Trajectory Soup: Pushing the Compute-Scaling Frontier of LLM Mid-training via Diverse Trajectories

Mid-training equips pretrained large language models with specialized and reasoning capabilities, but the returns of this stage are bounded since additional serial compute yields little further downstream improvement and can even degrade some capabilities, which places a practical ceiling on how much compute mid-training absorbs. We revisit how this compute should be allocated to a single run or multiple similar optimizations. We find that branches forked from a shared checkpoint under various controlled recipe reaches measurably different regions of parameter space, and establish a form of compatible diversity that extending one run cannot supply. Therefore, we introduce Trajectory Soup, which distributes a mid-training budget over several independent branches, and consolidates strongest checkpoints selected on validation through intra- and inter-trajectory averaging into a single model. A local bias and variance analysis separates the two averaging levels, showing that inter-trajectory averaging removes residual error beyond the reach of averaging within a trajectory, while checkpoint selection carries a bias that bounds how many checkpoints are worth merging. Across model scales, learning-rate schedules, token budgets, and trajectory counts, Trajectory Soup improves aggregate downstream performance over the strongest single-trajectory average under matched budgets and keeps improving as budgets expand, with the advantage preserved after an identical post-training pipeline. These results position trajectory allocation and merging as a practical way to extend the compute-scaling frontier of mid-training beyond serial saturation.