Inference by sampling in a model of ambiguous visual perception

Certain visual inputs can be consistently interpreted in more than one way. One classic example of this is the young-woman/old-woman puzzle:

"Boring figure", via Wikipedia user Bryan Derksen

An important finding related to these types of illusions is that we don’t perceive both possibilities at once, but rather switch spontaneously between them.

Buesing et al.’s recent study formalized a network model of spiking neurons, equivalent to sampling from a probability distribution, and used it on a quantifiable model of such visual ambiguity, binocular rivalry.

This allowed them to show how spontaneous switches between perceptual states can be caused by a sampling process which produces successively correlated samples.

In particular, they constructed a computational model with 217 neurons, and assigned each neuron a tuning curve with a preferred orientation such that the full set of orientations covered the entire 180° interval.

They then ran a simulation of these neurons according to their rules for spiking and refraction, computed the joint probability distribution, projected it in 2-d, and drew the endpoints of the projections as dots, shown below. They took samples every millisecond for 20 seconds of biological time.

the "prior distribution"; each colored dot is a sampled network state; the relative orientation of each dot corresponds to the primary orientation of the perception at that time point; a dot's distance from the origin encodes the perception's "strength"; doi:10.1371/journal.pcbi.1002211.g004 part d

Note that there is a fairly homogenous distribution across the whole orientation spectrum, indicating a lack of preference for one direction. You might think of the above as the resting state activity, as there was nothing to mimic external input to the system.

In order to add this input, the authors did another simulation in which they specified the states of a few of the neurons, “clamping” them to one value. In particular, they clamped two neurons with orientation preference ~45° to 1 (“firing”), two neurons with preference ~135° to 1, and four cells with preference ~90° to 0 (“not firing”).

Since the neurons set to firing are at opposite sides of the semicircle, this set-up mimics an ambiguous visual state. They then ran a simulation with the remaining 209 neurons as above, with the results shown below.

the "posterior distribution"; the black line shows the evolution of the network states z for 500 ms during a switch in perceptual state; doi:10.1371/journal.pcbi.1002211.g004 part e

As you can see, in this case the network samples preferentially from states that correspond to the clamped positions at either ~45° or ~135°. The black trace indicates that the network tends to remain in one high probability state for awhile and then shift rapidly to the other.

As compared to the above “prior” distribution, this “posterior” distribution has greatly reduced variance.

Although the ability of their network to explain perceptual bistability is fascinating, it is perhaps most interesting due to its broader implications for how cortical regions might be able to switch between cognitive states via sampling.

Reference

Buesing L, Bill J, Nessler B, Maass W (2011) Neural Dynamics as Sampling: A Model for Stochastic Computation in Recurrent Networks of Spiking Neurons. PLoS Comput Biol 7(11): e1002211. doi:10.1371/journal.pcbi.1002211