In plain sight: implicit priming of patterns and faces using change symmetry

The study of pattern structure has long been an important facet of psychological research. Issues of perceptual organization, structuring of information and mechanisms of structure processing have occupied researchers since the dawn of psychological science, especially in the context of experimental aesthetics (Fechner, 1876; Wundt, 1898). This line of research received a substantial impetus from the perspective of Gestalt psychology (e.g. Koffka, 1935), which focused on the relational aspects of perception and cognition. Somewhat later, the introduction of the Information theory (Shannon, 1948) revived interest in the relationship between pattern and information especially through the work of Attneave (1954, 1959) and Garner (e.g. 1974). Introduction of statistical methods into the study of pattern structure offered a promise of precise quantification of structural relationships within a pattern. Despite substantial interest in psychological complexity starting in the 1950s, progress has been slow (see Luce, 2003; Simon, 1972 for reviews) principally because traditional methods fail to capture the structural/relational properties of the pattern.

Investigations of pattern complexity in the 1970s and 1980s have provided evidence that processing of pattern structure has a hierarchical character—not unlike other processing domains (Alexander & Carey, 1968). Researchers, such as Chipman (1977), put forward a hypothesis according to which pattern processing is governed by two processes. One is primarily concerned with the quantitative aspects of a pattern—the number of elements or element clusters—whereas the other is responsible for processing pattern structure. Later work by Ichikawa (1985) demonstrated that the first process is fast and that the second requires more time. Quantitative processes focus on pattern elements, such as number of dots, runs or clusters. In contrast, structural processes are concerned with detecting periodicities, symmetries and other structural relationships. Consequently, Ichikawa proposed a two-stage model of structure processing. He named the first stage “primary” and the second “cognitive” linking them to processing time. With short stimulus presentation times, quantitative factors dominate the judgment and the structural aspects are discovered only at a given sufficient time.

One of the most important factors in determining complexity is symmetry (Weyl, 1952), a highly salient form of redundancy which consists in a repetition of a pattern which appears to disobey the rules of perceptual integration. Symmetrical repetitions can be singular or multiple, translational, mirror or rotational (Treder, 2010; Wagemans, 1997). The prototypical form of symmetry is mirror or central symmetry which can be decomposed into repetition plus rotation of the duplicated part by 180° horizontally. When the two halves are joined, we recognise a form of redundancy which is not only common in nature (plant, animal and human body shape) but is also ubiquitous in production, design and art. Mirror or central symmetry is highly salient and desirable and this has led to a number of theories linking it to the fundamentals of human existence, such as energy conservation and genetic inheritance. The special status of symmetry in perception has been confirmed both experimentally (Huang, Pashler, & Junge, 2004) and neurophysiologically (Sasaki, Vanduffel, Knutsen, Tyler, & Tootell, 2005), in that its processing does not require attention and is confined to a specific brain region. The question we wish to address in this paper is: is a higher, more abstract form of symmetry possible which is not noticeable even under attention? If so, would this kind of symmetry still impact the perception of related and unrelated qualities?

Recently, Aksentijevic et al. reported a complexity measure which connects the subjective perspective of the human observer and the third-person perspective of mathematics and science by acknowledging the importance of the processing cost (Aksentijevic–Gibson complexity; AG) (Aksentijevic, Mihailovic, & Mihailovic, 2020; Aksentijevic, Mihailovic, Kapor, Crvenkovic, Nikolic-Djoric, & Mihailovic, 2020; Aksentijevic & Gibson, 2012a, b). In contrast to current theories, Aksentijevic–Gibson complexity offers a simple, unifying definition of complexity, namely, change. Study of changes in sensation forms the foundation of psychology. Any account of sensory processing highlights the importance of change in parameters for stimulus encoding. Similarly, there is overwhelming evidence that the brain is primarily attuned to processing change. After all, the function of neurons is the registration of change in a binary manner. Change connects psychological, physical and computational meanings of information/entropy. Any perception, cognition or action must involve change as well as irreversible conversion of energy. Change equals increase in entropy, and this in turn equals cost. Unlike invariance, change can be easily defined and, while invariance can be easily described in terms of change, the converse is not straightforward (Cutting, 1998). Change allows direct quantification of the relationship between pattern elements. Structural information is contained in the transition from one symbol (or element) to another and not in the symbols themselves.

We tested AG using a large number of complexity-related data reported in the literature including subjective and objective complexities, subjective randomness, subjective and objective symmetry, subjective goodness, mean verbalization length, informational entropy, syntely, subsymmetries, partial symmetry, SIT information index, tapping variability, copying accuracy, memorization, sequential prediction, symmetropy and rhythm reproduction accuracy and variants of Kolmogorov complexity. We tested our measure on sequences and arrays, visual and auditory patterns, and without exception obtained significant correlations with data spanning 50 years of research. In contrast to other measures, our measure successfully models statistical properties of subjective complexity judgments. In addition, we were able to explain and quantify the changes in perceived complexity as the function of stimulus exposure time.¹ Besides generality and simplicity, the most valuable property of our model is the fact that it quantifies complexity at all structural levels. This allows us to examine subjective complexity performance in much more detail than possible with other measures and to investigate different levels of the structure-processing hierarchy. For example, we can model the quantitative stage with weights that favour short substrings of S, and the structural aspect with weights that favour all lengths equally (Aksentijevic, Mihailovic, Kapor, et al., 2020; Aksentijevic & Gibson, 2012b, Sect. 3.1).

As already stated, the basis of AG is the change profile which is obtained by scanning a string exhaustively (i.e. with maximum overlap) using windows of increasing length and tallying changes at each level. Unlike Shannon entropy, AG complexity scans the string completely redundantly (taking into account all overlaps), that is, the scanning window moves by one step at a time irrespective of size. For a stringwe scan for changes between individual symbols, pairs, triplets… all the way to level L − 1. This results in a directional tally of changes for all levels of the string (from left to right):

There are nine changes at the level of symbols, six at the level of pairs and so on. The complexity of the string is computed by multiplying individual entries by the weighting factor \({w}_{j}=\frac{1}{L-j}\) and summing the products.² Thus, the AG complexity \((C)\) for the above string iswhere \(L\) is string length (in this calculation \(L=12\) and \({p}_{j}\) is the number of changes at level \(j\)). In this example, \(j\) = 1, 2, 3… 12. Levels \(j\) are reciprocals of the number of possible scans at a particular level. For example, there are 12 possible scans at \(L\) = 1 and only one at \(L\) = 11. AG complexity is intimately connected to symmetry (Aksentijevic, Mihailovic, Kapor, et al., 2020). In the course of our work, we noticed that the efficiency of our measure in detecting pattern regularities was related to a hitherto unacknowledged form of palindromicity we call change symmetry (CS; also generalised palindrome). In normal usage, a palindrome is a sequence of characters which reads the same in both directions. In other words, palindromic strings possess central or mirror symmetry (e.g. 123454321). More generally, a string S can be called an alphabet palindrome (AP) if its reverse is either S or the complement of S. Finally, a change symmetry generalizes the concept of palindromicity even further—in terms of change. An AP of \(L > 2\) is a CS. The converse is not true for strings \(L \ge 9\). Informally, CSs are patterns that register no-change at the highest structural level (\(L - 1\)). This means that read from left to right and vice versa, the change profiles of the longest substrings are identical despite the fact that the pattern does not appear palindromic.

Applying the formula to the above string, we obtain:

As can be seen, at the very last level (\(L\) = 12; rightmost fraction), only one comparison is possible. This arrangement gives AG both theoretical substance (complexity is a hierarchical phenomenon) and it also lends flexibility to the measure—although the number of changes is fixed, the weighting at different substring lengths are open to adjustment—similar to the way in which human perception focusses on various information levels, depending on the context.

In the above string, the two substrings to be compared are 010110010010 (1 to \(L\) − 1) and 101100100101 (\(L\) to 2). The two substrings possess the same profile: 86475544321 and are, therefore, identical in terms of change. Figure 1 makes explicit the equivalence between the two substrings as well as the mirror symmetry of the two change profiles. When the whole string is observed, local asymmetry is in conflict with the global change symmetry (Fig. 1). Let us look at the above string from both ends simultaneously. 01 and 10 possess a single change. 010 and 101 contain two changes each. 0101 and 1010 contain three changes each at level 1 and no changes at level 2 all the way to \(L - 1\). In this sense, CSs are fully palindromic in terms of change. Thus, the critical difference between mirror symmetry and change symmetry is that the unit of comparison is not a pattern element (or a group of elements) but the relationship between elements.

This form of hidden symmetry opens up the possibility of dissociating perceptual and neural aspects of symmetry processing.³ It is possible that the brain responds to hidden structure by reducing its energetic demands despite observers’ inability to distinguish CSs from other patterns. The aim of the present study was to investigate the ability of CSs to dissociate overt and covert aspects of pattern structure processing. In other words, it is hypothesized that CS will implicitly prime symmetry perception despite not being discriminated overtly from similar patterns lacking this property. The aim of the current paper is to examine three questions. First, does the structure embedded within CSs affect perception implicitly? Second, can CS prime facial attractiveness? Finally, can 1D symmetry prime the perception of 2D stimuli? While the first two questions have not been posed before, there is some evidence that symmetry can be primed if the primes and targets are of the same dimensionality (Yamauchi, Cooper, Hilton, Szerlip, Chen, & Barnhardt, 2006).

As a first step, we needed to confirm that CS was perceptually indistinguishable from non-CS patterns. Since this is assumed to be a function of exposure time, an appropriate time window had to be found within which this would obtain. A pilot experiment showed that with 3000-ms presentation time participants were able to distinguish CSs and non-CSs in terms of complexity.⁴ Consequently, it was decided that presentation times of 750 and 1500 ms should be used.

Following Experiment 1, Experiments 2, 3 and 4 were planned and executed in the laboratory within a single session with the aim of testing how different CS priming techniques affected different aspects of symmetry processing. If CS is a form of symmetry, we could expect it to affect spatial perceptual judgments. To illustrate if a priming stimulus is laterally biased (asymmetrical), it might guide perception towards or away from the target which is located to the left or the right of it 50% of the time. By contrast, if the prime is perceived as symmetrical, the system will require longer time to decide which side to select. Equally, if the gaze is fixated on one side, a central symmetry might impede its shift to the other side. Figure 4 illustrates this assumption. If a priming stimulus is symmetrical and the fixation is central (a, inside out), there is no preferred direction to which gaze might be attracted. By contrast, if the prime is asymmetrical, it would draw attention to any salient feature (e.g. black cluster in b, inside out). If the gaze is fixated on the edge element of the prime, it will be attracted to the centre in case of symmetry (a, outside in) or again, to any salient features (b, outside in). This results in a bias for non-symmetrical primes (a 25% information gain) if the target is located on the same side as the salient feature. We hypothesised that CS primes would behave like visibly symmetrical stimuli and offer no lateral advantage relative to asymmetric stimuli.

Imagine a typical priming trial in which a prime is replaced by a target—a standard paradigm that has been used in psychology from its beginnings. The problem with using this kind of method to prime symmetry judgments is that the symmetry of the prime (or absence thereof) is very salient and difficult to mask. The local asymmetry of CS can be used profitably here. We have seen from Experiment 1 that a CS is recognised if presented at 1500 ms. Rather than presenting a single CS and hoping that it has lasted long enough to prime the target (and risk invalidating the experiment), we decided to use a novel priming method. Having selected 12 CSs of length 13 and having disrupted these to obtain 12 non-CS strings, we divided each string into an 11-element “lock” and two-side elements (“key”). If the former is presented first, its CS is completed only once the latter is added. Thus, both components of the pattern are necessary to perceive CS. We call this “lock and key” priming in that the two-side elements act as a key to (a) “fit into the lock and (b) “unlock” the hidden symmetry. Only when both parts of the prime have been presented can the CS be primed.

You will notice that all locks are laterally biased—they possess no central symmetry and consequently “pull” towards left or right (shaded segments in Table 2). The same is true of the completed primes—whether CS or non-CS. We assume that target registration is affected by this bias, in that the eye might be predisposed to favour one of the sides. However, given that any systematic bias was removed by counterbalancing and randomisation, no effects of accuracy were expected. In other words, both hit and false alarm rates would be equally affected. Consequently, we predicted that the presence of CS would slow down a target side decision by countering the feature-related bias and increasing the uncertainty about target location—without affecting response accuracy. Since we do not currently understand the underlying mechanism, we would equally correct in saying that non-CS patterns speeded up responses. Following the results of Experiment 1, we predicted that this effect would be observable at 1500 ms—after the lock has had sufficient time to embed itself in the memory and prime the symmetry response.

Although Experiment 2 produced an interesting finding, it would be difficult to make any substantive claims based on a relatively weak effect. While deliberating whether to keep using the lock and key technique, we decided to apply a technique that combines global structural priming with feature-level masking. Since individual CS patterns differ from each other in terms of the position of individual elements/features, a rapid sequential presentation ensures that the only aspect of the pattern that is reinforced is its global structure—which is not overtly perceivable. In Experiment 1, we established that the structure of CS of length 13 becomes detectable somewhere between 750- and 1500-ms exposure. Consequently, we decided to employ a novel priming technique which helps the cognitive system to extract the implicit symmetry information without the aid of feature cues. Interference priming combines the masking of individual stimulus features with the priming of the underlying structure. Note that this is not possible with overt mirror symmetry where the two halves remain visibly identical. We hypothesized that CSs would implicitly prime 2D arrays of differing degrees of symmetry.

Face perception represents one of the most researched areas in psychology and neuroscience partly because of its importance for basic psychological processes as well as developmental and clinical contexts (Bruce & Young, 2012; Liu, et al., 2010). Facial attractiveness is of particular interest since it has been hypothesized to reflect evolutionary and genetic advantages, and this in turn confers advantages in terms of mate selection, career choice and social advancement (Catena, Simmons & Roney, 2019). Importantly, there is significant agreement that central symmetry can enhance the attractiveness of a face as long as this is not exaggerated (Fink, et al., 2006; Rhodes, et al., 1998). The question that naturally arises is: is it possible to prime positive facial attractiveness ratings by means of symmetric geometrical patterns? In Experiment 4, we went one step further and asked if it was possible to improve facial attractiveness ratings by implicit priming of hidden (change) symmetry.

The present study investigated effects of a novel form of symmetry (change symmetry) on the perception of singleton targets, 2D arrays and faces. The concept of change symmetry (or general palindromicity) arises from a shift away from the focus on elements/features/objects to a more holistic Gestalt-like approach which acknowledges the importance of the relationships between objects. While the feature-based approach to perception has resulted in a number of interesting ideas and results, ultimately, it fails to address the most important question, namely how do we perceive the whole? This is clearly much more than a simple/linear agglomeration of features. Although obvious, this insight is not very helpful unless it can be translated into some kind of quantitative theory. Aksentijevic–Gibson complexity is one theory which translates the Gestalt insight into a quantitative model of perception. In the context of the current paper, the most relevant is the conceptual shift from objects to the relationship between them. The most basic relationship is identity/difference. In a dynamic context, this is translatable to change and absence of change, respectively. Aside from its theoretical advantages, using change to describe structure is efficient because it tells us something about the hierarchical ordering of information without having to rely on probability which hampers the quantification of higher structural levels (see e.g. Attneave, 1959).

We predicted that CSs would boost the perceived symmetry either directly or indirectly. To ensure absence of featural symmetry clues, we first established the time needed to perceive CS (Experiment 1) and then applied a couple of novel symmetry priming techniques. In Experiment 2, we applied a lock and key principle to avoid presenting the entire CS prime at the same time. The core of the pattern (lock) is presented and then extinguished to be replaced by the side elements (key). In Experiments 3 and 4, we presented priming stimuli rapidly and sequentially so that even if the symmetrical “essence” of an individual stimulus could be perceived, it would be erased and replaced by the succeeding pattern. In the latter experiments, we employed 2D targets to minimize any figural associations with the prime.

As demonstrated by the pilot experiment, under free-viewing conditions and a long presentation time (3000 ms), difference between CSs and non-CSs could be discerned—non-CS patterns were perceived as somewhat more complex (participants did not spot any structural differences). This compelled us to seek out a point in time at which the two types of pattern became indistinguishable. The results of Experiment 1 suggested that viewers required more than 750 ms to distinguish between them. One way of capitalising on this was to investigate how CS affected performance on an unrelated task (Experiment 2). A CS stimulus was never shown on the screen in its entirety and any effects of symmetry would have been caused by the completion of the pattern in a memory trace. The result confirmed that at 1500-ms duration of the lock segment, the presence of CS slowed down target detection.

To reduce the possibility of confounding by various stimulus-related factors, we designed a prime which was robust with respect to these. First, each priming stimulus was presented for 500 ms—time that is too short to permit the recognition of CS. Next, we created a priming “burst” containing 24 stimuli (two sets of 12 freshly randomised for every trial). This means that every prime is masked and erased by the next one. Added to the brief presentation time, this strategy ensures that information contained within a single priming stimulus cannot affect the participants’ response. All that is left is the “distillate” of high-level structure which is perceived implicitly. This is salient enough to bias the perceptual system even further towards a preference for symmetry.

The result of Experiment 3 can be explained in terms of energetic demands associated with perception and cognition. As elaborated elsewhere (e.g. Treder, 2010), complexity is intimately related to the cost of information processing. In that context, symmetry represents probably the most important redundancy signal in perception. The impact of visual symmetry on the perceiver is partly owed to the fact that a symmetrical form is easy to process, memorise and reproduce (e.g. Reber, Schwarz, & Winkielman, 2004). It could be said that the perceptual system is highly attuned to symmetry by the need to minimise effort (Falk & Konold, 1997). It seeks out symmetries and other informational shortcuts to direct effort towards stimuli that lack such shortcuts. Given the inherent symmetry bias, it is not surprising that presenting symmetric stimuli as primes should strengthen it. What is more interesting is that the presentation of 1D information which is not overtly perceived as symmetrical achieves the same result.

While the results of Experiment 3 are largely understandable if surprising, the findings of Experiment 4 are intriguing and challenging. The importance of facial and bodily symmetry has been linked to evolutionary advantages especially with respect to mate selection (Grammer & Thornhill, 1994; Møller & Thornhill, 1998). These qualities have been linked to a good genetic inheritance and health (Scheib, Gangestad, & Thornhill, 1999). Good health in turn ensures safe procreation and survival of one’s genetic line. Although not very romantic, the evolutionary explanation for the effects of facial symmetry on facial attractiveness is compelling. How then can one explain the fact that such an important evolutionary function is primed by a blurry sequence of black and white squares? Clearly, symmetry, even at a very high, abstract level, guides perception. Although this is not a new observation, the results of the present study demonstrate the profundity and power of its influence. One possible explanation concerns the concept of processing fluency which associates visual symmetry with positive effect that in our case is transferred to faces resulting in higher attractiveness judgment (Pecchinenda, Bertamini, Makin, & Ruta, 2014).

Regarding a specific mechanism, it is too early to speculate although recent work points at a possible way forward. Work by Kietzmann et al. (2017) has shown that the processing of different facial viewpoints produces distinct spatiotemporal patterns of cortical activation. Whereas the first and earliest viewpoint encoding scheme (60 ms post stimulus) encodes separate face orientations, the next one (peaking at approximately 115 ms), mirror symmetrical representations are recognised and the frontal representation is distinguished at about 280 ms post stimulus. FMRI results (e.g. Sasaki, et al., 2005; Tyler et al. 2005) place symmetry perception in the extra-striatal occipital lateral areas (OL). Assuming that CS takes longer to encode than visible symmetry, one could speculate that the “meeting” of symmetry and face-specific activation clusters occurs at approximately 300 ms post stimulus at the transitional area between the occipital lateral and parietal central areas. Once the structural effects of face and symmetry processing are merged, the structurally enhanced representation elicits a higher affective response.

Generally, we can locate our paradigm at the intersection of Gestalt perceptual organisation and hierarchical processing (Han & Humphreys, 1999). The distinction between local and global processing was established by means of suitable stimuli which could be manipulated to accentuate/attenuate either aspect (Navon, 1977). The main difference between Navon’s and our paradigm is the divergence between local asymmetry and global symmetry which enables us to dissociate the two levels more completely. With Navon-type stimuli, both the global and local information is equally available. Second, the function of Navon’s task is to diagnose the type of processing favoured in a particular experimental context. CS, on the other hand, can be used both as a prime and a target. More importantly, CS provides a more realistic definition of global processing in that the global configuration is not a simple sum of local elements (Nucci & Wagemans, 2007).

The observed effects of change symmetry allow us to theorise on the stages of perceptual processing. Very simple patterns (those containing few runs) are easily handled by both local or global strategies. For example, a pattern comprising few elements/clusters can be assimilated rapidly (e.g. black squares on the left; Aksentijevic & Gibson, 2012a; Glanzer & Clark, 1962). This agrees with the finding that grouping by proximity is faster than other forms of grouping (e.g. Ben-Av & Sagi, 1995) and that such Gestalt grouping processes are largely pre-attentional (Baylis & Driver, 1993; Humphreys, Olson, Romani, & Riddoch, 1996; Kahneman & Treisman, 1984; Kramer & Jacobson, 1991; Moore & Egeth, 1997). Here, one should note that a possible confounding with stimulus complexity and also that absence of attention do not necessarily imply conscious perception and categorisation—even when attention is involved. Furthermore, research has demonstrated that attention does not play a significant role in symmetry detection (Huang, et al., 2004) although the situation is not straightforward (Treder, 2010). Whether perfect or partial, symmetry is processed in parallel across the stimulus without capacity limit. This could be explainable by means of a mechanism which assesses incoming stimuli perhaps by means of hard-wired cross-cortical structures which perform comparisons of the two halves of the stimulus (Corballis & Roldan, 1974; Julesz, 1971).

As patterns become more complex, more time is required for their structure to be processed and this is where two-stage theories become relevant. Although it is clear that the brain requires time to absorb the featural arrangement (in agreement with Chipman. 1977; Ichikawa, 1985), we have no evidence that the effects of CS are conscious or based on a cognitive strategy. Rather, we believe that CS accesses the higher areas of the visual brain (V3 and above; Keefe, et al., 2018; Sasaki, et al., 2005; Tyler, Baseler, Kontsevich, Likova, Wade, & Wandell, 2005) extra-attentionally and from there guides the processing of the incoming structural information by looking for changes between the two halves of the stimulus.

One interesting aspect of our results is the dissociation between effects of exposure time and engagement of attention. On the one hand, some effects of CS emerge only after a long exposure (over a second; Experiments 1 and 2). On the other hand, the results of Experiments 3 and 4 suggest an extra-attentional effect by virtue of stimulus design (future research will investigate the precise timing mechanism of CS priming). The results of the first two experiments offer support for a two-stage model of pattern processing, such as Ichikawa’s (1985), according to which the primary stage of processing involves comparisons of surface/quantitative aspects of a pattern. These findings are also in agreement with the proposal by Behrmann and Kimchi (2003) who posit a distinction between low-level visual processes responsible for simple local grouping and higher-level processes responsible for holistic processing. Finally, the results of Experiments 1 and 2 appear compatible with the theorizing by Roelfsema (2006) which distinguishes between two types of grouping mechanism, namely fast “base-grouping” responsible for simple feature extraction and slower incremental grouping which governs higher-level structural processes. As shown by our results, holistic processing of structure and specifically symmetry, affects judgments which can be but do not have to be strictly perceptual. Although we were not able precisely to determine the underlying temporal mechanisms, CS “did its work” only after a period of about 1000–1500 ms. In perceptual research, such durations are commonly associated with conscious perception. However, here, the situation was a bit more complicated in that even prolonged exposure to the prime does not guarantee overt registration of the symmetry.

While Experiments 1 and 2 support two-stage accounts of structure processing, Experiments 3 and 4 indicate that however much time it takes for CS to be encoded, it behaves like a symmetry despite the fact that no symmetry in the accepted sense is present in the stimulus. This poses a question that needs to be addressed by future research, namely is it possible that CS behaves differently from visible symmetry in that its processing is slow yet extra-attentional? Thus, further research is needed to explore the attentional status of change symmetry. More research is also needed to establish a relationship between parameters, such as pattern length and time needed for the symmetry to become overtly available. At the same time, CS could represent a useful tool for probing certain aspects of early perceptual processing especially those pertaining to global vs. local processing. As hypothesized by Aksentijevic and Gibson (2012a), change conceptually precedes invariance and this could translate into “detection of change precedes detection of invariance”, thus allowing precise investigation of the time course of symmetry processing.

In conclusion, we present results of four experiments that demonstrate the effectiveness of a new form of symmetry in producing covert priming effects in three different experimental contexts. This “change symmetry” is not easily perceivable and as such offers a new venue for investigating perceptual processing of structural invariance.