(1) The -multigpu_strategy flag interacts with the -gpu flag: -gpu tells you which GPUs to use, and in what order to use them; -multigpu_strategy tells how to distribute layers across the different GPUs.

In starry_stanford.sh, we give the flag -gpu 0,1,2,3 which tells neural-style that we want to use 4 GPUs: GPU 0, 1, 2, and 3 in that order. The flag -multigpu_strategy 3,6,12 means to run layers 1-2 on GPU 0, layers 3-5 on GPU 1, layers 6-11 on GPU 2, and all remaining layers on GPU 3.

For this to work out, -multigpu_strategy needs to be a list with one element less than -gpu; the assertion error you are seeing checks that this is the case.

(2) L-BFGS and Adam are two different optimization algorithms; in general L-BFGS gives better results than Adam, but uses a lot more memory. The -lbfgs_num_corrections parameter lets you trade off memory usage and accuracy within the L-BFGS algorithm; the higher values of -lbfgs_num_corrections will use more memory but may give better results (the default is 100).

L-BFGS and Adam are both approximate second-order optimization algorithms, meaning that they use samples of the first derivative (slope, gradient) to approximate the second derivative (curvature, Hessian). L-BFGS (roughly speaking) keeps an explicit history of first derivatives while Adam uses various running averages of first derivative statistics; using explicit histories allows L-BFGS to better approximate the true second derivative, but keeping an explicit history takes a lot of memory. The -lbfgs_num_corrections argument controls the size of the gradient history that L-BFGS keeps, which can reduce the memory usage at the expense of less accurate estimates of the second derivative.