It is widely believed that the tuning of sensory neurons is adapted to the statistical structure of the signals they must encode (Sterling and Laughlin, 2015). This normative principle, known as efficient coding, has been successful in explaining many aspects of neural processing in vision (Atick and Redlich, 1990; Fairhall et al., 2001; Laughlin, 1981; Olshausen and Field, 1996; Pitkow and Meister, 2012), audition (Carlson et al., 2012; Smith and Lewicki, 2006) and olfaction (Teşileanu et al., 2019), including adaptation (Młynarski and Hermundstad, 2021) and gain control (Schwartz and Simoncelli, 2001). In Hermundstad et al., 2014, we reported that human sensitivity to visual textures defined by local multipoint correlations depends on the variability of such correlations across natural scenes. This allocation of resources to features that are the most variable in the environment, and thus more informative about its state, is accounted for by efficient coding, demonstrating its role as an organizing principle also at the perceptual level (Hermundstad et al., 2014; Tesileanu et al., 2020; Tkacik et al., 2010). However, it remains unknown whether this preferential encoding of texture statistics that are the most variable across natural images is a general principle underlying visual perceptual sensitivity across species. Although some evidence exists for differential neural encoding of multipoint correlations in macaque V2 (Yu et al., 2015) and V1 (Purpura et al., 1994), the sensitivity ranking we previously reported in Hermundstad et al., 2014 has not been investigated in any species other than humans (Hermundstad et al., 2014; Tesileanu et al., 2020; Tkacik et al., 2010; Victor and Conte, 2012). Moreover, while monkeys are standard models of advanced visual processing (DiCarlo et al., 2012; Kourtzi and Connor, 2011; Lehky and Tanaka, 2016; Nassi and Callaway, 2009; Orban, 2008), they are less amenable than rodents to causal manipulations (e.g. optogenetic or controlled rearing) to interrogate how neural circuits may adapt to natural image statistics. On the other hand, rodents have emerged as powerful model systems to study visual functions during the last decade (Glickfeld et al., 2014; Glickfeld and Olsen, 2017; Huberman and Niell, 2011; Katzner and Weigelt, 2013; Niell and Scanziani, 2021; Reinagel, 2015; Zoccolan, 2015). Rats, in particular, are able to employ complex shape processing strategies at the perceptual level (Alemi-Neissi et al., 2013; De Keyser et al., 2015; Djurdjevic et al., 2018; Vermaercke and Op de Beeck, 2012), and rat lateral extrastriate cortex shares many defining features with the primate ventral stream (Kaliukhovich and Op de Beeck, 2018; Matteucci et al., 2019; Piasini et al., 2021; Tafazoli et al., 2017; Vermaercke et al., 2014; Vinken et al., 2017). More importantly, it was recently shown that rearing newborn rats in controlled visual environments allows causally testing long-standing hypotheses about the dependence of visual cortical development from natural scene statistics (Matteucci and Zoccolan, 2020). Establishing the existence of a preferential encoding of less predictable statistics in rodents is therefore crucial to understand the neural substrates of efficient coding and its relationship with postnatal visual experience.

To address this question, we measured rat sensitivity to visual textures defined by local multipoint correlations, training the animals to discriminate binary textures containing structured noise from textures made of white noise (Figure 1A). The latter were generated by independently setting each pixel to black or white with equal probability, resulting in no spatial correlations. Structured textures, on the other hand, were designed to enable precise control over the type and intensity of the correlations they contained. To generate these textures we built and published a software library (Piasini, 2021) that implements the method developed in Victor and Conte, 2012. Briefly, for any given type of multipoint correlation (also termed a statistic in what follows), we sampled from the distribution over binary textures that had the desired probability of occurrence of that statistic, but otherwise contained the least amount of structure (i.e. had maximum entropy). The probability of occurrence of the pattern was parametrized by the intensity of the corresponding statistic, determined by a parity count of white or black pixels inside tiles of 1, 2, 3, or 4 pixels (termed gliders) used as the building blocks of the texture (Victor and Conte, 2012). When the intensity is zero, the texture does not contain any structure–it is the same as white noise (Figure 1A, left). When the intensity is +1, every possible placement of the glider across the texture contains an even number of white pixels, while a level of –1 corresponds to all placements containing an odd number of white pixels. Intermediate intensity levels correspond to intermediate fractions of gliders containing the even parity count. The structure of the glider and the sign of the intensity level dictate the appearance of the final texture. For instance (see examples in Figure 1A, right), for positive intensity levels, a one-point glider produces textures with increasingly large luminance, a two-point glider produces oriented edges and a four-point glider produces rectangular blocks. A three-point glider produces L-shape patterns, either black or white depending on whether the intensity is negative or positive.

Figure 1 with 1 supplement see all

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Notably, two-point and three-point gliders are associated to multiple distinct multipoint correlations, corresponding to different spatial glider configurations. For instance, two-point correlations can arise from horizontal (-), vertical (|) or oblique gliders (/, \), while three-point correlations can give rise to L patterns with various orientations (${\displaystyle {\theta }_{⌝}}$, ${\theta }_{\mathrm{\neg }}$, ${\displaystyle {\theta }_{⌞}}$, ${\displaystyle {\theta }_{⌟}}$). In our previous study with human participants (Hermundstad et al., 2014), we tested all these two-point, three-point, and four-point configurations, as well as 11 of their pairwise combinations, for a total of 20 different texture statistics. In that set of experiments, we did not test textures defined by one-point correlations because, by construction, the method we used to measure the variability of texture statistics across natural images could not be applied to the one-point statistic. In our current study, practical and ethical constraints prevented us from measuring rat sensitivity to a large number of statistic combinations, because a different group of animals had to be trained with each tested statistic (see below), meaning that the number of rats required for the experiments increased rapidly with the number of statistics studied. Therefore, we chose to test the 4-point statistic, as well as one each of the two-point and three-point statistics (those shown in Figure 1A). One of the three-point statistics (corresponding to the glider ${\displaystyle {\theta }_{⌟}}$) was randomly selected among the four available, since in our previous study no difference was found among the variability of distinct three-point textures across natural images, and aggregate human sensitivity to three-point correlations was measured without distinguishing among glider configurations. As for the two-point statistic, we selected one of the two gliders (the horizontal one) that yielded the largest sensitivity in humans, so as to include in our stimulus set at least an instance of both the most discriminable (two-point -) and least discriminable (three-point ${\displaystyle {\theta }_{⌟}}$) textures. In addition, we also tested the one-point statistic because, given the well-established sensitivity of the rat visual system to luminance changes (Minini and Jeffery, 2006; Tafazoli et al., 2017; Vascon et al., 2019; Vermaercke and Op de Beeck, 2012), performance with this statistic served as a useful benchmark against which to compare rat discrimination of the other, more complex textures. Finally, while in Hermundstad et al., 2014, both positive and negative values of the statistics were probed against white noise, here we tested only one side of the texture intensity axis (either positive, for one-, two-, and four-point configurations, or negative, for three-point ones) — again, with the goal of limiting the number of rats used in the experiment (see Materials and methods for more details on the rationale behind the choice of statistics and their polarity, and see Discussion for an assessment of the possible impact of these choices on our conclusions).

For each of the four selected image statistics, we trained a group of rats to discriminate between white noise and structured textures containing that statistic with nonzero intensity (Figure 1A). Each trial of the experiment started with the rat autonomously triggering the presentation of a stimulus by licking the central response port within an array of three (Figure 1B). The animal then reported whether the texture displayed over the monitor placed in front of him contained the statistic (by licking the left port) or white noise (by licking the right port). The rat received liquid reward for correct choices and was subjected to a time-out period for incorrect ones (Figure 1B). In the initial phase of the experiment, the intensity of the statistic was set to a single level, close to the maximum (or minimum, in case of the three-point statistic, for which we used only negative values), to make the discrimination between structured textures and white noise as easy as possible for naive rats that had to learn the task from scratch. The learning curves of four example rats, one per group, are shown in Figure 1—figure supplement 1A. In the following phase of the experiment, the intensity of the statistic was gradually reduced using an adaptive staircase procedure (see Materials and methods) to make the task progressively harder. The asymptotic levels of the statistics reached across consecutive training sessions by four example rats, one per group, are shown in Figure 1—figure supplement 1B. Following this training, rats were subjected to: (1) a main testing phase, where textures were sampled at regular intervals along the intensity level axis and were randomly presented to the animals; and (2) a further testing phase, where rats originally trained with a given statistic were probed with a different one (see Materials and methods for details on training and testing).

The main test phase yielded psychometric curves showing the sensitivity of each animal in discriminating white noise from the structured texture with the assigned statistic (example in Figure 2A, black dots). To interpret results, we developed an ideal observer model, in which the presentation of a texture with a level of the statistic equal to s produces a percept $x$ sampled from a truncated Gaussian distribution centered on the actual value of the statistic ($s$) with a fixed standard deviation σ (Fleming et al., 2013; Geisler, 2011). Here, σ measures the ‘blurriness’ in the animal's sensory representation for a particular type of statistic (i.e. the perceptual noise) and, consequently, its inverse 1/σ captures its resolution, or sensitivity — i.e., the perceptual threshold for discriminating a structured texture from white noise. As detailed in the Materials and methods, our ideal observer model yields the psychometric function giving the probability of responding ‘noise’ at any given level of the statistic $s$ as

Figure 2 with 1 supplement see all

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where $\mathrm{\Phi }(x)$ is the standard Normal cumulative density function, $\alpha$ captures the animal’s prior choice bias and $x^{*}(\alpha ,\sigma )$ is the decision boundary used by the animal to divide the perceptual axis into ‘noise’ and ‘structured texture’ regions. The two free parameters of the model (α and σ) parameterize the psychometric function (example in Figure 2A, blue curve) and can be estimated from behavioral data by maximum likelihood. Prior bias ($\alpha$) and sensitivity ($1/\sigma$) are related, respectively, to the horizontal offset and slope of the curve.

Fitting this model to the behavioral choices of rats in the four groups led to psychometric functions with a characteristic shape, which depended on the order of the multipoint statistic an animal had to discriminate (Figure 2B). In particular, the sensitivity $1/\sigma$ followed a specific ranking among the groups (Figure 2C), being higher for one- and two-point than for three-point (p₁<0.001 and p₂<0.001, two-sample t-test with Holm-Bonferroni correction) and four-point (p₁<0.001, p₂<0.001) correlations, and larger for four-point than three-point correlations (p<0.01). When focusing on the texture statistics that had been also tested in our previous study (i.e. two-point horizontal, three-point, and four-point correlations), this sensitivity ranking was the same as the one observed in humans and as the variability ranking measured across natural images (Hermundstad et al., 2014): two-point horizontal > four-point > three-point. Moreover, for the set of statistics that were studied both here and in Hermundstad et al., 2014, the actual values of the rat sensitivity matched, up to a scaling factor, both the human sensitivity and the standard deviation of the statistics in natural images (Figure 3). This match was quantified with the ‘degree of correspondence’, defined in Hermundstad et al., 2014, which takes on values between 0 and 1, with one indicating perfect quantitative match (see Materials and methods for details). The degree of correspondence was 0.986 between rat sensitivity and image statistics (p-value: 0.07, Monte Carlo test), and 0.990 between rat sensitivity and human sensitivity (p-value: 0.05, Monte Carlo test). For reference, Hermundstad et al., 2014 reported values between 0.987 and 0.999 for the degree of correspondence between human sensitivity and image statistics. This indicates not only a qualitative but also a quantitative agreement between our findings and the pattern of texture sensitivity predicted by efficient coding.

Figure 3

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To further validate these findings, we performed additional within-group and within-subject comparisons. To this end, each group of animals was either tested with a new statistic or was split into two subgroups, each tested with a different statistic. Results of these additional experiments are reported in Figure 4, comparing the sensitivity to the new statistic(s) with the sensitivity to the originally learned statistic (colored symbols without and with halo, respectively) for each group/subgroup. Rats trained on one- and two-point statistics (the most discriminable ones; see Figure 2C) performed poorly with higher-order correlations (compare the green and purple star with the red star, and the green and purple cross with the blue cross in Figure 4), while animals trained on the four-point statistic performed on two-point correlations as well as rats that were originally trained on those textures (compare the blue square to the blue cross). This shows that the better discriminability of textures containing lower order correlations is a robust phenomenon, which is independent of the history of training and observable within individual subjects. Moreover, performance on four-point correlations was higher than performance on three-point correlations for each group of rats (compare the green to the purple symbols connected by a line). This was true, in particular, not only for rats trained on four-point and switching to three-point (green vs. purple square, p < 0.01, paired one-tailed t-test) but even for rats trained on three-points and switching to four-point (green vs. purple triangle, p < 0.05, paired one-tailed t-test). This means that the larger discriminability of the four-point statistic, as compared to the three-point one, is a statistically robust phenomenon within individual subjects.

Figure 4

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Overall, our results show that rat sensitivity to multipoint statistics is similar to the one we previously observed in humans and to the variability of multipoint correlations we previously measured across natural images (Hermundstad et al., 2014; Tkacik et al., 2010). This agreement holds both qualitatively and quantitatively (Figures 2—4). Importantly, we found the expected sensitivity ranking (two-point horizontal > four-point > three-point) to be robust not only across groups (Figure 2C) but also for animals that were sequentially tested with multiple texture statistics (Figure 4) - and even at the within-subject level for the crucial three-point vs. four-point comparison. Moreover, we found a high degree of correspondence between rat and human sensitivities (Figure 3).

A potential limitation of our study is related to our stimulus choices, both in terms of selected texture statistics and polarity (i.e. negative vs. positive intensity). A first possible issue is whether the three texture statistics that were tested in both the present study and in Hermundstad et al., 2014 are sufficient to allow a meaningful comparison between rat and human sensitivities, as well as rat sensitivity and texture variability in natural scenes. We addressed this matter at the level of experimental design, by carefully choosing the three statistics that, based on the sensitivity ranking observed in humans, would have yielded the cleanest signature of efficient coding (Hermundstad et al., 2014). That is, we selected two statistics that were, respectively, maximally and minimally variable across natural images, and yielded the largest and lowest sensitivities in humans: horizontal two-point correlations and one of the three-point correlations. The four-point correlation was then a natural choice as the third statistic, as it was the only one characterized by a differently shaped glider. Additionally, human sensitivity to this statistic, as well as its variability across natural images, is only slightly larger than for the three-point configurations. Therefore, finding a reliable sensitivity difference between three-point and four-point textures also for rats would have provided strong evidence for matching texture sensitivity across the two species. Due to the experimental limitations discussed in the Results and the Materials and methods sections, we were unable to analyze one of the oblique two-point statistics, for which human sensitivity takes on an intermediate value between the two-point horizontal and three-point correlations, and that in humans allows one to differentiate between the predictions of efficient coding and those stemming from an oblique effect for patterns that are rotated versions of each other (Hermundstad et al., 2014).

The second potential limitation is related to the choice of polarity (positive or negative intensity values for the examined statistics). This choice was guided by different considerations depending on the kind of statistic. For one-point correlations we chose positive intensity values because they yield patterns that are brighter than white noise. Since previous work from our group has shown that rat V1 neurons are very sensitive to increases of luminance (Tafazoli et al., 2017; Vascon et al., 2019), our choice ensured that one-point textures were highly distinguishable from white noise (as indeed observed in our data; see Figure 2B–C), which was the key requirement for our benchmark statistic. This enabled us to guard against issues in our task design: if the animals had failed to discriminate one-point textures, this would have suggested an overall inadequacy of the behavioral task rather than a lack of perceptual sensitivity to luminance changes. For two-point and four-point statistics we also used positive intensity values — a choice dictated by the need of testing a rodent species that has much lower visual acuity than humans (Keller et al., 2000; Prusky et al., 2002; Zoccolan, 2015). Positive two-point and four-point correlations give rise to large features (thick oriented stripes and wide rectangular blocks made of multiple pixels with the same color), while negative intensities produce higher spatial frequency patterns, where color may change every other pixel (see Figure 2A in Hermundstad et al., 2014). Therefore, using negative two-point and four-point statistics would have introduced a possible confound, since low sensitivity to these textures could have been simply due to the low spatial resolution of rat vision. For three-point correlations, polarity does not affect the shape and size of the emerging visual patterns, but it determines their contrast. Positive and negative intensities yield L-shaped patches that are, respectively, white and black. In this case, we chose the latter to make sure that the well-known dominance of OFF responses observed across the visual systems of many mammal species would not play in favor of finding the lowest sensitivity for the three-point statistic. In fact, several studies have shown that primary visual neurons of primates and cats respond more strongly to black than to white spots and oriented bars (Liu and Yao, 2014; Xing et al., 2010; Yeh et al., 2009). A very recent study has shown that this is the case also for the central visual field of mice, although in the periphery OFF and ON response are more balanced (Williams et al., 2021). Indeed, the asymmetry begins already in the retina where there are more OFF cells than ON cells (Ratliff et al., 2010). Since in our behavioral rigs rats face frontally the stimulus display (Figure 1B) and maintain their head oriented frontally during stimulus presentation (Vanzella et al., 2019), it was important that the L-shaped patterns produced by three-point correlations had the highest saliency. Choosing negative intensity values ensured that this was the case, thus excluding the possibility that the low-sensitivity found for three-point textures (Figures 2—4) was partially due to presentation at a suboptimal contrast. Notwithstanding these considerations, one could wonder whether probing also the opposite polarities of those tested in our study would be desirable for a tighter test of the efficient coding principle. Previous studies, however, found human sensitivity to be nearly identical for negative and positive intensity variations of each of the statistic tested in our study: one-point, two-point, three-point, and four-point correlations (Victor and Conte, 2012), even in the face of asymmetries of the distribution of the corresponding statistic in natural images (see Figure 3—figure supplement 9 in Hermundstad et al., 2014). In the present work, we have accordingly decided to focus the available resources on the differences between different statistics, rather than between positive and negative intensities of the same statistic.

In summary, our choices of texture types and their polarity were all dictated by the need of adapting to a rodent species texture stimuli that, so far, have only been used in psychophysics studies with humans (Hermundstad et al., 2014; Tesileanu et al., 2020; Tkacik et al., 2010; Victor and Conte, 2012) and neurophysiology studies in monkeys (Purpura et al., 1994; Yu et al., 2015). Our goal was to maximize the sensitivity of the comparison with humans and natural image statistics, while reducing the possible impact of phenomena (such as rat low visual acuity and the dominance of OFF responses) that could have acted as confounding factors. Thanks to these measures, our findings provide a robust demonstration that a rodent species and humans are similarly adapted to process the statistical structure of visual textures, in a way that is consistent with the computational principle of efficient coding. This attests to the fundamental role of natural image statistics in shaping visual processing across species, and opens a path toward a causal test of efficient coding through the altered-rearing experiments that small mammals, such as rodents, allow (Hunt et al., 2013; Matteucci and Zoccolan, 2020; White and Fitzpatrick, 2007).

Experimental data are available at (Caramellino et al., 2021).

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Author details

1. Riccardo Caramellino

   Visual Neuroscience Lab, International School for Advanced Studies, Trieste, Italy

   Contribution

   Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Visualization, Writing - original draft

   Contributed equally with

   Eugenio Piasini

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-2201-8079

2. Eugenio Piasini

   Computational Neuroscience Initiative, University of Pennsylvania, Philadelphia, United States

   Present address

   Neural Computation Lab, International School for Advanced Studies, Trieste, Italy

   Contribution

   Conceptualization, Formal analysis, Methodology, Software, Writing – review and editing

   Contributed equally with

   Riccardo Caramellino

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-0384-7699

3. Andrea Buccellato

   Visual Neuroscience Lab, International School for Advanced Studies, Trieste, Italy

   Contribution

   Investigation

   Competing interests

   No competing interests declared

4. Anna Carboncino

   Visual Neuroscience Lab, International School for Advanced Studies, Trieste, Italy

   Contribution

   Investigation

   Competing interests

   No competing interests declared

5. Vijay Balasubramanian

   Computational Neuroscience Initiative, University of Pennsylvania, Philadelphia, United States

   Contribution

   Conceptualization, Funding acquisition, Supervision, Writing – review and editing

   For correspondence

   vijay@physics.upenn.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-6497-3819

6. Davide Zoccolan

   Visual Neuroscience Lab, International School for Advanced Studies, Trieste, Italy

   Contribution

   Conceptualization, Funding acquisition, Methodology, Project administration, Resources, Supervision, Writing – review and editing

   For correspondence

   zoccolan@sissa.it

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-7221-4188

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