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A common property of quantum computers is that they can exhibit instances of true randomness as opposed to pseudo-randomness obtained from classical systems. Investigating the effects of such true quantum randomness in the context of machine learning is appealing, and recent results vaguely suggest that benefits can indeed be achieved from the use of quantum random numbers. To shed some more light on this topic, we empirically study the effects of hardware-biased quantum random numbers on the initialization of artificial neural network weights in numerical experiments. We find no statistically significant difference in comparison with unbiased quantum random numbers as well as biased and unbiased random numbers from a classical pseudo-random number generator. 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