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A Appendix: Proofs and Algorithms A.1 Proofs of results in Section 4 Proof of Proposition 4.1. Plug B

Neural Information Processing Systems

(Bertsekas, 1999). Algorithm 1. Furthermore, we call ˆ f (), X We can show that | f () ˆ f () |, 8 2 [, ] . Besides, computing the upper bound claimed in Proposition 4.2 requires finding The second equality is from the fact that the objective function is affine w.r.t. Finally, we verify the rest two components. Finally, we verify the rest two components. This finishes the proof of our claim.







Mesh-TensorFlow: Deep Learning for Supercomputers

Neural Information Processing Systems

However,batch-splitting suffers from problems including the inability to train very large models (due to memory constraints), high latency, and inefficiency at small batch sizes. All of these can be solved by more general distribution strategies (model-parallelism). Unfortunately,efficient model-parallel algorithms tend tobe complicated todiscover, describe, and to implement, particularly on large clusters.