CARD: Towards Conditional Design of Multi-agent Topological Structures
Authors: Tongtong Wu
Yanming Li
Ziye Tang
Chen Jiang
Linhao Luo
Guilin Qi
Shirui Pan
Gholamreza Haffari
Venue: ICLR 2026 Poster (2026)
Keywords: Multi-Agent Systems
Graph Learning
Primary area: applications to computer vision, audio, language, and other modalities
TL;DR: We propose a dynamic-information-driven graph optimization framework that enables adaptive and robust communication structures.

Abstract: Large language model (LLM)-based multi-agent systems have shown strong capabilities in tasks such as code generation and collaborative reasoning. However, the effectiveness and robustness of these systems critically depend on their communication topology, which is often fixed or statically learned, ignoring real-world dynamics such as model upgrades, API (or tool) changes, or knowledge source variability. To address this limitation, we propose CARD (Conditional Agentic Graph Designer), a conditional graph-generation framework that instantiates AMACP, a protocol for adaptive multi-agent communication. CARD explicitly incorporates dynamic environmental signals into graph construction, enabling topology adaptation at both training and runtime. Through a conditional variational graph encoder and environment-aware optimization, CARD produces communication structures that are both effective and resilient to shifts in model capability or resource availability. Empirical results on HumanEval, MATH, and MMLU demonstrate that CARD consistently outperforms static and prompt-based baselines, achieving higher accuracy and robustness across diverse conditions. The source code is available at: https://github.com/Warma10032/CARD.

Published as a conference paper ICLR 2026
CARD: TOWARDS CONDITIONAL DESIGN OF MULTI-AGENT TOPOLOGICAL STRUCTURES
Tongtong Wul-si, Yanming Li Ziye Tang", Chen Jiang", Linhao Luo', Guilin QF, Shirui Pan",
Gholamreza Haffari
Monash University Southeast University *Griffith University
ABSTRACT
Large language model (LLM)-based multi-agent systems have shown strong capabilities in tasks such as code generation and collaborative reasoning. However, the effectiveness and robustness of these systems critically depend on their communication topology, which is often fixed or statically learned, ignoring real-world dynamics such as model upgrades, tool changes, or knowledge source variability. To address this limitation, propose CARD (Conditional Agentic Graph Designer), a conditional gyaph-generation framework that instantiates AMACP, protocol for adaptive multi-agent communication. CARD explicitly incorporates dynamic environmental signals into graph construction, enabling topology adaptation both training and runtime. Through conditional variational graph encoder and environment-es that are both effective and resilient to shifts in model capability or resource availability. Empirical results on HumanEval, MATH, and MMLU demonstrate that CARD consistently outperforms static and prompt-based baselines, achieving higher accuracy and robustness across diverse conditions. The source code is available at: https: // thub. com/ Warmaa00332/AAR
optimization, CARD produces communication structures
1 INTRODUCTION
Multi-agent systems (Liu et al. 2025 Li et al. 2026) powered by large language models (LLMs) (OpenAl 2024a: Chen 2024) have recently demonstrated remarkable capabilities across wide range of complex tasks, from code synthesis (Chen et al., (023) to collaborative reasoning (Liu et al. 2023). By integrating each model's internal knowledge, natural language generation, and inference abilities with external tools (Zhang
ct al. 20244] b) or peer LLMs. these systems effectively decompose problems (Yao et al.] (023). coordi-
nate subgoals (Liang et al. 2024), and integrate diverse information sources (Lee et al. 2023] Min et al.
2025). However, the communication topology, which specifies how agents are interconnected, significantly influences performance, affecting both solution quality and robustness to evolving conditions such as model
upgrades (Wu et al. 2024a), API modifications (Wu al. 2026 2024b), and fluctuating data sources (Min
et al. 2025).
Current topology design approaches typically fall into two categories (Bei et al. 2025 Liu et al. 2025). Many
systems depend on manually crafted pipelines (Hong et al. (2024) or predefined agent sequences (Wu et al. 2023), which perform effectively in stable, well-understood scenarios but lack adaptability. Conversely, recent methods automatically learn communication structures by backpropagating through "text gradients" (Zhuge et al. 2024) or parameterizing inter-agent connections via differentiable modules (Zhang et al., 2025a).
1x These authors contributed equally to this work. Corresponding author: tongtong wu @ monash.edu.

---

Published as a conference paper ICLR 2026
Agent Attributas
Multi Agent System with different configurations
Topology Vartations Under Different Configurations
Rale
S
Configuratinn
SigS Figooigiurration
Topology
Topology
Task
B
LLM BASE
COMo
CSDn
Ststente C
S(Extmmll Toutsource
E
duckaverton
Cson
Agent C
Agent C
ax
Programmer
Role: Pogrammer
LLM: Derpsack-V3
LLM: Owen-72B-Chon
Tool:
P
ython
Tool: Python
Knowledge
Knowledge
CSDN
source: Sackkverflow
Figure 1: Agent attributes and corresponding communication topologies under two environmental configura- tions, illustrating that topology is determined by both task requirements and the capabilities of the model base and available resources.
Yet, these learned topologies generally assume static environments, failing to account for transient external factors. Consequently, when conditions change, such as upgrading a model base (e.g. GPT-4o -> GPT-5), tool availability variations, or deterioration in data source quality, static naively learned topologies become fragile, resulting in redundant interactions or disrupted information flows (see Figure TT.
Adaptive LLM--asee Multi-agent Communication Protocol (AMACP):
Given a task/query y, an optimal communication topology for q should satisfy the following protocol logics: Effectiveness: The communication structure must effectively produce qualified solution for the given task q. Cost-efficiency: The communication structure should minimize the overall resource consumption (e.g., model usage, API calls, token cost) required to solve g under the given condition. Adaptiveness: The communication structure should dynamically adjust to varying conditions, ensuring robustness across diverse availability.
We address this gap by formalizing the Adaptive Multi-Agent Communication Protocol (AMACP) and instantiating via the Conditional Agentic gRaph Designer (CARD). CARD a conditional graph seaphaeeneattion framework that (i) represents each agent via profile and condition channels, (ii) encodes dynamic environment signals, and (iii) decodes an interaction graph whose edges adapt at training time and at runtime as conditions change without retraining. The objective balances task utility and condition-aware communication cost, enforcing effectiveness,, cost-efficiency, and adaptiveness required by AMACP. Empirically, on HUMANEVAL, MATH, and MMLU U with simulated environmental changes (model upgrades, tool availability, data-source perturbations), CARD yields substantial gains over static and prompt-only or naively learned topologies while remaining competitive in static regimes. Our primary contributions are:
Formalization of AMACP, protocol enabling adaptive multi-agent communication under dynamic external conditions.
Introduction of CARD, a conditional wraph-generation framework explicitly learning effective and adaptive agent topologies from environmental states.
2

---

Published as a conference paper ICLR 2026
Comprehensive empirical validation demonstrating that CARD consistently outperforms existing fixed and learned topology baselines under dynamic conditions.
Detailed analyses of topology adaptations, elucidating how environmental state conditioning en- hances the efficiency and robustness of multi-agent coordination.
2 RELATED WORK
Collaborative LLM Agents. Early work on L.LM- multi-agent communication has relied on manually
defined coordination pipelines, with ranging from non-interactive queries and chain-of-thought prompting
debate frameworks and fixed tree- or graph-based structures (Wei et al. 2022 Yao et al., 2023 Besta et al.
2024). To reduce the effort of handcrafting these pipelines, automated oopology-learing methods such GPT-Swarm (Zhuge et al., 2024), G-Designer (Zhang et al. 2025a), and Aflow (Zhang et al., (025b) have been developed. These approaches optimize agent connections via differentiable modules or heuristic search, yielding strong performance in static settings. However, they continue to assume a stationary environment (Hu jt al. 2025; Wang al.) 2025) and lack mechanisms respond changes in model capabilities, tool access, or data quality (Wu et al. 2024a).
Multi-Agents Graphs. Although a few dynamic communication protocols have been proposed in distributed-systemn literature (Wei et al. 2022 Yao et al. 2023 Liang et al., 2024), most learned topologies remain static and brittle under evolving conditions, such as model upgrades, fluctuations in external tool reliability, or shifts in data-source quality (Pareja et al. 2020 Chang et al., 2020). In these scenarios, pre- defined or naively optimized graphs can produce redundant interactions disrupted information flows (Liu et al. 2025). To bridge this gap, we introduce the Conditional Agentic Graph Designer, which explicitly conditions graph generation on external signals (e.g., model version, tool performance, data-source fidelity) to produce adaptive, robust multi-agent topologies.
3 PROBLEM FORMULATION
We begin by formalizing the topology and protocol design space for L..M- multi-agent systems (MAS), grounding the CARD framework (Figure in well-defined constructs.
Topological Structure of LLM-based Multi-Agent Systems. A multi-agent system is represented as y denotes an LLM--based agent and each directed
a directed graph G (V, E), where each node edge (v,, vy) E represents a communication path from v, to uy. Each agent v is described by: profile attributes P., including [role ident ity, model base, tool access, historical state] And condition attributes C, capturing runtime environmental conditions. We model the condition as a composition of multiple features, where each feature corresponds to distinct semantic aspect F such model type, tool availability, or task complexity. Formally,
C (c1, C2,-.,, (k), Gi Fr,
(1)
C C F= x x ... Fk:
(2)
To ensure semantic consistency across heterogeneous features, encode the structured condition using a unified pretrained language model, aligning all feature dimensions into a shared embedding space, enabling the model to handle unseen combinations of features during inference.
3.1 COMMUNICATION PIPELINE
Given a user query Q, our system executes K rounds of communication across a multi-agent topology g (V,E), where V fei,... Uy} } is the set of agents and & represents directed communication edges.
3

---

Published as conference paper ICLR 2026
Agent Representation
Conditional Graph Generation
Eriec reapet You plane
LLMBASE
"Eepptee Vn 4118
per praninn
Conditon
@Erainal SookS
CARD
Agent representation
Conditional Graph
Environment-Awwrr Training
Runtime Adaptation
Iteration
Configuration
Shift Condition
Configuration
Environment Group
Quara
OUE
LLM
anginn
Quara
DO
CARD
Environment-Awar Training
Runtime Adaptation via CARD
Figure 2: Overview of the Conditional Agentic Graph Designer (CARD) framework. Agent profiles and dynamic environment conditions are encoded into embeddings, which a conditional graph-generation module (Encoder > Condition Adaptation Decoder) uses to produce an adaptive communication topology. CARD then performs environment-awart training, itcratively refining graphs under changing resource configurations, and deploys runtime adaptation automatically update the multi-agent topology in response to new env environmental states.
To ensure valid information flow, a topological scheduling function &p determines a permutation {V(1).... ((N) of agents that respects acyelic dependencies:
Topological Scheduling.
8 - o, such that vj > i, VG)) & (v(o))
where (u(( denotes the set of upstream neighbors of agent 0(6)-
Message Propagation. At each communication round E {l,..., level prompt Pl (ii) user-level prompt P(O,, and (iii) the collection of responses from its incoming neighbors at the same round:
......,K K}. each agent o; receives (i) a system-
R = u. (()) PID, (R(): my e Mm((;)))
(4)
where R,00 the response generated by agent at round f.
Output Aggregation. After K rounds of interaction, the system aggregates the final-round outputs from all agents to form the final system response:
(K) Aggregate (
(K) ,..., R(K),
(5)
where Aggregate(-) denotes a task-specific aggregation function (e.g., voting, selection, or summarization) over the terminal responses.
4

---

Published as conference paper ICLR 2026
3.2 AMACP: ADAPTIVE MULTI-AGENT COMMUNICATION PROTOCOL
To ensure meaningful topology construction, define AMACP:
AMACP Definition
Given qitery Q, communication topology G must satisfy: 1. Effectiveness: Maximize condi-
tioned task utility (((() 2. Cost-efficiency: Minimize conditioned financial cost w(g:C); Adaptiveness: Adjust tepology in response environmental condition C shifts.
These objectives are jointly encoded in the following optimization problem:
min LAMACP(G; Q,C) = - C)) + w(G:C), DEG
(6)
where u(-) denotes the task-specific utility function, w(-) is the conditioned communication cost, and B E RR is tunable trade-off hyperparameter.
4 CONDITIONAL AGENTIC GRAPH DESIGNER
We introduce Conditional Agentic Graph Designer (CARD) that constructs adaptive, euvironment-condiiione multi-agent topologies. CARD comprises four key stages: (1) Agent representation, (2) Conditional graph gen- eration, (3) Environment-avaan training, and (4) Runtime adaptation. The complete workflow is summarized
in Algorithm D and visualized in Figure
Agent Representation. Given a query Q and an environment configuration C, CARD first constructs an initial multi-agen network. Each agent U E V is described by two components: Firstly, profile vector )], capturing static attributes of the agent, including its base model, language template function used verbalize categorical features (e.g., model name, role identity, plugin type) into a text embedding. Secondly, a condition vector C; (C,).. describing runtime environment status for Us such as model availability, token cost, or API reliability. The function Te(-) generates textual descriptions that encode dynamic system conditions. These representations are later encoded node features for conditional graph generation. See Appendix for template instantiations of Tp and Te.
P. [Tp (Base;)), (aaase,,,,oee;;
assigned role, and supported tools. Here, (-(.) denotes
Conditional Graph Generation Given a user query and an initial environment configuration, CARD constructs a preliminary agent graph I = (V, E) over N = |V] agents. Each agent 2 E V is associated with embedded as X²' and X;, respectively. Stacking across
a profile text PP and condition text C,, which agents yields Xp = [XT,... X and X, = [Xf..... ) The edge set initialized from an anchor topology A (c.g.. chain star), which provides structural priors for initial connectivity.
To obtain a refined, query- and context-aware communication topology, CARD applies an encoder-decoder graph generation module. The encoder comprises two learnable graph encoders, Øp and de. that produce latent representations for profile and condition channels:
H o H, A:
(7)
H = de H. X2,
(8)
where H = [bf.... .ff....,be h and H = hh.,.., h denote the latent states, and Op, O2 are encoder parame- ters. The decoder the then estimates pairwise edge probabilities conditioned these latent states and query
5

---

Published as a conference paper ICLR 2026
embedding he (the query treated as an auxiliary node that attends all agents in both channels):
(S Hp. H.)
II (Si) hy, hy, hy, ho: Oa) (.j
where Siz [0, 1] is the predicted link probability and O₂ decoder parameters. Finally, the communication topology obtained by thresholding the predicted adjacency:
Ecom = { vy) Sij > }},
Goom
Eoom),
(10)
with a user-specified or iulidation-selectte threshold T E (0, 1). The resulting 9com serves as the backbone for downstream multi-agent communication and reasoning, adaptively modulated by static profiles and dynamic runtime states.
Environment-Aware Training, Given a query Q and environment condition C (Section 3) CARD trains by iterating over sampled (Q,C) pairs and running E N rounds multi-agent interaction on Grom At communication round E {l,..., Kj. agent es receives a system-level prompt Zaya. user-level prompt Zusts and upstream messages {R. (0) V' E Ni (r:)), and produces response R².0) with equation 4 And after
K rounds, task-specific aggregation operator AGGREGATE(() (e.g., voting, selection, or summarization) combines terminal responses into the system output (K) with equation 5
Let Op, 2e Oa denote the parameters of the profile encoder dp. condition encoder de, and graph decoder vh. We optimize these parameters by gradient descent on a CARD loss that instantiates the AMACP objective (Eq. equation 6):
CC,RD(Q,C; Op, O., Oa) -u))) ((((()))
w(Gromii C)
(11)
condition-aware cost
task utility
where ul-) is task-specific utility (e.g., accuracy/probability of correctness), w(() measures the conditioned communication cost, and balances utility and cost. Specifically, to encourage communication efficiency
while preserving performance, we regularize the soft communication graph Foom output by the decoder. Let S [0, 1j be the predicted (directed) link-probability matrix and define Pij := Sij the probability that edge (w: - ) is active under condition C. Let Costij 2 O denote the expected token-level inference cost on edge (i.j) (a function of the base model(s) and the number of exchanged tokens). The condition-awe aware regularizer is:
min GeomEG
w (G.oo...) c)= =
Σ (1.j)e
Costy Pijs
(12)
where G is the space of admissible (soft) directed graphs over V. In practice, Goom used for execution is obtained by thresholding S: training backpropagates through update (Op, θ θa) via equation II
Runtime Adaptation via CARD. At deployment, when external conditions change (e.g., base model capability, tool reliability, or cost), CARD updates the communication topology without retraining by decoding new edges from refreshed condition signals:
Gaem = (Xp)), $o(X!"") A).
(13)
where X, encodes the agent profiles static (role, base model, and tools), X encodes the runtime conditions updated, &p. &e maps these latent node states, is the anchor prior (e.g. chain, star, or fully connected), and z decodes edge probabilities (thresholded at 7) to produce the revised adjacency. This one-pass recomputation preserves robust, cost-efficient collaboration under real-time shifts.
6

---

Published as conference paper ICLR 2026
5 EXPERIMENT
Datasets and Metrics. We assess CARD three standard benchmarks: programming code generation (HumanEval) et al. (021), mathematical reasoning (MATH) Hendrycks et al. (021b), and general reasoning and language understanding (HedUyyeendrycks al. 2021a).
Baselines and Setup. We compare our approach against three categories of methods: Vanilla LLM, using the model's native capabilities to produce direct answers; Manually designed agents, including Chain-of-Thought (CeT))Wei et al. 2022) in single-agent setup, and I.I.M-DebuteDDu et al.) (2024) and Random Graph in a multi-agenn configuration;; And Automatically optimized topologies, graph-learning techniques such as HPPT-warm(ZZuge
al. 2024) and G-Designer(Zhang et al., 2025a) (which share graph formulation), alongside the heuristic rule-based optimizer Aflow(Zhang et al. (0225). We evaluate diverse set of language models sourced from different providers, each representing distinet technical paradigms, training methodologies, and architectural designs. Please see Appendix C and G for more details.
5.1 MAIN RESULTS
Table 1: Evaluation of multi-agent and topology design methods on HumanFval, MATH, and MMLU. "Mul.", "Auto.", and "Cond." indicate support for multi-agent collaboration, automated topology design, and conditional configuration, where v indicates "Yes" and X indicates "No". "oo."" For automated methods, CYAN cells denote in-domain adaptation (trained and tested the same LLM), GREEN cells denote out-domain adaptation (generalization to unseen LLMs), and YELLOW cells denote the average performance.
Meibod
Mul.
Auto.
Cond
spido mini
deepseck-v3
Baaaz 70B
gpt4o
uwen 72B
Avg.
HumannEval
Vanilla
85.83
92.50
76.66
85.83
86.66
85.50
CoT
X
X
88.33
93.33
78.33
90.00
88.33
87.66
Random-grapp graph
X
87.50
94.16
73.33
90.00
85.00
86.00
LLM-Debate
X
91.66
95.00
75.83
87.50
GPTswarm
86
92.50
78.33
91.66
81.66
86.66
G-designer
89.16
94.16
75.00
88.33
85.83
86.50
CARD
MATH
Vanilla
59.16
74.16
41.66
70.00
71.66
63.33
Col
61.66
80.00
41.66
65.00
73.33
64.33
Random-graph
X
38.33
70.00
64.67
M.
59.16
85.00
46.66
71.66
71.66
66.83
GPTswarm
Allow
80.83
91.66
40.00
75.83
80.83
73.83
Gedesigner
CARD
73.33
91.66
48.33
76.67
82.50
74.50
MML.U
Vanilla
X
77.12
86.27
75.16
86.93
79.74
81.04
X
75.
Random- graph
X
X
79.74
90.85
75.82
86.93
83.000
83.27
Debatee
swam
82.35
89.54
77.78
86.27
84.31
84.05
G-designer
83
90.85
77. 12
86.93
84.31
84.44
CARD
84.97
93.46
80.39
89.54
86.67
Conditional design (CARD) consistently delivers the best overall performance. With 90.50% HumanEval, 74.50% on MATH, and 86.67% on MMLU, remarkably, CARD attains or ties for the top score combinations, demonstrating strong robustness across different LLM bases.
in 13 out of 15
7

---

Published as conference paper ICLR 2026
HumonEva
MATH
MVLU
19.16
94.22
75.00
N0.0
47.30
75.08
79.05
9:05
77.22
96.3
6431
E-42 90.33
0G
7441
0.90
MQ
SAZ 2.1
CM
Figure 3: Performance and gains of w/o Cond., w/ Cond.p, and CARD on HumanEval, MATH, and MMLU across LLM bases (MI-M5, same to Table T.. Top: absolute accuracy (%). Bottom: A accuracy (%) over the w/o Cond. baseline.
Gains accrue progressively with richer design abstractions. Single-agent methods (Vanilla, CoT) estab- lish competitive baseline but lack collaboration. Fixed multi-agent topologies (Random-grat graph, LLM-Debate) add modest gains (+0.5-2.0 pp) by enabling parallel reasoning. Automated topology learners (GPT-swarm, Aflow, G-designer) further boost performance (+1.0-4.0 pp) by optimizing static communication structures. Finally, CARD's conditional adaptation delivers an extra +0.5-3.0 pp advantage over these static designs by tailoring the topology to environmental signals.
Conditional adaptation pays off especially under out-of-domain settings. By explicitly conditioning model- and tool-state, CARD narrows the gap between in-domain and out-domain evaluations. For example, on MATH, G-designer's ' accuracy falls from 91.66% to 79. 16% when changing from deepseek-v3 qwen-72B, whereas CARD's drop is smaller (from 91.66% to 82.50%), underscoring its adaptability unseen settings.
5.2 How TO EMBED CONDITIONS IN LLM TOPOLOGY GENERATION?
Figure reports an ablation study on different ways to inject environmental conditions into the generation of multi-agent topologies. We compare unconditioned baseline (w/o Cond.), naive prompt-level injection (w/ Cond.p) that appends condition descriptors to the system prompt, and our CARD approach which embeds conditions directly within the graph-generan module. Each variant is evaluated in HumanEval, MATH, and MMLU on five LLM bases, reporting absolute precision and A precision relative to the unconditioned baseline.
CARD delivers robust, non-negative gains across all benchmarks. While simple prompt conditioning can backfire, causing up to a 122.50 % drop MATH with base M5 and -200 % on MMLU with base MI. CARD consistently yields positive improvements on every model-henchmark pair (e.g., +0.83 % to +3.34 MATH, +0.66 % to +2.62 % on MMLU, and +2.50 % to +23.33 % on HumanEval), proving structured topology adaptation far more reliable than prompt-only methods.
CARD compensates for weaker baseline models. The greatest uplifts appear in the most challenging settings, such as a +2.62 % gain on MMLU with M3 and a +3.34 % boost on MATH with M5, demonstrating the ability of CARD narrow out-of-domain performance gaps and mitigate the limitations of less capable
8

---

Published as a conference paper ICLR 2026
Combucity Sape
Saenbaad Fapee
Fam
38
-3
Figure 4: Visualization of CARD topology matrices (See Appendix Dor matrices and correlation analysis details.) under different conditions. Edge thickness reflects the communication probability between agents. Configurations 1 to (Table I0 are shown from left right.
LLM bases. Further analyses isolating source/tool effects and localized condition perturbations are in Appendix B.2
5.3 HOW DO ENVIRONMENTAL CONDITIONS SHAPE THE FINAL COMMUNICATION ARCHITECTURE?
In Figure we present four representative experimental configurations, combining two LLM capacities (GPT-4o-mini GPT-4o Llama3-70B) with two search engines (Google Search vs. Wiki Search) to illustrate CARD's conditional adaptation action. By visualizing the resulting topology matrices, we aim quantify how variations in model strength and retrieval quality drive changes in edge density, directional flow patterns, and overall graph structure. This case study validates CARD's 's ability to tailor multi-agent communication graphs dynamic environmental signals, providing insight into the practical behavior of the protocol under realistic operational changes.
Weaker Models Demand Denser Collaboration. In Configuration (GPT-4o-mini Google Search), the average edge weight is substantially greater than in Configuration 2 (GPT-4o + Google Search), demonstrating that the smaller model compensates for lower inherent capacity by intensifying multi-agent communication.
Search-Engine Swap Preserves Global Structure but Shifts Local Flows. Replacing Google with Wiki for GPT-40-mini (Config vs. 3) yields a Pearson correlation of r = 0.9797 and 0.0006 (Appendix D.2), confirming near-identical overall topology. Locally, however, the Knowledge -earcher edge weight decreases markedly, and the Searcher Searcher-Maatemaatee -aathematiiian link drops more than ing Nommin--seciffe retrieval efficacy differences.
reflect-
Lowest Capacity + Lower-Qualit Search Maximizes External-Knowleed Reliance. The Llama3- 70B Wiki configuration (Config 4) produces the densest graph with the highest average edge weights, demonstrating peak dependence external information when both model capacity and search quality are reduced (Config vs. 4: r = 0.7789, 0.0679 (Appendix D.2)).
We provide additional quantitative breakdowns by model capability and size in Appendix B.1 and by tools/knowledge sources in Appendix [B.2] Scalability under varying agent counts is detailed Appendix B.3 and robustness under targeted attacks and accuracy- cost trade-offs summarized in Appendix B.4

---

Published as conference paper ICLR 2026
6 CONCLUSION
We introduced AMACP, protocol for adaptive mullti-geet communication, and CARD, a conditional graph- gepph-eneration framework that tailors LLM-based agent topologies to dynamic environments. Experiments HumanEval, MATH, and MMLJU under simulated shifts (model upgrades, tool changes, and data per- turbations) show CARD outperforms static and prompt- based designs by up to three percentage points in accuracy while remaining cost-effective. Topology visualizations underscore CARD's capability adjust communication patterns based on agent capabilities and resource quality. Future work will scale to larger agent ensembles, integrate online reinforcement for continual adaptation, and validate CARD in real-world multi-agent applications. For detailed discussion of limitations and avenues for future work, please refer to Appendix
7
ETHICS STATEMENT
This work uses only publicly available datasets and models, and does not involve human subjects or private data. We acknowledge the broader societal risks of autonomous multi-agent LLM systems and encourage responsible deployment with appropriate safeguards.
8 REPRODUCIBILITY STATEMENT
To support reproducibility, provide the full source code, training and evaluation scripts, and prompt templates at htttps://ancnymouss 4open.sc scw.sciieinn wwweeeeeee//egggggeeeeeeee based on publicly available benchmarks (HumanFval, MATH, MMLU) and open-source APl-accessible LLMs, with full implementation details, model configurations, and hyperparameters documented in Appen- dices C-F, Results averaged over multiple runs, and all metries and visualizations are script-generated for easy verification.
FF9A All experiments are
REFERENCES
Yuanchen Bei, Weizhi Zhang, Siwen Wang, Weizhi Chen, Sheng Zhou, Hao Chen, Yong Li, Jiajun Bu, Shirui Pan, Yizhou Yu, Irwin King, Fakhri Karray, and Philip S. Yu. Graphs meet Al agents: Taxonomy, progress, and future opportunities. CoRR, abs/2506. 18019, 2025. URL https://doi.org
28550/arxiv.2506..om 18019
Maciej Besta, Nils Blach, Ales Kubicek, Robert Gerstenberger, Michal Podstawski, Lukas Gianinazzi, Joanna Gajda, Tomasz Lehmann, Hubert Niewiadomski, Piotr Nyczyk, and Torsten Hoefler. Graph of thoughts: Solving elaborate problems with large language models. Proceedings of AAAI, pp. 17682-17690, 2024.
hRRtss:s: org 10 609/60990 aaai, www.vv.v...... 29720
Xiaofu Chang, Xuqin Liu, Jianfeng Wen, Shuang Li, Yanming Fang, Le Song, and Yuan Qi. Continuous-time dynamic graph learning via neural interaction processes. In Proceedings of CIKM, pp. 145-154, 2020. URL
3411946
Bei Chen, Fengji Zhang, Anh Nguyen. Daoguang Zan, Zeqi Lin, Jian Man-Guang Lou, and Weizhu Chen. Codet: Code generation with generated tests. Proceedings of ICLR, 2023. [RRltttts///ppeeeeiiii
Huajun Chen. Large knowledge model: Perspectives and challenges. Data Intell., 6(3):587-620, 2024. URL httpp///ooll.oog//0..37222220- 210.000............... 0000
10

---

Published as a conference paper ICLR 2026
Mark Chen, Jerry Tworek, Heewoo Jun, Qiming Yuan, Henrique Ponde de Oliveira Pinto, Jared Kaplan, Harri Edwards, Yuri Burda, Nicholas Joseph, Brockman, et al. Evaluating large language models trained on code. CoRR, abs/2107. 03374, 2021. httlhttps//arxiv..ooo hbtgg//ab///1ae 03374
DeepSeek-AI, Aixin Liu, Bei Feng, Bing Xue, Bingxuan Wang, Bochao Wu, Chengda Lu, Chenggang Zhao, Chengqi Deng, Chenyu Zhang, Chong Ruan, Damai Dai, Daya Guo, Dejian Yang, Deli Chen, et al. Deepseek-v3 technical report. CoRR, abs/2412. 194377, 2024. URL http::t/tp....ooooo 40..g//11..55000
arXiv. 2412 19437
DeepSeck-AI, Daya Guo, Dejian Yang, Haowei Zhang, Junxiao Song, Ruoyu Zhang, Runxin Xu, Qihao Zhu, Shirong Ma, Peiyi Wang, Xiao Bi, et al. Deepseck-rl: Incentivizing reasoning capability in Ilms via reinforcement learning. CoRR, 0os/25011129453 2025. URL httptt://oi...oooo http:///to.og/////////
2501 12948
Yilun Du, Shuang Li, Antonio Torralba, Joshua B. Tenenbaum, and Igor Mordatch. Improving factuality and reasoning in language models through multiagent debate. In Proceedings of ICML, volume 235 of Proceedings of Machine Learning Research, pp. 11733-11763, 2024. URL BtLLtttts://ppreeddnng
mlr. www.ppssss23333 wwwp///22e....eeeeeoo html
Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al-Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Amy Yang. Angela Fan, Anirudh Goyal, and others. The llama 3 herd of models. CoRR, abs/2407.21783, 2024. URL https:: org/10 48550/arXiv.
21783
Dan Hendrycks, Collin Burns, Steven Basart, Andy Zou, Mantas Mazeika, Dawn Song, and Jacob Steinhardt. Measuring massive multitask language understanding. In Proceedings of ICLR. OpenReview.net, 2021a.
URL httLhttts///openrreee
ftnt//oormmiddddd/ JGmQ
Dan Hendrycks, Collin Burns, Saurav Kadavath, Akul Arora, Steven Basart, Eric Tang, Dawn Song, and Jacob Steinhardt. Measuring mathematical problem solving with the MATH dataset. In Proceedings of NewrlPS Datasets and Benchmarks, 2021b. URL
attps://dataser. wtw.seeeeeeeeeaaoooeoeeeeeeeeeee newrips. wttpps/cccppppp/e/eeeeeeeee pppppr//2//haa///// be933ab3e:d0cdb7733bb666.
Abbtt round
round2.
Sirui Hong, Mingchen Zhuge, Jonathan Chen, Xiawu Zheng, Yuheng Cheng, Jinlin Wang, Ceyao Zhang, Zili Wang, Steven Ka Shing Yau, Zijuan Lin, Liyang Zhou, Chenyu Ran, Lingfeng Xiao, Chenglin Wu, and Jürgen Schmidhuber. Metagpt: Meta programming for A multi-agent collaborative framework. In Proceedings of ICLR, 2024. https::/ //tprreve/eeeeeveeew net wtt.foormmm//m ?inerummmiiiiiiii -
Nan Hu. Yike Wu. Jiaye Li, Huikang Hu, Guilin Qi, Songlin Zhai, Yingrui Chen, Tianx- ing Wu, Tongtong Wu, Jiaoyan Chen, et al. Taxreasoning: Benchmarking knowledge- intensive mathematical reasoning with evolving tax laws. In Proceedings of AAAI, 2025.
URL https://research.
taxreasoning htw.:somrinnbbeennnnnrriii.. Seeermmarrktnngoooooeeeeeeieeeee
mathematical-reasoo
Sungwoo Lee, Younghyun Oh, Hyunhoe An, Hyebhin Yoon, Karl J. Friston, Seok Jun Hong, and Choong- Wan Woo. Life-inspired interoceptive artificial intelligence for autonomous and adaptive agents. CoRR, abs/2309.05999 2023. URL
otw//...org...... 48550/ (w1//55///.i...../ wttpaaaaiivvv.... 2309.,2....... 05999
Yanming Li, Xuelin Zhang, WenJic Lu, Ziye Tang, Maodong Wu, Haotian Luo, Tongtong Wu, Zijie Peng, Hongze Mi, Yibo Feng, Naiqiang Tan, Chao Huang, Hong Chen, and Li Shen. Who deserves the reward? sharp: Shapley credit-based optimization for multi-agent system, 2026. URL https
w/w.xiv..rg//b/////a/aa/ 08335
11

---

Published as conference paper ICLR 2026
Tian Liang, Zhiwei He, Wenxiang Jiao, Xing Wang, Yan Wang, Rui Wang, Yujiu Yang, Shuming Shi, and Zhaopeng Tu. Encouraging divergent thinking in large language models through multi-agent debate. In Proceedings of EMNLP, pp. 11889-17990) 2024. URL / wttp://////..././/..//// 11w.////.....111000000000 emn ma in. 992
Ruibo Liu, Jason Wei, Shixiang Shane Gu, Te-Yen Wu, Soroush Vosoughi, Claire Cui, Denny Zhou, and Andrew M. Dai. Mind's eye: Grounded language model reasoning through simulation. In Proceedings of net forum?
ICLR, 2023. URL https://
Yixin Liu, Guibin Zhang, Kun Wang. Shiyuan Li, and Shirui Pan. Graph-augmented large language
model agents: Current progress and future prospects. CoRR, abs/2507.21407, 2025. URL. https
48550/arXiv 7/doi / wwt.xiii.250.... .21407
Dehai Min, Kailin Zhang, Tongtong Wu, and Lu Cheng. Quco-rag: Quantifying uncertainty from the
pre-training corpus for dynamic regreeedl- generation. CoRR, abs/2512.91134 2025. URL
https://aoi.ozg// http:///......00.22222222222111
OpenAL. Hello gpt-4o, 2024a. URL http:t/r//peeea..cmm////e///////
OpenAL. Gpt-4o mini: advancing cost-efficient inteliigeee 2024b. URL https::/openai.comm
gennce/
Aldo Pareja, Giacomo Domeniconi, Jie Chen, Tengfei Ma, Toyotaro Suzumura, Hiroki Kanezashi, Tim Kaler, Tao B. Schardl, and Charles E. Leiserson. Evolvegen: Evolving graph convolutional networks for dynamic graphs. In Proceedings of AAAI, pp. 5363-5370, 2020. URL /ttetps://doi.ooo 1609//aa1
034104.5938
Yu Wang, Chi Han, Tongtong Wu, Xiaoxin He, Wangchunshu Zhou, Nafis Sadeq, Xiusi Chen, Zexue He, Wei Wang, Gholamreza Haffari, Heng Ji, and Julian J. McAuley. Towards lifespan cognitive systems. Trans. Mach. Learn. Res., 2025, 2025. URL
Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Brian Ichter, Fei Xia, Ed H. Chi, Quoc V. Le, and Denny Zhou, Chain-of-thouud -f-ouughtt prompting elicits reasoning in large language models. In Proceed- ings of NeurIPS, 2022. URL htthhtp:/// / /wpprspppps..es/aa/ nips cc/ wwwpaperppppppcceepppepeeee...ee fww.s/illpppee wttpee//ppppe/eeeee peaaper/2022haaa
Abst Abbstract-Coffeeeencee.. Conference, html
Qingyun Wu, Gagan Bansal, Jieyu Zhang, Yiran Wu, Shaokun Zhang, Erkang Zhu, Beibin Li. Li Jiang, Xiaoyun Zhang, and Chi Wang. Autogen: Enabling next-gen LLM applications via multi-agent conversation framework. CoRR, abs/2308.08 2023. URL https: org/ 48540/ 205.5/0/rxiiv2330 08155
Tongtong WU, Linhao Luo, Yuan-Fang Li, Shirui Pan, Thuy- Trang Vu, and Gholamreza Haffari. Continual learning for large language models: A survey. CoRR, abs/2402.01364, 2024a. URL https://doi
org/10 0tte/10.4855000 48550/855400 2...00/arxi....2
01364
Tongtong Wu, Weigang Wu. Xingyu Wang. Kang Xu, Suyu Ma, Bo Jiang, Ping Yang, Zhenchang Xing, Yuan-Fang Li, and Gholamreza Haffari. Versicode: Towards version-conttrolable code generation. CoRR, Abs/2406.07411, 2024b. htt.:ttts:://// :/dp:::://d.... /10 200.:0..55555.i.... 2206,, 2406. 07411
Tongtong Wu, Rongyi Chen, Wenjie Du, Suyu Ma, Guilin Qi, Zhenchang Xing, Shahram Khadivi, Ramesh Periyathambi, and Gholamreza Haffari. Environment-awwree code generation: How far are we? CORR, abs/2601. /tt
wtt..i.i........222222222 12262
12

---

Published as a conference paper ICLR 2026
An Yang, Baosong Yang, Binyuan Hui. Bo Zheng, Bowen Yu, Chang Zhou, Chengpeng Li, Chengyuan
Li, Dayiheng Liu, Fei Huang, et al. Qwen2 technical report. CoRR, abs/2407.10671, 2024. URL https://doks //oii wwwp:o..........oooooooooo 20w.5///axx..4007.........
Shunyu Yao, Dian Yu, Jeffrey Zhao, Izhak Shafran, Tom Griffiths, Yuan Cao, and Karthik Narasimhan. Tree of thoughts: Deliberate problem solving with large language models. In Proceedings of NeurlPS, 2023. URL
/
271 271199222....aaaaaaaaacec0aaaaa-
html
Guibin Zhang, Yanwei Yue, Xiangguo Sun, Guancheng Wan, Miao Yu, Junfeng Fang, Kun Wang. Tianlong Chen, and Dawei Cheng. G-designer: Architecting multi-agent communication topologies via graph neural networks. In Proceedings of ICML, 2025a. URL https: htttg:://operevveew... net/ forum?id-
LpE5 4NUm4N
Jiayi Zhang, Jinyu Xiang, Zhaoyang Yu, Fengwei Teng, Xiong-Hui Chen, Jiaqi Chen, Mingchen Zhuge, Xin Cheng, Sirui Hong. Jinlin Wang. Bingnan Zheng, Bang Liu, Yuyu Luo, and Chenglin Wu. AFlow: Automating agentic workflow generation. In Proceedings of 2025b. URUhttts://ppeeeeve/
Jintian Zhang, Xin Xu, Ningyu Zhang, Ruibo Liu, Bryan Hooi, and Shumin Deng. Exploring collaboration mechanisms for LLM agents: A social psychology view. In Proceedings of ACL, pp. 14544-14607, 2024a.
htthhtts:// /ttp:///..o.......000..//////0/.
Long. 782
Xilin Zhang, Zhixin Mao, Ziwen Chen, and Shen Gao. Effective tool augmented multi-agent framework for 3724/209-77204
data analysis. Data Intell., ((4):923-9455 2024b.
di 2024.042. 0013
Mingehen Zhuge, Wenyi Wang. Louis Kirsch, Francesco Faccio, Dmitrii Khizbullin, and Jürgen Schmidhuber. Gptswarm: Language agents as optimizable graphs. In Proceedings of ICMI., volume 235, pp. 62743- 62767, 2024. httss:/ts:/ http:::::/ppooceeliiie ngs. ml www.press//eee vv255/ zhuge24a html
13

---

Published as conference paper ICLR 2026
APPENDIX CONTENTS
A
Limitation
15
B
Analysis and Discussion
15
B.1
Quantitative Analysis of Conditions: Model Size and Reasoning Ability
15
B.2
Quantitative Analysis of Conditions: Tools and Knowledge Resources
16
B.3
Multi-agent Scalability Analysis
16
B.4
Multi-agent Robustness & Cost-Efficiency Analysis
17
Implementation Details
18
D Source Data
19
D.I Adjacency Matrix of Visualization
19
D.2 Correlation Analysis of Adjacency Matrix
20
Algorithm Workflow
20
F Prompt
21
Experiment Configuration Sets
26
14

---

Published as a conference paper ICLR 2026
A LIMITATION
This work focuses on conditional optimization and adaptation of multi-agent communication topologies. However, it does not explicitly update agent-level configurations such as individual prompts or internal profiles in response to environmental shifts. In practice, jointly optimizing both the communication topology and agent behaviors, including prompt augmentation and tool selection strategies, may further improve system performance. Exploring this direction remains an open avenue for future research. Additionally, while our formulation represents the multi-agent -agent system as a graph, which offers cognitively interpretable and analyzable abstraction, graph-based representations may insufficient for capturing domain-specits nuances in complex real-world settings. For example, in software engineering workflows, procedural constraints, tool dependencies, and execution semantics are often critical. Future work may incorporate sumann-nn-the-lon expertise, such software development best practices and debugging heuristics, and explore hybrid models that combine symbolic priors with learned agent adaptation mechanisms.
B ANALYSIS AND DISCUSSION
B.1 QUANTITATIVE ANALYSIS OF CONDITIONS: MODEL SIZE AND REASONING ABILITY
We conduct further experimental analysis to investigate how variations in model capability, model size, external tools, and knowledge sources impact multi-agent topology design and overall performance.
onan-72
decsaosi owenn
[b)
(C]
Humaneool
Wri
0daa
Gzea
30:53
Will
CARD
05
Accumey
Figure 5: Left: Accuracy on MATH and HumanEval across LLMs with different reasoning capabilities. Right: Accuracy across different model sizes within the same LLM family.
Stronger and larger base models yield higher multi-agent performance, with CARD amplifying these gains, but on simple tasks a single powerful LLM can outperform multi-agent coordination due to communication overhead On both MATH and HumanEval benchmarks, upgrading from qwen-7b to the higher-capability deepseek-distill--veen with CARD showing the largest absolute gains and the best performance(e.g. (e.g., MATH accuracy rises from 69. 16 % to 88.33 % (9719.7 pp)). However, on simple benchmarks with a capable model (Figure Rigght) Right), vanilla single-agent slightly outperforms multi-agent due to redundant communication. This underscores that multi-agent benefits require task complexity to outweigh coordination costs.
yields consistent accuracy improvements across all methods,
CARD exhibits superior robustness to variations in external tools and knowledge resources Evidence: When switching among Google Search, DuckDuckGo, and Wikipedia as the external tool, CARD's Hu- manEval accuracy only drops from 85.62 % 83.00 % Figure 6 Left), smaller decline than alternative methods. Similarly, across knowledge sources (Wikipedia, Tutorialspoint, Quora), CARD achieves its highest performance (85.62 %) on the richest data source and outperforms other approaches by 1-2 percentage points
15

---

Published as conference paper ICLR 2026
even less informative sources. This resilience highlights CARD's ability maintain strong multi-agent topologies under diverse resource conditions.
B.2 QUANTITATIVE ANALYSIS OF CONDITIONS: TOOLS AND KNOWLEDGE RESOURCES
Data Source Comparioon
Compation
G-bedgge
LNN cocate
hos loci Mos
Deb. 29.00
79:03
00.30
93-32
$3.03
94
66e
22:30
75.24
$3.70
-1
goo0
Figure Left: Performance comparison using different external knowledge sources. Central: Performance across various available tools (search engines). Right: Impact on multi-agent performance on HumanEval, when only a single node's condition updated instead of the global agent condition.
We evaluate how external conditions, namely knowledge sources and retrieval tools, affect performance the CARD framework. Experiments use HumanEval with the same base LLM and agent-role design as in the main paper. The only varying factors are the condition features: switching among three knowledge corpora (Wikipedia, Tutorialspoint, Quora), changing search tools (Google, DuckDuckGo, WikiSearch), and applying localized perturbations by modifying single node's s condition embedding. All configurations share the same retrieval budget, prompt formatting, and random seed.
Across source and tool variations, CARD consistently outperforms baselines and exhibits smaller performance drops under weaker conditions. Accuracy declines from 85.6% on Wikipedia 83.0% Quora, yet CARD maintains a clear margin over LLMM-Debate and G-Designer. This resilience stems from condition-aware graph generation that adapts edge density and agent coordination to upstream content quality. The results indicate that topology-Ieve adaptation provides stronger robustness than prompt-only conditioning when facing domain shift or noisy external knowledge.
In local perturbation tests, changing the condition for only one node, either the root or an intermediate node, preserves most performance at 88.3% and 85.0% respectively, substantially surpassing baselines. This shows that CARD enables low-cost, localized reconfiguration without full graph retraining. The modular design supports practical online adaptation in production, allowing lightweight updates in response to tool variability or hotfixes while maintaining stable accuracy under dynamic real-world constraints.
B.3 MULTI-AGENT SCALABILITY ANALYSIS
We evaluate the scalability and robustness of CARD against G-Designer by grouping base LLMs into in-domain copt4o-minis deepseek-v3, 1 1ama33 and out-of-domain (GPT-4o, qwen-72B) settings.
CARD scales more effectively than G-Designer as agent count increases, especially out-of-domain settings. As shown in Figure CARD consistently achieves higher MMLU scores the number of agents increases, with particularly pronounced gains the out-of-domain setting (up to +1.99 pp over G-Designer at 10 agents). In the in-domain case, both methods improve over Vanilla, but CARD shows steeper upward
16

---

Published as conference paper ICLR 2026
6el
(60
Figure 7: MMLU performance of CARD vs G-Designer across varying agent counts. CARD consistently outperforms G- G-Designer in both (a) in-domain and (b) out-of-domain settings, with larger gains under domain shift; shaded areas denote 95% confidence intervals.
Hi maneoal
Hath
122
112
L.N Debeer
Contre
Celo
UM Deww
G0
CATO
Adhesary Attook
Coal 151 in Scale
Figure 8: Left: Accuracy comparison before and after adversarial attacks across different methods. Right: The inference cost (USD per instance) across methods and L.Mss.
trend, with its advantage widening at 5-10 agents. This indicates that conditional topology generation in CARD helps agents coordinate more effectively as system size grows.
CARD also demonstrates stronger robustness under domain shift with comparable uncertainty. The method also exhibits greater robustness under distribution shift. While G-Designer's performance gains plateau in the out-of-domain setting, CARD continues to benefit from agent scaling. Moreover, CARD achieves these improvements with comparable or slightly lower confidence interval widths, suggesting more reliable and generalizable coordination gains. These results align with the design goal of CARD- to generate topology conditioned on external constraints (e.g., model type, cost, capability), enabling adaptive and scalable multi-agent collaboration even in unseen environments.
B.4 MULTI-AGENT ROBUSTNESS & COST-EFFICIENCE ANALYSIS
We evaluate both robustness and cost-efficiency by simulating targeted attacks and configuration faults at intermediate agents on the HumanEval benchmark measure resilience in accuracy, and by calculating total training and evaluation expenses across different LLM bases to quantify economic trade-offs, thereby enabling a systematic comparison of static, learned, and conditionally adapted communication topologies under both adverse conditions and budget constraints.
Robustness under attack markedly improved by conditional adaptation. As shown in Figure (Left), when agent node is attacked, LLM Debate, which relies fixed pairwise prompting without
17

---

Published as conference paper ICLR 2026
structural adaptation, and suffers the sharpest performance drop (-6.67 pp on HumanEval, -3.34 pp on MATH). G-Designer, trained under attack conditions, filters out the faulty node and shows smaller degradation (-1.24 pp on HumanEval, -3.33 pp on MATH), but loses generalization once the node recovers. contrast, CARD, trained under both attacked and clean conditions, not only outperforms G-Designer under attack (87.50% vs. 86. 66% on HvmanEval; 65. 65.83% vs. 60.00% on MATH), but also shows significantly greater recovery when the compromised node is restored (+3.33 pp +1.24 pp HumanEval; the accuracy under attack is even higher than non non-attacked on MATH, indicating that our topology is fully adaptable to both attacked and non-attacked conditions.) highlighting its superior resilience and adaptability across both degraded and recovered environments.
Localized condition updates recover most of the lost performance at minimal adaptation cost. Figure (Right) illustrates that, upon replacing only single node's condition rather than regenerating the entire communication graph, CARD retains 88.33 % accuracy under head-node perturbations and 85.00 % under intermediate-node perturbations, demonstrating overall superiority over both LLM-Debate and G-Designer, highlighting that fine-grained adaptation can preserve robustness with far lower computational overhead than global reconfiguration.
Conditional designs deliver the best accuracy-to-cost balance among all methods. In Figure (Right), CARD's configurations (e.g., achieving 94 % accuracy at evaluation cost of 4 x 10-3 USD) occupy the upper-left region of the cost-performance plane, while static multi-agent schemes like LLM-Debate and learned topologies such as G-Designer generally cost more to reach a lower accuracy; this confirms that conditionally adapted graphs not only boost resilience but also minimize economic expenditure for a given performance level.
C IMPLEMENTATION DETAILS
Specifically, we include OpenAl's GPT-4cOpenAl (2024a) and GPT-4o-min OpenA (024h)). DeepSeck's s -reepeee--VDDepSce--A..
al. (2024) (630B), Meta's - al. (2024). and the Qwen series from Alibaba, comprising Qwen-22 2.5 models (7B, 14B, and 72B Yang et al. (2024) as well the distilled variant Owen-2 5B These models differ across providers (capturing variations in technical trajectories and architectural choices), model sizes (correlating with computational capacity and performance), and domain specializations (affecting knowledge scope and inference behaviors). In addition, we examine the influence of external tools on multi-agent architectures by varying the underlying data sources and search engines. The search engines considered are Google Search, DuckDuckGo, and Wiki Search; the data sources include Quora, Mikipedia, and Tutorialspoint qualities and knowledge coverage levels. This setup is intended to emulate the dynamic evolution of resources real-world multi-agent systems, enhancing the robustness and adaptability of learned multi-agent topologies under changing conditions.
al. 2025 derived from
These configurations represent diverse retrieval
18

---

Published as conference paper ICLR 2026
D SOURCE DATA
D.1 ADIACENCY MATRIX OF VISUALIZATION
Table 2: Adjacency Matrix I: gpt-4o-mini + Google
Knowlegable Expert
Searcher
Philosopher
Mathematician
Critic
Knowlegable Expert
Masked
0.79
0.88
0.81
0.5
Searcher
0.17
Masked
0.79
0.69
0.34
Philosopher
0.11
0.17
Masked
0.81
0.5
Mathematician
0.15
0.21
0.15
Masked
0.37
Critic
0.25
0.22
0.25
0.23
Masked
Table Adjacency Matrix 2: gpt- 4o + Google
Knowlegable Expert
Searcher
Philosopher
Mathematician
Critic
Knowlegable Expert
Masked
0.54
0.15
0.4
0.14
Searcher
0.25
Masked
0.53
0.81
0.5
Philosopher
0.13
0.25
Masked
0.39
0.13
Mathematician
0.24
0.15
0.24
Masked 0.23
0.36
Critic
0.12
0.25
0.11
Masked
Table Adjacency Matrix 3: gpt 4o minn Wiki
Knowlegable Expert
Searcher
Philosopher
Mathematician
Critic
Knowlegable Expert
Masked
0.73
0.86
0.73
0.46
Searcher
0,2
Masked
0.76
0.57
0.3
Philosopher
0.12
0.18
Masked
0.75
0.5
Mathematician
0.2
0.25
0.19
Masked
0.29
Critic
0.25
0.21
0.25
0.21
Masked
Table 5: Adjacency Matrix 4: L.ama -3-00 Wiki
Knowlegable Expert
Searcher
Philosopher
Mathematician
Critic
Knowlegable Expert
Masked
0.84
0.73
0.8
0.5
Searcher
0.13
Masked
0.67
0.75
0.42
Philosopher
0.2
0.22
Masked
0.6
0.27
Mathematician
0.16
0.19
0.24
Masked
0.35
Critic
0.25
0.24
0.2
0.23
Masked
19

---

Published as conference paper ICLR 2026
D.2 CORRELATION ANALYSIS OF ADIACENCY MATRIX
CORRELATION ANALYSIS
Table 6: Pearson correlation between matrix pairs with corresponding strength and significance.
Comparison
r
Strength
Sig.
Matrix vs 2
0.32
0.54
Weak
No
Matrix vs 3
0.98
0.001
Very strong
Yes
Matrix vs 4
0.78
0.07
Strong
Marginal
E ALGORITHM WORKFLOW
Algorithm 1 Workflow CARD: Conditional Agentic Graph Designer
Input: Query set (QI.... QD), condition configurations (Ci..... Cc).
Graph auto-encoder fu (Astat: Adyn= 1) with parameters (0p: O, Oa), learning rate
1: for each query Qa E .Q...... 2n) do
2: for each condition C. E (CI....,Ce Cc} do
1* Construct agent features under condition C. */ 4: for agent 24 {VI,..., ] do
3:
5:
x + (Byse,,,, Role,, Plugini)
6:
x Te(a
7:
end for X, + .......x.
x T
X. + ix....., x
9:
query treated as virtual agent node Define anchor topology A (e.g., fully-connected + task node)
X2 + Embed 2a)
10:
11:
+ (1Xp, X2),
12:
1 Generate communication topology via encoder-decoder
13:
H, + op A), H. - Φx (A4
14:
S + (H. Har x2)
compute link probabilities D retain edges above threshold
15:
Goom + {(1.)) Sig >T
Multi Multi-agent collaboration under 9com for / to K do
17:
18:
for agent v; schedule (GCco) do
19:
((t) + [aa] U (R))) (R
U0 E (w:)
20:
R + (P(()) sys p(())
21:
end for (t))
Aggregate( (R. (8) ),
22:
23:
end for
24:
1th Optimize graph generation parameters */
25:
θ + a VoLCARD
26:
end for
27:
end for
20

---

Published as conference paper ICLR 2026
F РROMPT
LLM Dynamic Information Template
=
'Name's (model name) [medee_nnmm)',,
DDscciiption (MadelName)
[madel_type) model developed by + (developer), supporting (modalities). "I is optimized for Ikey wegy_strengths).
(ModelName) offers [performance_ddvantaae
TTe model costs $linput_con cost] per millicn input
tokens and $(cutput_cost) per millien output tokens.
evaluation =
'In (domain_a), (ModelName) achieves accuracy of (evaluatioo_score___)
'In (domain_bl, (ModelName) achieves an accuracy of ivallaatio_sccree ....
Search Engine Dynamic Information Template
trarrhhenniie_eempllee -
'Name' : "(engine_nane" name)',
'Description': ((EngineÑame) is (engine_type) develeped by (provider).
'It supports (supported_querr_ttyeee and delivers
results acress (content_scope]
'The engine integrates (additional [b6dttionai_featurres), making
it suitable for pepplicaaton_cceaatee
'evaluution infol'
evaluation_info
'In the task (task (task_name), (EngineName) achieved a score 3 (score_value) an the (metric_name) metric.
21

---

Published as conference paper ICLR 2026
HumanEval Role Profile
"Project Manager":
"You project manager.
"You will be given a function signature and its docstring by the
+ user.
"You are responsible for overseeing the overall structure of the code, ensuring that the code is structured to complete the task Implement code concisely and correctly without pursuing over-engineering.
"You need to suggest optimal design patterns to ensure that the code follows best practices for maintainability and flexibility. "You can specify the overall design of the code, including the
classes that need to defined (mayybe none) and the functions used (maybe only one function)
"I hope your reply will pe more cencise. Preferably within fifty
- words. Don't list too many points.",
"Algorithm Designer":
"You are algorithm designer.
"You will be given function signature and its docstring by the user.
"You need to specify the specific design of the algorithm, including
the classes that may be defined and the functions used.
"You need to generate the detailed decumentation including explanations of the algorithm, usage instructions and APT references. "
"When the implementation logic is complex, you can give the pseucocode logic of the main algerithm." "I hope your reply will be more concise. Preferably within fifty words. Don't list too many points.",
"Programming Expert";
"You
programming expert.
"You will be given a function signature and its docstring by the user.
"You may be able to get the output results of other agents. They may have passed internal tests, but they may not be completely correct.
"write your full implementation (restate the function signature). "Use a Python code block to write your response. For example: In pythh""""nnnn"r (arponnnnptit"Helllll ('Hello (orld!')\n"""
"Do not include anything other than Python code blocks in your response.
"Do not change function names and input variable types in tasks.",
" "Test Analyst":
"You are a test analyst.
"You will be given a function signature and its docstring by the
S user.
"You need to provide problems in the current code solution based the test data and possible test feedback in the question. " "You need to provide additional special use cases, boundary conditicns, etc. that should be paid attention to when writing code.
"You can point out any potential errors in the code."
"I hope your reply will be more concise. Preferably within fifty words. Don't 1ist too many points.", "Bug Fixer":
"You are a bug fixer."
"You will be given a function signature and its docstring by the user.
22
"You need to provide modified and improved python code based on the current overall code design, algorithm framework, code implementation or test problems.
(restate the function signature). "Use a Python code block to write your response. For ('Hello M
"Write your full implementation
example: " "pwphoeen
"Do not include anything other than Python code blocks in your
response
"Do not change function names and input variable types tasks",

---

Published as conference paper ICLR 2026
MATH Role Profile
"Math Solver":
"You math expert.
"You will be given a math problem and hints from other agents.
"Give your own solving process step by step based on hints.
"The last line of your output contains only the final result without any units, for example: The answer is 140 "You will be given some examples you may refer to.",
"Mathematical Analyst";
"You
mathematical analyst.
"You will be given a math problem, analysis and code from. other 4 agents.
"You need to first analyze the problem-solving process step by step, where the variables are represented by letters.
"Then you substitute the values into the analysis process perform calculations and get the results."
"The last line of your output contains only the final result without - any units, for example: The answer is 140
"You will be given some examples you may refer to.",
"Programming Expert":
"You
programming expert.
"You will be given math problem, analysis and code from other + agents.
"Integrate step-by-step reasoning and Python code to solve math problems.
"Analyze the question and write functions to solve the problem. "The function should not take any arguments and use the final result as the return value.
"The last line of code calls the function you wrote and assigns the a return value to the (answer\) variable.
"Use a Pythen code block to write your response. For
example:\n" "pythenknder fun ():n ylnanswer ()n \n"
10 y 20'n return x
"Do not include anything other than Python code blocks your - response."
"You will be given some examples you may refer to.", "Inspector":
"You are Inspector.
"You will be given math problem, analysis and code from. other of the problem em sclving and + analysis process is correct (if present).
4 agents.
"Check whether the aggic/calculatio
"Check whether the code corresponds to the solution analysis present).
"Give your solving process step by step based hints.
"The last line of your output contains only the final result without any units, for example: The answer is 140'n" "You will be given some examples you may refer to.",
23

---

Published as conference paper ICLR 2026
MMLU Role Profile
"Knowlegable Expert": =u"
You are a knowlegable expert questicn answering,
Please give less than key entities that need to be searched on the - Internet to solve the problem. Each entity must be wrapped with 8 symbols.
For example: @catfish effects, bbrcken window effects, @Shakespearee. IE there is entity in the question that needs to searched the a Internet, you don't have to provide it.
"Searcher":
You will be given question and Internet search overview of the key entities within it.
Please refer them step by step to give your answer. uun
"Critic":
You are an excellent critic.
Please point out potential issues in other agent's 's analysis point by point.
"Mathematician":
You are a mathematician who is good at arithmetic calculation and long-term planning.
You can your logic and reasoning skills solve problems step by step. wu.
"Philosopher":
You are philoscpher with deep knowledge in literature, history, and cultural studies.
You analyze texts critically, draw nuanced interpretations, and make connections across time, societies, and disciplines.
"Doctor": You are medical professional who goed biology, medicine, and health. You combine modern medicine with herbal and natural remedies.
You consider age, lifestyle, and medical history every recommendation. **.
"Programmer";
You are a programmer skilled in software development, systems design, and technical problen-solving.
You apply principles from computer science, engineering ng, and coding. You write clean, eificient code across diverse platforms. .n"
24

---

Published as conference paper ICLR 2026
Table 7: EvmanEval Environment Configuration Set
Configuration
L.M
Role
gpt-4o-mini
Project Manager
gpt-4o-mini
Algorithm Designer
Configuration
gpt-4o-mini
Programming Expert
gpt-4o-mini
Test Analyst
gpt-4o-mini
Bug Fixer
deepseck-v3
Project Manager
decpscck-v3
Algorithm Designer
Train Test Configuration
deepseck-v3
Programming Expert
deepseck-v3
Test Analyst
deepseck-v3
Bug Fixer
llama-3-70B
Project Manager
llama-3-70B
Algorithm Designer
Configuration
Ilama-3-70B
Programming Expert
Ilama-3-70B
Test Analyst
Ilama-3-70B
Bug Fixer
gpt-4o
Project Manager
gpt-4o
Algorithm Designer
Configuration
gpt-4o
Programming Expert
gpt-4o
Test Analyst
gpt-4o
Bug Fixer
Only Test
qwen-2.5-773
Project Manager
qwen-2.5-72BB
Algorithm Designer
Configuration
qwen-2.5-72BB
Programming Expert
qwen-2.5-72B
Test Analyst
qwen-2.5-72B
Bug Fixer
25

---

Published as conference paper ICLR 2026
G EXPERIMENT CONFIGURATION SETS
Table 8: MATH Environment Configuration Set
Configuration
LLM
Role
gpt-4o-mini
Math Solver
gpt-4o-mini
Mathematical Analyst
Configuration 1
gpt-4o-mini
Mathematical Analyst
gpt-4o-mini
Programming Expert
gpt-4o-mini
Inspector
deepseck-v3
Math Solver
deepseck-v3
Mathematical Analyst
Train Test
Configuration 2
deepseck-v3
Mathematical Analyst
deepseek-v3
Programming Expert
deepseck-v3
Inspector
llama-3-70B
Math Solver
lama--3-70B
Mathematical Analyst
Configuration 3
llama llama-3-70B 3-70B
Mathematical Analyst
llama-3-70B
Programming Expert
1lmma-3770B
Inspector
gpt-4o
Math Solver
gpt-4o
Mathematical Analyst
Configuration 4
gpt-4o
Mathematical Analyst
gpt-4o
Programming Expert Inspector
gpt-4o
Only Test
gwen-2.5-72B
Math Solver
qwen-2.5-72B
Mathematical Analyst
Configuration 5
qwen-2.5-72B
Mathematical Analyst
qwen-2.5-72B
Programming Expert
gwen-2.5-72B
Inspector
26

---

Published as conference paper ICLR 2026
Table 9: MMLU Environment Configuration Set
Configuration
LLM
Role
gpt-4o-mini
Mathematician
gpt-4o-mini
Programmer
Configuration
gpt-4o-mini
Critic
gpt-4o-mini
Doctor
gpt-4o-mini
Psychologist
deepseck-v3
Mathematician
deepseek-v3
Programmer
Train & Test
Configuration
deepseek-v3
Critic
deepseek-v3
Doctor
deepseek-v3
Psychologist
llama-3-70B
Mathematician
llama-3-70B
Programmer
Configuration
llama--770B
Critic
llama-3-70B
Doctor
llama--770B
Psychologist
gpt-4o
Mathematician
gpt-4o
Programmer
Configuration 4
gpt-4o
Critic
gpt-4o
Doctor
gpt-4o
Psychologist
Only Test
qwen-2.5-72B
Mathematician
qwen-2.5-72B
Programmer
Configuration
qwen-2.5-72B
Critic
qwen-2.5-72B
Doctor
qwen-2.5-72B
Psychologist
27

---

Published as conference paper ICLR 2026
Table 10: MMLU Environment Configuration Set with External Tools
Configuration
LLM
Role
External Tool (search engine)
gpt-4o-mini
Knowlegable Expert
gpt-4o-mini
Searcher
Google
Train & Test
Configuration
gpt-4o-mini
Psychologist
gpt-4o-mini
Mathematician
gpt-4o-mini
Critic
gpt-4o
Knowlegable Expert
gpt-4o
Searcher
Google
Configuration 2
gpt-4o
Psychologist
gpt-4o
Mathematician
gpt-4o
Critic
Only Test
gpt-4o-mini
Knowlegable Expert
gpt-4o-mini
Searcher
Wiki
Configuration 3
gpt-4o-mini
Psychologist
gpt-4o-mini
Mathematician
gpt-4o-mini
Critic
llama-3-70B
Knowlegable Expert
llama-3-70B
Searcher
Wiki
Train & Test
Configuration 4
llama-3-70B
Psychologist
llama-3-70B
Mathematician
llama-3-70B
Critic
28


Reviews:
[{"review_id": "bzwemkrCwn", "reviewer": "Reviewer_XpPo", "summary": "This paper introduces CARD, a framework that dynamically generates communication structures for multi-agent LLM systems by conditioning on real-time environmental signals like model capabilities and tool availability. It formalizes the AMACP protocol and demonstrates that CARD outperforms static topologies, achieving greater accuracy, robustness, and cost-efficiency on benchmarks like HumanEval, MATH, and MMLU, especially when adapting to unseen conditions.", "questions": "see weakness", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "Strengths:\n1.Novel Formulation of Adaptive Topology: The paper moves beyond static or naively learned communication graphs, which is a significant limitation in existing multi-agent systems. The formalization of the AMACP protocol and the CARD framework provides a principled approach for dynamic, condition-aware topology generation.\n2.Strong Empirical Validation: The paper provides comprehensive experiments across three major benchmarks (HumanEval, MATH, MMLU) and multiple LLMs. The results consistently show CARD outperforming strong baselines, particularly in \"out-of-domain\" settings and under simulated environmental changes, demonstrating superior generalization and robustness.\n3.Practical Runtime Adaptation: CARD can update the communication topology at deployment time in response to changing conditions without retraining, which is a crucial feature for real-world applications.", "weaknesses": "Weaknesses:\n1.Limited Agent-Level Adaptation: The paper adapts the communication topology but does not update agent-level configurations (e.g., individual agent prompts, internal reasoning steps, or tool-selection strategies) based on conditions. Jointly optimizing both topology and agent behaviors could lead to further performance gains.\n2.Scalability and Complexity: While a scalability analysis is provided, the computational overhead of the encoder-decoder graph generation module for very large agent ensembles (e.g., 50+ agents) remains a potential concern and is not thoroughly explored.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "5dCfR8mVJl", "reviewer": "Reviewer_2EJp", "summary": "This paper introduces **CARD (Conditional Agentic Graph Designer)**, a conditional graph-generation framework that dynamically designs LLM-based multi-agent communication topologies. It formalizes the **Adaptive Multi-Agent Communication Protocol (AMACP)** to jointly optimize for *effectiveness*, *cost-efficiency*, and *adaptiveness*. Through conditional variational encoding and environment-aware optimization, CARD enables real-time topology adjustment without retraining. Experiments on HumanEval, MATH, and MMLU show consistent improvements over static and prompt-based baselines.", "questions": "* Does CARD support localized topology updates rather than full recomputation?\n* Can the cost term \\$w(G;C)\\$ be generalized to other resource metrics such as latency or energy?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "* Technically innovative and conceptually unifying approach to dynamic topology learning.\n* Strong theoretical grounding with explicit optimization objectives (Eqs.6,11,12).\n* Robust empirical validation across multiple LLMs and benchmarks.\n* Intuitive and interpretable visualization of adaptive graph behavior.\n* Clear presentation and reproducible methodology with full prompts and configurations.", "weaknesses": "* **Hyperparameter Sensitivity:** Add performance–cost curves for different \\$\\beta\\$ values to visualize robustness.\n* **Empirical Validation of Assumptions:** Introduce experiments with fluctuating API or tool availability.\n* **Baseline Coverage:** Include stronger recent baselines such as reinforcement-based topology learning methods.\n* **Fixed Edge Threshold:** Consider adaptive or learnable \\$\\tau\\$ for improved flexibility.\n* **Scalability:** Extend evaluation beyond 10-agent systems to confirm convergence trends.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "je284dEgUs", "reviewer": "Reviewer_9BNN", "summary": "This paper introduces a framework (called CARD), which dynamically designs communication topologies for LLM-based multi-agent systems. CARD uses environmental signals to adapt agent connections in real-time. Experiments on three benchmarks show that CARD outperforms static baselines.", "questions": "Please refer to Weaknesses.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. This paper is well-organized. Most of the content is easy to understand.\n\n2. The proposed CARD framework is interesting and reasonable, which can be applied to various multi-agent cooperation scenarios.", "weaknesses": "1. The experimental improvements over the second-best baseline are modest and may not be statistically significant.\n\n2. It would be better to provide a case study to show the effectiveness of multi-agent communication.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "0zsRsgJ3cw", "reviewer": "Reviewer_XFA4", "summary": "This paper proposes CARD, a conditional multi-agent communication graph designer for LLM-based agent systems, along with AMACP, an explicit protocol for adaptive multi-agent communication. The core claim is that current multi-agent LLM systems typically assume a static or hand-crafted communication topology, which makes them brittle when the environment changes, for example upgraded language models, missing tools, degraded knowledge sources. CARD models topology as a directed communication graph and learns to generate that graph conditioned on two channels, static agent profiles, such as role, base model, available tools, and dynamic runtime conditions, such as API availability, token cost, search quality, model capability. The method uses a conditional variational-style graph encoder–decoder that embeds both channels, predicts an adjacency matrix of directed communication probabilities, and then thresholds it to get an executable communication protocol. Training optimizes a loss combining task utility, for example accuracy on HumanEval, MATH, MMLU, and a condition-aware communication cost term that reflects per edge token and model usage cost. At inference time, the system can update only the condition embeddings and re decode a new topology without retraining, allowing one shot adaptation when, say, the base LLM changes or a tool disappears. Experiments compare CARD to static topologies, to prompt only adaptations, and to recent automatically learned communication structures such as GPT-Swarm, Aflow, and G-Designer. On HumanEval, MATH, and MMLU, across multiple backbone LLMs, CARD delivers the highest average accuracy and is especially strong under out of domain conditions where model capacity or tool quality differs from training. The paper also analyzes how communication density, edge direction, and cost trade off as the model size, tool quality, or number of agents changes, and claims that CARD produces more robust, more cost efficient, and more easily scalable communication structures than existing approaches.", "questions": "Can you describe in more detail how gradients flow through K round communication during training, in particular, when you compute task utility after aggregation, how do you propagate credit to specific edges predicted by the decoder, and how do you avoid vanishing credit assignment for early round communication hops. Can you provide token budget and cost accounting for every baseline and confirm that CARD is not just buying accuracy by spending more interactions. In Table 1 and Figure 8, you mention accuracy versus USD per instance, can you include a strict Pareto style comparison where for each baseline you show its best achievable accuracy at or below CARD’s reported cost. How does CARD behave with simultaneous condition shifts, for example, weaker LLM plus degraded search plus high token cost. The single node perturbation study in Section B suggests graceful degradation, but can you show the multi factor case. How sensitive is the method to the choice of anchor topology A, you mention chain and star as priors, do different anchors converge to the same learned communication patterns, or does A bias the final structure. How much of the gain comes from the condition encoder versus just training a stronger static topology learner, a useful ablation would be to freeze condition embeddings to random noise at inference and see how far performance drops. Finally, what is the exact output metric for HumanEval, is this passpercentage style unit tests, or is it some text judged correctness proxy.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "The paper identifies a real and increasingly important gap. Most existing multi-agent LLM orchestration work either wires up agents in a fixed pipeline or learns a static graph tuned for one configuration, but in practice these systems run over evolving models, tool outages, and changing retrieval quality. The authors formalize this as AMACP, which states that an agent communication topology should be effective at solving the task, cost efficient under current resource constraints, and adaptive to runtime condition changes. They then actually implement that requirement. CARD is not just a heuristic, it is a trainable conditional graph generator that takes as input a structured description of each agent’s role, tools, and model identity, plus a structured description of the current environment, and predicts who talks to whom and in what order. This is materially different from simple prompt engineering, where you append “the math agent is weaker today, rely on search more” to a system prompt, because here the topology itself, the adjacency, changes. The empirical section is broad for this area. They test on coding, on math reasoning, and on MMLU style multi task QA, using several families of LLMs, and they evaluate not just accuracy but also robustness, for example node failures and adversarial perturbations, scalability with agent count, and accuracy versus token cost. CARD tends to either match or beat the best baseline and often keeps a smaller drop when conditions shift, in other words, the performance is more stable than G-Designer and Aflow when the backbone model or the available tool is swapped. The work also takes steps toward interpretability. The paper visualizes learned topologies and shows concrete behavioral adjustments, for instance, weaker models produce denser graphs with heavier reliance on other agents, and weaker retrieval sources change which agent edges carry information into the reasoning path. That makes the claim of conditional adaptation more convincing because we can see structure changes, not just accuracy deltas. Finally, runtime adaptation without retraining is compelling. The method can re instantiate a communication graph under new conditions by just re encoding the condition channel and passing it through the trained decoder, so deployment can, in principle, respond in real time to model upgrades or API outages, and this is exactly the sort of operational knob teams building agentic systems are asking for right now.", "weaknesses": "The technical depth is somewhat uneven. The AMACP objective is framed as a joint optimization over task utility and a communication cost term, but the training procedure in practice seems to boil down to supervised or weakly supervised gradient descent on an aggregate loss that mixes accuracy and a differentiable expected edge cost computed from soft edge probabilities. The paper gives the loss but does not fully unpack how gradients are attributed to edges through multi round communication, or how credit is assigned to long chain interactions, especially given that the system output aggregates all agent responses after several rounds. Without that, it is difficult to judge whether CARD is actually learning a policy for dynamic topology design, or if it is just fitting correlations between condition embeddings and good handcrafted structures. The experimental methodology raises some concerns. The benchmarks are HumanEval, MATH, and MMLU, which are popular and recognizable, but the evaluation protocol for multi agent interaction is only described at a high level, and does not clearly state how prompts are constructed, how tool calls are executed, and how many tokens are allowed per agent per round. HumanEval in particular is typically judged with execution based pass rates, but here it is treated more like accuracy in a dialogue pipeline, that needs to be spelled out precisely. The fairness of comparisons needs more clarity. Some baselines, like debate and chain of thought, are single round or pairwise prompting schemes, others like GPT-Swarm and G-Designer are graph learners, but I did not see cost normalized comparisons where all methods are given the same token budget, number of rounds, or number of agent calls. CARD explicitly optimizes a cost regularizer, so it is important to show, at equal or lower total spend, that it matches or beats baselines, and not just at whatever spend it happens to choose. The robustness and adversarial tests are promising, but they are still driven by synthetic manipulations of single nodes or tools, and they do not explore stronger failure modes like correlated tool outages or cascading hallucinations across agents. The work would feel stronger if it included at least one ablation where multiple nodes are simultaneously unreliable, or where a high capacity model silently degrades in a way that resembles realistic model version drift. Finally, while the paper repeatedly emphasizes adaptation to new models or tools without retraining, all evaluations still assume that you can embed those new conditions in a way the encoders can interpret. It would be good to quantify how far out of distribution you can go before the condition encoder fails, for example, can a model family never seen in training still be placed meaningfully in the graph, or does performance collapse there.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)