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We study the performance of a spiking network model based on integrate-and-fire neurons when performing a benchmark discrimination task. The task consists of determining the direction of moving dots in a noisy context. By varying the synaptic parameters of the integrate-and-fire neurons, we illustrate the counter-intuitive importance of the second-order statistics (input noise) in improving the discrimination accuracy of the model. Surprisingly, we found that measuring the firing rate (FR) of a population of neurons considerably enhances the discrimination accuracy as well, in comparison with the firing rate of a single neuron.

It is known that stimulus-evoked synchronization among neurons occurs in widely separated cortical regions. In this paper we test that how common, random but not deterministic inputs can synchronize groups of neurons with their parameters inside physiologically plausible regions. When a common, random input is presented, we find that a group of neurons—of integrate-and-fire or Hodgkin–Huxley models—are capable of rapidly synchronizing their firing. Interestingly the optimal average synchronization time occurs when the efferent spikes have a high coefficient of variation of interspike intervals (greater than 0.5).

We find that adding certain amounts of inhibitory inputs to a neuron improves its capability of accurately decoding the input information. The optimal ratio r of inhibitory to excitatory inputs for decoding the input information from an observation of the efferent interspike intervals is calculated. Surprisingly, the Fisher information could be zero for certain values of the ratio, seemingly implying that it is impossible to read out the encoded information at these values. By analyzing the maximum likelihood estimate of the input information, it is then concluded that the input information is, in fact, most easily estimated at the points where the Fisher information vanishes.

In terms of the Informax principle, and the input–output relationship of the integrate-and-fire (IF) model, IF neuron learning rules are developed and applied to blind separation tasks.

Effectively random firing occurs frequently in the brain. Random components of neuronal drive are therefore often major influences on activity. We describe here how level of drive, inhibitory/excitatory balance, correlation between input streams, EPSP/IPSP characteristics, the nature of the postsynaptic neuron all affect pattern and level of firing, the influence often interacting in complex ways. Random firing might also be instrumental in facilitating synchronized firing. These factors are possibly important elements of the mechanisms by which some neural networks encode information. Clarifying them might therefore facilitate a deeper understanding of the nature of the neural code.

For two-compartment models: the integrate-and-fire model and the Pinsky–Rinzel model, we show that the smaller the soma is, the faster and the more irregularly the neuron fires. We also find that when the soma is small, two-compartment models can be naturally employed as slope detectors.

Neurons are typically thought of as receiving information primarily through excitatory inputs, with inhibitory inputs playing a gating or regulating role. In this paper we demonstrate that increasing the strength of inhibitory inputs to the Hodgkin–Huxley and FitzHugh–Nagumo models can induce them to fire faster. This result is counter-intuitive and important in neural network modelling where inhibitory inputs are often neglected.

We compared the behavior of the Hodgkin–Huxley (HH) model subjected to two input regimes: firstly, discrete pulses from a Poisson process, and then to a diffusion approximation, constructed to share statistical properties with the discrete pulse input. The results show that under a wide range of physiologically plausible input conditions the diffusion process is equivalent to the pulse process, in terms of output interspike interval distribution. In this respect, the HH model differs from the integrate and fire model, which has been widely used to address a variety of questions in computational neuroscience.

The effects of positive and negative correlation, c, between (N=100) random synaptic inputs (each firing at 100 Hz) on the mean and coefficient of variation (CV) of interspike interval (ISI) of the Hodgkin–Huxley model are examined, for different IPSP/EPSP frequency ratios, r. Mean (ISI) and CV are approximately constant (30–40 ms, and 0.75, respectively) under independence for r∈[0,1], unlike the leaky IF small negative correlations (c≃−0.005) double mean ISI and increase CV by 25%.

We consider how correlated inputs can ensure a group of neurons (the integrate-and-fire model or the Hodgkin–Huxley model) to synchronize their activities. Without interactions, the shortest synchronization time occurs when the coefficient of variation of efferent spike trains of single neuron is greater than 0.5. The application of synchronization driven by correlated inputs to signal detection is also taken into account.

Previous studies have claimed that (a) an exact balance between numbers of randomly timed EPSPs and IPSPs and (b) high numbers of such inputs are necessary in single neuron models to obtain a coefficient of variation of interspike intervals in the physiological range (i.e. between 0.5 and 1). We show here that these are not necessary. For the perfect integrate-and-fire model, 0.5 r 0.5 whenever the ratio between the number of inhibitory and excitatory inputs, r , exceeds 0.27 for a total Poisson EPSP input rate of 10,000 Hz.

It has been reported that neurones in the visual cortex fire with a high CV (standard deviation/mean) of interspike interval, greater than 0.5. In terms of the integrate-and-fire model with and without reversal potentials, we elaborate the underlying mechanism of producing spike trains with CV greater than 0.5. When the attractor of deterministic part of models is above the threshold of the membrane potential, the firing is mainly due to deterministic forces and its output CV is usually lower than 0.5; whereas if the attractor is below the threshold, the generation of spikes results from random oscillations and the CV is usually greater than 0.5. The critical value of the number of active inhibitory synapses at which CV is greater or smaller than 0.5 is determined, which gives a clear picture of how neurones adjust their synaptic inputs to elicit irregular spike trains.

We first consider the convergence of the simple competitive learning with vanishing learning rate parameters (VLRPs). Examples show that even in this setting the learning fails to converge in general. This brings us to consider the following problem: to find out a family of VLRPs such that an algorithm with the VLRPs reaches the global minima with probability one. Here, we present an approach different from stochastic approximation theory and determine a new family of VLRPs such that the corresponding learning algorithm gets out of the metastable states with probability one. In the literature it is generally believed that a family of reasonable VLRPs is of the order of 1 t α for 1 2 , where t is the time. However, we find that a family of VLRPs which makes the algorithm go to the global minima should be between 1 log t and 1 √log t .