Inheritance as an Admission Test for LLM Prompt Merge Operators

Zan-Kai Chong; Hiroyuki Ohsaki; Bryan Ng

cs.AIOct 21, 2026

Inheritance as an Admission Test for LLM Prompt Merge Operators

Authors: Zan-Kai Chong, Hiroyuki Ohsaki, Bryan Ng

Organizations: School of Science and Technology, Kwansei Gakuin University, Sanda, Japan · School of Engineering & Computer Science, Victoria University of Wellington, Wellington, New Zealand

Abstract

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.

Figures & tables

Figure 1. The decomposition of Eq. 3 in the embedding. Points are population members

\psi(a)

. The child

x_{\mathrm{clone}}

is the recipient

x_{b}

plus a fraction

\tau

of the donor increment, the projection of Eq. 4 , plus the orthogonal residual

\xi

. The dashed polygon is the hull of

\psi(P_{t})

, which the residual may leave.

operator	model call	donor material	$\beta=0$ child
free rewrite	regenerates the whole prompt	trace, as context	paraphrase
constrained rewrite	rewrites, keeping unreplaced text verbatim	trace, as context	original, if honoured
tactic append	abstracts the trace into short rules only	rules, appended	recipient
template append	none	raw trace lines, appended	recipient

Table 1. The four merge operators. Each takes a recipient prompt, a donor trace and a requested dose

\beta

. The rewrites pass

\beta

to the model as a requested percentage. Template append uses

\beta

as a count of grafted lines and makes no model call. Tactic append calls the model for short rules, then appends that count mechanically.

System. [the strategy’s own prompt] You are negotiating over three indivisible issues: patent, territory, staffing. Each must go entirely to A or to B. You are side A. Your private values are patent 50, territory 30, staffing 20. This is message 5 of 6; 1 message remains after yours. Reply with propose or accept and an allocation. If no agreement is reached by the last message both sides score zero.

User. Negotiation so far:

A: propose patent A, territory A, staffing B. my terms

B: propose patent B, territory B, staffing A. staffing is all I can give

A: propose patent A, territory B, staffing A. I need the patent

B: propose patent B, territory B, staffing A. unchanged, take it or leave it

Your move.

Listing 1: One of the eight scripted situations, at side A’s final message. The strategy’s prompt is prepended to the system message, and the four B lines are fixed text. Accepting here scores 20, and any other move scores zero.

Figure 2. Two free-rewrite pairs, with the recipient at 0 and the donor at 1. The filled

\beta=0

marker is the zero-dose child that serves as the baseline, and the hollow marker is the no-donor control of Table 2 , the same rewrite instruction with the rival block removed.

operator	$s(0)$	$\Delta s$ ( $0.15$ )	$\Delta s$ ( $0.30$ )	bound (probe 1)	bound (re-probe)	ratio	held-out $\Delta s$	held-out bound	verdict
tactic append	$0$	$+0.33$	$+0.33$	$+0.21$	$+0.19$	7.9	$+0.23$	$+0.15$	admitted
constrained rewrite	$0$	$+0.15$	$+0.40$	$+0.23$	$+0.21$	5.6	$+0.29$	$+0.16$	admitted
template append	$0$	$+0.41$	$+0.35$	$+0.17$	$+0.11$	7.6	$+0.18$	$+0.10$	undetermined
free rewrite	$0.30$	$+0.06$	$+0.10$	$+0.05$	$+0.06$	6.5	$+0.14$	$+0.03$	rejected
free rewrite, no donor	$0.39$	–	–	–	–	7.9	–	–	–

Table 2. Transmission and drift for the operators of Table 1 over sixteen recipient-donor pairs.

s(0)

: median position of the operator’s own

\beta=0

child.

\Delta s

: median movement beyond that child at each dose, on the first probe of the full battery. Bound: one-sided 95% lower confidence bound on

\Delta s

\beta=0.30

, on the first probe and on the re-probe of the same children. Ratio: off-segment residual over the convex null at

\beta=0.30

. Held-out:

\Delta s

\beta=0.30

on the five held-out situations, and its bound. Verdict: admitted when both full-battery bounds reach half the dose,

0.15

, rejected when a shortfall below the dose is detected, and otherwise undetermined.

operator	$\Delta s$	ratio	verdict	loop $\Delta s$	runs past best seed	child increment
	Section 4 (open loop)			Section 5 (closed loop)
tactic append	$+0.33$	7.9	admitted	$+0.19$	3/3	$+0.028$
template append	$+0.35$	7.6	undetermined	$+0.17$	3/3	$+0.011$
free rewrite	$+0.10$	6.5	rejected	$+0.00$	0/3	$-0.001$

Table 3. Open-loop verdict (Table 2 ,

\beta=0.30

) beside closed-loop outcome.

\Delta s

and ratio: as in Table 2 . Verdict: the open-loop verdict. Loop

\Delta s

: median

\Delta s

of sampled closed-loop children on the same battery. Runs past best seed: runs whose final mean beats the pooled bar of 0.771. Child increment: mean panel gain from recipient to child.

Figure 3. Thin curves are each run and the solid curve is their mean, both mean reference performance

\bar{\theta}_{t}

on the frozen generation-zero panel. The dotted line is the pooled best generation-zero score of 0.771, the bar for every run.

Language Model Merging

Language model merging combines capabilities from multiple models or adapters by composing their weights, updates, or outputs.

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Abstract

Language Model Merging

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