PaperlayerView exact revision on arXiv

Source-linked AI summary

Bayes-Sufficient Compression Is Not Enough: How Does Communication Help Multi-Agent Systems?

Yi Xie, Zhanke Zhou, Yi Fan, Yong Ge, Bo Han, Bo Liu

arXiv:2610.03769v1cs.LGcs.ITcs.MAmath.IT

TL;DR

Multi-agent LLM systems must decide how to communicate from a sender with broader context to an executor with a limited local view. The paper models message utility relative to the receiver’s next decision and analyzes compression, usability, and receiver burden. Across benchmarks, one fixed Qwen protocol helps on ContextBench but hurts on ToolSandbox, motivating adaptive protocol selection.

  • Problem

    In multi-agent LLM systems, it is unclear when a short message improves an executor’s next decision rather than adding burden, and aggregate task metrics conflate distinct sources of failure.

    Source: §1 · p. 1

  • Method

    The paper introduces a step-level framework that values communication by receiver gain minus protocol tax and develops an inference-time selector for communication actions.

    Source: §1 · p. 2, §2.2 · p. 3

  • Results

    The same Qwen protocol raises ContextBench joint accuracy from 0.633 to 0.775 but lowers ToolSandbox accuracy from 0.889 to 0.653, while fixed-message replay exposes cases where correct artifact recovery does not yield the correct action.

    Source: §5 · p. 10

  • Takeaways & Limitations

    Compression is useful only when tax savings exceed omitted information and decoder mismatch, and Bayes sufficiency alone does not ensure that a bounded executor can use a message.

    Source: §2.3 · p. 4

    The receiver is representation-sensitive: a fixed model, prompt, parser, context window, and tool interface may not support arbitrary recodings of a compressed message.

    Source: §2.3 · p. 4

Abstract

from arXiv · show

Multi-agent LLM systems pair a sender with broad context and an executor with a limited local view. We study when a short message improves the executor's next decision, when raw context is preferable, and when a stronger sender helps. Our framework, \emph{receiver-relative bounded coordination}, expresses message utility as receiver gain minus protocol tax. Compression beats raw context when tax savings exceed losses from omitted information and decoder mismatch. Even \emph{Bayes-sufficient} compression can fail when a bounded executor cannot use its surface form. A three-stage decomposition separates externalization, absorption, and \emph{action closure}, explaining how errors remain after the correct content reaches the receiver. Under a single-crossing condition, sender upgrades help above a receiver-burden threshold. Across six benchmarks, the same Qwen protocol raises ContextBench joint accuracy from $0.633$ to $0.775$ but lowers ToolSandbox from $0.889$ to $0.653$. Fixed-message replay reveals closure failures despite correct artifact recovery. These results guide an inference-time selector that improves the accuracy-cost frontier on the evaluated communication regimes.

1 Introduction

Multi-agent systems must decide whether to expose raw context or send a short message to an executor with a limited local view. The paper analyzes communication at the executor’s next decision and tests how its effects vary across tasks and receiver interfaces.

1 Introduction

  • Communication should be evaluated at the receiver’s next decision because aggregate task metrics conflate uninformative messages, messages the receiver fails to use, and errors carried across steps.The framework defines usefulness against an action-sufficient target and models the executor as a bounded decoder.Source: §1 · p. 2
  • The framework treats message value as receiver-side gain minus protocol tax, with compression trading tax savings against omitted information and decoder mismatch.Bayes sufficiency preserves information but does not guarantee receiver usability; fixed-message replay separates content recovery from conversion into an action.Source: §1 · p. 2
  • Across six benchmark families, communication helped when local views lacked useful context, while its effects varied across receiver interfaces on locally informative tasks.The experiments include receiver-only, full-context, multi-agent, fixed-message replay, and sender-swap comparisons.Source: §1 · p. 2
  • The paper introduces a step-level theory, an inference-time protocol selector, and empirical tests of compression, action-closure failures, sender-upgrade thresholds, and accuracy-cost improvements.The selector scores communication actions using estimated gain, protocol burden, and cost.Source: §1 · p. 2

2 A Theoretical Framework for Bounded Coordination

The framework evaluates communication by its effect on a bounded receiver’s next action, rather than by information transfer alone. It specifies when messages help, why correct content can still fail to produce a correct action, and when stronger senders are useful.

2.1 Setup

  • The setup defines an action-sufficient target as sender-side state needed for the receiver’s next action beyond its local view, and models the receiver with a bounded decoder class.The class includes a map that ignores the message, while a larger probe class separates message recoverability from receiver usability.Source: §2.1 · p. 3

2.2 One-Step Utility

  • A message helps exactly when its receiver-side gain exceeds the protocol tax it induces.Positive tax is an increase in the deployed protocol’s gap from the best decoder in the same bounded class, and can reflect parsing burden, distraction, or interface mismatch.Source: §2.2 · p. 3

2.3 Representation-Aware Compression

  • Compression beats raw context when tax savings exceed omitted target information and decoder mismatch; an action-sufficient message wins if it also is no harder for the executor to use.Bayes sufficiency alone is not a usability guarantee for a representation-sensitive bounded receiver.Source: §2.3 · p. 4
  • Even proper Bayes-sufficient compression can incur error of at least 1/2 −ε when raw context yields zero error for a representation-sensitive receiver.The failure can occur despite correct artifact and action information if the executor cannot use the message’s surface form.Source: §2.3 · p. 4

2.4 Where Post-Message Loss Remains

  • For a bottleneck-factorized receiver, total post-message loss decomposes into nonnegative externalization, absorption, and action-closure terms.Fixed-message replay cancels sender-side externalization, so paired receiver differences depend on absorption and action closure.Source: §2.4 · pp. 4–5

2.5 When Stronger Upstream Agents Help

  • Under continuity and single crossing, a stronger upstream agent changes from harmful to helpful at a unique receiver-burden threshold.The upgrade can add protocol tax through longer messages, less compatible surface forms, or greater executor reasoning burden.Source: §2.5 · p. 5

3 Dynamic Coordination and Protocol Control

The section models how communication errors can persist in shared-state workflows and turns receiver-relative utility into a selector over discrete protocol actions.

3.1 Residual Risk in Shared-State Workflows

  • When residuals persist between steps, local errors can carry forward as future risk, while later observations or repairs may shrink the gap.The propagation result applies when both trajectories remain in the carry regime; the gap vanishes only when the perturbed residual is fully resolved.Source: §3.1 · pp. 5–6

3.2 Analysis-Guided Protocol Control

  • The selector scores skip, bounded compression, raw context, escalation, or refresh using receiver-relative utility minus immediate cost and estimated residual risk.Raw context remains an option because Bayes-sufficient compression may still fail for a bounded executor.Source: §3.2 · p. 6
  • Calibration fixes action-level offsets, a local-sufficiency threshold, and cost weights before evaluation, using instance-disjoint records.The selector then reads instance-level signals at test time.Source: §3.2 · p. 6
  • In the online ToolSandbox path, the gate can skip before sender calls; otherwise, cached candidate messages support receiver probes before one selected action executes.The probes are capped at four tokens, and raw reads full upstream context.Source: §3.2 · p. 6

4 Experiments

Across six benchmark families, communication effects vary with the task, receiver, and protocol. The experiments also examine representation sensitivity, receiver-side action closure, sender upgrades, and protocol selection.

4.1 Experimental Setup

  • The evaluation pairs receiver-only, full-context, and multi-agent runs across six benchmark families, with fixed-message replay and sender swaps to test communication and receiver effects.Primary accuracy is hit_joint; the content and closure diagnostics distinguish artifact recovery from action conversion.Source: §4 · p. 7, §4.1 · p. 7, Table 2 · p. 8

4.3 When Compression Beats Raw Context

  • ContextBench joint accuracy rises from 0.633 to 0.775, while ToolSandbox falls from 0.889 to 0.653 under the default Qwen protocol.Figure 3 groups six benchmarks by communication effect and compares Qwen and OpenAI receiver protocols for ContextBench and BFCL.Source: Figure 3 · p. 8, §4.3 · p. 8

4.2 Benchmark-Wide Numerical Summary

  • ContextBench’s paired MA–RO gain is 0.1711 (95% CI [0.1417, 0.2012]), and RepoBench’s is 0.1611 ([0.1340, 0.1891]).The estimates cover 2,390 steps and 799 instances for ContextBench, and 2,396 steps and 800 instances for RepoBench.Source: §4.2 · p. 8

4.3 When Compression Beats Raw Context

  • Strict recoding lowers accuracy by 13.5 points on τ-bench, 6.0 on ContextBench, and 3.5 on ToolSandbox, while BFCL is unchanged.The controlled probe holds the target fixed while changing the message form.Source: §4.3 · p. 9

4.4 Closure-Dominated Receiver-Side Loss

  • Receivers can recover artifacts yet fail to convert them into actions: GLM-5, o3, and MiniMax-M2.5 have action-conversion rates of 0.545, 0.195, and 0.053.In fixed-message replay, wrong-action rates among parse-valid outputs with correct artifact recovery are 44.5% for GLM-5, 94.0% for MiniMax-M2.5, and 40.8% for o3.Source: §4.4 · p. 9

4.5 The Stronger-Sender Threshold

  • Stronger senders help on SWE-Lite, ContextBench, and RepoBench but hurt the other three Qwen conditions, with 34 of 38 nonzero anchors following a single positive-to-negative crossing.The reported effects are +0.52, +0.21, and +0.09 on the three helped conditions, versus −0.03 on τ-bench, −0.26 on ToolSandbox, and −0.16 on BFCL.Source: §4.5 · p. 9, Figure 5 · p. 10

4.6 Inference-Time Protocol Selection in Practice

  • On the 300-record ContextBench audit, the selector reaches 0.7367 accuracy at 1,735 tokens per step, recovering 8.67 points over always-skip while using 46.4% fewer tokens than always-send.On the 36-step ToolSandbox audit, early-skip reaches 1.000 accuracy with 919.4 prompt-plus-completion tokens, versus 0.8056 with 3,085.4 tokens for always-send.Source: Figure 6 · p. 10, §4.6 · p. 10

5 Conclusion

The conclusion frames communication as a receiver-relative trade-off among information, decoder compatibility, protocol tax, and local burden. It connects that account to benchmark reversals and an inference-time selector.

5 Conclusion

  • Compression pays off only when protocol-tax savings exceed omitted information and decoder mismatch, and Bayes sufficiency alone does not ensure receiver usability.The conclusion separates externalization, absorption, and action closure as sources of post-message loss.Source: §5 · p. 10
  • The same Qwen protocol raises ContextBench joint accuracy from 0.633 to 0.775 but lowers ToolSandbox from 0.889 to 0.653.Fixed-message replay also finds receivers that recover the correct artifact but choose the wrong action.Source: §5 · p. 10
  • The resulting selector adapts communication to receiver needs on the evaluated communication regimes.The conclusion points to trajectory-level success and calibration across interfaces as further discussion in Appendix E.Source: §5 · p. 10

AI use statement

The statement describes the authors’ use of Codex during revision, while the included appendix passages map supporting material and situate the paper’s contribution among related work.

AI use statement

  • Codex assisted with language editing, formatting, consistency checks, code and result-record inspection, and presentation of existing results; no new experimental runs were conducted.Implementation settings were incorporated following author confirmation, and the authors take responsibility for the final paper.Source: AI use statement · p. 14

Appendix Contents

  • The appendix organizes related-work discussion, proofs, experimental details, trajectory case studies, and expanded scope and limitations by the body sections they support.Appendix C contains experimental details and supporting results, while Appendix E expands scope and limitations.Source: Appendix Contents · p. 15

A Extended Related Work

  • The paper distinguishes its receiver-bounded, step-level focus from work on training or restructuring teams, descriptive communication taxonomies, and broad coordination benchmarks.It presents same-message replay and sender swaps as diagnostics for separating receiver-side from sender-side failures.Source: A Extended Related Work · pp. 16–17
  • The paper frames protocol selection as inference-time control using receiver-relative gain, communication tax, and dynamic residual risk, rather than as a new routing architecture.This formulation links modeling, diagnosis, and protocol selection for bounded receivers.Source: A Extended Related Work · p. 17

B Additional Theory and Proofs

This appendix develops formal results on compression, receiver limitations, and coordination, including loss decomposition, sender upgrades, state propagation, protocol selection, and idealized specializations. It also extends the experimental record with robustness, protocol, and shared-state analyses, and explains how benchmark-native supervision becomes action-sufficient scoring targets.

B.1 One-Step Utility and Representation-Aware Compression

  • Compression dominates raw context exactly when its saved protocol tax exceeds the bounded-receiver representation gap.If that gap is bounded by κ_t, the condition gives a compatibility-based sufficient condition for compression to win.Source: §B.1 · pp. 18–19

B.2 Bayes-Sufficient Compression and Receiver Compatibility

  • Bayes-sufficient compression can still fail for a bounded receiver because preserving target information does not guarantee a usable message representation.Receiver compatibility requires the required fields to be extractable and converted into a valid action by the deployed interface.Source: §B.2 · p. 19, For the threshold class · p. 21

For the threshold class

  • An α-proper Bayes-sufficient message can leave a bounded threshold receiver near chance error even when raw context is decoded perfectly.Alternating labels on the compressed message axis force threshold error of at least (m −1)/(2m).Source: For the threshold class · pp. 19–21

B.3 Bottleneck Decomposition and Fixed-Message Replay

  • The bottleneck loss decomposes into externalization, absorption, and action-closure losses; fixed-message replay cancels the shared sender-side externalization term.Paired receiver comparisons therefore isolate absorption and action closure.Source: §B.3 · p. 22

B.4 Sender-Gap Identity and Burden Threshold

  • Under a continuous, strictly single-crossing gain-minus-tax function, a stronger sender helps only above the unique receiver-burden threshold.The crossing occurs when extra gain and extra tax balance.Source: §B.4 · p. 22, Figure 7 · p. 22

B.5 State Propagation

  • When clipping is inactive for both residual trajectories, their difference propagates linearly; clipping either trajectory ends that regime and permits resynchronization.For vector residuals, the argument applies componentwise when the carry condition holds componentwise.Source: §B.5 · p. 23

B.6 Protocol-Control Regret Bound

B.7 Idealized Specializations

  • Under additive loss and independent artifact and action predictors, both class-optimal risk and receiver-relative gain decompose into artifact and action components.This is an idealized specialization under the stated factorization assumptions.Source: §B.7 · p. 24
  • Under additive loss and a product receiver class, joint prediction risk and receiver-relative gain decompose into artifact and action components.The proof obtains this by separately optimizing the artifact predictor and action predictor.Source: §B.7 · p. 24
  • In the zero-slack log-loss specialization, receiver-relative gain equals conditional mutual information, yielding a variational lower bound for uniformly bounded critics.The proof identifies conditional mutual information with KL divergence and applies the Donsker–Varadhan representation restricted to the critic class; the tax certificate follows by rearranging Proposition 1.Source: §B.7 · p. 24

C Additional Experimental Details and Results

  • The appendix extends the main experimental claims with robustness checks, protocol variants, cross-family sweeps, and shared-state perturbation and repair studies.Its additional analyses cover token accounting, no-overflow controls, strict recoding, gain-surrogate diagnostics, replay variants, sender replacement, protocol knobs, and selector results.Source: C Additional Experimental Details and… · p. 24
  • The appendix centralizes the default sender/receiver pair, message budget, and benchmark roles in its benchmark-and-protocol summary.Evaluation support is table-specific, and paired analyses use common instance-step keys; protocol accuracies and comparisons retain their stated supports.Source: C Additional Experimental Details and… · p. 24, Table 4 · p. 25
  • Benchmark scoring projects native supervision into acceptable artifact/action target pairs, while senders, receivers, and selectors do not observe those targets.Joint hits require matching an acceptable pair; artifact hits score the artifact component, and action correctness is conditional on artifact correctness.Source: Table 5 · p. 25

C.1 Benchmark and Protocol Summary

The appendix documents the benchmark supports and scoring projections, then reports how communication regimes and paired diagnostic controls vary across benchmarks. It also details uncertainty estimates and receiver-side outcomes on SWE-Lite.

C.1 Benchmark and Protocol Summary

  • The appendix’s main benchmark comparisons use six benchmark families, while LongCLI is reserved for shared-state analyses; default runs use a Qwen sender, Qwen receiver, and 128-token message budget.SWE-Lite uses Qwen3-Coder-Next-FP8 for the main multi-agent sender condition.Source: §C.1 · pp. 25, 28
  • ContextBench and RepoBench are context-heavy, while BFCL and ToolSandbox have high local sufficiency; SWE-Lite probes capability transfer and τ-bench is weakly helpful and protocol-sensitive.LongCLI is reserved for dynamic shared-state analyses.Source: §C.1 · p. 28

Appendix diagnostic controls

  • Communication effects remained positive on ContextBench and RepoBench, negative on BFCL and ToolSandbox, and near zero on τ-bench under paired diagnostic comparisons.ContextBench, RepoBench, SWE-Lite, and BFCL remained significant after Bonferroni correction; τ-bench had p = 1.0.Source: Appendix diagnostic controls · p. 29
  • The paired uncertainty analysis uses instance-clustered bootstrap intervals and exact McNemar tests on strict common instance-step keys, with larger diagnostic supports for ContextBench and RepoBench.Appendix numerical families use table-specific supports rather than replacing the main-text evaluation supports.Source: Appendix diagnostic controls · p. 29, Table 6 · p. 29, Table 8 · p. 30
  • On ToolSandbox’s 72-step common support, RO had 64 correct outputs and MA had 47, a descriptive RO advantage of 17/72 or 23.6 percentage points.Clustered intervals on BFCL and τ-bench were wider than their step-level intervals while retaining the same conclusions.Source: Appendix diagnostic controls · p. 29
  • SWE-Lite receiver-only joint scores could be zero despite artifact accuracy of 0.885–0.917, because most audited outputs chose read or run_test where the repair target was edit.Final SWE-bench correctness is determined by patch and test execution, not these next-action scores.Source: Appendix diagnostic controls · p. 30

C.2 Extended Compression Results

Extended controls show that receiver size, context overflow, message truncation, message form, and recoding all shape communication outcomes. The same added message content can help on context-heavy tasks yet impose burden on locally informative tasks.

Extended compression results

  • On ToolSandbox, substantial error remained with 80B and 397B receivers and with raw-context access, motivating evaluation by receiver and interface.These controls complement the main 9B receiver results.Source: §C.2 · p. 30, Table 9 · p. 31
  • On no-overflow subsets, ContextBench still had MA above RO and SF, while ToolSandbox had MA below RO and SF.The filter retained 100 ContextBench rows and 39 ToolSandbox rows where all compared protocols used at most 8192 input tokens.Source: §C.2 · p. 30, Table 10 · p. 31
  • ContextBench accuracy was 0.633/0.294/0.775 for RO/SF/MA overall, and MA exceeded both alternatives in capped and uncapped message groups.All 404 capped messages retained action_type and target_artifact, and the receiver followed both fields in 402 cases.Source: §C.2 · p. 30, Table 11 · p. 31
  • On a common ToolSandbox slice, canonical JSON and a decision-header template both reached 0.750 accuracy, versus 0.556 for prose, a 19.4 pp difference.These comparisons varied user-turn content while keeping the receiver system prompt fixed.Source: §C.2 · p. 31
  • As more sender-message content was exposed, ContextBench improved from B = 4 to B ≥16 while ToolSandbox degraded, showing budget effects depended on task.The sweep used stored Qwen sender messages and varied only the visible coordination-message budget.Source: §C.2 · pp. 31–32, Table 12 · p. 32
  • Strict recoding preserved the scorer target but reduced joint accuracy on ContextBench, ToolSandbox, and especially τ-bench; BFCL was unaffected.Only the receiver-facing representation changed, making the probe a test of bounded receiver compatibility.Source: §C.2 · p. 32, Table 13 · p. 32
  • The high gain-surrogate bin occurred in both helpful and harmful communication regimes, so the gain component alone does not establish deployed utility without protocol tax.The surrogate is based on hit changes on a coarse scale, not measured log-probability reductions.Source: §C.2 · p. 32, Figure 9 · p. 33

C.3 Extended Closure Results

Extended replay analyses show that post-message errors can remain action-closure failures even when the correct artifact is recovered. This pattern persists across replay partitions, receivers, and RepoBench.

C.3 Extended Closure Results

  • The content/closure split remains evident across easy and hard replay partitions, additional receivers, and RepoBench.RepoBench changes the absolute accuracy scale but preserves the interpretation of the bottleneck axes.Source: §C.3 · p. 34, Figure 10 · p. 34
  • With the sender message fixed, post-message error can concentrate in action closure rather than message content.The additional partitions and receivers extend the fixed-message replay analysis.Source: §C.3 · p. 34
  • 40.8–94.0% of valid outputs with the correct artifact still selected the wrong action, while permissive parsing changed validity by at most 0.2 pp.The replay used a gpt-5.4 sender and robust and permissive parsers.Source: §C.3 · p. 34
  • 41 of 52 SF losses in the 300 paired o3 steps retained the correct artifact but selected the wrong action.The audit reproduced RO/SF accuracies of 0.223/0.133.Source: §C.3 · p. 34

C.4 Extended Stronger-Sender Results

Expanded sender-swap analyses support a task-dependent crossover: stronger senders tend to help when receiver-only accuracy is low, but their value can turn negative as it rises. Sender helpfulness depends on the sender–receiver–task combination, not a fixed model ranking.

C.4 Extended Stronger-Sender Results

  • Across additional sender families, the strong-sender effect’s sign and rough ranking remained task-dependent, with the threshold also visible in sender-family matrices and pilot-set frontiers.The analyses extend the sender-gap result beyond a same-family comparison.Source: §C.4 · p. 34, Figure 11 · p. 35
  • With the Qwen3.5-9B receiver fixed, non-GLM strong senders beat RO on ContextBench, while some strong senders fell below RO on ToolSandbox.On ToolSandbox, local sufficiency was already high; the study attributes regime-specific helpfulness to varying receiver-relative gain and protocol tax.Source: §C.4 · p. 35, Figure 12 · p. 35
  • Fixing sender pairs while varying benchmark regimes, then fixing receiver and benchmark while varying sender identity, ties the threshold to the full sender–receiver–task combination.Within-family self-pair controls separate sender-identity changes from adding a same-family message channel.Source: §C.4 · pp. 35–36, Table 17 · p. 36
  • The fitted zero-crossing was RO = 0.638, with bootstrap 95% interval [0.491, 0.780], but few very-low-RO cells limit interpretation as a universal scaling law.A segmented hinge fit had a similar R2 and a wider interval.Source: §C.4 · p. 36, Table 15 · p. 36
  • Expanding the paired anchor set from 22 to 41 narrowed the crossover interval to [0.552, 0.706]; 34 of 38 nonzero effects agreed with one positive-to-negative crossing.The hierarchical model preferred this structure to linear/no-threshold and two-crossing alternatives on all 10 anchor-separated folds.Source: §C.4 · p. 36, Table 16 · p. 36

C.5 Cross-Family Model Ablations

Cross-family ablations preserve ContextBench communication gains but show that ToolSandbox outcomes vary with receiver and protocol. Closure diagnostics and weak-family baselines further qualify those comparisons.

C.5 Cross-Family Model Ablations

  • On four benchmarks, the OpenAI extension evaluated six API model aliases in SF, RO, and gpt-5.4-to-receiver MA configurations.The extension preserves ContextBench communication gains and shows a different ToolSandbox response from the default Qwen receiver.Source: §C.5 · pp. 36–37, Table 18 · p. 37, Table 19 · p. 37
  • On ContextBench, OpenAI MA exceeds SF for each displayed receiver; on ToolSandbox, MA improves over RO for OpenAI receivers but reduces accuracy for the default Qwen receiver.The SF and MA endpoints often approach ceiling on ToolSandbox.Source: §C.5 · p. 37
  • Non-reasoning OpenAI receivers remain largely content-limited, while reasoning receivers continue to show closure-sensitive behavior.The latter is the cross-family analog of the earlier closure diagnostic.Source: §C.5 · p. 37
  • At smaller scale, matched MA falls below RO even on ContextBench; five-seed BFCL and ToolSandbox results at temperature 0.3 add replication checks.The weak-family result matches the sender-gap account when extra gain fails to cover protocol tax.Source: §C.5 · p. 37, Figure 13 · p. 38

C.6 Protocol-Level Tax Knobs

The protocol studies compare routing, costs, and shared-state propagation. The selector’s accuracy–cost trade-off and the effect of repair or fresh observations vary across evaluated regimes.

C.6 Protocol-Level Tax Knobs

  • Removing gain made the selector choose skip on every step and reduced accuracy from 0.737 to 0.650; removing tax left choices unchanged on this support.Removing cost changed the action mixture, while always-send had the highest raw accuracy and the highest cost.Source: §C.6 · p. 39, Table 20 · p. 39
  • On ToolSandbox, the adaptive static controller reached 1.000 accuracy at 581 input tokens per step; on τ-bench, rewriting exceeded the controller’s accuracy, 0.139 versus 0.083, at nearly identical cost.The τ-bench costs were 2,506 versus 2,504 tokens.Source: §C.6 · p. 39, Table 21 · p. 40
  • Protocol comparisons include skip, bounded compression, evidence rewriting, and selective suppression, while format and budget sweeps vary preserved content, decoder compatibility, and protocol tax.The raw action retains its full-context meaning.Source: §C.6 · p. 39, Figure 14 · p. 40, Table 22 · p. 40
  • Across calibration fractions from 5% to 40%, mean accuracy spanned 0.90 pp and cost relative to always-send spanned 0.30 pp.The sensitivity study used 20 instance-disjoint splits per fraction.Source: §C.6 · p. 39, Table 23 · p. 41
  • The receiver-relative selector had the highest accuracy minus token cost among evaluated routing policies, reaching 0.7425 accuracy at 1,732.9 tokens per step versus always-send’s 0.7917 at 3,227.0 tokens.Utilities use the same 10^-4 token-cost weight.Source: §C.6 · p. 41, Table 24 · p. 41
  • The pre-sender gate reduced ToolSandbox tokens by 70.2% and latency by 31.0% on 36 online steps relative to always-send.The separate five-seed endpoint comparison reduced tokens by 57.9% and latency by 26.0%; online and endpoint supports differ.Source: §C.6 · pp. 38, 41, Table 26 · p. 42

C.7 Conditional Propagation in Shared-State Tasks

  • LongCLI and higher-coupling ToolSandbox show downstream deficits after local perturbations, with repair only partly closing the gap; broader ToolSandbox effects are mostly local and resynchronize.The studies test coupling dependence in shared-state tasks.Source: §C.7 · p. 42, Figure 15 · p. 42
  • Stale LongCLI observations degrade downstream performance even without an injected perturbation, while fresh ToolSandbox observations largely neutralize downstream effects in broader conditions.Targeted repair helps most under stale conditions.Source: §C.7 · p. 42, Figure 16 · p. 43

D Illustrative Case Studies

The case studies show that messages can help by transferring context unavailable to the receiver, harm by redirecting a locally correct choice, or fail after correct artifact recovery when the receiver emits the wrong action.

Case D.1: Message overrides a correct local view (noise regime)

  • On ToolSandbox’s find_temperature step, the sender redirects a correct receiver-only tool target to messages, and the receiver follows the wrong target.The receiver-only output names search_weather_around_lat_lon; the sender instead directs it to messages.Source: D Illustrative Case Studies · p. 44

Case D.2: Sender provides cross-module context the receiver lacks (helpful coordination)

  • The receiver edits the correct cascade-deletion file after the sender supplies cross-module context missing from its local view.Without the sender, it edits the wrong file; the message identifies deletion.py and Collector.collect.Source: D Illustrative Case Studies · p. 44

Case D.3: Same message and different action compliance (conversion bottleneck)

  • With the same frozen message and correct target artifact, GLM-5 emits read instead of edit, while the Qwen-9B receiver emits edit.The case separates artifact recovery from action closure: the target file is correct even when the emitted action is not.Source: D Illustrative Case Studies · p. 45

E Scope and Limitations

The paper bounds its account to receiver-relative, step-level communication and discusses what remains for trajectory-level success. It also documents the evaluation, reproducibility, compute, and broader-impact considerations in its checklist.

E Scope and Limitations

  • The framework isolates message-conditioning at the step level; extending its account to end-to-end task success requires modeling cross-step error correlation.The selector is analysis-guided, with strongest gains when closure failure or protocol tax dominates; gain and tax also depend on the bounded decoder class.Source: E Scope and Limitations · p. 45
  • The paper identifies lower inference cost and latency as potential benefits while noting risks from incorrect directives, sensitive-context exposure, and scaling harmful workflows.It recommends limiting shared context to task-relevant information and validating consequential actions against the user request and available tool state.Source: E Scope and Limitations · p. 45, NeurIPS Paper Checklist · p. 50

NeurIPS Paper Checklist

  • The checklist reports benchmark and model settings, paired contrasts, replay and selector calibration details, released records and recomputation scripts, and statistical intervals and tests.It notes that the repository does not include the full benchmark-running harness and that experiments are inference-only, with compute and evaluated step counts reported.Source: NeurIPS Paper Checklist · pp. 47–49

Related papers

Loading 2610.03769v1…