Certified Approximation for Interpretable Representer Landmarks

תקציר מקורי באנגליתarXiv:2609.38901v1 Announce Type: new Abstract: Representer explanations rank the training landmarks that most influence a self-supervised representation. At scale, this ranking rests on up to four stacked approximations of the empirical neural tangent kernel (eNTK). These are random output heads, a parameter sketch, landmark sampling and a coefficient fit. Existing analyses bound each approximation separately, but none certifies the top-$K$ set against their combined error. We introduce CAIRN (Certified Approximation for Interpretable Representer laNdmarks), a framework that carries this error through to the ranking. We derive the exact variance of the sketched multi-head eNTK, which matches measurement within $4\%$ where Johnson-Lindenstrauss bounds err by up to $2.5\times$. This yields