Little Room for Second-Order Rules in a Delta-Rule Testbed: Oracle Gains and an Evolution-Strategy Learner

Four pre-registered attempts to learn second-order modulation in a minimal plasticity testbed found nothing, and the learners failed their own positive controls. Before improving the learners further, this note measures whether anything was there to find, by comparing hand-built (oracle) second-order rules with the best uniform gain. A regime-dependent scalar oracle (49 gain pairs, chosen on a selection tape, scored on a fresh evaluation tape) gave no measurable benefit (mean evaluation error 0.13192 vs 0.13198; wins 20/60). An evolution-strategy learner failed the explicit-context gate (17/60 wins). A relation-specific oracle gating built from the true supports of the two transition matrices beat the best uniform gain in 36/60 systems (median +0.77%, mean −0.41%) and beat a random gating of the same size in 59/60 (median +2.07%), but missed the pre-registered criteria (3% over uniform; a 2-point gap over random gating, missed by 0.002). In this engine and task family, a structure-aware second-order rule carries a real, structure-dependent but sub-percent benefit over a tuned uniform rule, so the emergence tests were uninformative by construction; the toy result that a regime-dependent gain strictly beats any uniform gain does not transfer to this engine. Unpublished draft, not peer reviewed; synthetic systems only; it neither supports nor refutes the conjecture. The bundle reproduces every quoted number with verify_paper5.py (31 checks). AI use: simulations were written and executed by an AI coding model under written specifications and audited by a second AI system; the author is responsible for all content.