observed in every X LGN cell; in all but one it accounted for about as many anonymous spikes as the discharge in the excitatory phase. No delayed discharge of anonymous spikes was ever observed in the Y LGN cells.
Since the delayed discharge of anonymous spikes is unique to X LGN cells, it is tempting to examine that discharge for an explanation of the difference between X and Y pairs in linearity of the variance of rate. However, some Y cell pairs show an increase in slope of log variance of rate versus log rate between retina and LGN, but nevertheless are devoid of this discharge. And a comparison of the strength of this discharge in X cells with the extent of their change in slope reveals no relationship. It is also is hard to imagine why an added discharge during the relatively low rate response phase would increase slope: It would increase variability (and rate), bringing the data points at the low end up toward those at the high end. Further analyses will be needed to explain how the variance of rate is made proportional to rate, and to define the role (if any) of the delayed burst in this process.
Finally, might the anonymous spikes actually be "learned" across the cycles of a repeated stimulus? Might they be an anticipatory response to the next cycle, such as has been observed even in retina ? To test for this, the PSTHs of triggered and anonymous spikes were plotted for the first three cycles and the last three cycles of stimulation. No differences could be discerned across cycles in the latencies to each response, or in the size of the delayed discharges of X cells. A simple spike count in the excitatory phase of the responses did show one significant effect: In both X and Y ganglion cells there was a tendency to fire fewer spikes in the final cycles than the first (t=3.35, p<0.01). This effect of fatigue or habituation was not significant in either the triggered or anonymous spikes of the LGN, although the tendency was in the same direction.
It appears that the variance of rate is more nearly proportional to rate in the X cells of the LGN than in their corresponding retinal drivers; this is likely a step on the way to the direct proportionality reported for primary cortex [43, 45, 46] and the V4 "color and pattern" (parvocellular) area of primate higher cortex . If this is truly an effect of the X system and not of the Y, as seems likely, it would seem that the features of the cortical variance are set more by X inputs than by Y. This could support the idea that the Y system plays a minor part in the main processing task of the cortex, the analysis of visual shape and form.
There is another possible implication to the finding that variance of rate is made proportional to rate: From equation (1), it may be seen that CV will be constant. That is, the signal to noise ratio will be independent of response strength if the intervals convey the neural code.
What advantage might be bestowed by having the signal to noise ratio held constant? If the function of the neural network (higher visual cortex) is to extract an image, or percept, the percept should not vary with the stimulus strength. The same solution should be found regardless of image quality, as long as the image is not too degraded to comprehend. We perceive that poorer images are "grayer" or "dirtier" than high quality images, but we still extract the same perception, recognize the same pattern in both. Lateral antagonism, light adaptation, contrast gain controls, and similar mechanisms known to function in the visual system serve to produce the constancy that permits us to see the same object regardless of lighting. Perhaps variability is part of an analogous process, and so must be similarly adjusted to maintain object constancy.
A role for noise has been postulated in terms of neural network problem solving: Variability is useful for preventing a problem-solving network from settling into a local minimum in the multidimensional solution space it is searching. Noise can be used to extricate the network from local minima, but the computational dilemma is how to keep the noise from dislodging the network from the correct solution [e.g.: 7]. Adjusting the amplitude of the variability to match the signal strength may be part of the answer. The variability is strong where the signal is strong, so there is sufficient dither to escape local minima (but the signal can still prevail). The variability weakens where the signal is weak, so there is minimal noise to prevent the network from taking account of subtle cues. It appears that a scaling of variability is precisely what the X system achieves.
I wish to thank Dr. Brian Cleland, who conducted all the retina/LGN pair experiments while I did what I could to assist. That work was supported by the NH&MRC of Australia, and by the Fogarty Center of NIH (TW01317). I am grateful to all the colleagues with whom I have worked over the years, especially to Drs. Laura Frishman and