Towards High Semantic Fidelity: Hyperdimensional Symbolic Messages in Multi-Agent Communication

Shoucheng Song; Chang Yao; Hao Wu; Youfang Lin; Sheng Han; Kai Lv

cs.MAOct 16, 2026

Towards High Semantic Fidelity: Hyperdimensional Symbolic Messages in Multi-Agent Communication

Authors: Shoucheng Song, Chang Yao, Hao Wu, Youfang Lin, Sheng Han, Kai Lv

Organizations: School of Computer Science & Technology, Beijing Jiaotong University, Beijing, China · Beijing Key Laboratory of Traffic Data Mining and Embodied Intelligence, Beijing, China · Institute of Artificial Intelligence of China Telecom (TeleAI), Beijing, China

Abstract

Semantic fidelity is essential for multi-agent communication under non-ideal channels, comprising transmission fidelity and conversion fidelity. Yet existing numerical and neural message formats cannot simultaneously achieve both. To address this, we propose a novel message format-Hyperdimensional Symbolic Messages (HSM) and its corresponding communication framework Herm. For transmission fidelity, Herm suppresses semantic entanglement via an entity-attribute-value structured encoding pipeline. For conversion fidelity, Herm first leverages a receiver-centric ego-binding mechanism to align semantics. Then, a similarity-aware dual-branch fusion module is proposed to prevent critical semantic dilution. To realize explicit message-semantic conversion, we devise an iterative decoding scheme via algebraic inverse operations. Experiments exhibit that Herm outperforms baselines across various noisy scenarios while maintaining superior structural readability.

Figures & tables

Figure 1: Comparison of Semantic Fidelity of Messages. The left shows the conversion fidelity in terms of the embedding process, message format, and semantic content. The right employs t-SNE to exhibit their transmission fidelity when exposed to noise.

Figure 2: Framework of Herm. (a) The agent network comprises a trajectory-encoding module and a communication module, with their outputs serving as inputs to the local Q-function. (b) On the sender side, the agent encodes its entity-wise observations and historical actions into HSM. (c) On the receiving side, the agent performs ego-binding and fuses messages based on similarity metrics.

Figure 3: Performance in Noise-Free Environments. Each curve represents the average across four random seeds. (a)-(b) Hallway. (c)-(e) LBF . (f)-(h) SMAC. (i)-(j) SMACv2.

Figure 4: Robustness Evaluation in Randomly Noisy Environments.

Scenario	Method	No-Adv	FGSM (0.1)	FGSM (0.3)	FGSM (0.5)	PGD (5, 0.3)	PGD (5, 0.5)
5m_large	CroMAC	$16.3\pm 0.2$	$10.7\pm 0.1$	$3.1\pm 0.4$	$0.5\pm 0.9$	$9.2\pm 0.3$	$1.6\pm 0.7$
	MAIC-AME	$48.9\pm 0.8$	$44.1\pm 0.6$	$26.5\pm 0.5$	$15.1\pm 0.2$	$42\pm 3.3$	$\mathbf{36\pm 2.8}$
	Herm (Ours)	$\mathbf{67.2\pm 0.5}$	$\mathbf{58.3\pm 0.4}$	$\mathbf{31.8\pm 0.1}$	$\mathbf{18.6\pm 0.3}$	$\mathbf{43.5\pm 1.4}$	$33.9\pm 3.2$
5z_vs_1ul	CroMAC	$64.5\pm 0.1$	$10.5\pm 0.8$	$0.3\pm 0.2$	$0.8\pm 0.5$	$31.4\pm 0.9$	$24.7\pm 0.1$
	MAIC-AME	$77.8\pm 0.3$	$60.8\pm 0.7$	$34.2\pm 0.6$	$6.2\pm 0.1$	$\mathbf{65.2\pm 2.4}$	$37.5\pm 3.3$
	Herm (Ours)	$\mathbf{79.0\pm 0.2}$	$\mathbf{68.5\pm 0.9}$	$\mathbf{35.5\pm 0.3}$	$\mathbf{25.1\pm 0.4}$	$63.5\pm 4.1$	$\mathbf{58.5\pm 3.7}$

Table 1: Robustness Evaluation in Adversarially Noisy Environments.

Figure 5: Message-Semantic Transformation in LBF. The upper displays entity-wise similarity measurements, while the lower shows: the raw observations, manually translated observation texts, and the decoded semantics. The black box highlights the value exhibiting maximum similarity.

Panel of Figure 6 — Figure 6: Ablation and Parameter Analysis on the Communication Process.

Task	Encoding	noise=0	noise=0.5	noise=1.0	noise=1.5	noise=2.0
$9\times 9$	HDC	$\textbf{0.878}\pm\textbf{0.017}$	$\textbf{0.872}\pm\textbf{0.020}$	$\textbf{0.785}\pm\textbf{0.034}$	$\textbf{0.678}\pm\textbf{0.047}$	$\textbf{0.615}\pm\textbf{0.050}$
$9\times 9$	Neural	$0.862\pm 0.039$	$0.825\pm 0.045$	$0.720\pm 0.075$	$0.595\pm 0.070$	$0.440\pm 0.048$
$11\times 11$	HDC	$\textbf{0.882}\pm\textbf{0.028}$	$\textbf{0.875}\pm\textbf{0.020}$	$\textbf{0.785}\pm\textbf{0.028}$	$\textbf{0.705}\pm\textbf{0.030}$	$\textbf{0.592}\pm\textbf{0.038}$
$11\times 11$	Neural	$0.858\pm 0.040$	$0.815\pm 0.022$	$0.695\pm 0.072$	$0.510\pm 0.118$	$0.385\pm 0.082$

Table 2: Spearman Correlation Coefficient

\rho

under Noise (mean

\pm

std)

Appendix figures & tables19 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 7: Communication-Intensive Tasks in SMAC [ 14 ] . Enemies are highlighted in blue circles, while allies are marked in red.

Parameter	Value
Optimizer	Adam
Learning Rate	$5\times 10^{-4}$
Batch Size	32
Discount Factor	0.99
GRU Hidden State Dim	64
Mixing Hidden Dim	32

Appendix

Table 3: Default Parameters

Symbol	Description	Value
$\mathcal{H}$	Dimension of the hyperdimensional space	$\{64,128,256\}$
$w$	Length of historical action sequences	$\{1,3,4\}$
$Bin$	Number of discretized partitions	$\{5,10\}$

Appendix

Table 4: Method-Specific Parameters

	MAIC	T2MAC	CoDe	TGCNET	Herm (Ours)	Herm + Cache
Params (K)	50.79	50.70	49.39	827.01	46.88	46.88
Times (s)	1.481	1.528	1.363	1.656	1.993	1.392

Appendix

Table 5: Comparison on Model Size and Efficiency

Figure 8: Additional Robustness Comparison.

Figure 9: Performance Comparison with Different HDC Framework.

Task	$\mathcal{H}$	Noise Level
Task	$\mathcal{H}$	0	0.5	1.0	1.5	2.0
Hallway-4	MAIC	100 $\pm$ 0.0	95.6 $\pm$ 1.7	58.4 $\pm$ 1.9	37.4 $\pm$ 3.3	20.0 $\pm$ 3.9
	MAIC-E ( $\mathcal{H}=256$ )	98.4 $\pm$ 0.5	96.8 $\pm$ 0.8	94.5 $\pm$ 0.7	64.5 $\pm$ 2.6	44.6 $\pm$ 4.1
	MAIC-E ( $\mathcal{H}=512$ )	100.0 $\pm$ 0.0	100.0 $\pm$ 0.0	100.0 $\pm$ 0.0	100.0 $\pm$ 0.0	85.5 $\pm$ 1.3
	MAIC-E ( $\mathcal{H}=1024$ )	100.0 $\pm$ 0.0	100.0 $\pm$ 0.0	100.0 $\pm$ 0.0	100.0 $\pm$ 0.0	100.0 $\pm$ 0.0
5z_vs_1ul	MAIC	78.8 $\pm$ 1.2	72.4 $\pm$ 1.9	50.2 $\pm$ 2.6	24.0 $\pm$ 4.2	16.6 $\pm$ 4.1

Appendix

Table 6: Performance with HSM-Enhancement

Panel of Figure 10 — Figure 10: Performance with Policy-based Extension.

Task	Variant	0.0	0.5	1.0	2.0
$9\times 9$	Herm	99.1 $\pm$ 0.5	97.6 $\pm$ 1.2	94.8 $\pm$ 0.9	84.7 $\pm$ 1.1
	Herm_ne	$94.8\pm 0.28$	$89.6\pm 3.9$	$87.4\pm 3.2$	$80.5\pm 4.1$
	Herm_mf	$93.4\pm 0.4$	$93.6\pm 0.2$	$87.8\pm 1.3$	$80.8\pm 1.6$
	Herm_is	$92.2\pm 0.7$	$92.8\pm 1.1$	$83.6\pm 0.8$	$76.1\pm 1.2$
	Herm_ne_mf	$90.9\pm 2.5$	$87.9\pm 2.2$	$83.7\pm 3.8$	$78.2\pm 4.4$
$11\times 11$	Herm	96.1 $\pm$ 0.3	94.1 $\pm$ 0.2	90.8 $\pm$ 1.1	81.8 $\pm$ 1.4

Appendix

Table 7: Ablation of Herm’s Variant under Noise

Figure 11: Conversion Fidelity in SMAC with Different Message Length.

Figure 12: Conversion Fidelity in LBF with Different Message Length.

Figure 13: Decoding Accuracy in SMAC with Different Message Length.

Figure 14: Observation Similarity Visualization in SMAC. Triangles denote “stalker” and squares denote “zealot”. Subfigures b, c, and d present the observation encoding similarity matrices under different noise conditions.

Figure 15: Analysis of the Ego-Binding on Similarity.

Attribute	Explanation	Independence	Discrete	Value Range
Agent ID	Unique Identifier	Independent	Yes	$\{1,\cdots,N_{entity}\}$
HP	Current Health Value	Associated	No	$[0,1]$
Relative X	Normalized X-position Relative to Agent	Associated	No	$(-1,1)$
Relative Y	Normalized Y-position Relative to Agent	Associated	No	$(-1,1)$
Unit Type	Race of the Unit	Independent	Yes	$\{1,\cdots,N_{type}\}$
Visibility	Binary Visibility Indicator	Independent	Yes	$\{0,1\}$

Appendix

Table 8: Attribute Properties Specification in SMAC

Attribute	Explanation	Independence	Discrete	Value Range
Agent ID	Unique Identifier	Independent	Yes	$\{1,\cdots,N_{entity}\}$
Absolute X	Absolute X-position in the Map	Associated	Yes	$\{0,\cdots,X\}$
Absolute Y	Absolute Y-position in the Map	Associated	Yes	$\{0,\cdots,Y\}$
Level	Capture Ability (Predator) / Escape Ability (Prey)	Independent	Yes	$\{1,\cdots,Level\}$
Visibility	Binary Visibility Indicator	Independent	Yes	$\{0,1\}$
Identity	Indicator Whether the Unit is Self, Predator, or Prey	Independent	Yes	$\{0,1,2\}$

Appendix

Table 9: Attribute Properties Specification in LBF

Attribute	Explanation	Independence	Discrete	Value Range
Agent ID	Unique Identifier	Independent	Yes	$\{1,\cdots,N_{agent}\}$
Position	Position in its Line	Associated	Yes	$\{0,\cdots,X\}$
Time	Time Window Index	Associated	No	$\{-1,\cdots,-w\}$

Appendix

Table 10: Attribute Properties Specification in Hallway

$\mathcal{H}$	Task	Herm	DeepSeek-V3.2	GLM-4-7	Doubao-Seed-1.6
256	5z_vs_1ul	79.0 $\pm$ 0.2	68.4 $\pm$ 3.7	31.6 $\pm$ 3.6	53.8 $\pm$ 3.5
	2s3z_vs_1ul	81.9 $\pm$ 0.6	64.3 $\pm$ 3.3	35.6 $\pm$ 4.8	60.5 $\pm$ 3.1
	1c4z_vs_1ul	75.1 $\pm$ 1.5	52.6 $\pm$ 3.4	28.5 $\pm$ 3.3	44.6 $\pm$ 4.2
512	5z_vs_1ul	80.3 $\pm$ 0.8	73.4 $\pm$ 2.2	34.3 $\pm$ 1.5	58.0 $\pm$ 2.6
	2s3z_vs_1ul	80.6 $\pm$ 0.5	66.8 $\pm$ 3.7	37.2 $\pm$ 3.4	59.8 $\pm$ 2.8
	1c4z_vs_1ul	76.5 $\pm$ 0.8	55.2 $\pm$ 2.8	30.5 $\pm$ 3.1	46.3 $\pm$ 3.5

Appendix

Table 11: Performance of Algorithm-LLM Hybrid Decision Making

Y_{j}=r_{j}+\gamma(1-\mathrm{done}_{j})\cdot{Mixing}^{\mathrm{target}}(y_{1}^{j},\dots,y_{N}^{j};\beta^{-})

Appendix

Algorithm 1 Training Process in Herm

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Shannon's information theory deliberately excludes message semantics. This paper develops a rigorous framework for semantic communication that integrates formal proof systems with Shannon-theoretic tools. We introduce an axiomatic information model comprising Lsem-definable state sets linked by computable enabling maps, and define the semantic channel as a composition of Markov kernels whose supports respect the enabling structure. A fixed proof system induces an irredundant semantic core and a derivation-depth stratification, enabling four distortion measures of increasing semantic depth: Hamming, closure, depth, and a parameterized composite. Six families of computable semantic channel invariants are defined and their inter-relationships established, including a data processing bound, a semantic Fano bound, and an ideal-channel collapse theorem. The central quantitative result is a deductive compression gain: under closure-based fidelity, the minimum block length is determined by the irredundant core size rather than the full knowledge-base size. We instantiate the framework for heterogeneous multi-agent communication, introducing an overlap decomposition that yields necessary and sufficient conditions for closure-reliable communication. A semantic bottleneck phenomenon is identified in broadcast settings: vocabulary mismatch imposes irreducible fidelity limitations even over noiseless carriers. All results are verified on an explicit Datalog instance.

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