Laboratory of Neuropsychology, National Institute of Health
Assessing information processing in V1 neurons across stimulus sets
A linear relationship between log(mean) and log(variance) of spike counts elicited by different stimuli has been observed in many parts of the brain (Tolhurst et al. 1981, Dean 1981, Tolhurst et al. 1983, van Kan et al. 1985, Vogels et al. 1989, O'Keefe et al. 1997, Gershon et al. 1998, Lee et al. 1998). The means and variances of responses to individual stimuli scatter around the regression line. Under the assumption that true log(mean) and log(variance) of all response distributions fall on this line, the scatter is due to variability in sample estimates of mean and variance. Fitting the linear relation to the sample means and variances uses information from the responses to all tested stimuli to help describe the distribution of responses to each individual stimulus.
If we assume that the distribution of spike counts elicited by each stimulus is completely specified by its mean and variance (e.g. Gaussian), the linear relation between log(mean) and log(variance) characterizes the set of possible response distributions, in that the variance can be determined from the mean using the mean-variance relation. Now the distribution of responses to any stimulus can be described using the slope and intercept of this relation - a single slope and intercept for each neuron - and a single additional number - the mean response to that stimulus. Since the responses to any stimulus have some mean (even if it is zero), this is a model of all possible response distributions. According to this model two stimuli that elicit the same mean response from a neuron elicit identical response distributions, and so form a single equivalence class of stimuli for that neuron. Therefore, the set of all possible stimuli is reduced to the set of equivalence classes, which can in turn be represented by all possible mean responses (at whatever resolution is desired).
Because the mean-variance model characterizes all of a neuron's response distributions, it can be used to calculate a neuron's channel capacity - that is, the maximum information the neuron could transmit using a particular neural code. Channel capacity has been calculated in this way for the spike count code (Gershon et al., 1998; Wiener & Richmond, 1998) and for a two-dimensional principal component code. While transmitted information depends on which stimuli are used in an experiment and the frequency with which each stimulus is presented, channel capacity depends only on the neuron's noise characteristics and range of possible responses. A change in the mean-variance relation indicates either a change in how a neuron processes its inputs or a change in the nature of those inputs (or both). Channel capacity quantifies the effect of any changes on the neuron's ability to transit information.
To investigate the consistency of the mean-variance relation, we recorded the responses of neurons in monkey primary visual (V1) cortex using stimuli of four different kinds: bars, sine-wave gratings, Walsh patterns, and digitized photographs of scenes and objects. The mean-variance relation did not change across these stimulus sets. A related issue is whether small eye movements during fixation affect response variability (Gur et al. 1997, O'Keefe et al. 1997). We find no evidence that eye movements affect the linear relation between log(mean) and log(variance) of spike count. Thus neither the neuron's processing of its inputs nor the nature of its inputs changed across stimulus set or eye movement.
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