Since a network doesn't learn colors and computer don't understand anything other than 1's and 0's, does this mean an input image in a CNN model should only have 1's and 0s as its matrix entries?
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Neural networks do learn colors, and you have a big misunderstanding on how data types work on programming languages/computers. Any tutorial wil show you how to learn a NN on color images directly. – Dr. Snoopy May 20 '20 at 09:16
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Colors are represented by the color-channels RGB (red, green, blue), usually with 8-bit intensities ranging from 0 to 255.
If you only have 0 and 1 you only would have black and white pixels. However if you use a range from 0 to 255 you can also represent gray-ish values between black and white. Now for colorful images you can adjust the intensity for each channel in such a way that the added three RGB-values can represent any color.

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