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Communication between Frozen Large Language Models via Prompt Optimization in a Referential Game

Vivek Anand, Muthu Chandrasekaran, Shiva Chaitanya

arXiv:2609.31989v1cs.CLcs.AIcs.LGcs.MA

TL;DR

The paper tests whether two frozen LLMs with different backbones can establish a shared code through prompt optimization in a referential game. Positional codes generalize to held-out objects, while targeted harness changes enable place-value communication in some runs.

  • Problem

    Evidence on whether frozen LLMs with different backbones can establish a shared communication protocol remains limited.

    Source: §1 · p. 1

  • Method

    Two frozen LLMs play a referential game and independently optimize prompts from scored interactions, with only messages and reward shared.

    Source: §1 · p. 2, §3.4 · p. 11

  • Results

    The positional-game agents establish a shared code that generalizes to unseen objects, and targeted harness changes yield a working place-value protocol in successful runs.

    Source: §1 · p. 2, §5 · p. 26

  • Takeaways & Limitations

    In successful runs, optimized prompts contain the protocol in readable form, and positional-game communication persists without the memory window.

    Source: §5 · p. 26

    Outcomes are stochastic: Rocky settles in only four of seven reported attempts with the auxiliary, and runs take hundreds of rounds and many hours and dollars.

    Source: §5 · p. 26

Abstract

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We study communication between two frozen large language models from different providers, with different tokenizers, accessed through their API endpoints. The two play a referential game: one sees an object and describes it in a short fixed-length message over a small alphabet; the other must pick that object out of a candidate set. Neither model's weights are updated. Each agent's prompt is rewritten by an isolated prompt optimizer whose reflection model reads that agent's scored interactions. In the positional setting, optimized prompts carry a shared code that generalizes to held-out objects above a measured no-codebook baseline, including when the memory window is removed. In a second setting, independent per-letter blocks no longer fit within the message, although a whole-object place value code does. The base system fails to establish reliable communication: the sender struggles to retain an injective rule, and the receiver has too few confirmed examples in view. A sender collision penalty, retention of successful interactions, and sequential optimization enable successful place value communication in some runs. Outcomes vary across runs and reflection models. In successful runs, the protocol is written into the optimized prompts, where it can be read and audited directly.

1 Introduction

The paper asks whether frozen LLMs with different backbones can establish a shared communication protocol without a predefined code. In referential games, prompt optimization yields structured codes that generalize in the positional setting and, with targeted changes, in successful place-value runs.

1 Introduction

  • The study asks whether frozen agents with differences in tokenization, architecture, pretraining, and post-training can communicate, against a backdrop of protocol overhead and limited evidence for cross-backbone communication.Prior frozen-LLM studies closest to this work use one model in both roles.Source: §1 · pp. 1–2
  • The positional-game agents converge on a shared injective code that generalizes to objects never seen in play.The harness uses two models with different backbones, and communication is optimized through prompts rather than weight updates.Source: §1 · p. 2
  • Successful positional-game prompts retain the protocol even when the memory window is removed, with the code written into both agents’ prompts.The paper presents this as a readable artifact that can be inspected directly.Source: §1 · p. 2
  • Successful runs produce a compositional positional code in one game and a systematic place-value code in the other, measured after optimization rather than used to select prompts.Source: §1 · p. 2
  • In successful place-value runs, a sender collision penalty, keep-wins memory for the receiver, and optimizing the sender first can enable a generalizing code.The base harness struggles to retain an injective sender code and gives the receiver too few confirmed examples.Source: §1 · pp. 2–3

2 Related work

Related work connects language emergence and compositionality to learning bottlenecks, and traces emergent communication from trained toy agents to frozen LLMs. The paper distinguishes its cross-backbone, fixed-channel setting and uses prompt optimization to adapt frozen agents.

Language emergence and compositionality

  • Iterated-learning work links compositionality to languages passed through learners with limited fragments, while another account frames it as a balance between learnability and expressiveness.This paper instead constrains memory while optimized prompts persist across rounds.Source: §2 · p. 3
  • Prior emergent-communication studies train recurrent agents, but report different relationships between compositional structure and generalization.One study finds no correlation but reports that more compositional languages are easier for fresh listeners to learn.Source: §2 · p. 3

Referential and reconstruction games

  • Referential games give the receiver a candidate set and binary success feedback, whereas reconstruction asks the receiver to recover the target from the message alone.The supervision and candidate-set size affect game difficulty.Source: §2 · p. 4

Emergent communication with frozen LLMs

  • Closest frozen-LLM studies use one model for both roles; one permits variable-length messages and obtains a non-injective code, while another compares hand-designed memory harnesses.Source: §2 · p. 4

Prompt optimization

  • The paper uses GEPA, which proposes prompt changes from scored rollouts and retains candidates that improve validation performance, while keeping agent architecture fixed.Each agent optimizes its own genes independently.Source: §2 · p. 4

3 Methods

The methods define a referential game between a sender and receiver, compare positional and place-value encodings, and use independently optimized prompts and bounded memory to support communication. The two game sizings differ in whether independent per-letter blocks fit in the message channel.

3.1 The referential game

  • Rocky sends a message for a hidden object, and Grace selects from candidates; both receive a binary reward while the target and candidate set remain private.The agents share the message and reward, but neither sees the other’s committed rule.Source: §3.1 · p. 5

3.2 The two sizings

  • In POSGAME, four letters each receive a fixed three-symbol block, exactly filling the 12-symbol channel.A confirmed pair can reveal up to four distinct letter-to-block facts; repeated letters reveal fewer.Source: §3.2 · p. 7, Figure 3 · p. 7
  • In PVGAME, three independent three-bit letter blocks need nine bits, so the eight-bit channel instead uses a base-6 whole-object value written in binary.Grace must invert the whole-number mapping; a confirmed pair constrains the full rule rather than individual letter blocks.Source: §3.2 · pp. 7–8

3.3 The agents

  • Each agent has a reasoner and answerer, while its memory window holds at most 19 selected interaction rows and cannot store a lookup table.Rocky’s rows contain object, message, and reward; Grace’s contain message, candidates, pick, and reward.Source: §3.3 · pp. 9–10

3.4 Prompt optimization

  • GEPA independently updates each agent’s prompts from scored rollouts, selecting candidates on validation data; held-out objects evaluate the resulting arms, including optimized prompts without memory.For place-value experiments, only the reasoner genes remain optimizable from the third attempt onward after codebooks appeared in answerer genes.Source: §3.4 · p. 11

3.5 The harness around the genes

The harness is fixed prompt text surrounding each optimizable gene, with role-specific inputs for Rocky and Grace and a separate reflection harness for GEPA. The experiments use different frozen player models and a reflection model, while provider reliability limits exact reproducibility.

3.5 The harness around the genes

  • The harness is fixed input text around the genes, while each agent has a reason gene and an answer gene that can be optimized.The gene and harness render together in each model request.Source: §3.5 · p. 11, Figure 6 · p. 12

3.5.1 Rocky’s harness and seed genes

  • Rocky’s harness supplies the target object and carried rule to the reasoner, then has the answerer emit the fixed-length message.The reasoner is instructed to state and retain its committed rule unless memory contradicts it.Source: §3.5.1 · pp. 12–13

3.5.2 Grace’s harness and seed genes

  • Grace’s harness supplies the message and unlabelled candidate set, and requires the answerer to choose one listed candidate.Its history records the candidates and whether the choice earned reward 1 or 0.Source: §3.5.2 · p. 13

3.5.3 The Reflection Model’s harness

  • GEPA’s reflection harness combines its fixed template, the incumbent gene, and scored rollouts so the reflection model can propose a candidate gene for validation.The reflection model reads each agent’s own interactions; it does not see the other agent’s private information.Source: §3.5.3 · p. 14, Figure 7 · p. 14

3.6 Models

  • Rocky is GLM-5 and Grace is DeepSeek-V4-Flash, with Claude Opus 4.8 proposing genes; provider reliability changes may prevent exact reproduction of experimental conditions.The player models are accessed through APIs and their weights, decoding settings, and architectures are not updated.Source: §3.6 · p. 15

4 Experiments

The experiments test whether prompt optimization can establish and retain shared codes between frozen models in positional and place-value games, including targeted changes to sender selection and receiver memory. They examine whether memory updates and sequential optimization support communication, with outcomes varying by reflection model and successful prompts encoding the protocol directly.

4.1.1 Accuracy baseline

  • The measured no-codebook baseline is 0.589 in POSGAME and 0.056 on held-out PVGAME objects, versus chance of 0.125 and 0.050, respectively.Accuracy above this baseline is necessary, but not sufficient, evidence of code acquisition; topsim is compared with the perfect code on the same objects, while pvfit measures agreement with a fitted place-value rule.Source: §4.1.1 · p. 16, Place value metrics · pp. 17–18

4.2 Experiment 1: POSGAME with the base harness

  • The POSGAME evaluation grid used three evaluation draws on 99 held-out objects per cell, with chance 0.125 and ceiling 0.589.The fifth cell re-evaluates the prompt-opt@mem arm’s genes with the window off.Source: Table 6 · p. 18
  • The optimized genes carry the same injective positional code, and communication remains possible without the memory window at evaluation.Prompt optimization with no window reaches 0.451 accuracy; prompt-opt@mem reaches 0.95 of the perfect code’s topsim and has high positional disentanglement and consistency.Source: §4.2 · pp. 18–19

4.3.1 The base harness in the PVGAME

  • In PVGAME, the base harness’s best cell reaches 0.112, above the 0.056 baseline but not establishing reliable communication, although Grace reaches 0.968 accuracy when given Rocky’s rule.The handed-rule probe compares 0.968 with a perfect-code score of 1.00, indicating Grace can execute the supplied rule but does not acquire enough information to do so unaided.Source: §4.3.1 · pp. 19–20, Table 8 · p. 19, Table 9 · p. 20

4.3.2 Grace’s half: the starvation hurdle

  • Grace’s 19-row FIFO window averages 1.17 confirmed pairs, has no pair in 31% of play rounds, and contains at least three in only 15%.Three pairs are a floor for identifying a place-value rule when the code family is already known; at this win frequency, the passage estimates 47 rows would be needed to average three.Source: §4.3.2 · pp. 20–21, Table 11 · p. 21

4.3.3 Rocky’s half: the selection hurdle

  • Rocky’s selection signal can reward lossy codes: the diagnostic reports 13% of confirmed pairs as collisions and a lower pvfit for the memory arm than the no-memory arm.The passage reports pvfit values of 0.750 and 0.028, respectively, while diagnosing that the window and small validation set can let a lossy code win by luck.Source: §4.3.3 · p. 21, Table 12 · p. 21

4.4.1 Fixing Rocky: the selection hurdle

  • Experiment 3 adds a self-supervised collision penalty to Rocky’s optimizer; about half of attempts settle on a high-pvfit base-6 rule, while about half fail.The penalty discourages reusing a message for a different object, but proposed base-6 rules may not be retained when Grace performs at chance, so the repair is necessary but not sufficient for communication.Source: §4.4.1 · pp. 22–23

4.4.2 Fixing Grace: the starvation hurdle

  • Grace’s keep-wins policy evicts losing rows before confirmed pairs, preserving wins longer without adding labels or increasing memory size.Experiment 3 also optimizes Rocky before Grace and evaluates the changes individually and together.Source: §4.4 · p. 22, §4.4.2 · p. 23
  • Keep-wins improves Grace’s accuracy and retained-pair supply over fifo during 400 rounds against frozen Rocky, without optimization.Grace may still fail to infer the rule because its 13-pair window can contain errors or collisions, even though three pairs uniquely identify a place-value rule in 69% of draws; given the true rule, Grace achieves near-perfect accuracy.Source: §4.4.2 · pp. 23–24

4.4.3 Both together: the two outcomes

  • Nine of 10 Opus 4.8 runs end partial and one full; partial and full outcomes average 0.141 and 0.878 held-out accuracy, respectively, while GPT-5.6 Sol produces four full outcomes in four runs.Runs optimize Rocky first and then Grace; accuracy is measured over the last 600 of 1,200 rounds.Source: §4.4.3 · p. 24, Table 15 · p. 24
  • Partial genes derive the six-value alphabet but treat messages as three independent groups, whereas the full gene learns and computes the base-6 mapping.Partial genes show some communication, at about 2.5 times baseline, but do not converge to the base-6 rule.Source: §4.4.3 · p. 24, Figure 10 · p. 25
  • With the full system, prompt-opt-both@nomem achieved communication even under the default model; without prompt optimization and memory, accuracy was significantly lower, while Opus 4.8 succeeded once and Sol 5.6 achieved full outcomes in all four runs.Source: §4.4.3 · p. 25
  • The results cover only GLM-5 sending to DeepSeek-V4-Flash receiving; role swaps and a different Rocky model are examined in appendix ablations.The authors report that outcomes vary across random seeds and reflection models.Source: §4.4.3 · pp. 25–26

5 Conclusion

With the models’ weights fixed, prompt optimization and harness design let Rocky and Grace establish shared communication codes. The conclusion reports success in the positional game and in some place-value runs, alongside substantial variability and cost.

5 Conclusion

  • In POSGAME, both optimized prompts retain the shared protocol even after the memory window is removed.The optimizers wrote the identical protocol into both agents’ prompts.Source: §5 · p. 26
  • In PVGAME, a sender collision auxiliary, keep-wins memory for Grace, and sequential optimization enable a working protocol in many runs.The base harness fails in this harder game; the modified setup keeps the same frozen base models.Source: §5 · p. 26
  • Outcomes remain stochastic: Rocky settles in four of seven reported auxiliary runs, and selection uses small, noisy validation sets.Runs take hundreds of rounds and many hours and dollars; both agents also use the same reflection model, and the experiments do not explain how much structure comes from model priors.Source: §5 · p. 26
  • The authors identify reliability, robustness, predictability, communication among more agents, and code cost as open research directions.They also propose studying two-way communication and harder codes.Source: §5 · p. 26

A The prompts every run starts from

This appendix documents the prompts and harness used in the runs, distinguishing optimizable instruction text from fixed surrounding text and showing how memory and optimizer feedback are rendered.

A The prompts every run starts from

  • Each agent has a reason gene and an answer gene; the fixed harness surrounds them, so the model receives the rendered combination.Genes are optimizable instructions, while the harness includes task text, memory headers and legends, and the committed-rule line.Source: A The prompts every run starts from · p. 29

A.1 The four seed genes, code-free by construction

  • The sender sees a fixed-length object-to-message task, scores 1 for exact reconstruction, and is prompted to state and retain a reusable rule.The seed instructions say to restate the committed rule unless memory contradicts it, and to explain any revision.Source: §A.1 · p. 29
  • The receiver chooses among listed candidates, with reward 1 for selecting the sender’s object and 0 otherwise.The seed instruction says the answer must be one of the candidates, never an object outside the list.Source: §A.1 · p. 29

A.2 The memory window as the agent sees it

  • At round 400, the illustrated keep-wins receiver window contains 19 confirmed WAS pairs.The window renders one row per remembered round, with the message beside its outcome.Source: §A.2 · p. 30

A.3 The updated harness, assembled

  • The updated harness leaves fixed prompt templates unchanged while collision feedback affects Rocky’s metric and keep-wins changes memory eviction.The retained window contents can change during play even though the prompt templates do not.Source: §A.3 · p. 31
  • The harness specifies three-character objects, eight-character messages, and a receiver choice among 20 candidates.The sender and receiver specifications list the object and message alphabets, and the receiver must select one listed candidate.Source: §A.3 · p. 31
  • The window legends distinguish fit, legal output, whether a program ran, and the remembered outcome.The outcome legend labels confirmed objects as WAS and alternatives as NOT.Source: §A.3 · p. 32
  • On a collision, Rocky’s reflection feedback states that the message was also emitted for another object; Grace has no such auxiliary.The passage says a tested counterpart for Grace was harmful at both seeds and was excluded from the claimed system.Source: §A.3 · p. 32

B The genes the optimizer wrote

This section reproduces the prompts behind the claim that the code is written into prompt text.

B The genes the optimizer wrote

B.1 The optimized positional genes, πreason

The optimized positional genes encode each object as four consecutive three-character blocks, using a fixed bijection between blocks and letters. The receiver checks confirmed message matches in memory before relying on the substitution table.

B.1 The optimized positional genes, πreason

  • The sender’s gene specifies the mapping b=ggg, z=ggm, n=gmg, v=gmm, k=mgg, j=mgm, q=mmg, and x=mmm.The sender is instructed to apply it character by character and concatenate the blocks.Source: §B.1 · pp. 33–34
  • Each object character maps to one distinct three-character block, and the four blocks are concatenated in order to form the message.The code is a bijection between the eight possible blocks and eight letters.Source: §B.1 · pp. 33, 35
  • The receiver first uses an exact-message WAS memory match; otherwise, it decodes with confirmed mappings or the working table and chooses among the candidates.The gene warns that the working table has produced a wrong answer and prioritizes memory-derived mappings.Source: §B.1 · p. 35

B.2 The first settled place value sender gene, πreason

The sender’s settled place-value rule maps a three-character object to an eight-bit message. The gene was warm-started into Grace runs naming a Rocky with pvfit 0.918, while prior reward-zero failures were attributed to message-length errors.

B.2 The first settled place value sender gene, πreason

  • The settled base-6 sender gene had pvfit 0.918 and was warm-started byte for byte into every Section 4.4.3 Grace run naming a 0.918 Rocky, including the full run.The passage describes reuse of the sender gene, not a change to its encoding rule.Source: §B.2 · p. 36
  • The sender maps each three-character object to a base-6 value, converts it to an eight-bit binary string, and maps 0 to p and 1 to w.The rule uses x=0, z=1, j=2, k=3, q=4, b=5 and left-pads the binary representation to eight bits.Source: §B.2 · p. 36
  • Past reward-zero failures were attributed to assembling messages with the wrong length, including nine-character strings that were truncated from the intended eight.The gene therefore requires constructing and checking exactly eight message characters.Source: §B.2 · p. 36
  • The gene treats the base-6-to-eight-bit whole-object code as the allowed scheme and rejects fixed-width per-character blocks as too long.It states that three bits per character would require nine bits, exceeding the eight-character message.Source: §B.2 · p. 37

B.3 One failed settling attempt, before and after

A seed-8 attempt first adopted a whole-object base-6 rule, then replaced it with per-letter blocks after zero rewards, although those blocks were said not to fit. The passages describe both the code’s injectivity and its failure to yield successful decoding in this attempt.

B.3 One failed settling attempt, before and after

  • At the second firing, the seed-8 rewrite banned the base-6 rule adopted at the first firing and returned Rocky to per-letter blocks that the text says cannot fit.Between firings, only the scoring batch changed; Grace scored with the window off, and the reflection model treated base-6 zero rewards as evidence about the code.Source: §B.3 · p. 37
  • The whole-object base-6 conversion was injective but repeatedly scored zero, with the passage attributing this to cross-character arithmetic that the partner could not independently decode.The examples listed include jzb, qqk, and bbj, each receiving reward 0.Source: §B.3 · p. 38
  • The hybrid overflow-flag scheme scored zero and was not injective: zxx and xbj shared the same message.The passage says the shared flag logic was ambiguous to the partner.Source: §B.3 · p. 38
  • The proposed per-character alternative keeps character contributions contiguous and independent, but three full three-bit blocks require nine bits for an eight-bit message.The passage presents the block-length conflict alongside the failures of base conversion and the hybrid scheme.Source: §B.3 · p. 38

B.4 The full run’s receiver gene, πreason

The full-run receiver gene decodes an eight-character p/w message as a binary number and converts that value into three base-6 digits. It then maps those digits to letters and selects a matching candidate, using position-by-position matching if no exact candidate is present.

B.4 The full run’s receiver gene, πreason

  • The receiver gene includes position weights and division-and-remainder arithmetic, and instructs the receiver to verify its digit table against the memory window each round.The prompt contains no message-to-object lookup entry.Source: §B.4 · p. 39
  • The receiver reads p/w characters as binary bits, sums the weights of w positions, converts the resulting number into three base-6 digits, and maps digits to letters.The gene assigns left-to-right bit weights 128, 64, 32, 16, 8, 4, 2, 1 and uses 0→x, 1→z, 2→j, 3→k, 4→q, 5→b.Source: §B.4 · p. 39
  • The listed calibration pairs are consistent with the stated digit-to-letter table.Examples include pppwwppw→xqz and wpppwwwp→kbq.Source: §B.4 · pp. 39–40
  • The gene says to choose the exact decoded object if it appears among the candidates; otherwise, it chooses the closest positional match, using memory exclusions to break ties.It also instructs the receiver to select only from the candidate list.Source: §B.4 · p. 40

C The swaps

The swaps compare alternatives with the default GLM-5 sender and DeepSeek-V4-Flash receiver. Table 17 reports the default pair’s prompt-opt-both@nomem cell, while role-swap rows have no cell when Rocky did not settle.

C The swaps

  • The role swap exchanges Rocky’s and Grace’s base models.Source: C The swaps · p. 41
  • Table 17 compares swaps against the default GLM-5-sender, DeepSeek-V4-Flash-receiver pair, whose prompt-opt-both@nomem cell uses three draws on 98 held-out objects and has a 0.056 ceiling.Source: Table 17 · p. 41
  • A Grace read behind a Rocky that did not settle is void, so role-swap rows carry no cell.Source: Table 17 · p. 41

C.1 Model identities and generation

The appendix identifies the API models used for the main pair and swaps, and records generation and reflection settings alongside gaps in per-run configuration records.

C.1 Model identities and generation

  • The main pair uses z-ai/glm-5 for Rocky and deepseek/deepseek-v4-flash for Grace; swaps exchange their roles or replace the sender with deepseek/deepseek-v4-pro-0813.Source: §C.1 · p. 41
  • Reflection defaults to anthropic/claude-opus-4.8, while the receiver-reflection swap uses openai/gpt-5.6-sol with the previously optimized sender retained.Source: §C.1 · p. 41
  • Provider settings require launch records as well as metadata, and fully resolved settings and versioned model snapshots were not recorded for every run.Source: §C.1 · p. 41
  • The reasoner and answerer limits are 2000 and 250 tokens, respectively; task temperature and complete per-run token-limit overrides were not archived.Source: §C.1 · p. 41

C.2 Optimization and evaluation

Optimization uses recorded DSPy and GEPA configurations with validation-based candidate selection. Evaluation repeats responses for fixed optimized pairs, rather than measuring variation across optimization runs.

C.2 Optimization and evaluation

  • Candidate selection uses validation performance, and saved firing logs record selected candidates, scores, configured metric-call budgets, and actual calls.Source: §C.2 · p. 41
  • Both genes were editable in positional experiments, while the answerer freeze later restricted proposals to the reasoner; reflection used minibatches of three training examples.Source: §C.2 · p. 41
  • Evaluation reports three draws per cell using the same held-out targets and object-seeded candidate sets, with fresh model responses.Source: §C.2 · p. 41
  • Genes, windows, and carried rules remain fixed within an evaluation cell; memory-off clears the window and carried rule, and repeated draws are not independent optimization runs.Source: §C.2 · p. 42
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