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The implementation makes sense from what the equations say but I was confused for a minute with using the term beta_prod_t.
What is beta?
beta = 1 - alpha
and
alpha_prod_t = prod(alpha_0, alpha_1, ...., alpha_t)
What will be the product of beta till timestep t?
(IIUC) beta_prod_t = prod(1-alpha_0, 1-alpha_1, ..., 1-alpha_t)
which is not equivalent to 1 - alpha_prod_t
What do you think?
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