We present a novel non-parametric method for finding a subspace of stimulus features that contains all information about the response of a system. Our method generalizes similar approaches to this problem such as spike triggered average, spike triggered covariance, or maximally informative dimensions. Instead of maximizing the mutual information between features and responses directly, we use integral probability metrics in kernel Hilbert spaces to minimize the information between uninformative features and the combination of informative features and responses. Since estimators of these metrics access the data via kernels, are easy to compute, and exhibit good theoretical convergence properties, our method can easily be generalized to populations of neurons or spike patterns. By using a particular expansion of the mutual information, we can show that the informative features must contain all information if we can make the uninformative features independent of the rest.

The timescale-invariant recognition of temporal stimulus sequences is vital for many species and poses a challenge for their sensory systems. Here we present a simple mechanistic model to address this computational task, based on recent observations in insects that use rhythmic acoustic communication signals for mate finding. In the model framework, feedforward inhibition leads to burst-like response patterns in one neuron of the circuit. Integrating these responses over a fixed time window by a readout neuron creates a timescale-invariant stimulus representation. Only two additional processing channels, each with a feature detector and a readout neuron, plus one final coincidence detector for all three parallel signal streams, are needed to account for the behavioral data. In contrast to previous solutions to the general time-warp problem, no time delay lines or sophisticated neural architectures are required. Our results suggest a new computational role for feedforward inhibition and underscore the power of parallel signal processing.

Channel noise is the dominant intrinsic noise source of neurons causing variability in the timing of action potentials and interspike intervals (ISI). Slow adaptation currents are observed in many cells and strongly shape response properties of neurons. These currents are mediated by finite populations of ionic channels and may thus carry a substantial noise component. Here we study the effect of such adaptation noise on the ISI statistics of an integrate-and-fire model neuron by means of analytical techniques and extensive numerical simulations. We contrast this stochastic adaptation with the commonly studied case of a fast fluctuating current noise and a deterministic adaptation current (corresponding to an infinite population of adaptation channels). We derive analytical approximations for the ISI density and ISI serial correlation coefficient for both cases. For fast fluctuations and deterministic adaptation, the ISI density is well approximated by an inverse Gaussian (IG) and the ISI correlations are negative. In marked contrast, for stochastic adaptation, the density is more peaked and has a heavier tail than an IG density and the serial correlations are positive. A numerical study of the mixed case where both fast fluctuations and adaptation channel noise are present reveals a smooth transition between the analytically tractable limiting cases. Our conclusions are furthermore supported by numerical simulations of a biophysically more realistic Hodgkin-Huxley type model. Our results could be used to infer the dominant source of noise in neurons from their ISI statistics.

Spike-frequency adaptation is a prominent feature of neural dynamics. Among other mechanisms, various ionic currents modulating spike generation cause this type of neural adaptation. Prominent examples are voltage-gated potassium currents (M-type currents), the interplay of calcium currents and intracellular calcium dynamics with calcium-gated potassium channels (AHP-type currents), and the slow recovery from inactivation of the fast sodium current. While recent modeling studies have focused on the effects of specific adaptation currents, we derive a universal model for the firing-frequency dynamics of an adapting neuron that is independent of the specific adaptation process and spike generator. The model is completely defined by the neuron's onset f-I curve, the steady-state f-I curve, and the time constant of adaptation. For a specific neuron, these parameters can be easily determined from electrophysiological measurements without any pharmacological manipulations. At the same time, the simplicity of the model allows one to analyze mathematically how adaptation influences signal processing on the single-neuron level. In particular, we elucidate the specific nature of high-pass filter properties caused by spike-frequency adaptation. The model is limited to firing frequencies higher than the reciprocal adaptation time constant and to moderate fluctuations of the adaptation and the input current. As an extension of the model, we introduce a framework for combining an arbitrary spike generator with a generalized adaptation current.