Not sure what you mean, why wouldn't there be a gradient? There is a problem that small changes to weights may have no effect (eg ((0 + 0.3) + 0.3) + 0.4 = 0 if

Not sure what you mean, why wouldn't there be a gradient? There is a problem that small changes to weights may have no effect (eg ((0 + 0.3) + 0.3) + 0.4 = 0 if you have to round the result to 0 or 1 after every step), but to fix this I believe everyone maintains high precision weights for the backwards pass, from which the quantized weights are derived.