Abstract

Deep convolutional neural networks are a class of machine-learning algorithms capable of solving non-trivial tasks, such as object recognition, with human-like performance. Little is known about the exact computations that deep neural networks learn, and to what extent these computations are similar to the ones performed by the primate brain. Here, we investigate how color information is processed in the different layers of the AlexNet deep neural network, originally trained on object classification of over 1.2M images of objects in their natural contexts. We found that the color-responsive units in the first layer of AlexNet learned linear features and were broadly tuned to two directions in color space, analogously to what is known of color responsive cells in the primate thalamus. Moreover, these directions are decorrelated and lead to statistically efficient representations, similar to the cardinal directions of the second-stage color mechanisms in primates. We also found, in analogy to the early stages of the primate visual system, that chromatic and achromatic information were segregated in the early layers of the network. Units in the higher layers of AlexNet exhibit on average a lower responsivity for color than units at earlier stages.

© 2018 Optical Society of America

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References

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2018 (1)

2016 (2)

T. M. Sanada, T. Namima, and H. Komatsu, “Comparison of the color selectivity of macaque v4 neurons in different color spaces,” J. Neurophysiol. 116, 2163–2172 (2016).
[Crossref]

E. Provenzi, J. Delon, Y. Gousseau, and B. Mazin, “On the second order spatiochromatic structure of natural images,” Vis. Res. 120, 22–38 (2016).
[Crossref]

2015 (3)

O. Russakovsky, J. Deng, H. Su, J. Krause, S. Satheesh, S. Ma, Z. Huang, A. Karpathy, A. Khosla, M. Bernstein, A. C. Berg, and L. Fei-Fei, “ImageNet large scale visual recognition challenge,” Int. J. Comput. Vis. 115, 211–252 (2015).
[Crossref]

U. Güçlü and M. A. van Gerven, “Deep neural networks reveal a gradient in the complexity of neural representations across the ventral stream,” J. Neurosci. 35, 10005–10014 (2015).
[Crossref]

K. T. Mullen, D. H. Chang, and R. F. Hess, “The selectivity of responses to red-green colour and achromatic contrast in the human visual cortex: an fMRI adaptation study,” Eur. J. Neurosci. 42, 2923–2933 (2015).

2014 (1)

S.-M. Khaligh-Razavi and N. Kriegeskorte, “Deep supervised, but not unsupervised, models may explain it cortical representation,” PLoS Comput. Biol. 10, e1003915 (2014).
[Crossref]

2013 (2)

T. Hansen and K. R. Gegenfurtner, “Higher order color mechanisms: evidence from noise-masking experiments in cone contrast space,” J. Vis. 13(1):26 (2013).
[Crossref]

C. J. Kellner and T. Wachtler, “A distributed code for color in natural scenes derived from center-surround filtered cone signals,” Front. Psychol. 4, 661 (2013).
[Crossref]

2012 (2)

G. D. Horwitz and C. A. Hass, “Nonlinear analysis of macaque v1 color tuning reveals cardinal directions for cortical color processing,” Nat. Neurosci. 15, 913–919 (2012).
[Crossref]

J. J. DiCarlo, D. Zoccolan, and N. C. Rust, “How does the brain solve visual object recognition?” Neuron 73, 415–434 (2012).
[Crossref]

2011 (1)

R. Shapley and M. J. Hawken, “Color in the cortex: single-and double-opponent cells,” Vis. Res. 51, 701–717 (2011).
[Crossref]

2009 (2)

B. R. Conway, “Color vision, cones, and color-coding in the cortex,” Neuroscience 15, 274–290 (2009).

J. J. Nassi and E. M. Callaway, “Parallel processing strategies of the primate visual system,” Nat. Rev. Neurosci. 10, 360–372 (2009).
[Crossref]

2007 (2)

B. R. Conway, S. Moeller, and D. Y. Tsao, “Specialized color modules in macaque extrastriate cortex,” Neuron 56, 560–573 (2007).
[Crossref]

K. T. Mullen, S. O. Dumoulin, K. L. McMahon, G. I. De Zubicaray, and R. F. Hess, “Selectivity of human retinotopic visual cortex to s-cone-opponent, l/m-cone-opponent and achromatic stimulation,” Eur. J. Neurosci. 25, 491–502 (2007).
[Crossref]

2006 (1)

M. Kusunoki, K. Moutoussis, and S. Zeki, “Effect of background colors on the tuning of color-selective cells in monkey area v4,” J. Neurophysiol. 95, 3047–3059 (2006).
[Crossref]

2005 (1)

E. M. Callaway, “Structure and function of parallel pathways in the primate early visual system,” J. Physiol. 566, 13–19 (2005).
[Crossref]

2004 (1)

M. S. Caywood, B. Willmore, and D. J. Tolhurst, “Independent components of color natural scenes resemble v1 neurons in their spatial and color tuning,” J. Neurophysiol. 91, 2859–2873 (2004).
[Crossref]

2003 (3)

H. S. Friedman, H. Zhou, and R. Heydt, “The coding of uniform colour figures in monkey visual cortex,” J. Physiol. 548, 593–613 (2003).
[Crossref]

K. R. Gegenfurtner, “Cortical mechanisms of colour vision,” Nat. Rev. Neurosci. 4, 563–572 (2003).
[Crossref]

K. R. Gegenfurtner and D. C. Kiper, “Color vision,” Annu. Rev. Neurosci. 26, 181–206 (2003).
[Crossref]

2002 (4)

F. A. Wichmann, L. T. Sharpe, and K. R. Gegenfurtner, “The contributions of color to recognition memory for natural scenes,” J. Exp. Psychol. 28, 509–520 (2002).
[Crossref]

R. Shapley and M. Hawken, “Neural mechanisms for color perception in the primary visual cortex,” Curr. Opin. Neurobiol. 12, 426–432 (2002).
[Crossref]

S. Shipp and S. Zeki, “The functional organization of area V2, I: specialization across stripes and layers,” Vis. Neurosci. 19, 187–210 (2002).
[Crossref]

T.-W. Lee, T. Wachtler, and T. J. Sejnowski, “Color opponency is an efficient representation of spectral properties in natural scenes,” Vis. Res. 42, 2095–2103 (2002).
[Crossref]

2001 (4)

A. Skodras, C. Christopoulos, and T. Ebrahimi, “The jpeg 2000 still image compression standard,” IEEE Signal Process. Mag. 18(5), 36–58 (2001).
[Crossref]

T. Wachtler, T.-W. Lee, and T. J. Sejnowski, “Chromatic structure of natural scenes,” J. Opt. Soc. Am. A 18, 65–77 (2001).
[Crossref]

E. N. Johnson, M. J. Hawken, and R. Shapley, “The spatial transformation of color in the primary visual cortex of the macaque monkey,” Nat. Neurosci. 4, 409–416 (2001).
[Crossref]

J. Tanaka, D. Weiskopf, and P. Williams, “The role of color in high-level vision,” Trends Cognit. Sci. 5, 211–215 (2001).
[Crossref]

2000 (8)

K. R. Gegenfurtner and J. Rieger, “Sensory and cognitive contributions of color to the recognition of natural scenes,” Curr. Biol. 10, 805–808 (2000).
[Crossref]

R. L. De Valois, N. P. Cottaris, S. D. Elfar, L. E. Mahon, and J. A. Wilson, “Some transformations of color information from lateral geniculate nucleus to striate cortex,” Proc. Natl. Acad. Sci. USA 97, 4997–5002 (2000).

A. Hanazawa, H. Komatsu, and I. Murakami, “Neural selectivity for hue and saturation of colour in the primary visual cortex of the monkey,” Eur. J. Neurosci. 12, 1753–1763 (2000).
[Crossref]

A. Bartels and S. Zeki, “The architecture of the colour centre in the human visual brain: new results and a review,” Eur. J. Neurosci. 12, 172–193 (2000).

P. O. Hoyer and A. Hyvärinen, “Independent component analysis applied to feature extraction from colour and stereo images,” Network 11, 191–210 (2000).
[Crossref]

A. Hyvärinen and E. Oja, “Independent component analysis: algorithms and applications,” Neural Networks 13, 411–430 (2000).
[Crossref]

A. Hyvärinen and P. Hoyer, “Emergence of phase-and shift-invariant features by decomposition of natural images into independent feature subspaces,” Neural Comput. 12, 1705–1720 (2000).
[Crossref]

D. R. Tailor, L. H. Finkel, and G. Buchsbaum, “Color-opponent receptive fields derived from independent component analysis of natural images,” Vis. Res. 40, 2671–2676 (2000).
[Crossref]

1999 (1)

J. W. Tanaka and L. M. Presnell, “Color diagnosticity in object recognition,” Percept. Psychophys. 61, 1140–1153 (1999).
[Crossref]

1998 (3)

H. Komatsu, “Mechanisms of central color vision,” Curr. Opin. Neurobiol. 8, 503–508 (1998).
[Crossref]

J. H. Van Hateren and A. van der Schaaf, “Independent component filters of natural images compared with simple cells in primary visual cortex,” Proc. R. Soc. London B 265, 359–366 (1998).

D. L. Ruderman, T. W. Cronin, and C.-C. Chiao, “Statistics of cone responses to natural images: Implications for visual coding,” J. Opt. Soc. Am. A 15, 2036–2045 (1998).
[Crossref]

1997 (2)

Q. Zaidi, “Decorrelation of l-and m-cone signals,” J. Opt. Soc. Am. A 14, 3430–3431 (1997).
[Crossref]

D. C. Kiper, S. B. Fenstemaker, and K. R. Gegenfurtner, “Chromatic properties of neurons in macaque area v2,” Vis. Neurosci. 14, 1061–1072 (1997).

1996 (1)

N. K. Logothetis and D. L. Sheinberg, “Visual object recognition,” Annu. Rev. Neurosci. 19, 577–621 (1996).
[Crossref]

1994 (2)

G. K. Humphrey, M. A. Goodale, L. S. Jakobson, and P. Servos, “The role of surface information in object recognition: studies of a visual form agnosic and normal subjects,” Perception 23, 1457–1481 (1994).
[Crossref]

K. R. Gegenfurtner, D. C. Kiper, J. M. Beusmans, M. Carandini, Q. Zaidi, and J. A. Movshon, “Chromatic properties of neurons in macaque MT,” Vis. Neurosci. 11, 455–466 (1994).

1993 (1)

L. H. Wurm, G. E. Legge, L. M. Isenberg, and A. Luebker, “Color improves object recognition in normal and low vision,” J. Exp. Psychol. 19, 899–911 (1993).
[Crossref]

1990 (1)

P. Lennie, J. Krauskopf, and G. Sclar, “Chromatic mechanisms in striate cortex of macaque,” J. Neurosci. 10, 649–669 (1990).

1988 (1)

D. S. Massey and N. A. Denton, “The dimensions of residential segregation,” Soc. Forces 67, 281–315 (1988).
[Crossref]

1987 (1)

D. J. Felleman and D. C. Van Essen, “Receptive field properties of neurons in area v3 of macaque monkey extrastriate cortex,” J. Neurophysiol. 57, 889–920 (1987).
[Crossref]

1984 (3)

L. G. Thorell, R. L. de Valois, and D. G. Albrecht, “Spatial mapping of monkey VI cells with pure color and luminance stimuli,” Vis. Res. 24, 751–769 (1984).
[Crossref]

M. S. Livingstone and D. H. Hubel, “Anatomy and physiology of a color system in the primate visual cortex,” J. Neurosci. 4, 309–356 (1984).

A. M. Derrington, J. Krauskopf, and P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. 357, 241–265 (1984).
[Crossref]

1983 (1)

G. Buchsbaum and A. Gottschalk, “Trichromacy, opponent colours coding and optimum colour information transmission in the retina,” Proc. R. Soc. London B 220, 89–113 (1983).
[Crossref]

1982 (1)

J. Krauskopf, D. R. Williams, and D. W. Heeley, “Cardinal directions of color space,” Vis. Res. 22, 1123–1131 (1982).
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1980 (1)

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Figures (6)

Fig. 1.
Fig. 1. Preferred tuning directions of first-layer kernels in RGBPCA coordinates. Kernel tuning directions represented in RGBPCA coordinates. In the left panel, individual dots are preferred elevationPCA angles (in absolute value) plotted against preferred azimuthPCA angles for each kernel in the first layer of all 35 training instances of AlexNet. Dotted lines represent the 45° threshold elevation value employed to classify kernels as either color (ϕ45°) or luminance (ϕ45°) kernels. The right panel shows the histogram of preferred elevationPCA values across all azimuthsPCA. The top panel shows the histogram of preferred azimuthPCA values across color kernels only.
Fig. 2.
Fig. 2. Kernels of the first layer of AlexNetB. Kernels are displayed according to their index order in the architecture. The top group of 48 kernels was trained on GPU1. The bottom group of 48 kernels was trained on GPU2. Outlined in black are those kernels classified as luminance kernels following the procedure described in Section 2.F. Note how the majority of GPU1 kernels are color kernels, while the majority of GPU2 kernels are luminance kernels.
Fig. 3.
Fig. 3. Azimuth tuning distributions of color kernels in RGBPCA. (a) Circular histogram displaying the distribution of preferred azimuthPCA of all color kernels in the first layer of all 35 AlexNet training instances. (b–d) Distributions of preferred azimuthPCA of color, first-layer kernels for three individual AlexNet training instances selected from our set of 35. (e) Same as (b–d), except for the AlexNetB network instantiation provided within the CAFFE framework.
Fig. 4.
Fig. 4. Color tuning curves from representative kernels in the different AlexNet layers. In each panel, the dotted curve represents the response of a kernel, plotted as a function of the azimuthPCA of the input stimulus. The continuous line is the tuning curve of filter that linearly combines chromatic input, fitted to the kernel response using the formula in Eq. (2). The horizontal dashed line is the kernel’s response to an achromatic (gray) stimulus with the same spatial and intensity characteristics as the colored stimuli.
Fig. 5.
Fig. 5. Linearity, responsivity, and color responsivity of kernels across the different AlexNet layers. (a) Fit accuracy plotted as a function of network depth (i.e., layer number). Accuracy data are the r2 score between kernel responses to colored stimuli and the model response of a linear chromatic filter [Eq. (2)] fit to the measured kernel responses. Filled dots are mean accuracy at each network layer, computed across all kernels and across all 35 AlexNet training instances. (b) Proportion of kernels with different chromatic processing characteristics as a function of layer number. The full bold line gives the proportion of kernels which have no response to our stimuli. Dashed-dotted line gives the proportion of kernels with a sensitivity to intensity contrastsPCA at least two times superior to their sensitivity to chromatic contrastsPCA (=elevationPCA>63° in layer 1, color responsivity>1/5). Full fine line is the proportions of kernels with sensitivity to chromatic contrastPCA at least two times superior to intensity contrastsPCA (=elevationPCA<27° in layer 1, color responsivity>1/2). Dashed line is the proportion of kernels sensitive to both intensity and chromatic contrastsPCA (63°>elevationPCA>27° in layer 1, 1/2>color responsivity>1/5). All data are the mean proportions, computed across all 35 AlexNet training instances. (c) Color responsivity [as computed from Eq. (3)] in all five convolutional layers. Data are the mean color responsivity computed across all kernels and across all 35 AlexNet training instances. (d) Proportion of kernels with color responsivities superior to different thresholds, computed across all 35 AlexNet training instances. In panels (a) and (c), error bars represent the standard deviation across the 35 training instances.
Fig. 6.
Fig. 6. Accuracy as a function of the index of dissimilarity in layer 1. Correlation of the top 1 accuracy, computed on the whole validation dataset, of the training instances of AlexNet with the degree of segregation (ID, cf. Section 2.G) in layer 1. The right axis shows the number of successful classifications among the 50,000 images of the validation dataset. The white dot stands for the AlexNetB training instance provided with CAFFE. Kernels in the first layer of AlexNetB are shown in Fig. 2.

Tables (1)

Tables Icon

Table 1. Proportions of Color and Luminance Kernels in the Color and Luminance Groups of the First Two Layers and Corresponding Indexes of Dissimilarity

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

Yϕ,ψK=maxjRϕ,ψKj,
Rϕ(ψ)=B+A|b+cos(ψaz)|,
CR=max response to colorresponse to graymax response to color+response to gray,
ID=12(|c1Cl1L|+|c2Cl2L|),