finding

active

finding:a-nonempty-convex-set-in-r-d-is-patch-closed-if-and-only-if-it-is-an-axis-aligned-hyperrectangle

A nonempty convex set in R^d is patch-closed if and only if it is an axis-aligned hyperrectangle

Mathematical characterization showing only hyperrectangles avoid divergence under coordinate patching

Source paper

extracted_from

Addressing divergent representations from causal interventions on neural networks

(2025) · Satchel Grant · Simon Jerome Han · Alexa R. Tartaglini · Christopher Potts

Neighborhood — ranked by edge-count

Findings (1)

finding

Coordinate patching on circular manifolds guarantees off-manifold representations for boundary point pairs with orthogonal deviations
supports
Theoretical proof that patching produces divergent representations for most manifold geometries

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