Decoding spike timing: The differential reverse-correlation method

Abstract

It is widely acknowledged that detailed timing of action potentials is used to encode information, for example in auditory pathways; however the computational tools required to analyze encoding through timing are still in their infancy. We present a simple example of encoding, based on a recent model of time-frequency analysis, in which units fire action potentials when a certain condition is met, but the timing of the action potential depends also on other features of the stimulus. We show that, as a result, spike-triggered averages are smoothed so much they do not represent the true features of the encoding. Inspired by this example, we present a simple method, differential reverse correlations, that can separate an analysis of what causes a neuron to spike, and what controls its timing. We analyze with this method the leaky integrate-and-fire neuron and show the method accurately reconstructs the model's kernel.The receptive field of a sensory neuron is defined as an area in the stimulus parameter space in which the presence of a stimulus significantly affects the firing behavior of the neuron. For example, visual neurons may fire when a stimulus at a given position in space and with a given orientation or velocity is presented; in this case, the receptive field of that neuron will be a region in the (5-dimensional) space of position, orientation and velocity.Methods to reconstruct receptive fields are many, and the details of the receptive field thus reconstructed are often dependent on which method is used, underscoring that the definition of a receptive field given above is rather loose. For example, in primary visual cortex there is a distinction between the "classical" receptive field (namely, the location and orientation where a single small line segment on a uniform background will, when presented by itself, elicit firing) and various "non-classical" receptive fields, i.e. regions of stimulus space where the presentation of a single segment can alter sub-threshold electrical activity, or where the presentation of a second segment alters the firing rate elicited by a first segment located within the classical receptive field [1]. This distinction dates back to Kuffler, who in 1953 observed the effect of lateral inhibition by illuminating the retina with two spots of light instead of only one, and consequently stated that "not only the areas from which responses can actually be set up by retinal illumination may be included in a definition of the receptive field but also all areas which show a functional connection, by an inhibitory or excitatory effect on a ganglion cell" [2,3].In order to accelerate the characterization of receptive fields, various approaches are often employed in which stimuli are drawn at random from the stimulus parameter space and presented to a given neuron, whereupon all those that elicit firing are averaged together. This method is thus referred to as spike-triggered averaging of the stimuli [4]. While superficially

Learning Quadratic Receptive Fields from Neural Responses to Natural Stimuli

“…. , k K · s) differential reverse correlation (dRC) spike triggering snippet linear feature that predicts spike timing (Tkačik & Magnasco, 2008) (reverse correlation)…”

Context-dependent selectivity to natural scenes in the retina

“…Compared to our study, the change in that study was evoked by a transient and dynamical change in one stimulus property, while we measured the LSTAs for flashed natural images. The results of (Geffen et al, 2007) suggest that extending our paradigm to a spatio-temporal case (Ferrari et al, 2017;Tkačik & Magnasco, 2008), by applying perturbations on top of a scene with natural dynamics, could reveal even more complexity in the LSTA dependence on context. Maheswaranathan et al, 2019 learned a deep network model on retinal responses to natural movies and noticed that the gradient of the stimulus-response function, estimated with their network model, could change polarity depending on the content of the natural scene.…”

Degraded Time-Frequency Acuity to Time-Reversed Notes

“…This is the result we would expect on the grounds of optimal-information transfer: statistical priors of a rapid-attack, slow-decay form. The reverse-correlation method, however, has only a limited ability to reconstruct auditory filters, even in the case of simulated data [11]. Additionally, such spectral methods are thrown into doubt by the existence of essential nonlinearities in the cochlea [12], [13] and the recent results that human auditory perception is more precise than any linear (spectral) method can account for [14].…”