Theory of Spike Timing-Based Neural Classifiers

1998

The statistical properties of spike trains generated by a sensory neuron are studied. It is shown that the spike trains exhibit universal statistical behavior over short times, modulated by a strongly stimulusdependent behavior over long times. This decomposition is accounted for by a "frequency integrator" model, under conditions of time scale separation. We provide explicit formulas for the statistical properties in both the universal and the stimulus-dependent regimes, which are in very good agreement with the data. The universal regime is characterized by a dimensionless free parameter, which is observed experimentally to remain constant under different external stimuli. [S0031-9007(98)07566-8]

Neural Computation, 2005

We develop new data-robust lower-bound methods to quantify the information carried by the timing of spikes emitted by neuronal populations. These methods have better sampling properties and are tighter than previous bounds based on neglecting correlation in the noise entropy. Our new lower bounds are precise also in the presence of strongly correlated firing.

2015

Odyssée is a joint project between ENPC-ENS Ulm-INRIA * * Ce travail a été partiellement financé par la Communauté Européenne dans le cadre du projet numéro 15879, FACETS.

2009

In the present overview, our wish is to demystify some aspects of coding with spike-timing, through a simple review of well-understood technical facts regarding spike coding. Our goal is a better understanding of the extent to which computing and modeling with spiking neuron networks might be biologically plausible and computationally efficient. We intentionally restrict ourselves to a deterministic imp lementation

Neural Computation, 2009

The winner-take-all (WTA) computation in networks of recurrently connected neurons is an important decision element of many models of cortical processing. However, analytical studies of the WTA performance in recurrent networks have generally addressed rate-based models. Very few have addressed networks of spiking neurons, which are relevant for understanding the biological networks themselves and also for the development of neuromorphic electronic neurons that commmunicate by action potential like address-events. Here, we make steps in that direction by using a simplified Markov model of the spiking network to examine analytically the ability of a spike-based WTA network to discriminate the statistics of inputs ranging from stationary regular to nonstationary Poisson events. Our work extends previous theoretical results showing that a WTA recurrent network receiving regular spike inputs can select the correct winner within one interspike interval. We show first for the case of spik...

1999

Stochastic nature of precisely timed spike patterns in visual system neuronal responses. J. Neurophysiol. 81: 3021-3033, 1999. It is not clear how information related to cognitive or psychological processes is carried by or represented in the responses of single neurons. One provocative proposal is that precisely timed spike patterns play a role in carrying such information. This would require that these spike patterns have the potential for carrying information that would not be available from other measures such as spike count or latency. We examined exactly timed (1-ms precision) triplets and quadruplets of spikes in the stimulus-elicited responses of lateral geniculate nucleus (LGN) and primary visual cortex (V1) neurons of the awake fixating rhesus monkey. Large numbers of these precisely timed spike patterns were found. Information theoretical analysis showed that the precisely timed spike patterns carried only information already available from spike count, suggesting that the number of precisely timed spike patterns was related to firing rate. We therefore examined statistical models relating precisely timed spike patterns to response strength. Previous statistical models use observed properties of neuronal responses such as the peristimulus time histogram, interspike interval, and/or spike count distributions to constrain the parameters of the model. We examined a new stochastic model, which unlike previous models included all three of these constraints and unlike previous models predicted the numbers and types of observed precisely timed spike patterns. This shows that the precise temporal structures of stimulus-elicited responses in LGN and V1 can occur by chance. We show that any deviation of the spike count distribution, no matter how small, from a Poisson distribution necessarily changes the number of precisely timed spike patterns expected in neural responses. Overall the results indicate that the fine temporal structure of responses can only be interpreted once all the coarse temporal statistics of neural responses have been taken into account. PREDICTING REPLICATING PATTERNS OF SPIKE ARRIVAL TIMES

2003

Temporal precision of spiking response in cortical neurons has been a subject of intense debate. Using a canonical model of spike generation, we explore the conditions for precise and reliable spike timing in the presence of Gaussian white noise. In agreement with previous results we find that constant stimuli lead to imprecise timing, while aperiodic stimuli yield precise spike timing. Under constant stimulus the neuron is a noise perturbed oscillator, the spike times follow renewal statistics and are imprecise. Under an aperiodic stimulus sequence, the neuron acts as a threshold element; the firing times are precisely determined by the dynamics of the stimulus. We further study the dependence of spike-time precision on the input stimulus frequency and find a non-linear tuning whose width can be related to the locking modes of the neuron. We conclude that viewing the neuron as a non-linear oscillator is the key for understanding spike-time precision.

Physical Review E, 2014

Understanding how stimuli and synaptic connectivity influence the statistics of spike patterns in neural networks is a central question in computational neuroscience. Maximum Entropy approach has been successfully used to characterize the statistical response of simultaneously recorded spiking neurons responding to stimuli. But, in spite of good performance in terms of prediction, the fitting parameters do not explain the underlying mechanistic causes of the observed correlations. On the other hand, mathematical models of spiking neurons (neuro-mimetic models) provide a probabilistic mapping between stimulus, network architecture and spike patterns in terms of conditional probabilities. In this paper we build an exact analytical mapping between neuro-mimetic and Maximum Entropy models.

Neurocomputing, 2002

We provide a mathematical method to determine the distribution of synaptic strengths formed by any types of spike-timing-dependent plasticity (STDP). This becomes possible by applying the theory of Ornstein-Uhlenbeck process in determining the Fokker-Planck equation that characterizes the distribution. We verify our novel method by reproducing quantitative properties of STDP observed in previous simulation results. We apply our method to CA1-type window function and electric ÿsh-type window function to demonstrate possible implications of STDP. Moreover, we derive basic properties of STDP from our formalism. Especially, we determine the optimal window function for synaptic competition.

2007

This paper describes some preliminary results of a research program for characterizing the statistics of spikes trains for a variety of commonly used neuron models in the presence of stochastic noise and deterministic input. The main angle of attack of the problem is through the use of stochastic calculus and ways of representing (local) martingales as Brownian motions by changing the time scale.