Title: Clarifying Pipeline Parallelism: The Initial Theoretical Framework for PipeDream

Abstract: As the training of contemporary machine learning models expands across numerous accelerators, distribution of computational load becomes essential. While data parallelism is the standard approach, frequently combined with tensor-parallel sharding, model parallelism becomes a necessity when parameters, activations, or optimizer states exceed the capacity of a single device. This study investigates pipeline model parallelism by focusing on PipeDream (PD) (Harlap et al., 2018). We present three primary contributions. First, we offer a theoretical advancement by introducing Randomized PipeDream (RPD), an abstraction based on stale block-SGD that provides, to our knowledge, the first rigorous nonconvex convergence guarantee for methods following the PD style. Second, we conduct a scaling analysis, demonstrating that the delay inherent in steady-state PD increases as $S^2 - S/2 + O(1)$ for $S$ stages. Consequently, the stale-read component in the convergence theorem scales as $\Theta(\gamma^2 S^4)$, which is equivalent to $\Theta(S^4/K)$ in the tuned-rate formulation. Third, we compare PD with LocalSGD, noting that LocalSGD exchanges weight staleness for synchronization bubbles through periodic model averaging. Our simulated-time experiments reveal that performance varies by objective: PD outperforms LocalSGD on quadratic objectives and a small language-modeling training-loss task, whereas LocalSGD proves superior in logistic regression as the number of stages grows.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC