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Let's assume I have a simple feedforward neural network whose input contains binary 0/1 features and output is also binary two classes.

Is it better, worse, or maybe totally indifferent, for every such binary feature to be in just one column or maybe it would be better to split one feature into two columns in a way that the second column will have the opposite value, like that:

feature_x (one column scenario) 

[0]

[1]

[0]


feature_x (two columns scenario)

[0, 1]

[1, 0]

[0, 1]

I know this might seem a bit weird and probably it is not necessary, but I have a feeling like there might be a difference for a network especially for its inner workings and how neurons in the next layers see such data. Has anyone ever researched that aspect?

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You're simply adding a redundant feature by having it as two: $X_2 = 1 - X_1$. It would be equally useful to duplicate the first column. At best this will not improve your model, at worst it will decrease accuracy.

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