Large-scale ranking and recommendation models of Web platforms benefit from increased compute much as large language models do, and their scaling behavior is broadly power-law in form. Yet ranking models have heterogeneous architectures which makes their scaling law less straightforward than that of LLMs. We address how to discover the scaling law of an arbitrary ranking model efficiently. We introduce a scaling layer, which groups primitive architecture parameters into semantically coherent groups and defines how they co-vary, inducing a mapping from a low-dimensional space of hyper-hyperparameters into the full architecture space. On top of it, Axia fits scaling-informed surrogates, selects configurations by a posterior-based acquisition criterion, and returns a Pareto frontier from which per-model operating points are validated -- replacing exhaustive sweeps with a small number of informative runs. A fleet-level evaluation protocol, computed on a fixed representative model set under matched trial budgets, makes refinements to either component measurable. Our contribution is an automated system that learns model-specific complexity-quality relationships and gives uncertainty-aware guidance for allocating compute across a heterogeneous model ecosystem. Across 34 model iterations in two development cycles on Meta's ads ranking and retrieval system, the workflow yielded a mean 0.66% offline normalized-entropy improvement and 0.36% cumulative online lift.

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