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Domain-Adapted Granger Causality for Real-Time Cross-Slice Attack Attribution in 6G Networks

Conference: NEURIPS2025 arXiv: 2510.05165 Code: To be confirmed (authors declare Apache 2.0 open-source release) Area: Causal Inference Keywords: Granger causality, 6G network slicing, cross-slice attack attribution, resource contention, real-time security

TL;DR

This paper proposes a domain-adapted Granger causality framework for 6G network slicing that integrates enhanced Granger causality testing with network resource contention modeling to enable real-time cross-slice attack attribution, achieving 89.2% accuracy and 87 ms response time across 1,100 attack scenarios, substantially outperforming existing statistical, deep learning, and causal discovery methods.

Background & Motivation

Core Problem: 6G networks partition shared physical infrastructure into multiple logical networks via network slicing to serve diverse services (eMBB/URLLC/mMTC), but resource sharing allows attacks to propagate across slices, making attribution extremely challenging.

Limitations of Prior Work: Existing approaches suffer from three major deficiencies: (a) correlation-based methods (e.g., Pearson correlation) yield high false positive rates (30.6%) and cannot distinguish causal from spurious associations; (b) deep learning methods (e.g., Transformer-XL) achieve relatively high accuracy but exceed 200 ms response time, failing to meet real-time requirements; (c) purely statistical causal methods (e.g., VAR-Granger) neglect resource contention—a domain-specific causal pathway.

Opportunity and Limitation of Granger Causality: Classical Granger causality infers causation from improvements in time-series prediction and is a canonical framework for temporal causal inference. However, when directly applied to multi-slice 6G scenarios, shared resources (CPU/memory/network) act as important confounders, generating numerous spurious causal relationships if left uncontrolled.

Real-Time Constraint: 6G security orchestration requires sub-100 ms response times, ruling out computationally expensive methods (PC algorithm: 156 ms; Transformer-XL: 234 ms).

Interpretability Requirement: Automated security orchestration systems require interpretable causal explanations to guide response strategies, which black-box deep learning methods cannot readily provide.

Industrial Urgency: In IoT and industrial automation scenarios, cross-slice attacks can cause real production-safety hazards (e.g., manufacturing control system latency violations triggering emergency shutdowns).

Method

Overall Architecture

The Domain-Adapted Granger Causality framework receives security telemetry streams \(\{x_t^{(i)}\}\) from \(N\) slices together with resource allocation data \(A(t)\), and operates through three core components working in concert: (1) enhanced Granger causality testing to eliminate resource-induced confounding; (2) resource contention modeling to capture domain-specific causal pathways; and (3) integrated causal strength scoring combined with the Viterbi algorithm to extract the optimal attack path. The overall algorithmic complexity is \(O(N^2 \cdot W \cdot (p+q+K) + N^3 \cdot \log N)\), which guarantees sub-100 ms execution under typical deployments (\(N \leq 50\), \(W = 300\)).

Module 1: Enhanced Granger Causality Testing

  • Function: For each slice pair \((s_i, s_j)\), tests whether the telemetry time series of \(s_i\) has statistically significant causal predictive power over \(s_j\), while controlling for confounding effects of shared resources.
  • Mechanism: Shared resource control terms \(Z_t = [Z_{1,t}, \ldots, Z_{K,t}]^\top\) are introduced into the standard Granger regression. The unrestricted model is \(Y_t = \sum \alpha_i Y_{t-i} + \sum \beta_j X_{t-j} + \sum \gamma_k Z_{k,t} + \varepsilon_t\); the restricted model (\(H_0: \beta_j = 0\)) is \(Y_t = \sum \alpha_i Y_{t-i} + \sum \gamma_k Z_{k,t} + \eta_t\). The enhanced F-statistic is \(F = \frac{(RSS_R - RSS_U)/q}{RSS_U/(T-p-q-K-1)}\), which follows an \(F(q,\, T-p-q-K-1)\) distribution under \(H_0\).
  • Design Motivation: Shared resources are the primary confounding source in 6G scenarios—two slices may exhibit correlated telemetry solely because they share a CPU. The resource conditioning term \(\gamma_k Z_{k,t}\) explicitly blocks the confounding path \(X \leftarrow R \rightarrow Y\). Compared with standard Granger causality, resource conditioning yields an 8.2 percentage-point accuracy gain (74.1% → 82.3%).

Module 2: Resource Contention Modeling

  • Function: Captures causal pathways mediated through shared resource mechanisms that are missed by purely statistical methods, by modeling inter-slice resource contention intensity.
  • Mechanism: Contention intensity is defined as \(\rho_{ij}(t) = \sum_k w_k \cdot A_{ik}(t) \cdot A_{jk}(t) \cdot \sigma(U_{k,t} - \tau_k)\), where \(A_{ik}(t)\) is the normalized resource allocation ratio, \(U_{k,t}\) is the resource utilization rate, \(w_k\) are learnable criticality weights, \(\tau_k\) are contention thresholds, and \(\sigma(\cdot)\) is the sigmoid function.
  • Design Motivation: The product term \(A_{ik} \cdot A_{jk}\) acts as a logical AND gate—contention arises only when both slices simultaneously use the same resource. The sigmoid term implements a threshold effect—contention becomes significant only after resource utilization exceeds the threshold. Linear weighted summation allows the model to automatically learn the relative importance of different resources (CPU/memory/network). Weights learned in experiments (CPU 0.45, memory 0.31, network 0.24) are intuitively consistent. This module contributes an additional 4.7 percentage-point accuracy gain (82.3% → 87.0%).

Module 3: Integrated Causal Strength and Attack Path Extraction

  • Function: Fuses statistical and domain causal evidence into a unified score and extracts the optimal attack path from the causal graph.
  • Mechanism: The integrated causal strength is \(\Gamma_{ij}(t) = \omega_1 \cdot \phi(F_{ij}(t)) + \omega_2 \cdot \rho_{ij}(t)\), where \(\phi\) denotes min-max normalization and \(\{\omega_1, \omega_2\}\) are learned via MLE (optimal values: \(\omega_1 = 0.67\), \(\omega_2 = 0.33\)). Benjamini–Hochberg correction controls the FDR at 0.05; edges satisfying the threshold \(\tau_{\text{causal}}\) form the causal graph \(G\), and the Viterbi algorithm solves for the optimal path \(C^* = \arg\max \prod \Gamma_{ij}(T)\).
  • Design Motivation: Linear fusion offers better algorithmic stability and interpretability than nonlinear fusion in real-time systems. BH correction addresses the multiple comparison problem arising from \(N(N-1)\) pairwise tests. Sensitivity analysis shows that accuracy fluctuates by only \(\pm 1.5\) percentage points for \(\omega_1 \in [0.55, 0.80]\), demonstrating robustness to parameter tuning.

Loss & Training

  • Parameters \(\theta = \{w_1, \ldots, w_K,\, \tau_1, \ldots, \tau_K,\, \omega_1, \omega_2\}\) are learned by maximizing the regularized log-likelihood: \(\mathcal{L}(\theta) = \sum_m \log P(C^{(m)} \mid X^{(m)}, A^{(m)}, \theta) - \lambda \|\theta\|_2^2\).
  • Hyperparameters are selected via 5-fold cross-validation (optimal \(\lambda^* = 10^{-3}\)).
  • Theoretical guarantees: Theorem 1 proves the asymptotic \(F\)-distribution of the enhanced F-statistic under \(H_0\); Theorem 2 proves that causal relationships are uniquely identified with probability \(\geq 1 - N(N-1)\alpha\) under the DAG assumption.

Key Experimental Results

Table 1: Main Performance Comparison (N = 1,100 attack scenarios, 5-fold cross-validation)

Method Accuracy (%) Precision (%) Recall (%) FDR (%) Response Time (ms)
Pearson Correlation 72.9±1.8 69.4±2.1 76.2±1.9 30.6±2.1 21±3
Transfer Entropy 78.4±1.5 75.8±1.7 81.3±1.6 24.2±1.7 58±7
VAR-Granger 74.1±1.7 71.2±1.9 77.6±1.8 28.8±1.9 43±5
PC Algorithm 76.2±1.6 73.5±1.8 79.4±1.7 26.5±1.8 156±20
GraphSAGE 76.8±1.6 74.3±1.8 79.9±1.7 25.7±1.8 142±18
LSTM-Attention 79.1±1.4 76.7±1.6 82.2±1.5 23.3±1.6 167±22
Transformer-XL 81.3±1.3 78.9±1.5 84.1±1.4 21.1±1.5 234±31
Ours 89.2±0.9 87.6±1.1 91.1±1.0 12.4±1.1 87±9

Table 2: Extended Metric Comparison

Method AUC-ROC AUC-PR F1 MCC Memory (MB)
Correlation 0.742±0.018 0.689±0.021 0.726±0.019 0.461±0.024 12±2
Transfer Entropy 0.798±0.015 0.751±0.017 0.784±0.016 0.572±0.019 28±4
Transformer-XL 0.827±0.013 0.789±0.015 0.815±0.014 0.634±0.017 756±48
Ours 0.921±0.009 0.876±0.011 0.892±0.010 0.785±0.012 67±8

Key Findings

  1. The proposed method outperforms the strongest baseline, Transformer-XL, by 7.9 percentage points in accuracy (\(p < 0.001\), Cohen's \(d > 1.5\)), while achieving 2.7× faster response (87 ms vs. 234 ms) and requiring only 1/11 of its memory.
  2. Ablation studies quantify individual component contributions: resource conditioning +8.2 pp, resource contention modeling +4.7 pp, and integrated learning +2.2 pp, all significant at \(p < 0.001\).
  3. The framework maintains 84.3% accuracy under 60% partial observability, exhibiting graceful performance degradation.
  4. In an industrial IoT attack case study, the complete 5-hop attack chain is reconstructed with 96.3% accuracy, zero false positives, and 73 ms response time, whereas the traditional correlation method produces 11 false alarms.

Highlights & Insights

  1. Principled Integration of Statistical Causality and Domain Knowledge: Rather than naively stacking components, the framework learns optimal fusion weights via MLE, and the necessity of each component is theoretically and empirically substantiated through ablation studies.
  2. Rare Achievement of Both Real-Time Performance and High Accuracy: The 87 ms response time satisfies the strict real-time constraints of 6G security orchestration while surpassing the heavyweight Transformer-XL in accuracy.
  3. Interpretable Outputs: Each causal edge is supported by dual explanations—an F-statistic p-value and a resource contention score—making the framework suitable for automated security decision-making.
  4. Elegant Design of Resource Contention Modeling: The three-layer product–sigmoid–weighted structure is simultaneously compact and physically intuitive.

Limitations & Future Work

  1. The weak stationarity assumption may be violated during rapid nonlinear attack evolution; although resource conditioning partially mitigates this, fundamentally non-stationary scenarios (e.g., abrupt changes in attack patterns) may still cause failures.
  2. Reliable attribution requires approximately 2 seconds of telemetry data, which may be insufficient for ultra-fast attacks.
  3. The \(O(N^3 \log N)\) complexity requires approximation algorithms for very large-scale deployments (\(N > 50\)).
  4. The product-weighted linear structure of the resource contention model may inadequately capture more complex nonlinear interference patterns.
  5. Experiments are conducted on a single production-grade testbed, lacking generalization validation across operators or geographic regions.
  • Classical Granger Causality [Granger, 1969; Shojaie & Fox, 2024]: The core methodological foundation of this work; the enhancements lie in resource conditioning and domain fusion.
  • Transfer Entropy [Schreiber, 2000]: An information-theoretic approach to temporal causal inference, achieving 78.4% accuracy in the experiments—inferior to the resource conditioning strategy proposed here.
  • Graph Neural Network Methods [GraphSAGE, Hamilton et al., 2017]: Learn the spatial structure of slice relationships but lack temporal causal reasoning and resource contention modeling.
  • Granger Causality in IoT Security [Begum et al., 2025; Lv et al., 2024]: Preliminary applications of Granger causality to IoT scenarios, without domain adaptation tailored to resource contention characteristics of 6G multi-slice networks.
  • Causal Discovery Methods [PC, DirectLiNGAM]: Structural learning based on conditional independence testing; computationally expensive and unsuitable for real-time scenarios.

Rating

  • Novelty: ⭐⭐⭐⭐ — Innovatively combines Granger causality with network resource contention modeling, opening a new direction in 6G security research.
  • Experimental Thoroughness: ⭐⭐⭐⭐ — Comprehensive coverage across 1,100 scenarios, multiple baselines, ablation analysis, sensitivity analysis, and an industrial case study.
  • Writing Quality: ⭐⭐⭐⭐ — Clear framework description, complete algorithmic pseudocode, rigorous theoretical proofs, and rich figures and tables.
  • Value: ⭐⭐⭐⭐ — Provides a practical framework for 6G network security attribution; theoretical guarantees combined with real-time performance make it deployment-ready.