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arXiv · 2505.23225

Generalizability vs. Counterfactual Explainability Trade-Off

Fabiano Veglianti·Flavio Giorgi·Fabrizio Silvestri·Gabriele Tolomei
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Abstract

In this work, we investigate the relationship between model generalization and counterfactual explainability in supervised learning. We introduce the notion of $\varepsilon$-valid counterfactual probability ($\varepsilon$-VCP) -- the probability of finding perturbations of a data point within its $\varepsilon$-neighborhood that result in a label change. We provide a theoretical analysis of $\varepsilon$-VCP in relation to the geometry of the model's decision boundary, showing that $\varepsilon$-VCP tends to increase with model overfitting. Our findings establish a rigorous connection between poor generalization and the ease of counterfactual generation, revealing an inherent trade-off between generalization and counterfactual explainability. Empirical results validate our theory, suggesting $\varepsilon$-VCP as a practical proxy for quantitatively characterizing overfitting.

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Fabiano Veglianti, Flavio Giorgi, Fabrizio Silvestri, Gabriele Tolomei. 2025-05-29. Generalizability vs. Counterfactual Explainability Trade-Off. https://arxiv.org/abs/2505.23225

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