Feature-Aware Anisotropic Local Differential Privacy for Utility-Preserving Graph Representation Learning in Metal Additive Manufacturing

1. Problem Statement

The paper addresses two critical, interrelated challenges in Metal Additive Manufacturing (AM), specifically in Directed Energy Deposition (DED) processes:

• Relational Modeling Gap: Existing defect detection models (e.g., CNNs, LSTMs) typically treat melt-pool observations as independent samples. This ignores the physical reality of AM, where defect formation (specifically porosity) is governed by layer-wise physical couplings, such as heat accumulation from adjacent scan tracks and thermal history from underlying layers.
• Privacy-Utility Trade-off: Collaborative quality assurance requires sharing sensor data, but raw data contains proprietary "process fingerprints" (thermal signatures, scan paths). While Local Differential Privacy (LDP) offers formal privacy guarantees, standard LDP mechanisms inject isotropic noise (uniform noise across all dimensions). In high-dimensional manufacturing embeddings, this uniformly corrupts both task-critical thermal signatures and redundant dimensions, leading to severe degradation in defect detection utility.

Goal: Develop a framework that enables collaborative, privacy-preserving graph learning for porosity prediction without destroying the structural information necessary for accurate defect detection.

---

2. Methodology: FI-LDP-HGAT

The authors propose FI-LDP-HGAT, a computational framework combining two novel components:

A. Feature-Importance-Aware Anisotropic LDP (FI-LDP)

Instead of uniform noise injection, FI-LDP redistributes the privacy budget based on the predictive importance of feature dimensions.

• Supervised Warmup: Before privatization, a lightweight classifier is trained on the raw data to estimate a global feature importance prior ($q$). This identifies which embedding coordinates are most critical for distinguishing porous from non-porous regions.
• Anisotropic Allocation: Using a temperature-controlled power-law allocation, the total privacy budget ($\epsilon$) is redistributed.
  • High-importance dimensions: Assigned a larger $\epsilon$ (weaker noise).
  • Low-importance dimensions: Assigned a smaller $\epsilon$ (stronger noise).
• Mechanism: An anisotropic Gaussian mechanism adds coordinate-wise noise with dimension-dependent scales ($\sigma_d$), ensuring formal $(\epsilon, \delta)$-LDP guarantees while preserving the geometry of task-critical subspaces.

B. Stratified Hierarchical Graph Attention Network (HGAT)

To capture the physical couplings ignored by independent-sample models, the framework uses a specialized Graph Neural Network.

• Layer-Stratified Graph Construction: Nodes represent melt-pool observations. Edges are restricted to within-layer neighborhoods to respect the physical layering of AM.
• Hybrid kNN Edges: Connectivity is determined by a hybrid distance metric combining:
  1. Spatial proximity (in-layer coordinates).
  2. Thermal embedding similarity (learned features).
• Edge-Affinity Biased Attention: The HGAT incorporates the hybrid distance as an edge prior ($w_{ij}$) into the attention mechanism. This biases message passing toward neighbors that are both spatially close and thermally similar, effectively modeling heat accumulation and track interactions.

C. Data Augmentation Strategy

To address the severe class imbalance (only ~4.5% porous samples), the authors employ porous-targeted augmentation. Transformations (noise, brightness scaling, rotation, interpolation) are applied only to the minority class (porous frames) during training to increase defect-signal diversity without distorting the majority class distribution.

---

3. Key Contributions

1. FI-LDP Mechanism: A novel, non-interactive local privacy mechanism that uses a supervised warmup signal to guide anisotropic noise allocation. It provides a principled bridge between feature importance and privacy budget distribution, outperforming isotropic LDP.
2. Physics-Informed Graph Modeling: A stratified HGAT architecture that explicitly encodes manufacturing priors (layer restrictions, thermal coupling) into the graph topology and attention mechanism, moving beyond generic graph learning.
3. Comprehensive Evaluation: A rigorous benchmarking against classical ML, standard GNNs, and alternative privacy methods (DP-SGD, Uniform-LDP) on a real-world DED porosity dataset.

---

4. Experimental Results

The framework was evaluated on a Ti-6Al-4V thin-wall dataset (1,564 observations) with a 60/20/20 split.

• Utility Recovery:
  • At a moderate privacy budget ($\epsilon = 4$), FI-LDP-HGAT achieved 81.5% utility recovery relative to the non-private oracle (F1 score of 0.767 vs. 0.941).
  • At a strict budget ($\epsilon = 2$), it maintained a defect recall of 0.762, significantly outperforming baselines.
• Comparison with Baselines:
  • vs. DP-SGD: DP-SGD training suffered catastrophic utility loss (F1 < 0.21) due to gradient noise disrupting rare-event learning.
  • vs. Uniform-LDP: FI-LDP improved AUC by 3.3% and Recall by 7.2% at $\epsilon=2$, demonstrating that importance-guided noise allocation preserves rare-defect signals better than uniform corruption.
  • vs. Standard GNNs: The proposed HGAT (with edge priors) achieved a calibrated F1 of 0.941 (non-private), outperforming GCN and Vanilla GAT, which tended to over-predict the minority class.
• Mechanistic Validation:
  • Analysis confirmed a strong negative correlation (Spearman $\rho = -0.81$) between feature importance and noise magnitude. This proves that FI-LDP systematically assigns less noise to critical features, validating the "principled anisotropic allocation" hypothesis.

---

5. Significance and Impact

• Reconciling Privacy and Utility: The paper demonstrates that privacy-induced utility loss is not inevitable. By aligning the perturbation mechanism with the structure of the learned embedding (anisotropy), high-fidelity defect detection can be maintained even under strict privacy constraints.
• Enabling Collaborative AM: FI-LDP-HGAT provides a pathway for multi-stakeholder manufacturing ecosystems to share sensitive process data for collective quality improvement without exposing proprietary "process fingerprints."
• Beyond Heuristics: Unlike previous image-level de-identification or heuristic privacy methods, this approach offers formal $(\epsilon, \delta)$-LDP guarantees while preserving the geometric structure required for downstream graph-based inference.
• Future Directions: The framework sets the stage for federated learning in AM, physics-informed graph biases, and privacy-preserving autonomous closed-loop control systems.

In conclusion, this work establishes that feature-aware anisotropic perturbation combined with physics-informed graph learning is a viable and superior strategy for secure, high-utility quality assurance in advanced manufacturing.