Improved Predictive Performance and Interpretability for Mesomorphic Neural Networks Using Local Fidelity Regularization

Technical Summary: Improved Predictive Performance and Interpretability for Mesomorphic Neural Networks Using Local Fidelity Regularization

Problem Statement
Interpretable Mesomorphic Neural Networks (IMNs) were proposed to bridge the gap between the predictive power of deep learning and the interpretability of linear models. In an IMN, a neural network backbone dynamically generates weights for a linear output layer, allowing for instance-wise feature attribution. However, the original formulation suffers from a critical vulnerability: the model is underdetermined. Because the neural network backbone is highly expressive, it can achieve optimal predictive performance by collapsing all explanatory variance into a single weight (often the intercept) while suppressing others. This "degenerate" behavior results in predictions that are mathematically accurate but interpretations that are completely unfaithful to the underlying data relationships. Paradoxically, the L1 penalty originally proposed to encourage sparsity exacerbates this issue by incentivizing such degenerate configurations.

Methodology: Local Fidelity Regularization (LFR)
To address this, the authors introduce Local Fidelity Regularization (LFR), a novel penalty term designed to align the generated linear weights with the local variations present in the training data.

• Theoretical Basis: Ideally, the generated weights $w_j(x_i, \theta)$ should correspond to the partial derivatives of the prediction function with respect to each feature ($\nabla f(x_i)$). However, relying on analytical gradients is computationally expensive (requiring double backpropagation) and prone to capturing infinitesimal noise rather than macroscopic trends.
• SMOTE-Inspired Interpolation: To overcome these issues, LFR avoids exact derivatives. Instead, it constructs a local neighborhood around an anchor point $x_i$ by generating synthetic samples using a strategy inspired by the Synthetic Minority Over-sampling Technique (SMOTE). For a given anchor, $K$ synthetic points $\tilde{x}_k$ are created via linear interpolation with neighboring data points: $\tilde{x}_k = x_i + \alpha_k(x' - x_i)$.
• The Penalty: The LFR loss ($L_{LFR}$) enforces that the linear approximation anchored at $x_i$ (using the generated weights) must accurately extrapolate to the full neural network's prediction at these synthetic points. The penalty is the mean squared difference between the linear extrapolation and the full network forward pass across the synthetic neighborhood.
• Optimization: The total objective function combines the original prediction loss, the L1 sparsity penalty, and the new LFR penalty. The authors propose a tuning strategy using a composite score $S(\gamma)$ that balances predictive performance (e.g., AUROC or $R^2$) and explanation fidelity (measured by the reduction in infidelity relative to the unregularized model).

Key Contributions

1. Novel Regularization Mechanism: The introduction of LFR, which prevents weight collapse by grounding interpretations in the geometric structure of the data via local fidelity constraints.
2. Dual Performance Improvement: Empirical evidence demonstrating that LFR not only resolves interpretability flaws but also consistently enhances predictive performance, yielding results competitive with state-of-the-art black-box models.
3. Open-Source Implementation: A modular Python implementation of the LFR-IMN framework with a scikit-learn style API, made publicly available.

Experimental Results
The paper evaluates the proposed method across synthetic and real-world benchmarks:

• Synthetic Experiments: On a synthetic dataset with known ground-truth local effects (including interaction terms), the unregularized IMN failed to recover true effects, driving feature weights to near zero and absorbing magnitude into the intercept. In contrast, LFR-IMN successfully recovered the true local gradients. Notably, when using a complex TabResNet backbone, LFR-IMN achieved significantly lower test MSE (0.0244) compared to the unregularized IMN (0.0444), demonstrating that interpretability constraints can improve generalization.
• XAI-Bench Evaluation: Using the XAI-Bench framework with known ground-truth importances, the authors compared LFR-IMN against unregularized IMN and standard post-hoc explainers (LIME, SHAP) applied to black-box models. The study utilized a new metric, Scaled Infidelity, to measure the accuracy of local gradients. Results indicated that LFR-IMN provided highly faithful explanations while maintaining or improving predictive accuracy (AUROC) over the unregularized baseline.
• Real-World Benchmarks: Evaluations across the OpenML benchmark suite showed that LFR-IMN achieved AUROC scores highly competitive with top-tier methods like CatBoost and TabNet, without compromising accuracy for the sake of explainability.

Significance and Claims
The paper claims that LFR-IMN provides a dual benefit: it guarantees reliable, faithful interpretations by preventing the model from exploiting degenerate solutions, and it simultaneously improves predictive performance. The authors argue that, contrary to the common assumption of a trade-off between accuracy and interpretability, enforcing local fidelity can lead to more robust decision boundaries. The method is presented as a practical solution for safety-critical applications (e.g., healthcare, finance) where both high performance and trustworthy explanations are prerequisites. The work is supported by an open-source repository to facilitate adoption and further research.