SPARe: Stacked Parallelism with Adaptive Reordering for Fault-Tolerant LLM Pretraining Systems with 100k+ GPUs

TL;DR

SPARe - Stacked Parallelism with Adaptive Reordering - a fault-tolerance framework that masks node failures during gradient synchronization by stacking redundant data shards across parallelism groups and adaptively reordering execution achieves availability comparable to traditional replication while maintaining near-constant computation overhead of only 2~3x.

Abstract

In large-scale LLM pre-training systems with 100k+ GPUs, failures become the norm rather than the exception, and restart costs can dominate wall-clock training time. However, existing fault-tolerance mechanisms are largely unprepared for this restart-dominant regime. To address this challenge, we propose SPARe - Stacked Parallelism with Adaptive Reordering - a fault-tolerance framework that masks node failures during gradient synchronization by stacking redundant data shards across parallelism groups and adaptively reordering execution. SPARe achieves availability comparable to traditional replication while maintaining near-constant computation overhead of only 2~3x, even under high redundancy where traditional replication would require linearly inflating overhead. We derive closed-form expressions for endurable failure count and computation overhead, validate them via SimGrid-based discrete-event simulation, and jointly optimize redundancy and checkpointing to minimize time-to-train. At extreme scale with up to 600k GPUs, SPARe reduces time-to-train by 40~50% compared to traditional replication.

Figures (9)

• Figure 1: Synchronous Data Parallelism.
• Figure 2: Traditional Replication $r=3$.
• Figure 3: (a): Example of SPARe at $N=9$, $r=3$. (b): Before any failure, all partial gradients can be collected after computing the $1^{\mathrm{st}}$ stack. (c): With group $1$ failure, system needs to compute up to $2^{\mathrm{nd}}$ stack to collect all types. (d): If group $2$ fails later, type $2$ partial gradient cannot be collected within the $2^{\mathrm{nd}}$ stack of shards. (e): However, all partial gradients can be collected after computing up to $2^{\mathrm{nd}}$ stack when group $8$ stack is reordered.
• Figure 4: Average endurable failure count by redundancy $r$.
• Figure 5: Average computation overhead by redundancy $r$.

Theorems & Definitions (12)

• Theorem 4.1: Average Failure Count
• proof
• Theorem 4.2: Average Computation Overhead
• proof
• Theorem 4.3: Optimal $r^\star$ for minimal time-to-train
• proof
• Definition 2.1: Cyclic Golomb Ruler distribution rule
• Lemma 2.2
• proof
• proof