Emergent color categorization in a neural network trained for object recognition

  1. Jelmer P de Vries
  2. Arash Akbarinia
  3. Alban Flachot
  4. Karl R Gegenfurtner

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    This paper addresses the long-standing problem of color categorization and the forces that bring it about, which can be potentially interesting to researchers in cognition, visual neuroscience, society, and culture. In particular, the authors show that as a "model organism", a Convolutional Neural Network (CNN) trained with the human-labelled image dataset ImageNet for object recognition can represent color categories. The finding reveals important features of deep neural networks in color processing and can also guide future theoretical and empirical work in high-level color vision.

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Abstract

Color is a prime example of categorical perception, yet it is unclear why and how color categories emerge. On the one hand, prelinguistic infants and several animals treat color categorically. On the other hand, recent modeling endeavors have successfully utilized communicative concepts as the driving force for color categories. Rather than modeling categories directly, we investigate the potential emergence of color categories as a result of acquiring visual skills. Specifically, we asked whether color is represented categorically in a convolutional neural network (CNN) trained to recognize objects in natural images. We systematically trained new output layers to the CNN for a color classification task and, probing novel colors, found borders that are largely invariant to the training colors. The border locations were confirmed using an evolutionary algorithm that relies on the principle of categorical perception. A psychophysical experiment on human observers, analogous to our primary CNN experiment, shows that the borders agree to a large degree with human category boundaries. These results provide evidence that the development of basic visual skills can contribute to the emergence of a categorical representation of color.

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  1. Version published to 10.7554/elife.76472 on eLife
  2. eLife

    Author Response

    Reviewer #1 (Public Review):

    1. One nagging concern is that the category structure in the CNN reflects the category structure baked into color space. Several groups (e.g. Regier, Zaslavsky, et al) have argued that color category structure emerges and evolves from the structure of the color space itself. Other groups have argued that the color category structure recovered with, say, the Munsell space may partially be attributed to variation in saturation across the space (Witzel). How can one show that these properties of the space are not the root cause of the structure recovered by the CNN, independent of the role of the CNN in object recognition?

    We agree that there is overlap with the previous studies on color structure. In our revision, we show that color categories are directly linked to the CNN being trained on the objectrecognition task and not the CNN per se. We repeated our analysis on a scene-trained network (using the same input set) and find that here the color representation in the final layer deviates considerably from the one created for object classification. Given the input set is the same, it strongly suggests that any reflection of the structure of the input space is to the benefit of recognizing objects (see the bottom of “Border Invariance” section; Page 7). Furthermore, the new experiments with random hue shifts to the input images show that in this case stable borders do not arise, as might be expected if the border invariance was a consequence of the chosen color space only.

    A crucial distinction to previous results is also, is that in our analysis, by replacing the final layer, specifically, we look at the representation that the network has built to perform the object classification task on. As such the current finding goes beyond the notion that the color category structure is already reflected in the color space.

    1. In Figure 1, it could be useful to illustrate the central observation by showing a single example, as in Figure 1 B, C, where the trained color is not in the center of the color category. In other words, if the category structure is immune to the training set, then it should be possible to set up a very unlikely set of training stimuli (ones that are as far away from the center of the color category while still being categorized most of the time as the color category). This is related to what is in E, but is distinctive for two reasons: first, it is a post hoc test of the hypothesis recovered in the data-driven way by E; and second, it would provide an illustration of the key observation, that the category boundaries do not correspond to the median distance between training colors. Figure 5 begins to show something of this sort of a test, but it is bound up with the other control related to shape.

    We have now added a post-hoc test where we shift the training bands from likely to unlikely positions using the original paradigm: Retraining output layers whilst shifting training bands from the left to the right category-edge (in 9 steps) we can see the invariance to the category bounds specifically (see Supp. Inf.: Figure S11). The most extreme cases (top and bottom row) have the training bands right at the edge of the border, which are the interesting cases the reviewer refers to. We also added 7 steps in between to show how the borders shift with the bands.

    Similarly, if the claim is that there are six (or seven?) color categories, regardless of the number of colors used to train the data, it would be helpful to show the result of one iteration of the training that uses say 4 colors for training and another iteration of the training that uses say 9 colors for training.

    We have now included the figure presented in 1E, but for all the color iterations used (see SI: Figure S10. We are also happy to include a single iteration, but believe this gives the most complete view for what the reviewer is asking.

    The text asserts that Figure 2 reflects training on a range of color categories (from 4 to 9) but doesn’t break them out. This is an issue because the average across these iterations could simply be heavily biased by training on one specific number of categories (e.g. the number used in Figure 1). These considerations also prompt the query: how did you pick 4 and 9 as the limits for the tests? Why not 2 and 20? (the largest range of basic color categories that could plausibly be recovered in the set of all languages)?

    The number of output nodes was inspired by the number of basic color categories that English speakers observe in the hue spectrum (in which a number of the basic categories are not represented). We understand that this is not a strong reason, however, unfortunately the lack of studies on color categories in CNNs forced us to approach this in an explorative manner. We have adapted the text to better reflect this shortcoming (Bottom page 4). Naturally if the data would have indicated that these numbers weren’t a good fit, we would have adapted the range. (if there were more categories, we would have expected more noise and we would have increased the number of training bands to test this). As indicated above, we have now also included the classification plots for all the different counts, so the reader can review this as well (SI: Section 9).

    1. Regarding the transition points in Figure 2A, indicated by red dots: how strong (transition count) and reliable (consistent across iterations) are these points? The one between red and orange seems especially willfully placed.

    To answer the question on the consistency we have now included a repetition of the ResNet18, with the ResNet34, ResNet50 and ResNet101 in the SI (section 1). We have also introduced a novel section presenting the result of alternate CNNs to the SI (section S8). Despite small idiosyncrasies the general pattern of results recurs.

    Concerning the red-orange border, it was not willfully placed, but we very much understand that in isolation it looks like it could simply be the result of noise. Nevertheless, the recurrence of this border in several analyses made us confident that it does reflect a meaningful invariance. Notably:

    • We find a more robust peak between red and orange in the luminance control (SI section 3).

    • The evolutionary algorithm with 7 borders also places a border in this position.

    • We find the peak recurs in the Resnet-18 replication as well as several of the deeper ResNets and several of the other CNNs (SI section 1)

    • We also find that the peak is present throughout the different layers of the ResNet-18.

    1. Figure 2E and Figure 5B are useful tests of the extent to which the categorical structure recovered by the CNNs shifts with the colors used to train the classifier, and it certainly looks like there is some invariance in category boundaries with respect to the specific colors uses to train the classifier, an important and interesting result. But these analyses do not actually address the claim implied by the analyses: that the performance of the CNN matches human performance. The color categories recovered with the CNN are not perfectly invariant, as the authors point out. The analyses presented in the paper (e.g. Figure 2E) tests whether there is as much shift in the boundaries as there is stasis, but that’s not quite the test if the goal is to link the categorical behavior of the CNN with human behavior. To evaluate the results, it would be helpful to know what would be expected based on human performance.

    We understand the lack of human data was a considerable shortcoming of the previous version of the manuscript. We have now collected human data in a match-to-sample task modeled on our CNN experiment. As with the CNN we find that the degree of border invariance does fluctuate considerably. While categorical borders are not exact matches, we do broadly find the same category prototypes and also see that categories in the red-to-yellow range are quite narrow in both humans and CNNs. Please, see the new “Human Psychophysics” (page 8) addition in the manuscript for more details.

    1. The paper takes up a test of color categorization invariant to luminance. There are arguments in the literature that hue and luminance cannot be decoupled-that luminance is essential to how color is encoded and to color categorization. Some discussion of this might help the reader who has followed this literature.

    We have added some discussion of the interaction between luminance and color categories (e.g., Lindsay & Brown, 2009) at the bottom of page 6/ top of page 7. The current analysis mainly aimed at excluding that the borders are solely based on luminance.

    Related, the argument that “neighboring colors in HSV will be neighboring colors in the RGB space” is not persuasive. Surely this is true of any color space?

    We removed the argument about “neighboring colors”. Our procedure requires the use of a hue spectrum that wraps around the color space while including many of the highly saturated colors that are typical prototypes for human color categories. We have elected to use the hue spectrum from the HSV color space at full saturation and brightness, which is represented by the edges of the RGB color cube. As this is the space in which our network was trained, it does not introduce any deformations into the color space. Other potential choices of color space either include strong non-linear transformations that stretch and compress certain parts of the RGB cube, or exclude a large portion of the RGB gamut (yellow in particular).

    We have adapted the text to better reflect our reasoning (page 6, top of paragraph 2).

    1. The paper would benefit from an analysis and discussion of the images used to originally train the CNN. Presumably, there are a large number of images that depict manmade artificially coloured objects. To what extent do the present results reflect statistical patterns in the way the images were created, and/or the colors of the things depicted? How do results on color categorization that derive from images (e.g. trained with neural networks, as in Rosenthal et al and presently) differ (or not) from results that derive from natural scenes (as in Yendrikhovskij?).

    We initially hoped we could perhaps analyze differences between colors in objects and background like in Rosenthal, unfortunately in ImageNet we did not find clear differences between pixels in the bounding boxes of objects provided with ImageNet and pixels outside these boxes (most likely because the rectangular bounding boxes still contain many background pixels). However, if we look at the results from the K-means analysis presented in Figure S6 (Suppl. Inf.) of the supplemental materials and the color categorization throughout the layers in the objecttrained network (end of the first experiment on page 7) as well as the color categorization in humans (Human Psychophysics starting on page 8), we see very similar border positions arise.

    1. It could be quite instructive to analyze what's going on in the errors in the output of the classifiers, as e.g. in Figure 1E. There are some interesting effects at the crossover points, where the two green categories seem to split and swap, the cyan band (hue % 20) emerges between orange and green, and the pink/purple boundary seems to have a large number of green/blue results. What is happening here?

    One issue with training the network on the color task, is that we can never fully guarantee that the network is using color to resolve the task and we suspected that in some cases the network may rely on other factors as well, such as luminance. When we look at the same type of plots for the luminance-controlled task (see below left) presented in the supplemental materials we do not see these transgressions. Also, when we look at versions of the original training, but using more bands, luminance will be less reliable and we also don’t see these transgressions (see right plot below).

    1. The second experiment using an evolutionary algorithm to test the location of the color boundaries is potentially valuable, but it is weakened because it pre-determines the number of categories. It would be more powerful if the experiment could recover both the number and location of the categories based on the "categorization principle" (colors within a category are harder to tell apart than colors across a color category boundary). This should be possible by a sensible sampling of the parameter space, even in a very large parameter space.

    The main point of the genetic algorithm was to see whether the border locations would be corroborated by an algorithm using the principle of categorical perception. Unfortunately, an exact approach to determining the number of borders is difficult, because some border invariances are clearly stronger than others. Running the algorithm with the number of borders as a free parameter just leads to a minimal number of borders, as 100% correct is always obtained when there is only one category left. In general, as the network can simply combine categories into a class at no cost (actually, having less borders will reduce noise) it is to be expected that less classes will lead to better performance. As such, in estimating what the optimal category count would be, we would need to introduce some subjective trade-off between accuracy and class count.

    1. Finally, the paper sets itself up as taking "a different approach by evaluating whether color categorization could be a side effect of learning object recognition", as distinct from the approach of studying "communicative concepts". But these approaches are intimately related. The central observation in Gibson et al. is not the discovery of warm-vscool categories (these as the most basic color categories have been known for centuries), but rather the relationship of these categories to the color statistics of objects-those parts of the scene that we care about enough to label. This idea, that color categories reflect the uses to which we put our color-vision system, is extended in Rosenthal et al., where the structure of color space itself is understood in terms of categorizing objects versus backgrounds (u') and the most basic object categorization distinction, animate versus inanimate (v'). The introduction argues, rightly in our view, that "A link between color categories and objects would be able to bridge the discrepancy between models that rely on communicative concepts to incorporate the varying usefulness of color, on the one hand, and the experimental findings laid out in this paragraph on the other". This is precisely the link forged by the observation that the warmcool category distinction in color naming correlates with object-color statistics (Gibson, 2017; see also Rosenthal et al., 2018). The argument in Gibson and Rosenthal is that color categorization structure emerges because of the color statistics of the world, specifically the color statistics of the parts of the world that we label as objects, which is the same approach adopted by the present work. The use of CNNs is a clever and powerful test of the success of this approach.

    We are sorry we did not properly highlight the enormous importance of these two earlier papers in our previous version of the manuscript. We have now elaborated our description of Gibson’s work to better reflect the important relation between the usefulness of colors and color categories (Page 2, middle and Page 19 par. above methods). We think our work nicely extends the earlier work by showing that their approach works even at a more general level with more color categories,

  3. eLife

    eLife assessment

    This paper addresses the long-standing problem of color categorization and the forces that bring it about, which can be potentially interesting to researchers in cognition, visual neuroscience, society, and culture. In particular, the authors show that as a "model organism", a Convolutional Neural Network (CNN) trained with the human-labelled image dataset ImageNet for object recognition can represent color categories. The finding reveals important features of deep neural networks in color processing and can also guide future theoretical and empirical work in high-level color vision.

  4. eLife

    Reviewer #1 (Public Review):

    This is a fascinating paper that takes up an important question with a creative and new approach. We have a few suggestions that we hope are constructive for the authors.

    1. One nagging concern is that the category structure in the CNN reflects the category structure baked into color space. Several groups (e.g. Regier, Zaslavsky, et al) have argued that color category structure emerges and evolves from the structure of the color space itself. Other groups have argued that the color category structure recovered with, say, the Munsell space may partially be attributed to variation in saturation across the space (Witzel). How can one show that these properties of the space are not the root cause of the structure recovered by the CNN, independent of the role of the CNN in object recognition?

    2. In Figure 1, it could be useful to illustrate the central observation by showing a single example, as in Figure 1 B, C, where the trained color is not in the center of the color category. In other words, if the category structure is immune to the training set, then it should be possible to set up a very unlikely set of training stimuli (ones that are as far away from the center of the color category while still being categorized most of the time as the color category). This is related to what is in E, but is distinctive for two reasons: first, it is a post hoc test of the hypothesis recovered in the data-driven way by E; and second, it would provide an illustration of the key observation, that the category boundaries do not correspond to the median distance between training colors. Figure 5 begins to show something of this sort of a test, but it is bound up with the other control related to shape. Similarly, if the claim is that there are six (or seven?) color categories, regardless of the number of colors used to train the data, it would be helpful to show the result of one iteration of the training that uses say 4 colors for training and another iteration of the training that uses say 9 colors for training. The text asserts that Figure 2 reflects training on a range of color categories (from 4 to 9) but doesn't break them out. This is an issue because the average across these iterations could simply be heavily biased by training on one specific number of categories (e.g. the number used in Figure 1). These considerations also prompt the query: how did you pick 4 and 9 as the limits for the tests? Why not 2 and 20? (the largest range of basic color categories that could plausibly be recovered in the set of all languages)?

    3. Regarding the transition points in Figure 2A, indicated by red dots: how strong (transition count) and reliable (consistent across iterations) are these points? The one between red and orange seems especially willfully placed.

    4. Figure 2E and Figure 5B are useful tests of the extent to which the categorical structure recovered by the CNNs shifts with the colors used to train the classifier, and it certainly looks like there is some invariance in category boundaries with respect to the specific colors uses to train the classifier, an important and interesting result. But these analyses do not actually address the claim implied by the analyses: that the performance of the CNN matches human performance. The color categories recovered with the CNN are not perfectly invariant, as the authors point out. The analyses presented in the paper (e.g. Figure 2E) tests whether there is as much shift in the boundaries as there is stasis, but that's not quite the test if the goal is to link the categorical behavior of the CNN with human behavior. To evaluate the results, it would be helpful to know what would be expected based on human performance.

    5. The paper takes up a test of color categorization invariant to luminance. There are arguments in the literature that hue and luminance cannot be decoupled-that luminance is essential to how color is encoded and to color categorization. Some discussion of this might help the reader who has followed this literature. Related, the argument that "neighboring colors in HSV will be neighboring colors in the RGB space" is not persuasive. Surely this is true of any color space?

    6. The paper would benefit from an analysis and discussion of the images used to originally train the CNN. Presumably, there are a large number of images that depict man-made artificially coloured objects. To what extent do the present results reflect statistical patterns in the way the images were created, and/or the colors of the things depicted? How do results on color categorization that derive from images (e.g. trained with neural networks, as in Rosenthal et al and presently) differ (or not) from results that derive from natural scenes (as in Yendrikhovskij?).

    7. It could be quite instructive to analyze what's going on in the errors in the output of the classifiers, as e.g. in Figure 1E. There are some interesting effects at the crossover points, where the two green categories seem to split and swap, the cyan band (hue % 20) emerges between orange and green, and the pink/purple boundary seems to have a large number of green/blue results. What is happening here?

    8. The second experiment using an evolutionary algorithm to test the location of the color boundaries is potentially valuable, but it is weakened because it pre-determines the number of categories. It would be more powerful if the experiment could recover both the number and location of the categories based on the "categorization principle" (colors within a category are harder to tell apart than colors across a color category boundary). This should be possible by a sensible sampling of the parameter space, even in a very large parameter space.

    9. Finally, the paper sets itself up as taking "a different approach by evaluating whether color categorization could be a side effect of learning object recognition", as distinct from the approach of studying "communicative concepts". But these approaches are intimately related. The central observation in Gibson et al. is not the discovery of warm-vs-cool categories (these as the most basic color categories have been known for centuries), but rather the relationship of these categories to the color statistics of objects-those parts of the scene that we care about enough to label. This idea, that color categories reflect the uses to which we put our color-vision system, is extended in Rosenthal et al., where the structure of color space itself is understood in terms of categorizing objects versus backgrounds (u') and the most basic object categorization distinction, animate versus inanimate (v'). The introduction argues, rightly in our view, that "A link between color categories and objects would be able to bridge the discrepancy between models that rely on communicative concepts to incorporate the varying usefulness of color, on the one hand, and the experimental findings laid out in this paragraph on the other". This is precisely the link forged by the observation that the warm-cool category distinction in color naming correlates with object-color statistics (Gibson, 2017; see also Rosenthal et al., 2018). The argument in Gibson and Rosenthal is that color categorization structure emerges because of the color statistics of the world, specifically the color statistics of the parts of the world that we label as objects, which is the same approach adopted by the present work. The use of CNNs is a clever and powerful test of the success of this approach.

  5. eLife

    Reviewer #2 (Public Review):

    Vries et al. investigated the mechanism of the color categorical perception and tried to answer the question of whether it develops universally or it is relative to local communication. So they investigated whether a categorical representation of color emerges from a Convolution Neural Network (CNN) that is trained to perform an object recognition task. The results indicate that the CNN has a categorical representation of color, which suggests that the color categorical perception might emerge from the object recognition.

    In general, I think the results are interesting. They performed a psychophysical experiment with the CNN, which shows the border of color category was largely invariant to the training colors. Also, further experiments with the evolution algorithm and other experiments confirm this.

    However, I think the approaches to address this question are not straightforward. All of the approaches in the paper rely on the retraining of the last layer. I was hoping they would provide more direct evidence to support their claim. Also, if they can show the color categorical information revealed by the CNN is similar to the human's color perception, that would help to strengthen their claim.

  6. eLife

    Reviewer #3 (Public Review):

    This paper investigates the emergence of color categories as a result of acquiring object recognition. The authors find that color categorization is an emergent property of a Convolutional Neural Network (CNN) trained with ImageNet for object recognition. In short, they find CNN, precisely a ResNET, can represent color in a categorical manner. They also show the categories obtained through the model are meaningful for more complex images and tasks. Analyzing how deep neural networks represent color categories is an under-studied but important problem in cognition and the authors did an excellent job presenting their analysis and results. The finding reveals features of deep neural networks in color processing and can also guide future theoretical and empirical work in high-level color vision. The method can be used to investigate other questions in high-level vision.

    Strength:

    The current modeling results support the immediate conclusion that color categories can emerge from learning object recognition. The method is novel and the result is intriguing. Most of the analysis is clear and the paper is easy to follow. Extensive experiments are done with the model and convincing results are presented.

    Weakness:

    The main weakness of the paper is the scope. In many places in the paper, the authors write that the results support several unsolved issues in biological color processing and color categorization. I am not convinced how the results, purely obtained from modeling CNN, connect to the biological color processing as the authors speculated in many places in the article including Introduction and Discussion. To support these claims, psychophysical data or experimenting with published psychophysical data are needed.

    Specifically, I find the following speculations not immediately supported by the results from this paper.

    First, I am not sure about the connection the author draws between the emergence of color categories from CNN (findings in this paper) with the debate of Universalists and Relativists, and support that "categories can emerge independent of language development". The fact that output layers of CNN trained on object recognition can cluster color into categories does not mean the color categories used in humans are formed before they have language. Even though the network isn't explicitly trained with color names, the CNN has been trained with object labels. Aren't the object labels part of language acquisition?

    Second, the authors wrote "The current findings can explain why the general development of categories is so similar across languages: If color categorization is a side effect of acquiring basic visual skills (given relatively similar circumstances across the globe) color categories are expected to shape in a similar fashion throughout many cultures". There are no explicit measurements of how different cultures would agree on these color categories. The current results only support that CNN trained on object recognition can discover limited color categories. It doesn't say anything about human color categorization across cultures.

    Third, in the Discussion, the authors wrote "they can explain why the emergence of color categories over cultures broadly follows a universal pattern". How can a CNN trained with ImageNet explain broad cultures? Even though ImageNet contains common objects labeled mostly by people from western countries, they do not represent a diversity of cultures. The current results suggest a relationship between object recognition and color categorization. But this relationship may vary from culture to culture.

    Finally, it would be great if the authors can experiment with network architectures other than ResNET. An alternative model trained on different image datasets can answer the question of under what circumstance color categories emerge from pre-trained models.

  7. Version published to 10.1101/2021.06.28.450097v2 on bioRxiv
  8. Version published to 10.1101/2021.06.28.450097v1 on bioRxiv