Interpretability-Accuracy Tradeoff

The inherent capacity of the student model defines the upper bound of the tradeoff. A high-bias model like a linear proxy cannot faithfully capture a teacher's non-linear decision boundary, forcing a strict accuracy sacrifice. Conversely, a transparent-by-design student with higher capacity, such as an Explainable Boosting Machine (EBM), can achieve higher fidelity by learning additive feature functions with pairwise interactions. The structural prior—whether the student is a decision tree, GAM, or rule list—determines the shape of the achievable frontier.

The nature of the input data dictates the severity of the tradeoff. Problems with a low intrinsic dimensionality and strong, monotonic feature relationships are easily approximated by simple surrogates with minimal accuracy loss. However, tasks involving high-dimensional, unstructured data—like image recognition or raw text—require hierarchical feature extraction that is fundamentally opaque. In these regimes, a global surrogate will suffer a catastrophic fidelity drop, making local explanations or feature-based distillation necessary.

The tradeoff is measured by the specific fidelity metric chosen. Global fidelity—matching the teacher's predictions across the entire input space—is a stricter constraint than local fidelity, which only requires accuracy in the neighborhood of a specific instance. A decision tree surrogate may have poor global fidelity but serve as a perfect local explanation. Furthermore, fidelity can be measured on output logits (soft targets) or final class predictions, with the former preserving the teacher's dark knowledge and uncertainty calibration.

The temperature scaling parameter in distillation directly modulates the tradeoff. High temperatures soften the teacher's output distribution, revealing the dark knowledge of inter-class similarities and preventing the student from overfitting to the teacher's overconfident errors. This richer supervisory signal allows a simple student to achieve higher fidelity than training on hard labels alone. The optimal temperature balances the signal-to-noise ratio, transferring generalization ability without amplifying the teacher's miscalibration.

The sequence of training imposes different constraints on the tradeoff. In post-hoc distillation, the teacher is fixed and the student must adapt to its pre-existing decision boundary, which may be arbitrarily complex. In a distilled-by-design paradigm, the teacher can be regularized during its own training—via rule-regularized distillation or attention transfer—to produce smoother, more explainable internal representations. This co-design approach shifts the entire frontier, enabling high accuracy and high interpretability simultaneously.

The acceptable operating point on the tradeoff curve is determined by the deployment context. In high-stakes domains like credit underwriting or medical diagnosis, a legally mandated right to explanation may force the use of a fully transparent model, accepting a hard accuracy ceiling. In lower-stakes applications, a complex black-box model with post-hoc local surrogate explanations may be sufficient. The tradeoff is thus not purely technical but a socio-technical constraint defined by the cost of errors versus the cost of opacity.