Estimating neural scaling laws involves an end-to-end pipeline: designing a scaling recipe, training models across scales, evaluating models on a target metric, and deploying an algorithm to fit a scaling law to the resulting data. This final fitting stage is often treated as routine: standard procedures minimize a non-convex fitting loss using local optimization from a grid of initializations, and return the best solution found. Yet such heuristic searches can fail in two distinct ways: they offer no guarantee of returning a nearly optimal solution, and they obscure whether fundamentally different parameter choices fit the data nearly as well. Indeed, we show that standard scaling law fitting is subject to a Rashomon effect (Breiman, 2001): the sublevel sets of near-minimizers correspond to broad parameter regions whose extrapolations diverge substantially at scale. We resolve these issues with a deterministic branch-and-bound algorithm that guarantees nearly optimal fitting loss and exhaustively maps the near-minimizers to the implied range of scaling curves.

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