History-dependent changes of Gamma distribution in multistable perception

Multistable perception – spontaneous switches of perception when viewing a stimulus compatible with several distinct interpretations – is often characterized by the distribution of durations of individual dominance phases. For continuous viewing conditions, these distributions look remarkably similar for various multistable displays and are typically described using Gamma distribution. Moreover, durations of individual dominance phases show a subtle but consistent dependence on prior perceptual experience with longer dominance phases tending to increase the duration of the following ones, whereas the shorter dominance leads to similarly shorter durations. One way to generate similar switching behavior in a model is by using a combination of cross-inhibition, self-adaptation, and neural noise with multiple useful models being built on this principle. Here, we take a closer look at the history-dependent changes in the distribution of durations of dominance phases. Specifically, we used Gamma distribution and allowed both its parameters – shape and scale – to be linearly dependent on the prior perceptual experience at two timescales. We fit a hierarchical Bayesian model to five datasets that included binocular rivalry, Necker cube, and kinetic-depth effects displays, as well as data on binocular rivalry in children and on binocular rivalry with modulated contrast. For all datasets, we found a consistent change of the distribution shape with higher levels of perceptual history, which can be viewed as a proxy for perceptual adaptation, leading to a more normal-like shape of the Gamma distribution. When comparing real observers to matched simulated dominance phases generated by a spiking neural model of bistability, we found that although it matched the positive history-dependent shift in the shape parameter, it also predicted a negative change of scale parameter that did not match empirical data. We argue that our novel analysis method, the implementation is available freely at the online repository, provides additional constraints for computational models of multistability. Author Summary Multistable perception occurs when one continuously views a figure that can be seen in two distinct ways. A classic old-young woman painting, a face-vase figure, or a Necker cube are examples easy to find online. The endless spontaneous switches of your perception between the alternatives inform us about the interplay of various forces that shape it. One way to characterize these switches is by looking at their timing: How long was a particular image dominant, how did that reflect what you have seen previously, the focus of your attention, or the version of the figure that we showed you? This knowledge allows us to build models of perception and test them against the data we collected. As models grow more elaborate, we need to make tests more elaborate as well and for this, we require more precise and specific ways to characterize your perception. Here, we demonstrate how your recent perceptual experience – which of the alternative images did you see and for how long – predicts subtle but consistent changes in the shape of the distribution that describes perceptual switching. We believe it to be a more stringent test by demonstrating how a classical model of bistability fails on it.


24
Necker cube, and kinetic-depth effects displays, as well as data on binocular rivalry in children and 25 on binocular rivalry with modulated contrast. For all datasets, we found a consistent change of the 26 distribution shape with higher levels of perceptual history, which can be viewed as a proxy for 27 perceptual adaptation, leading to a more normal-like shape of the Gamma distribution. When 28 comparing real observers to matched simulated dominance phases generated by a spiking neural 29 model of bistability, we found that although it matched the positive history-dependent shift in the 30 shape parameter, it also predicted a negative change of scale parameter that did not match 31 empirical data. We argue that our novel analysis method, the implementation is available freely at 32 the online repository, provides additional constraints for computational models of multistability. that we showed you? This knowledge allows us to build models of perception and test them 41 against the data we collected. As models grow more elaborate, we need to make tests more 42 elaborate as well and for this, we require more precise and specific ways to characterize your 43 perception. Here, we demonstrate how your recent perceptual experience -which of the 44 alternative images did you see and for how long -predicts subtle but consistent changes in the 45 shape of the distribution that describes perceptual switching. We believe it to be a more stringent 46 test by demonstrating how a classical model of bistability fails on it.

68
When multistable displays are presented continuously, their perception is often characterized by a 69 distribution of duration times or, conversely, by the alternation rate. Although duration times vary 70 strongly between subjects, the shape of the distributions is remarkably similar [6], see Figure 1D.

120
In the present study, we sought to characterize the changes to gamma distribution using prior

223
In addition, we included the effect of contrast and participants' age for, respectively, contrast and 224 development data sets.

225
The shape and scale parameters of the fitted gamma distributions (without effects of history, 226 contrast, and age) for all participants are plotted in Figure 4A. They show typical values with most 227 shape parameters clustering between 2 and 4 and similarly tight clustering for the scale parameter.

228
For the data set that used contrast manipulation, the effect of contrast matches that reported by 229 van Ee [20]. Specifically, higher contrast led to a positive change for the shape parameter but a 230 negative one for scale parameter (Figure 4B, left panel). However, we found no effect of age on 231 either parameter of the gamma distribution ( Figure 4B

240
The history dependence of the parameters for both timescales is summarized in Figure 5. For the 241 short timescale perceptual history, we found a consistent positive shift for the shape parameter 14 242 across all five data sets, although the effect was weaker for Necker Cube (NC). For the scale 243 parameter, we also found a generally positive effect, although it was weaker and less consistent 244 across the data sets than that for the shape. The effect of the history for longer time scale was 245 more variable with mostly negative changes to both parameters indicating an overall speed-up 246 trend for perceptual alternations over time. We also compared the dominance phases of real observers with that generated by a spiking neural 258 model of bistability [22]. The model was fit so as to match distributions of individual participants in 259 three data sets (BR, KD, and NC) as closely as possible (see Methods for details). However, the 260 simulated data was not optimized with respect to history-dependence, as the latter was not 261 included in the fitness function. In addition, the selected model does not generate a long-term 262 trend and, therefore, we opted to use only the short timescale history. The comparison of the main 263 effect of perceptual history is presented in Figure 6 with the results matching those of the real 264 observers only partially. Although we found a similar positive shift for the shape parameter, we 265 also observed a consistent negative history-dependent shift for the scale parameter. This contrasts 266 simulated data with that from human observers, as for the latter we found a small and inconsistent 267 but mostly positive change for the scale parameter (gray histograms in (Figure 6). Interestingly, 268 the effect of short timescale history for the model was similar to that of contrast ( Figure 4B).  capturing the underlying dynamics. We must note, however, that the model parameters were not 312 optimized for history-dependence only for the overall match of the distribution shapes.

313
Accordingly, the observed history-dependence in simulated data was not there by choice but was a 314 product of the model itself. Therefore, it is possible that more thorough parameter-matching could 315 produce a better match. Nonetheless, this discrepancy shows the usefulness of our approach for 316 in-depth analysis of computational models of multistable perception.

317
To conclude, we presented a novel analysis method, the implementation is available freely at the 318 online repository, which improves our ability to characterize the history-dependence of time-series 319 of perceptual alternations, provides additional constraints for computational models of 320 multistability.