Summation overi I decouples i from j and allows reuse of computation overj.

As a result, the explanation generated is painstakingly customized foreachinstance.

There are20complexes in the training set and 26,303 conformations in total.

We first prove the direction that efficiency ordering implies Loewner ordering. Next we want to showlimt (I γA)t = 0. Since we assume0 < γ < 2/ A 2, we have I γA 2 = maxi=1,2,,n|1 γλi(A)| < 1, where λi(A) > 0 is thei-the eigenvalue of the positivedefinite matrixA. For the original functionG: Rd V Rd, we define another functionΦ: Rd E Rd such thatΦ(θ,eij) = G(θ,j). This is true for periodic Markov chain, and is shown in the following lemma. Due to its random nature across each epoch, random shuffling is not a Markov chain on state space[n].