Lineage Is Memory: Parent Inheritance and Feedback Disclosure in Short-Budget LLM-Guided Optimization

Large language model (LLM) agents are often improved by iterating until a fixed verifier is done. Once that verifier saturates, the loop has nothing left to climb. We instead score agents against the current population, and a frozen panel records whether anyone got better. The panel mean can rise inside the seeds by elimination alone. We therefore count a run as training only when its final mean beats the best generation-zero member. A merge is admitted only when the child moves toward the donor, past the child the same operator produces at zero dose, and the lower confidence bound on that movement reaches half the requested dose. That is the admission test. A detectable shortfall rejects the operator, and the test is otherwise undetermined. We keep realised fitness φas the selector and reference performance θas the unused ruler. Every measurement uses gemini-3.1-flash-lite on one negotiation task, and no fixed-oracle arm was run. In the open loop, tactic append grafts short donor rules and is admitted. Free rewrite moves only a third of the requested dose and is rejected. Template append pastes raw donor replies into the child. Its movement clears the bound on the first probe but not on the re-probe, and it is left undetermined. A held-out re-probe on the five situations the merge never saw confirms that both appends move, and it does not rescue free rewrite. Neither append rises with the dose. Constrained rewrite is admitted in the open loop and was not run in the closed loop, which changes only the operator. The population, the scores and the task stay fixed. No free-rewrite run beats the best generation-zero member. Every tactic-append run and every template-append run does. Sampled loop children keep that split. Free rewrite moves no further toward the donor, and both appends still clear the bound, by less than in the open loop.

LLM-guided search loops propose a modified candidate, score it, and keep it if it scores better. When both candidates are re-scored at every comparison, as in the minibatch acceptance gates of prompt optimizers, keep-if-better is a reversible Markov chain if the score difference is logistic and the mutation operator is reversible, and its stationary law is the mutation equilibrium tilted by exp(beta f). For any continuous symmetric noise difference the same tilt is the stationary law of a small-step diffusion limit, with beta = 4F'(0); for a minibatch gate beta grows with the square root of the minibatch size. Caching the incumbent's score instead inflates the recorded score. We test the tilt as a prediction for LLM-guided program search, committing each prediction from calibration data before the search runs. The level after 150 steps rises with the minibatch size in six of seven settings, but its predicted value fails: on bin packing, search attains 62-88% of the predicted gain when the proposer edits the parent and 109-119% when it writes new heuristics. The attained fraction falls with the parent-child quality correlation of unselected mutation; a registered test on two new settings confirmed the direction, but not the quantitative agreement after a correction. Further registered tests found that runs started from a good program kept losing quality over 300 steps, more so from starts that search had selected, by a margin that passed its registered rule narrowly. Runs from different starts had not reached a common level, so whether the tilt describes the stationary law of LLM editing remains open. A registered test in prompt optimisation on frozen task-model scores failed: search exceeded the tilt, and the bin-packing relation did not transfer.

Parent selection significantly affects exploration, exploitation, and complexity control in genetic programming (GP) for symbolic regression. It is unclear whether large language models (LLMs) can synthesize effective operators in a zero-shot setting without iterative meta-evolution. Here, zero-shot means that the model receives only the task description, with no reference operators or iterative feedback. In this work, we benchmark zero-shot synthesis of parent-selection operators across eight LLMs within a standard GP framework for symbolic regression. Each model receives the same natural-language prompt to generate a parent-selection operator, which is then evaluated in a standard GP framework with only the parent-selection operator replaced, while all other components and the evolutionary-search budget are held constant. For each LLM, ten independent zero-shot operators are evaluated on twelve OpenML regression benchmarks and compared against automatic lexicase and tournament selection baselines. Claude Sonnet4.6 and Gemini3.1 Pro stand out for consistently strong performance on both training and held-out test $R^2$. The strongest operator in our benchmark---a Kimi~K2.5 zero-shot synthesis---surpasses the automatic lexicase and tournament baselines in search effectiveness. These results suggest that zero-shot LLM synthesis is a viable approach to generating competitive GP selection operators. Analysis shows that many generated operators use semantics to guide selection, suggesting that LLMs can produce non-trivial search heuristics from the task description alone. We also examine the relationship between public LLM leaderboard rankings and GP performance. Widely used benchmarks, such as Humanity's Last Exam and SWE-bench Verified, strongly correlate with training $R^2$, while their relationship to held-out test $R^2$ is weaker and less clear.