cs.LGJun 2, 2026

Demystifying Pipeline Parallelism: First Theory for PipeDream

Authors: Ivan IlinPeter Richtárik

Organizations: KAUST

Abstract

Training modern machine learning models increasingly requires computation to be distributed across many accelerators. Data parallelism remains the default choice and is often paired with tensor-parallel sharding, but model parallelism becomes unavoidable once parameters, activations, or optimizer states no longer fit on a single device. This paper studies pipeline model parallelism through the lens of PipeDream (PD) (Harlap et al., 2018). Our first contribution is theoretical: we introduce Randomized PipeDream (RPD), a stale block-SGD abstraction that yields, to our knowledge, the first clean nonconvex convergence guarantee for a PD-style method. Our second contribution is a scaling diagnosis: we prove that the delay induced by steady-state PD grows as S2S/2+O(1)S^2 - S/2 + O(1) for SS stages, so the stale-read contribution in the convergence theorem scales as Θ(γ2S4)Θ(γ^2 S^4), equivalently as Θ(S4/K)Θ(S^4/K) in the tuned-rate form. Our third contribution is a comparison with LocalSGD, whose periodic model averaging trades weight staleness for synchronization bubbles. In our reported simulated-time experiments, the better-performing method depends on the objective: PD performs better on the quadratic objective and on a small language-modeling training-loss task, while for logistic regression LocalSGD becomes superior as the number of stages increases.

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