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I believe it has no impact on the training. The reason I use the multiplication of 2 is that I want to keep the total weights the same as addition.
In the direct addition case, X + Y is actually 1 * X + 1 * Y, the sum of the weight is 2. However, in a soft selection way, M(X+Y) * X + (1 - M(X+Y)) * Y, the sum of the weight is 1, so I multiply 2 to keep them the same. Then the only difference between 1 * X + 1 * Y and 2 * M(X+Y) * X + 2 * (1 - M(X+Y)) * Y is the dynamic weight allocation, but the sum of the weights keeps the same.
xo = 2 * x * wei + 2 * residual * (1 - wei)
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