When a neuronal spike train is observed, what can we deduce from it about the properties of the neuron that generated it? A natural way to answer this question is to make an assumption about the type of neuron, select an appropriate model for this type, and then choose the model parameters as those that are most likely to generate the observed spike train. This is the maximum likelihood method. If the neuron obeys simple integrate-and-fire dynamics, Paninski, Pillow, and Simoncelli ( 2004 ) showed that its negative log-likelihood function is convex and that, at least in principle, its unique global minimum can thus be found by gradient descent techniques. Many biological neurons are, however, known to generate a richer repertoire of spiking behaviors than can be explained in a simple integrate-and-fire model. For instance, such a model retains only an implicit (through spike-induced currents), not an explicit, memory of its input; an example of a physiological situation that cannot be explained is the absence of firing if the input current is increased very slowly. Therefore, we use an expanded model (Mihalas & Niebur, 2009 ), which is capable of generating a large number of complex firing patterns while still being linear. Linearity is important because it maintains the distribution of the random variables and still allows maximum likelihood methods to be used. In this study, we show that although convexity of the negative log-likelihood function is not guaranteed for this model, the minimum of this function yields a good estimate for the model parameters, in particular if the noise level is treated as a free parameter. Furthermore, we show that a nonlinear function minimization method (r-algorithm with space dilation) usually reaches the global minimum.

We present a first-order nonhomogeneous Markov model for the interspike-interval density of a continuously stimulated spiking neuron. The model allows the conditional interspike-interval density and the stationary interspike-interval density to be expressed as products of two separate functions, one of which describes only the neuron characteristics and the other of which describes only the signal characteristics. The approximation shows particularly clearly that signal autocorrelations and cross-correlations arise as natural features of the interspike-interval density and are particularly clear for small signals and moderate noise. We show that this model simplifies the design of spiking neuron cross-correlation systems and describe a four-neuron mutual inhibition network that generates a cross-correlation output for two input signals.

We present a multichip, mixed-signal VLSI system for spike-based vision processing. The system consists of an 80 × 60 pixel neuromorphic retina and a 4800 neuron silicon cortex with 4,194,304 synapses. Its functionality is illustrated with experimental data on multiple components of an attention-based hierarchical model of cortical object recognition, including feature coding, salience detection, and foveation. This model exploits arbitrary and reconfigurable connectivity between cells in the multichip architecture, achieved by asynchronously routing neural spike events within and between chips according to a memory-based look-up table. Synaptic parameters, including conductance and reversal potential, are also stored in memory and are used to dynamically configure synapse circuits within the silicon neurons.