arXiv AI By Antonio Di Cecco

The Quadrilateral Loss: Additivity as a Measurable Behavior of Dense Neural Networks

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arXiv:2607. 20201v1 Announce Type: cross Abstract: Additive models buy interpretability by forbidding feature interactions, a constraint that neural instantiations enforce architecturally.

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The Quadrilateral Loss: Additivity as a Measurable Behavior of Dense Neural Networks

Additive models buy interpretability by forbidding feature interactions, a constraint that neural instantiations enforce architecturally. We introduce the quadrilateral loss, a differentiable penalty that treats additivity as a measurable behavior instead: a second-order mixed difference on pairs of training points swapping one coordinate, which vanishes if and only if the coordinate carries no interaction, remains informative for piecewise-linear networks, and equals in expectation the per-coordinate interaction mass of the interventional Shapley-GAM.