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Inheritance as an Admission Test for LLM Prompt Merge Operators
Zan-Kai Chong, Hiroyuki Ohsaki, Bryan Ng
TL;DR
Fixed-verifier iteration can stop at saturation, while population scoring can show apparent gains from eliminating weaker seeds rather than inheritance. The paper proposes a zero-dose admission test and a best-seed criterion for closed-loop training; its append operators move behavior toward donors, while free rewrite is rejected and template append remains undetermined.
Problem
A fixed verifier stops offering progress once satisfied, and a rising population-panel mean can reflect elimination rather than donor inheritance.
Source: §1 · p. 1Method
The paper tests merges against the same operator’s zero-dose child and counts closed-loop training only when the final mean beats the best generation-zero member.
Source: §1 · p. 1Results
Tactic append was admitted, free rewrite was rejected, and template append was undetermined; in the closed loop, every append run beat the best generation-zero member, while no free-rewrite run did.
Source: §6 · p. 7Takeaways & Limitations
The admission test distinguishes movement inherited from a donor from drift produced by the merge operator itself.
Source: §1 · p. 1Measurements use one model on one negotiation task, with sixteen open-loop pairs and three closed-loop runs per operator; both appends drive the population toward copies of a few agents.
Source: §6 · p. 7
Abstract
from arXiv · showhide
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 \phi as the selector and reference performance \theta as 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.
1 INTRODUCTION
The paper tests whether merge operators transmit donor behavior, since a rising panel mean can reflect elimination rather than inheritance. It introduces a zero-dose admission test and a closed-loop training criterion based on beating the best generation-zero member.
1 INTRODUCTION
- A rising panel mean can result from eliminating weaker seeds, so it does not establish that children inherit behavior from donors.The paper therefore treats transmission as a property of the merge operator.Source: §1 · p. 1
- Each agent is a frozen LLM with a system prompt, and a merge combines a recipient prompt, donor behavior trace, and requested dose into a child prompt.Transmission is measured through behavior profiles on a fixed battery of scripted negotiation situations.Source: §1 · p. 1
- An operator is admitted when the lower confidence bound on movement toward the donor, beyond its own zero-dose child, reaches half the requested dose.A detectable shortfall rejects it; otherwise, the verdict is undetermined.Source: §1 · p. 1
- Measurements use gemini-3.1-flash-lite on one negotiation task, and the study makes no efficiency comparison with a fixed-verifier arm.The paper measures transmission, not whether competitive scoring trains faster.Source: §1 · p. 1
- The admission test uses the operator’s zero-dose child as its baseline, separating inherited movement from paraphrase drift.The closed-loop protocol counts training only when the final mean exceeds the best generation-zero member, which elimination alone cannot achieve.Source: §1 · p. 1
2 RELATED WORK
Prior prompt-optimization and evolutionary approaches generate complete prompts or programs, whereas this paper studies recipient-preserving merges. Its related-work framing connects those merges to prompt grafting, later LLM evolution, and classical evolutionary computation while distinguishing the paper’s zero-dose audit.
2 RELATED WORK
- Prompt-optimization methods use textual gradients or LLM optimizers, while evolutionary prompt search samples complete prompts from parent examples rather than keeping the recipient and appending the donor.The latter includes language-model crossover and self-referential prompt evolution.Source: §2 · p. 2
- The merge audit compares a recipient-and-donor operation with its own zero-dose child, unlike crossover that replaces a parent with a random individual.Experience-distillation systems append rules from an agent’s own history [23] [30], while this paper uses a rival’s trace.Source: §2 · p. 2
- Later LLM evolution methods edit prompts or programs, but the cited methods do not score changes against the operator’s own zero-dose child [16] [1] [9] [29] [28].Source: §2 · p. 2
- The paper situates its setting in competitive coevolution and self-play, while distinguishing prompt inheritance from code-level search [3].It contrasts a blend, which stays on the seed segment, with hull escape sought by open-ended and quality-diversity search.Source: §2 · p. 2
3 A COEVOLUTIONARY TRAINING MODEL
The model separates population selection from donor inheritance by measuring progress against a fixed reference panel and decomposing child movement into inherited and residual components. It analyzes how merge fidelity, operator bias, and rank-weighted removal shape population performance.
3 A COEVOLUTIONARY TRAINING MODEL
- A fixed-size population adds k children from merge operators and removes k agents by rank-proportional elimination, without updating model weights.Strategies are prompts and configurations, and each child is produced from a recipient, donor, and requested dose.Source: §3 · p. 2, §3.2 · p. 2
3.1 Population, Competitive Fitness, and Reference Performance
- Realised fitness φ scores agents against current-population rivals, while reference performance θ uses a fixed panel that is never subject to selection.The strategy embedding is a measurement instrument for transmission; convexity of the strategy space is not assumed.Source: §3.1 · p. 2
3.2 Reproduction Operator
- A child decomposes into the recipient, a fraction τ of the donor increment, and an orthogonal residual; operator assumptions specify the residual and bias behavior.The residual may leave the population hull, and requested dose β can differ from fidelity τ; a dose rule based on donor advantage may under-deliver when fidelity is small or flat.Source: §3.2 · pp. 2–3, Figure 1 · p. 3
3.3 Population Dynamics
- Selection can raise the reference mean even without inheritance: the exact one-generation decomposition holds for k = 1 and to leading order in k/N otherwise.Its terms are fidelity, operator bias, and rank-weighted removal.Source: §3.3 · p. 3
3.4 Fidelity and the Operator Envelope
- When fidelity is dose-invariant, increasing requested dose adds no inherited movement; a noiseless blend with vanishing residual cannot exceed the best seed.Leaving the parent line is necessary, but not sufficient, to clear the best seed.Source: §3.4 · p. 3
4 IDENTIFYING FIDELITY ON LLM MERGE OPERATORS
The paper tests whether prompt-merge operators transmit donor behavior beyond their own zero-dose children, using a confidence-bound admission test. In single-merge experiments, tactic append and constrained rewrite are admitted, free rewrite is rejected, and template append remains undetermined.
4.1 Task and Operators
- Agents are frozen gemini-3.1-flash-lite models with different system prompts, evaluated in a structured negotiation task using scripted situations and a fixed behavior-profile battery.The merge model sees three donor replies; the task is a six-message negotiation over three indivisible issues.Source: §4.1 · p. 4, §4.2 · p. 4
4.2 Two Tests on Single Merges
- Free rewrite can drift toward the donor even at zero dose, so the operator’s own zero-dose child—not the recipient—is the baseline for measuring dose-driven movement.The with-trace child is beyond the no-donor child on eight of sixteen pairs, but the median gap is within the noise floor.Source: §4.2 · p. 4
- The admission test compares a child’s movement toward the donor with the same operator’s zero-dose child, admitting only when the lower confidence bound reaches half the requested dose.A detectable shortfall rejects an operator; otherwise, a result that does not clear the bound is undetermined.Source: §4.2 · p. 5
4.3 Admitting the Operators
- Template append moves on the five held-out situations, but its re-probe bound falls below the admission bar and six weak pairs leave its verdict undetermined.Neither append tracks requested dose: tactic append moves by the same +0.33 at both doses, while template append moves further at β=0.15 than at β=0.30.Source: §4.3 · p. 5
- At the requested dose, every operator departs from the recipient–donor line by 5.6–7.9 times the convex null, but this residual does not distinguish the four operators.Source: §4.3 · p. 5
- Tactic append and constrained rewrite are admitted, free rewrite is rejected, and template append is undetermined under the full-battery admission test.Tactic append’s median movement is +0.33 at both doses; free rewrite moves +0.10 at β=0.30, while template append’s re-probe bound falls below the half-dose bar.Source: §4.3 · p. 5, Table 2 · p. 6
5 THE CLOSED LOOP ON LLM AGENTS
With the population, scores, and task fixed, the closed-loop results separate the operators: tactic and template append pass the best-seed training criterion, while free rewrite does not. Sampled children preserve the open-loop admission split, though the append operators clear the bound by small margins.
5 THE CLOSED LOOP ON LLM AGENTS
- The closed loop changes only the merge operator and uses the same model, negotiation task, and twelve seed prompts.It runs 12 strategies for 40 generations, with turnover of 2, across three coevolutionary runs.Source: §5 · p. 6
- Every tactic-append and template-append run beats the pooled best generation-zero score of 0.771; no free-rewrite run does.Mean reference performance rises under all three operators, but only those append runs count as training under the stated criterion.Source: §5 · p. 6
- Sampled loop children preserve the admission split: both appends clear the half-dose bound, while free rewrite has a detectable shortfall.Tactic append has median Δs +0.19 and bound +0.01; template append has median Δs +0.17 and bound +0.02; free rewrite has Δs +0.00 and is rejected.Source: §5 · p. 6
- Mean panel-score increments are +0.028 for tactic append, −0.001 for free rewrite, and +0.011 for template append.By generation 40, append runs have five to ten copies among twelve agents, compared with one to three under free rewrite.Source: §5 · p. 6
6 CONCLUSION
The paper uses a frozen-panel best-seed threshold to distinguish population progress from gains caused by elimination. In the closed loop, the operator-specific outcomes align with the open-loop verdicts for decided operators, within a narrow evaluation scope.
6 CONCLUSION
- The closed-loop outcome table places the open-loop verdict beside sampled-child movement, runs past the best seed, and child panel increments.The caption identifies the table’s comparison fields but does not state their values.Source: Table 3 · p. 7
- Training is read against the best seed, because selection alone can raise the frozen-panel mean without agents leaving the seeds.Figure 3 marks the pooled best generation-zero score, 0.771, as the bar for every run.Source: §6 · p. 7, Figure 3 · p. 7
- No free-rewrite run beats the best generation-zero member, while every tactic-append and template-append run does.Sampled loop children retain that split, and both append operators pass the admission bound inside the loop.Source: §6 · p. 7
- The study measures transmission, not efficiency, using one model on one negotiation task and three closed-loop runs per operator.Both append operators also drive the population toward copies of a few agents.Source: §6 · p. 7