Question about softmax

[morgan-bc]

In the softmax in PyG is

N = maybe_num_nodes(index, num_nodes)
src_max = scatter(src, index, dim, dim_size=N, reduce='max')
src_max = src_max.index_select(dim, index)
out = (src - src_max).exp()
out_sum = scatter(out, index, dim, dim_size=N, reduce='sum')
out_sum = out_sum.index_select(dim, index)

out = out / (out_sum + 1e-16)

The equation corresponding the code is

The original softmax equation is

Why dose the PyG softmax subtract the max value of the neighborhood nodes ?

[wsad1]

Both the equations you pasted will yield the same output, as softmax(x) = softmax(x+c) where c is some constant.
Now setting c to max(x) makes the softmax more stable by preventing underflow and overflow, read more here.