Fidelity-Evaluated Student

Fidelity quantifies the agreement rate between a teacher model's predictions and a student model's predictions on unseen data. Unlike standard accuracy, which measures performance against ground-truth labels, fidelity measures how well the student mimics the teacher's learned function. A high-fidelity student captures the teacher's decision boundaries, including its systematic errors and biases, making it a faithful surrogate for explanation purposes.

These two metrics serve fundamentally different purposes in the distillation pipeline:

• Accuracy: Measures student predictions against ground-truth labels. A student can be highly accurate but low-fidelity if it solves the problem differently than the teacher.
• Fidelity: Measures student predictions against teacher predictions. High fidelity is essential when the goal is explanation, not deployment.
• Tradeoff: Maximizing fidelity often requires the student to replicate teacher errors, which can reduce ground-truth accuracy.

Fidelity is computed by passing a held-out dataset through both models and comparing outputs:

• Classification: Simple agreement rate — the percentage of instances where student and teacher predict the same class.
• Regression: Correlation coefficient or R² score between teacher and student continuous outputs.
• Soft Fidelity: Kullback-Leibler divergence between the full probability distributions, capturing how well the student replicates the teacher's confidence across all classes, not just the top prediction.

Fidelity can be evaluated at different scopes depending on the explanation use case:

• Global Fidelity: Measures how well the student approximates the teacher across the entire input space. Essential for understanding overall model behavior and extracting global rules.
• Local Fidelity: Measures approximation quality in the neighborhood of a specific instance. Critical for explaining individual predictions, where the student must faithfully replicate the teacher's local decision boundary.
• A student may exhibit high global fidelity but poor local fidelity in sparse regions of the feature space.

A rigorous fidelity evaluation follows a structured protocol:

• Hold-out Set: Fidelity must be measured on data never seen by either model during training to avoid overfitting.
• Statistical Significance: Use confidence intervals or bootstrap resampling to ensure fidelity estimates are reliable.
• Subgroup Analysis: Disaggregate fidelity across data slices to detect systematic failures in specific demographic or operational segments.
• Adversarial Testing: Probe the student with inputs near the teacher's decision boundary to stress-test local fidelity.

Common scenarios where fidelity breaks down:

• Capacity Mismatch: The student's architecture is too simple to capture the teacher's complex, non-linear decision boundaries.
• Distribution Shift: The student is evaluated on data from a different distribution than the teacher was trained on, causing divergent behavior.
• Soft Target Collapse: The student overfits to the teacher's hard predictions rather than learning from the rich soft probability distributions.
• Feature Access Asymmetry: The interpretable student may lack access to complex engineered features the teacher relies on, creating an inherent fidelity ceiling.

The quantitative measure of agreement between the student and teacher model's predictions on unseen data. Unlike standard accuracy, fidelity evaluates how faithfully the interpretable model replicates the black-box teacher's decision logic.

• Top-1 Fidelity: Percentage of instances where student and teacher predict the same class
• Top-k Fidelity: Agreement within the top k predicted classes
• R² Fidelity: For regression tasks, the coefficient of determination between teacher and student outputs
• AUC Fidelity: Area under the ROC curve for binary classification agreement

A high-fidelity student may sacrifice ground-truth accuracy to faithfully replicate the teacher's behavior, including its errors. This tradeoff is central to interpretability: the goal is explaining what the model does, not what it should do.

• Fidelity-first: Prioritizes matching teacher predictions, even when teacher is wrong
• Accuracy-first: Prioritizes ground-truth correctness, potentially diverging from teacher
• Balanced approach: Weighted combination in the distillation loss function
• Error fidelity: Measures whether student replicates teacher's specific mistakes

Techniques for identifying regions of the input space where the student model diverges significantly from the teacher, indicating low fidelity zones that undermine the explanation's trustworthiness.

• Residual analysis: Plotting teacher-student prediction differences across the feature space
• Disagreement clustering: Grouping instances where models diverge to find patterns
• Adversarial fidelity testing: Generating inputs that maximize teacher-student disagreement
• Confidence calibration comparison: Checking if student uncertainty aligns with teacher confidence

The systematic process of choosing the optimal interpretable student architecture by comparing fidelity scores across candidate models. Higher fidelity indicates a more faithful approximation of the teacher's decision boundary.

• Candidate models: Decision trees, rule lists, GAMs, linear models, EBMs
• Cross-validated fidelity: Evaluating fidelity on held-out data to prevent overfitting
• Parsimony penalty: Balancing fidelity with model complexity for human interpretability
• Local fidelity: Measuring agreement on individual predictions, not just global averages

Training methodologies that enforce a minimum fidelity threshold as a hard constraint during the distillation process, ensuring the resulting student model meets explainability requirements.

• Constrained optimization: Adding fidelity lower bounds to the training objective
• Rejection regions: Identifying input areas where student cannot achieve target fidelity
• Adaptive temperature scaling: Dynamically adjusting softmax temperature to improve fidelity
• Ensemble student: Using multiple simple models to collectively achieve higher fidelity

Continuous tracking of student-teacher agreement in production to detect fidelity degradation caused by data distribution shifts or model updates. Essential for maintaining trustworthy explanations over time.

• Drift metrics: Tracking fidelity scores across time windows
• Alerting thresholds: Automated notifications when fidelity drops below acceptable levels
• Retraining triggers: Initiating student retraining when drift exceeds bounds
• Attribution comparison: Monitoring if feature importance explanations remain consistent