Moving the Mean Toward the Known Good, Not Beyond It: What Inference-Time Interventions and Weight Consolidation Buy in Open-Ended Generation

arXiv:2608.28886v2 Announce Type: replace-cross Abstract: What does a generation loop gain from learning on its own verified successes? In cycles of generate, verify, select and LoRA-consolidate on online bin packing, training on value-filtered candidates shifts what the model writes on held-out variants toward value (-1.7 points of excess, p=0.008; -3.1 against a random-consolidation control, p=0.004) while the best observed candidate converges to the classic heuristic's level and no further. A confirmation battery replicates the whole procedure three times, with fresh seeds and a never-consulted held-out set read exactly once: the mean was nearly identical in all three lineages (-2.0, -1.8, -1.9), and after aggregating within held-out variant all seven evaluable variants favored consolidation (p=0.008). The best observed candidate moved to the classic heuristic's level, exactly (0.021028, the lowest variant's classic level, in all three lineages and both arms); attract never went beyond its variant's classic level, while the random control did in 7 of 24 lineage-variant cells. A matched SFT-only control shows the supervised anchor, not repulsion from bad candidates, does the concentrating (96% of candidates land exactly at the classic heuristic's level). On far families the tails cut both ways: consolidation lowers the per-candidate rate of better-than-classic candidates (10% to 3.9%) while its larger production yields more such candidates absolutely (5 against 1, on few events). As motivation we report the inference-time ledger that led here: a model-written schematic recap buys judged document integration and nothing buys development; a verifier written into the stream is imitated, 16.4 fabricated verdict lines per notebook. In this arrangement (an 8-bit model in MLX, five cycles), mean quality among valid candidates can be bought and replicated; under attraction the observed best goes to the classic and, so far, never beyond it.