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Auditing Cascading Risks in Multi-Agent Systems via Semantic-Geometric Co-evolution

Zixun Luo, Yuhang Fan, Hengyu Lin, Yufei Li, Youzhi Zhang

Abstract

Large Language model (LLM)-based Multi-Agent Systems (MAS) are prone to cascading risks, where early-stage interactions remain semantically fluent and policy-compliant, yet the underlying interaction dynamics begin to distort in ways that amplify latent instability or misalignment. Traditional auditing methods that focus on per-message semantic content are inherently reactive and lagging, failing to capture these early structural precursors. In this paper, we propose a principled framework for cascading-risk detection grounded in semantic--geometric co-evolution. We model MAS interactions as dynamic graphs and introduce Ollivier--Ricci Curvature (ORC) -- a discrete geometric measure -- to characterize information redundancy and bottleneck formation in communication topologies. By coupling semantic flow signals with graph geometry, the framework learns the normal co-evolutionary dynamics of trusted collaboration and treats deviations from this coupled manifold as early-warning signals. Experiments on a suite of cascading-risk scenarios aligned with the risk category demonstrate that curvature anomalies systematically precede explicit semantic violations by several interaction turns, enabling proactive intervention. Furthermore, the local nature of Ricci curvature provides principled interpretability for root-cause attribution, identifying specific agents or links that precipitate the collapse of trustworthy collaboration.

Auditing Cascading Risks in Multi-Agent Systems via Semantic-Geometric Co-evolution

Abstract

Large Language model (LLM)-based Multi-Agent Systems (MAS) are prone to cascading risks, where early-stage interactions remain semantically fluent and policy-compliant, yet the underlying interaction dynamics begin to distort in ways that amplify latent instability or misalignment. Traditional auditing methods that focus on per-message semantic content are inherently reactive and lagging, failing to capture these early structural precursors. In this paper, we propose a principled framework for cascading-risk detection grounded in semantic--geometric co-evolution. We model MAS interactions as dynamic graphs and introduce Ollivier--Ricci Curvature (ORC) -- a discrete geometric measure -- to characterize information redundancy and bottleneck formation in communication topologies. By coupling semantic flow signals with graph geometry, the framework learns the normal co-evolutionary dynamics of trusted collaboration and treats deviations from this coupled manifold as early-warning signals. Experiments on a suite of cascading-risk scenarios aligned with the risk category demonstrate that curvature anomalies systematically precede explicit semantic violations by several interaction turns, enabling proactive intervention. Furthermore, the local nature of Ricci curvature provides principled interpretability for root-cause attribution, identifying specific agents or links that precipitate the collapse of trustworthy collaboration.
Paper Structure (54 sections, 13 equations, 4 figures, 3 tables)

This paper contains 54 sections, 13 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Safety and Robustness in Multi-Agent Systems.
  4. Semantic Safety and Adversarial Attacks.
  5. Graph Geometry and Structural Anomaly Detection.
  6. Methodology: Semantic–Geometric Co-evolutionary Auditing
  7. Auditing Manifold and Co-evolution Assumption
  8. Semantic Representation.
  9. Principle of Co-evolution.
  10. Directed Semantic Flow Induction
  11. Geometric Profiling via Ollivier–Ricci Curvature
  12. SCCAL: Coupled Dynamics Predictor
  13. Geometry-Aware Semantic Predictor ($\psi$).
  14. Semantic-Tension Geometric Predictor ($\phi$).
  15. Anomaly Detection and Root-Cause Attribution
  16. ...and 39 more sections

Figures (4)

  • Figure 1: Architecture of the Semantic-Curvature Co-evolution Auditing Loop (SCCAL). The framework treats multi-agent interactions as a dynamic graph stream $\mathcal{G}_t = (\mathcal{V}, \mathcal{E}_t)$ and operates via three integrated stages: (1) Dual-View Feature Extraction: Interaction data is decoupled into Semantic Content (node-level latent manifolds $\mathcal{M}_s$ via frozen encoders) and Interaction Topology (edge-level geometry). (2) Geometric Quantization: We utilize Ollivier-Ricci Curvature (ORC) to identify structural patterns; positive curvature indicates information redundancy (potential echo chambers), while negative curvature highlights structural bottlenecks (vulnerability for cascading risks). (3) Proactive Audit Loop: By monitoring Consistency Residuals between semantic and geometric flows, the system triggers Audit Feedback—a control signal that serves as an early-warning intervention to steer agents away from identified geometric traps before explicit semantic violations occur.
  • Figure 2: Overview of the proposed Semantic-Curvature Co-Evolution Loop Framework. The framework models Multi-Agent interaction risks through four distinct stages: (A) Semantic Encoding: Agent-generated messages are mapped into a latent space using a frozen SBERT to decouple representation from dynamics. (B) Semantic Flow Induction: A weighted interaction graph $G_f$ is constructed based on semantic transmissibility and a Perplexity Filter. (C) Coupled Dynamics Modeling: The core module $\Phi_\theta$ jointly models the bidirectional constraints between semantic updates and local topological evolution. Here, Curvature $\bar{\kappa}$ (Orange Box) represents the aggregated Ollivier-Ricci Curvature across a sliding interaction window, serving as a geometric descriptor of structural stability. (D) Anomaly Detection: Risk signals are identified by the joint prediction residual. The Geometric Response (Green Box) quantifies the system's structural reaction to semantic shifts; a high deviation between the predicted and observed Geometric Response indicates a consistency violation, flagging potential cascading risks before they manifest semantically.
  • Figure 3: Illustration of the Semantics-Geometry Detection Lag. The evolution of a cascading risk scenario across three phases: (Phase $t_0$) The system operates in a stable state with balanced topology. (Phase $t_1$) A structural "echo chamber" forms (indicated by high Ollivier-Ricci Curvature, $\kappa > 0.3$) as agents align tightly. Crucially, semantic content remains benign and policy-compliant, causing traditional semantic auditors to miss this latent risk. (Phase $t_2$) Semantic violations finally erupt and cascade along the high-curvature paths established in $t_1$. This demonstrates that geometric collapse precedes semantic violation, validating our approach of structural early warning.
  • Figure 4: Event-aligned time-lag analysis of curvature and semantic risk signals. The dashed line denotes the semantic risk onset ($t=0$).