It is well known that pauses in the presentation of an ambiguous display may stabilize its perceptual appearance. Here we show that this stabilization depends on an extended history spanning several dominance periods, not merely on the most recent period. Specifically, appearance after a pause often reflects less recent (but longer) dominance periods rather than more recent (but shorter) periods. Our results imply the existence of a short-tem memory for perceptual appearance that builds up over seconds, decays over minutes, and is robust to perceptual reversals. Although this memory is most evident in paused displays, it influences perceptual reversals also when display presentation continues: while the memory of one appearance prevails over that of the other, successive dominance durations are positively correlated. This highly unusual successive dependence suggests that multi-stable perception is not the memoryless ‘renewal process’ as which it has long been regarded. Instead, a short-term memory of appearance must be added to the multiple processes that jointly produce reversals of perceptual appearance.

*multi-stable perception,*which has intrigued scientific minds for two centuries, continues to be investigated with a large variety of both binocular (Blake & Logothetis, 2002) and monocular displays (Leopold & Logothetis, 1999). Surprisingly, the perceptual fluctuations elicited by widely different kinds of displays exhibit a universal stochastic nature (e.g., Brascamp, van Ee, Pestman, & van den Berg, 2005): perceptual dominance times are distributed statistically (approximating a Gamma distribution) and successive dominance periods are independent (Fox & Herrmann, 1967; Levelt, 1967).

^{2}.

^{2}), uniformly covering the surface of a virtual sphere, were projected orthographically. The virtual sphere (diameter 5.6°) rotated 0.25 Hz about a vertical axis and was centered 3.2° above or below fixation (depending on the observer's preference). This display is ambiguous and consistent with two opposite rotations in depth. Phenomenal appearance is bi-stable and alternates between the two possible rotations.

*P*

_{survival}), defined as the probability that the same appearance will dominate before and after the blank period (e.g., Leopold et al., 2002). If

*A*

_{1},

*A*

_{2}, and

*A*

_{3}denote the respective appearances of the first, second, and third dominance periods during a display period (see Figures 1B and 1C) and if

*i*is the index of the display period, ‘survival’ of phenomenal appearance is defined as

*A*

_{2}

^{i}=

*A*

_{1}

^{i+1}in Experiment 1 and

*A*

_{1}

^{i}=

*A*

_{3}

^{i}=

*A*

_{1}

^{i+1}in Experiment 2.

*i*to

*i*+ 1 was compared to the duration of dominance periods

*T*

_{1},

*T*

_{2}, and

*T*

_{3}in display period

*i*( Figures 1B and 1C). As mean dominance times varied significantly between different observers and between different experimental sessions with each observer, dominance durations are reported as multiples of the mean dominance duration 〈

*T*

_{dom}〉 for each session. This session mean was computed as the average of (up to) 30 values of

*T*

_{1}in Experiment 1 and 30 values of

*T*

_{1}and

*T*

_{2}in Experiment 2.

*T*

_{2}after the

*first*phenomenal reversal was reported ( Figure 1B).

*T*

_{2}remained constant during each block but ranged between 0.0 and 0.9 times 〈

*T*

_{dom}〉 in different blocks. At the beginning of each session, the mean dominance duration 〈

*T*

_{dom}〉 was established for each observer under conditions of continuous stimulation. A second estimate of 〈

*T*

_{dom}〉 was obtained from the main experiment.

*T*

_{RT}= 385 ± 100 ms and used this value to correct for the inevitable delay between a phenomenal reversal and its voluntary report by the observer. Specifically, dominance times

*T*

_{1}and

*T*

_{2}were computed as

*T*

_{1}+

*T*

_{2}) in order to minimize adaptation effects (Petersik, 2002). In absolute numbers, the blank period ranged from 1700 to 7700 ms with a mean of 2924 ms. In this range of durations, blank periods are expected to stabilize perception and reduce the frequency of reversals (Kornmeier, 2002; Kornmeier, Ehm, Bigalke, & Bach, 2007).

*second*phenomenal reversal was reported ( Figure 1C). The duration of

*T*

_{3}, which could not be measured, was assumed to be equal to the observer's reaction time

*T*

_{RT}(see above). To correct for reporting delays, dominance durations were computed as

*T*

_{1}+

*T*

_{2}+

*T*

_{3}). In absolute terms, the blank period ranged from 1834 to 4321 ms in this experiment.

*T*

_{1}was terminated by a spontaneous reversal of appearance, while the second period

*T*

_{2}ended artificially with the display period.

*T*

_{2}was kept constant for each block but varied systematically between blocks. Each display period was followed by a blank period of equal duration (

*T*

_{1}+

*T*

_{2}). In the analysis of this experiment,

*P*

_{survival}

^{2}is the probability that onset appearance agrees with the most recent dominance period (prior to the interruption), while

*P*

_{survival}

^{1}= 1 −

*P*

_{survival}

^{2}is the probability that it is consistent with the less recent dominance period. Further details may be found in the Methods section.

*T*

_{1}exhibited the characteristic variability of multi-stable percepts ( Figure 2C). Typically, both appearances were reported at the onset of display periods, although this varied between sessions and observers. Figure 2D shows the distribution of report fractions

*A*

_{right}/(

*A*

_{right}+

*A*

_{left}) over all sessions and observers (average 0.46 ± 0.28). Thus, we cannot confirm that observers consistently favor one particular onset appearance, as reported recently for another type of multi-stable display (Carter & Cavanagh, 2007).

*P*

_{survival}

^{2}, which lay

*below*0.5 for most observers, ranging from 0.268 to 0.54 for individual observers and averaging to 0.38 ± 0.12 over all observers ( Figure 2E). Thus, appearances before and after the interruption

*disagreed*more often than not. This results contrast markedly from the values of

*P*

_{survival}> 0.8 obtained when only one dominance period is allowed per display period (Leopold et al., 2002; Maier et al., 2003; Pearson & Clifford, 2005).

*P*

_{survival}

^{ i}on

*T*

_{1}and

*T*

_{2}, we took advantage of the fact that

*T*

_{1}varied between display periods and

*T*

_{2}varied between blocks. Specifically, we sorted display periods into bins according to the value of

*T*

_{1}and computed the average value of

*P*

_{survival}

^{1}for each bin ( Figure 3A). Similarly, we computed the dependence of

*P*

_{survival}

^{2}on the value of

*T*

_{2}( Figure 3B) and on the value of

*T*

_{2}−

*T*

_{1}( Figure 3C). In each case, the results show that the probability of a particular appearance after the interruption increases with length of time for which this appearance was dominant prior to the interruption.

*less recent*)

*T*

_{1}than for (the

*more recent*)

*T*

_{2}. Note, however, that the range of values sampled for

*T*

_{2}was less than half that for

*T*

_{1}. Presumably,

*P*

_{survival}

^{2}would have reached larger values if longer durations of

*T*

_{2}could have been explored. This expectation was borne out by the dependence of

*P*

_{survival}

^{2}on

*T*

_{2}−

*T*

_{1}( Figure 3C): for positive

*T*

_{2}−

*T*

_{1},

*P*

_{survival}rises steeply with the value of

*T*

_{2}−

*T*

_{1}. Accordingly, the

*most recent*appearance persists whenever it outlasts the

*less recent*appearance, regardless of absolute duration.

*P*

_{survival}(KS test,

*n*= 10,

*D*= 0.2,

*p*> 0.2). However, the mean run length decreased significantly with increasing

*T*

_{2}( Figure 4A). This fits with the idea that onset appearance is determined by ‘lingering biases’: when

*T*

_{2}is much shorter than

*T*

_{1}, the onset appearance leaves the stronger ‘bias’ and becomes self-perpetuating, resulting in long COPs. As

*T*

_{2}increases toward

*T*

_{1}, the ‘bias’ from the second appearance grows, increasing the likelihood of an inconsistent onset and thus curtailing COPs.

*T*

_{1}were significantly correlated between successive display periods ( Figure 4B). This violation of sequential independence was limited to successive display periods falling within the same COPs, with correlation coefficients as high as 0.55. For successive display periods falling outside COPs, no correlation between the values of

*T*

_{1}was evident.

*T*

_{1}and

*T*

_{2}) lasted until appearance reversed spontaneously, while the third period (

*T*

_{3}) was terminated by the end of the display period.

*T*

_{3}was kept as short as possible and not varied systematically. Each display period was followed by a blank period of equal duration (

*T*

_{1}+

*T*

_{2}+

*T*

_{3}). In the context of this experiment,

*P*

_{survival}

^{1,3}is the probability that onset appearance matches the most recent dominance period (prior to the interruption), while

*P*

_{survival}

^{2}= 1 −

*P*

_{survival}

^{1,3}is the probability that it matches the less recent dominance period. For further details, the reader is referred to the Methods section.

*T*

_{1}and

*T*

_{2}varied stochastically, exhibiting typical Gamma-like distributions ( Figure 5C). No observer consistently reported one particular appearance at the onset of display periods ( Figure 5D). The survival probability

*P*

_{survival}

^{1,3}of the most recent appearance averaged 0.62 ± 0.17 across observers ( Figure 5E).

*P*

_{survival}

^{ i}depends on the dominance times of the preceding display period, we sorted display periods into bins according to the value of

*T*

_{1}+

*T*

_{3}and computed the average value of

*P*

_{survival}

^{1,3}for each bin ( Figure 6A). Similarly, we computed the dependence of

*P*

_{survival}

^{2}on the value of

*T*

_{2}( Figure 6B) and of

*P*

_{survival}

^{1,3}on the value of

*T*

_{1}−

*T*

_{2}+

*T*

_{3}( Figure 6C). As in the first experiment, we observed that a particular onset appearance becomes the more likely, the longer it had been dominant during the preceding display period. This demonstrates that at least three dominance periods influence a subsequent onset appearance.

*P*

_{survival}(KS test,

*n*= 10,

*D*= 0.36,

*p*> 0.1). As in Experiment 1, individual values of

*T*

_{1}and

*T*

_{2}were correlated in successive display periods, provided these fell into the same COP ( Figure 7). The observed correlation was stronger for the appearance not dominating the onsets of the COP (

*T*

_{2}).

*A*

_{ i}(

*i*∈ {1,2}) dominates perception, the associated bias

*B*

_{ i}increases exponentially with time constant

*τ*

_{rise}( Equation 6). When

*A*

_{ i}is suppressed or the display interrupted, bias

*B*

_{ i}decreases exponentially with time constant

*τ*

_{fall}( Equation 7).

*t*is time during the dominance period,

*t*

_{0}is the time at the beginning of the dominance period, and

*τ*

_{rise}and

*τ*

_{fall}are the time constants of the rise and fall, respectively.

*B*is the minimal differential bias needed to sway appearance at onset and

*A*

_{preferred}is the intrinsic preference of the observer.

*τ*

_{rise},

*τ*

_{fall}, Δ

*B,*and

*A*

_{preferred}) and the reported dominance periods for each block of trials, we can calculate the absolute and relative bias strength at the time of each display onset and thus predict onset appearance.

*A*

_{preferred}was determined by noting the initial appearance at the start of each block, while

*τ*

_{rise},

*τ*

_{fall}, and Δ

*B*were determined by fitting the model to our observations. The fraction of correctly predicted onset appearances served as a measure of the quality of fit.

*τ*

_{rise}/〈

*T*

_{dom}〉 = 0.3 ± 0.5,

*τ*

_{fall}/〈

*T*

_{dom}〉 = 31 ± 18, and Δ

*B*= 0.02 ± 0.005, where the error ranges correspond to a fit quality of >95% of the optimal fit. Although the error ranges of individual parameters are fairly broad, the narrow and elongated shape of the parameter region providing the best fits shows that

*τ*

_{fall}is approximately two orders of magnitude larger than

*τ*

_{rise}( Figure 8B). These values for

*τ*

_{rise}and

*τ*

_{fall}are in good agreement with recent empirical measurements (Pastukhov & Braun, 2007b), which determined the dependence of

*P*

_{survival}on the duration of a single, preceding dominance period (to obtain

*τ*

_{rise}) and on the duration of the blank period (to obtain

*τ*

_{fall}). In those measurements, we had obtained values of

*τ*

_{rise}/〈

*T*

_{dom}〉 = 0.4 ± 0.1 and

*τ*

_{fall}/〈

*T*

_{dom}〉 = 30 ± 10.

*P*

_{survival}

^{ i}on dominance times is quantitatively reproduced ( Figures 9A– 9F), although at times the model predicts more extreme values of

*P*

_{survival}

^{ i}than are actually observed. This includes the dependencies on

*T*

_{2}and

*T*

_{2}−

*T*

_{1}in Experiment 1 ( Figures 9B and 9C), as well as the dependencies on

*T*

_{1}+

*T*

_{3}and

*T*

_{1}−

*T*

_{2}+

*T*

_{3}in Experiment 2 ( Figures 9D– 9F).

*T*

_{ON}terminated after one or two reversals,

*T*

_{OFF}equal to the preceding

*T*

_{ON}) and analyzed the predicted relationship between dominance times and onset appearance. As mentioned by Noest and colleagues, the particular (linear) type of adaptive decay implemented in their model predicts only marginal effects on onset appearance for

*T*

_{OFF}≫

*τ*

_{adaptation}, that is, for the regime of long

*T*

_{OFF}investigated by us. However, this shortcoming can easily be remedied by introducing a “long-tailed” adaptive decay. As an alternative to extending the persistence of adaptation effects, we computed the predicted onset appearance for shorter

*T*

_{OFF}(average

*T*

_{OFF}equal to

*τ*

_{adaptation}). Noise level and

*τ*

_{adaptation}were fit to our observations. All other parameters were left unchanged.

*P*

_{survival}on the duration of the most recent appearance (before the interruption, Figure 10B), it does not account for the dependence on less recent appearances ( Figures 10A– 10C), which constitutes the critical evidence for a memory-like process.

*τ*

_{adaptation}must be comparable to 〈

*T*

_{dom}〉 in order to contribute to phenomenal reversals,

*τ*

_{fall}must be an order of magnitude larger than 〈

*T*

_{dom}〉 to produce the observed persistence of ‘positive bias’. The second difficulty is posed by persistence across several dominance periods. While adaptive states must decay within a dominance period (to permit phenomenal reversals), the positive bias must ‘linger’ over several dominance periods to account for our observations.

*τ*

_{rise}and

*τ*

_{fall}, respectively. Quantitative analysis suggests that decay rates are at approximately two orders of magnitude slower than accumulation rates, consistent with earlier observations (Pastukhov & Braun, 2007b).

^{2+}-gated K

^{+}-channels (McCormick & Williamson, 1989).