1,329 research outputs found
Balanced networks of spiking neurons with spatially dependent recurrent connections
Networks of model neurons with balanced recurrent excitation and inhibition
produce irregular and asynchronous spiking activity. We extend the analysis of
balanced networks to include the known dependence of connection probability on
the spatial separation between neurons. In the continuum limit we derive that
stable, balanced firing rate solutions require that the spatial spread of
external inputs be broader than that of recurrent excitation, which in turn
must be broader than or equal to that of recurrent inhibition. For finite size
networks we investigate the pattern forming dynamics arising when balanced
conditions are not satisfied. The spatiotemporal dynamics of balanced networks
offer new challenges in the statistical mechanics of complex systems
Estimating the efficient price from the order flow: a Brownian Cox process approach
At the ultra high frequency level, the notion of price of an asset is very
ambiguous. Indeed, many different prices can be defined (last traded price,
best bid price, mid price,...). Thus, in practice, market participants face the
problem of choosing a price when implementing their strategies. In this work,
we propose a notion of efficient price which seems relevant in practice.
Furthermore, we provide a statistical methodology enabling to estimate this
price form the order flow
On the relationship between predictive coding and backpropagation
Artificial neural networks are often interpreted as abstract models of
biological neuronal networks, but they are typically trained using the
biologically unrealistic backpropagation algorithm and its variants. Predictive
coding has been offered as a potentially more biologically realistic
alternative to backpropagation for training neural networks. In this
manuscript, I review and extend recent work on the mathematical relationship
between predictive coding and backpropagation for training feedforward
artificial neural networks on supervised learning tasks. I discuss some
implications of these results for the interpretation of predictive coding and
deep neural networks as models of biological learning and I describe a
repository of functions, Torch2PC, for performing predictive coding with
PyTorch neural network models
Learning fixed points of recurrent neural networks by reparameterizing the network model
In computational neuroscience, fixed points of recurrent neural network
models are commonly used to model neural responses to static or slowly changing
stimuli. These applications raise the question of how to train the weights in a
recurrent neural network to minimize a loss function evaluated on fixed points.
A natural approach is to use gradient descent on the Euclidean space of
synaptic weights. We show that this approach can lead to poor learning
performance due, in part, to singularities that arise in the loss surface. We
use a re-parameterization of the recurrent network model to derive two
alternative learning rules that produces more robust learning dynamics. We show
that these learning rules can be interpreted as steepest descent and gradient
descent, respectively, under a non-Euclidean metric on the space of recurrent
weights. Our results question the common, implicit assumption that learning in
the brain should necessarily follow the negative Euclidean gradient of synaptic
weights
Estimation de Volatilité en Présence de Bruit de Microstructure Endogène
International audienceCe papier considère des procédures statistiques facilement implémentables pour l'estimation de mesures de volatilité haute fréquence pour des actifs financiers. Le modèle de microstructure sous-jascent se base sur un prix efficient de type semi-martingale continue et permet de reproduire les principales caractéristiques empiriques des données ultra haute fréquence. Dans ce modèle, le bruit de microstructure est endogène mais ne dépend pas uniquement du prix efficient. En utilisant les prix de transaction observés, nous développons une nouvelle approche permettant d'approximer les valeurs du prix efficient à certains instants aléatoires. En se basant sur ces valeurs approchées, on construit un estimateur de la volatilité intégrée et on fournit sa théorie asymptotique. On donne aussi un estimateur consistant de la co-volatilité intégrée dans le cas où deux actifs (asynchrones par construction du modèle) sont observés
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