The Sign Rule and Beyond: Boundary Effects, Flexibility, and Noise Correlations in Neural Population Codes
Figure 1
Different structures of correlated trial-to-trial variability lead to different coding accuracies in a neural population.
(Modified and extended from [5].) We illustrate the underlying issues via a three neuron population, encoding two possible stimulus values (yellow and blue). Neurons' mean responses are different for each stimulus, representing their tuning. Trial-to-trial variability (noise) around these means is represented by the ellips(oid)s, which show 95% confidence levels. This noise has two aspects: for each individual neuron, its trial-to-trial variance; and at the population level, the noise correlations between pairs of neurons. We fix the former (as well as mean stimulus tuning), and ask how noise correlations impact stimulus coding. Different choices (A–D) of noise correlations affect the orientation and shape of response distributions in different ways, yielding different levels of overlap between the full (3D) distributions for each stimulus. The smaller the overlap, the more discriminable are the stimuli and the higher the coding performance. We also show the 2D projections of these distributions, to facilitate the comparison with the geometrical intuition of [5]. First, Row A is the reference case where neurons' noise is independent: zero noise correlations. Row B illustrates how noise correlations can increase overlap and worsen coding performance. Row C demonstrates the opposite case, where noise correlations are chosen consistently with the sign rule (SR) and information is enhanced compared to the independent noise case. Intriguingly, Row D demonstrates that there are more favorable possibilities for noise correlations: here, these violate the SR, yet improve coding performance vs. the independent case. Detailed parameter values are listed in Methods Section “Details for numerical examples and simulations”.