RF-LISSOM model of tilt aftereffects

(First be sure to try out the tilt aftereffect on yourself so that you are familiar with the phenomenon.)

The RF-LISSOM self-organizing brain model exhibits tilt aftereffects that closely match the measured values in humans:

TAE w.r.t. Angle

The blue dots and their error bars show the TAE from a human subject (Mitchell and Muir, Vision Research 16:609-613, 1976). The red line and its error bars are the corresponding results for the RF-LISSOM model from our 2000 Neural Computation paper. A version of this page with larger pictures is also available.

Because the model is implemented as a computer program, we can study it very easily and in great detail to find out how the aftereffects occur, while it is currently impossible to do such detailed analysis in humans or experimental animals. Thus the model may help us to understand how and why aftereffects occur in the real cortex, as we explain below. To follow this discussion, first check out the simple orientation perception demo to become familiar with the images we use on this page, as well as with my basic model of orientation perception.

Adaptation

An orientation map was self-organized (the equivalent of being raised from birth to adulthood), then trained for an absurdly long time on a single vertical stimulus (the equivalent of staring at one of the TAE patterns for several hours) with only lateral inhibitory weights adapting. (These conditions were chosen to magnify the effects so that they can be seen more easily in the plots; see the 2000 Neural Computation paper for more details.) The result:

Retina and initial response Settled response Orientation key
a b c
d e
f
Key:
  1. retinal image presented to the orientation map
  2. initial response of the cortex to that image
  3. orientation histogram of the initial response
  4. settled response of the cortex to that image
  5. orientation histogram of the settled response
  6. key showing color assigned to each angle
A version of this page with larger pictures is also available.

These animations repeat at regular intervals, starting over with the unadapted response and showing how the response to the test line changes during adaptation. Each animation has a logarithmic timebase, meaning that even though the changes look regular in real-time, each subsequent step actually took twice the previous time-step.

The input (left) and initial activity (next to left) remain constant, but as the network adapts to the given line, the most active units gain inhibitory connections through Hebbian learning. This causes the settled activity and histogram plots (right) to broaden, as neurons near vertical reduce their activity, while the surrounding ones increase theirs. Since the histogram remains centered at vertical throughout (see key at far right), there is no change in the orientation perceived, just as you didn't notice any change in the orientation of the central lines above while you stared at them.

Direct TAE

However, while training on the above stimulus, the average response to a nearby angle becomes very different:

Retina and initial response Settled response Orientation key
a b c
d e
f

In this case, the orientation histogram shifts markedly upwards, i.e. away from the adaptation line, just as the lines at the left side of the TAE figure seemed to twist away from the ones at which you had been staring. In the model, this change occurs because the units preferring vertical lines gain strong inhibitory connections during adaptation, while those preferring distant lines lose their connections to these units. Thus units preferring slightly tilted lines become activated more strongly at the expense of those preferring vertical lines or lines tilted the other way. The psychological result is that the average orientation changes, and thus that the perceived orientation is different than it would be otherwise (the direct tilt aftereffect). But the functional result is that small differences in orientation from the adaptation line are greatly amplified, which makes the detection of a change in orientation much easier.

Indirect TAE

The response to a distant angle goes through the opposite changes:

Retina and initial response Settled response Orientation key
a b c
d e
f

In this case, the average of the orientation histogram shifts slightly downwards, i.e. towards from the adaptation line, just as the lines at the right of the TAE figure seemed to twist slightly towards the ones you were staring at. The same forces are at work again, but the result differs because the bulk of the units activated are distant from the adaptation line's orientation. At this distance, the units were either unaffected (if they were quite different in orientation) or have primarily lost inhibitory connections rather than gained them. The result is an increase in response for those that were close enough to lose inhibitory connections, and thus an overall perceived orientation shift towards the adaptation orientation (the indirect tilt aftereffect).

Thus simple local interactions between neurons in the primary visual cortex can explain both the indirect and direct tilt aftereffects, though only the direct effect had been thought to occur at such a low level previously. For more info, including relevant publications, see the full TAE page.