An Analytical Model of Compute-limited Multistage Training Pipelines

arXiv:2611.13276v1 Announce Type: new Abstract: Modern foundation models are trained through multiple stages, yet how these stages interact and how compute should be allocated across them remain poorly understood. We introduce an analytically tractable high-dimensional model combining unsupervised pretraining with a linear autoencoder, supervised fine-tuning (SFT) with noisy stepwise labels, and reinforcement learning (RL) with sparse episodic rewards. Using random matrix theory and an operator-projection closure, we derive approximate low-dimensional learning dynamics that closely match simulations.