How many LLM-labelled rows does a decision encoder need, and how wrong can the labels be?

arXiv:2611.16498v1 Announce Type: new Abstract: A decision encoder such as Laya reads a question with named options (for example, which department should handle a ticket) and a text, and picks an option. It reads both in one forward pass and returns a probability for every option, without writing any text. We ask how many LLM-written training rows such an encoder needs and how wrong those labels may be. We ran 19 fine-tunes of Laya (ModernBERT-large) on nested subsets of a 2,818-row pool and scored them on 1,065 held-out items from the same generator, so every test item is in-distribution and no out-of-family test was run. Accuracy rises from 69.4% before fine-tuning to 74.3% with 5% of the rows, 84.8% with 50% and 86.9% with all rows. The curve flattens, and a saturating fit with bootstrap intervals cannot pin down its plateau. Seed spread at 20% of the rows (s.d. 1.6 points) exceeds some of the steps between sizes. Giving small subsets as many updates as the full pool gains 1.9 points at 5% and 1.9 points at 20% of the rows (one seed; p=0.14 and 0.13), and at 20% that is below the 2.3-point difference between two ordinary seeds. A single run with 10% symmetric label noise shows no detectable change (-0.2 points, 95% interval -1.7 to +1.4); 20% costs 3.4 points and 40% costs 8.7 points. Confusable-pair noise at 20% costs 7.4 points, and under noise the model moves from over-confident to under-confident. An independent labeller disagrees with the gold labels on 3.5% of held-out items, and about half of its choice disagreements (16 of 33, leaving each item out of the partner map) name the partner option that the confusable-pair noise uses. Laya is +0.9 points ahead of a TF-IDF classifier trained on the same rows at full size (the interval includes zero) and +21.1 points ahead at 5% of the rows. Everything is synthetic, LLM-labelled and from one backbone, one trainer and mostly one seed.