling based loss function for training Long Short-Term
Memory (LSTM) networks for small-footprint keyword spotting (KWS), with low
CPU, memory, and latency requirements. The max-pooling loss training can be
further guided by initializing with a cross-entropy loss trained network. A
posterior smoothing based evaluation approach is employed to measure keyword
spotting performance. Our experimental results show that LSTM models trained
using cross-entropy loss or max-pooling loss outperform a cross-entropy loss
trained baseline feed-forward Deep Neural Network (DNN). In addition,
max-pooling loss trained LSTM with randomly initialized network performs better
compared to cross-entropy loss trained LSTM. Finally, the max-pooling loss
trained LSTM initialized with a cross-entropy pre-trained network shows the
best performance, which yields relative reduction compared to baseline
feed-forward DNN in Area Under the Curve (AUC) measure
Unified framework for the entropy production and the stochastic interaction based on information geometry
We show a relationship between the entropy production in stochastic
thermodynamics and the stochastic interaction in the information integrated
theory. To clarify this relationship, we newly introduce an information
geometric interpretation of the entropy production for a total system and the
partial entropy productions for subsystems. We show that the violation of the
additivity of the entropy productions is related to the stochastic interaction.
This framework is a thermodynamic foundation of the integrated information
theory. We also show that our information geometric formalism leads to a novel
expression of the entropy production related to an optimization problem
minimizing the Kullback-Leibler divergence. We analytically illustrate this
interpretation by using the spin model.Comment: 13pages, 4 figure
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