With Tom Sullivan, another graduate student, we have been constructing models to test our ideas about learning rules and connectivity in the early visual cortical areas. We have shown that complex cells can develop from retinal waves and a persistence of activation in the neurons. This had been shown previously for very artificial waves and neurons; Tom's model uses more realistic waves and neurons and develops a smooth map of cortical complex cells. More recently we have contrasted the assumption of activation pattern seen with optical imaging and used in our model and many others to the sparse coding literature. As mentioned earlier, we have also continued exploring the conundrum of cortical feedback connections - how can feedback give a net inhibitory effect when it is known that the direct connections are almost purely excitatory (from excitatory neurons to excitatory neurons)? We have more recently investigated the computational properties of the recently discovered homeostatic synaptic plasticity finding where neurons regulate their synapse strength according to their average firing rate. We have shown that this rule is mathematically related to the commonly used (but unmotivated) weight normalization rule and that it can lead to stable map learning, particularly if it is implemented during sleep.
In addition to constructing models based on physiological data, we are also building models to explain psychophysical behavior. Our work builds on the ODOG model of Blakeslee and McCourt -- a mechanistic model that can simultaneously account for several seemingly contradictory psychophysical results. The ODOG model can account for the simultaneous brightness contrast effect (where a gray square surrounded by black appears lighter than one surrounded by white) as well as the more surprising ``White's effect'' (where a gray patch in a vertical grating appears lighter when surrounded by more white than black.) It also accounts for many other lightness illusions. We created a more biologically plausible version of the model using normalization that is local in space and spatial frequency. With the new model we are able to account for several more brightness illusions. Our next step is to create a more realistic model with actual lateral connections. We will relate the optimal size of the lateral connections in the model to anatomical data on the lengths and connectivity patterns of cortical horizontal connections. This work will be an important link between anatomy and physiology, and perception and behavior.