TrustFlow: Topic-Aware Vector Reputation Propagation for Multi-Agent Ecosystems

Volodymyr Seliuchenko

cs.MAMar 19, 2026

TrustFlow: Topic-Aware Vector Reputation Propagation for Multi-Agent Ecosystems

Authors: Volodymyr Seliuchenko

Abstract

We introduce TrustFlow, a reputation propagation algorithm that assigns each software agent a multi-dimensional reputation vector rather than a scalar score. Reputation is propagated through an interaction graph via topic-gated transfer operators that modulate each edge by its content embedding, with convergence to a unique fixed point guaranteed by the contraction mapping theorem. We develop a family of Lipschitz-1 transfer operators and composable information-theoretic gates that achieve up to 98% multi-label Precision@5 on dense graphs and 78% on sparse ones. On a benchmark of 50 agents across 8 domains, TrustFlow resists sybil attacks, reputation laundering, and vote rings with at most 4 percentage-point precision impact. Unlike PageRank and Topic-Sensitive PageRank, TrustFlow produces vector reputation that is directly queryable by dot product in the same embedding space as user queries.

Figures & tables

Symbol	Definition
$N$	Number of agents
$E$	Embedding dimensionality (e.g., 384 for E5)
$D$	Number of discrete domains
$R[i]\in\mathbb{R}^{E}$	Reputation vector of agent $i$
$e_{ij}\in\mathbb{R}^{E}$	Unit interaction embedding for edge $i\to j$
$T[j]\in\mathbb{R}^{E}$	Teleportation prior of agent $j$

Table 1: Notation summary.

Operator	Output rank	Blind preservation	Cross-domain isolation	Convergence
Squared gating	Up to $E$	$\cos=1.0$	Soft (per-dim filter)	Always
Projection	1	$\cos\approx 0$	Maximum	Always
Hadamard relu	Up to $E$	$\cos=0.71$	Moderate (relu clips)	Always
Scalar-gated	Up to $E$	Full (when gate opens)	Binary	Always ( $\sigma$ clamped)
Hybrid	Up to $E$	Tunable	Tunable	Always

Table 2: Transfer operator properties.

Figure 1: Convergence of TrustFlow under projection and squared-gating transfer, with and without per-iteration normalization. The log-scale residual decreases linearly, confirming the contraction mapping rate

\alpha=0.85

. Squared gating converges faster in unnormalized mode due to higher self-alignment.

Metric	Discrete (8D)	Continuous (norm)	Continuous (unnorm)
Convergence iterations	8	9	11
P@5 (labeled, 70 edges)	74.0%	68.0%	72.0%
P@5 (combined, 682 edges)	—	78.0%	72.0%
Cross-domain alignment	0.65 / 0.10	0.20 / 0.06	0.20 / 0.06

Table 3: Discrete vs. continuous formulations. Cross-domain alignment reports primary / secondary domain cosine for a representative biostatistics agent.

Operator	Labeled P@5	Combined P@5	$\Delta$
Squared gating $R\odot e^{2}$	72.0%	72.0%	0.0pp
Projection $\sigma(R\cdot e)\cdot e$	68.0%	78.0%	+10.0pp
Scalar-gated $\sigma(\hat{R}\cdot e)\cdot R$	74.0%	62.0%	$-12.0$ pp
Hadamard relu $\sigma_{vec}(R\odot e)$	68.0%	68.0%	0.0pp
Hybrid proj + sq-gating	68.0%	76.0%	+8.0pp

Table 4: Discovery quality (P@5) by transfer operator. Combined graph = 682 edges.

Operator	Uniform $e$	avg(caller, callee) proxy
Squared gating $R\odot e^{2}$	1.000	0.682
Projection $\sigma(R\cdot e)\cdot e$	0.004	0.740
Scalar-gated $\sigma(\hat{R}\cdot e)\cdot R$	1.000 (40% of edges)	1.000
Hadamard relu	0.710	0.017

Table 5: Directional preservation on blind edges.

Operator	Labeled P@5	Combined P@5	Iterations
Squared gating	72.0%	72.0%	4
Projection	72.0%	72.0%	12
Scalar-gated	74.0%	70.0%	12
Hybrid	72.0%	72.0%	6

Table 6: Unnormalized iteration.

Variant	Self-alignment	P@5
No gating	0.730	68.0%
KL $\lambda=1.0$	0.908 (+24.5%)	76.0%
KL $\lambda=5.0$	1.000 (+37.1%)	72.0%

Table 7: KL-divergence gating. All results on labeled-only graph.

Scenario	P@5	$\Delta$	Verdict
Baseline	78.0%	—	—
Cross-domain sybil	78.0%	0pp	Structurally resistant
Same-domain sybil	74.0%	$-4$ pp	Bounded, flaggable
Reputation laundering	78.0%	0pp	Structurally resistant
Vote ring	80.0%	+2pp	Bounded by contraction
Flag defense	78.0%	0pp	Effective neutralization

Table 8: Attack resistance summary.

Figure 2: P@5 under four adversarial scenarios. The dashed line marks the 78% baseline. All attacks produce

{\leq}4

pp impact; cross-domain sybil and reputation laundering are structurally resisted.

Configuration	Strict P@5	Multi-label P@5
Sparse (70 edges, norm)	68.0%	78.0%
Dense (156 edges, norm)	78.0%	86.0%
Dense (156 edges, unnorm)	80.0%	88.0%
Dense + blind (768 edges, norm)	78.0%	88.0%

Table 9: Effect of graph density.

Figure 3: P@5 scales with interaction data. Moving from 70 to 768 edges improves strict P@5 by 10pp and multi-label P@5 by 10pp. The y-axis begins at 60% to highlight the improvement range.

Operator	Sparse P@5	Dense P@5	Dense multi-label
Projection	68.0%	78.0%	86.0%
Squared gating	72.0%	72.0%	82.0%
Scalar-gated	74.0%	88.0%	98.0%
Hybrid	68.0%	78.0%	86.0%

Table 10: Transfer operators on dense graph.

Strategy	P@5	$\Delta$ vs. cosine
Pure cosine (direction only)	78.0%	baseline
Log-dampened ( $\beta=0.1$ )	76.0%	$-2.0$ pp
Log-dampened ( $\beta=0.3$ )	76.0%	$-2.0$ pp
Inner product ( $\beta=1.0$ )	76.0%	$-2.0$ pp
Domain-boosted ( $\beta=0.05$ )	78.0%	0.0pp
Multi-query RRF	78.0%	0.0pp

Table 11: Retrieval strategy comparison (mean-centered embeddings).

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Trust via Reputation of Conviction

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The question of knowledge, truth and trust is explored via a mathematical formulation of claims and sources. We define truth as the reproducibly perceived subset of knowledge, formalize sources as having both generative and discriminative roles, and develop a framework for reputation grounded in the conviction -- the likelihood that a source's stance is vindicated by independent consensus. We argue that conviction, rather than correctness or faithfulness, is the principled basis for trust: it is regime-independent, rewards genuine contribution, and demands the transparent and self-sufficient perceptions that make external verification possible. We formalize reputation as the expected weighted signed conviction over a realm of claims, characterize its behavior across source-claim regimes, and identify continuous verification as both a theoretical necessity and a practical mechanism through which reputation accrues. The framework is applied to AI agents, which are identified as capable but error-prone sources for whom verifiable conviction and continuously accrued reputation constitute the only robust foundation for trust.

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