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

arXiv: https://arxiv.org/abs/2608.28886 · HTML: https://mlsanity.com/paper/2608.28886/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 16 references that are in the map.
- First posted on arXiv 28 Aug 2026.

## Builds on (most cited first, 9 of 9)

- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [Illuminating search spaces by mapping elites](https://mlsanity.com/paper/1504.04909/) (2015)
- [Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Models](https://mlsanity.com/paper/2312.06585/) (2023)
- [LoongFlow: Directed Evolutionary Search via a Cognitive Plan-Execute-Summarize Paradigm](https://mlsanity.com/paper/2512.24077/) (2025)
- [Curriculum Reinforcement Learning Can Incentivize Reasoning Capacity in LLMs Beyond the Base Model](https://mlsanity.com/paper/2606.22317/) (2026)
- [Interrupting the Loop: Periodic Subject Changes Raise Judged Surprise and Connection in Base Language Models](https://mlsanity.com/paper/2608.19893/) (2026)

## Abstract (arXiv)

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 in all three lineages, for attract and for the random control alike), and never beyond it. 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). 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. Mean quality among valid candidates can be bought and replicated; the observed best goes to the classic and, so far, never beyond it.