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Why noise with normal distribution is used as input to GAN? What will happen if we will use uniform noise or just random binary vector?

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You don't have to use a normal distribution to generate noise for starting. You can use a uniform distribution too. It's all depending on your preference, your data and your training results. If the uniform distribution noise helps to make training short and not compensate for the output, you can definitely switch.

Reference: https://medium.com/@jonathan_hui/gan-why-it-is-so-hard-to-train-generative-advisory-networks-819a86b3750b

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