There is extensive evidence that biological neural networks encode information in the precise timing of the spikes generated and transmitted by neurons, which offers several advantages over rate-based codes. Here we adopt a vector space formulation of spike train sequences and introduce a new liquid state machine (LSM) network architecture and a new forward orthogonal regression algorithm to learn an input-output signal mapping or to decode the brain activity. The proposed algorithm uses precise spike timing to select the presynaptic neurons relevant to each learning task. We show that using precise spike timing to train the LSM and selecting the readout presynaptic neurons leads to a significant increase in performance on binary classification tasks, in decoding neural activity from multielectrode array recordings, as well as in a speech recognition task, compared with what is achieved using the standard architecture and training methods.

Inferring mathematical models of sensory processing systems directly from input-output observations, while making the fewest assumptions about the model equations and the types of measurements available, is still a major issue in computational neuroscience. This letter introduces two new approaches for identifying sensory circuit models consisting of linear and nonlinear filters in series with spiking neuron models, based only on the sampled analog input to the filter and the recorded spike train output of the spiking neuron. For an ideal integrate-and-fire neuron model, the first algorithm can identify the spiking neuron parameters as well as the structure and parameters of an arbitrary nonlinear filter connected to it. The second algorithm can identify the parameters of the more general leaky integrate-and-fire spiking neuron model, as well as the parameters of an arbitrary linear filter connected to it. Numerical studies involving simulated and real experimental recordings are used to demonstrate the applicability and evaluate the performance of the proposed algorithms.

Integrate-and-fire neurons are time encoding machines that convert the amplitude of an analog signal into a nonuniform, strictly increasing sequence of spike times. Under certain conditions, the encoded signals can be reconstructed from the nonuniform spike time sequences using a time decoding machine. Time encoding and time decoding methods have been studied using the nonuniform sampling theory for band-limited spaces, as well as for generic shift-invariant spaces. This letter proposes a new framework for studying IF time encoding and decoding by reformulating the IF time encoding problem as a uniform sampling problem. This framework forms the basis for two new algorithms for reconstructing signals from spike time sequences. We demonstrate that the proposed reconstruction algorithms are faster, and thus better suited for real-time processing, while providing a similar level of accuracy, compared to the standard reconstruction algorithm.