Conflicting Supervision Moves Commitment, Not Capability: A 12.29σ arrangement effect that is exactly zero under a convention-agnostic score

Wenhui Chen

"Train a model on the same problems written under two incompatible conventions, both correct, and ask what the ordering of that data writes into the parameters. The learning-rate schedule is not a background condition for that question. It is the averaging operator, and it decides the answer. We prove a bound in which the arrangement and the schedule enter the ordering effect as separate multiplied factors: the arrangement only as a block period, the schedule only as how much weight the endpoint can place on any one moment of the run. A decaying schedule cannot put a large step size and an uncontracted remainder at the same moment; a constant one does exactly that at the last step. That decay moderates ordering effects has been reported in pretraining; the mechanism, the separation, and a controlled measurement of both halves are ours. Ten orderings of one corpus, one budget, everything but the path held fixed, run twice under families differing in lr_scheduler_type and nothing else: at a constant rate the interior spans 0.2221 in allocation, 11.63 contrast floors, monotone in how blocked the arrangement is. Under the single cosine every published arm uses, the same ten arms…