Synthetic Anomaly Score

The score is fundamentally a log-likelihood ratio or a reconstruction error magnitude. It quantifies how many standard deviations a sample sits from the centroid of the nominal data manifold.

• Gaussian Assumption: In models like VAEs, the score often represents the negative log-likelihood under a multivariate Gaussian prior.
• Reconstruction Residual: In autoencoder-based models, it is the L2 norm of the difference between the input and its reconstruction.
• Discriminator Confidence: In GAN-based approaches, it maps directly to the discriminator's probability that a sample is real versus synthetic.

Unlike binary classifiers, a continuous score allows operational tuning of the detection threshold without retraining. This decouples model training from business risk tolerance.

• Precision-Recall Trade-off: Lowering the threshold increases recall for micro-defects but raises false positive rates.
• Cost-Matrix Integration: The threshold can be set to minimize a custom cost function, e.g., $Cost = (FN * $Scrap) + (FP * $Rework).
• Dynamic Adjustment: Thresholds can be modulated in real-time based on downstream process parameters or product SKU criticality.

Because the model is trained on a Synthetic Defect Library covering the long tail of failure modes, the score distribution for known anomalies is well-characterized.

• Open-Set Recognition: The score naturally supports out-of-distribution detection; novel defect types not seen in the synthetic library will still produce high anomaly scores if they deviate from the nominal manifold.
• Domain Gap Invariance: Training with Domain Randomization ensures the score is sensitive to structural defects, not lighting or texture variations.
• Calibrated Confidence: The score can be statistically calibrated using Fréchet Inception Distance metrics to ensure it correlates with true physical deviation.

An anomaly score is not just a single-point metric; its trajectory over time provides a leading indicator of process drift or tool wear.

• Cumulative Sum Control: Applying CUSUM charts to the anomaly score stream detects subtle, sustained shifts in the production distribution before individual units fail inspection.
• Predictive Maintenance Input: A rising baseline anomaly score across a batch signals degrading tool health, serving as a feature for Predictive Maintenance Algorithms.
• Root Cause Correlation: Spikes in anomaly scores can be correlated with specific sensor readings from the Digital Twin to isolate the upstream process variable causing the deviation.

In complex inspection systems, individual anomaly scores from different sensor modalities are fused into a single, robust composite metric.

• Sensor Fusion Frameworks: A vision-based score for surface defects can be combined with a vibration-based score for structural integrity using a Bayesian fusion layer.
• Depth Map Synthesis: An anomaly score derived from 3D point cloud reconstruction can be weighted against a 2D texture score to resolve ambiguities.
• Late Fusion Architecture: Each modality computes an independent anomaly score; a final lightweight classifier learns the optimal weighting to produce a unified decision statistic.

To meet Algorithmic Explainability requirements, a high anomaly score must be decomposable into its constituent feature contributions.

• Pixel Attribution: Techniques like Grad-CAM can highlight the specific pixels in the input image that most contributed to the high reconstruction error.
• Latent Traversal: For VAE-based scores, traversing the latent space along the vector of deviation reveals the specific defect morphology the model detected.
• Counterfactual Generation: The system can generate a 'repaired' version of the defective sample by projecting it onto the nominal manifold, visually explaining the detected anomaly.