Thank you for the thoughtful comment. Your questions are valid given the title, which I used to make the post more accessible to a general HN audience. To clarify: the core distinction here is not kernelization vs kNN, but field evaluation vs point selection (or selection vs superposition as retrieval semantics). The kernel is just a concrete example.

FAISS implements selection (argmax ⟨q,v⟩), so vectors are discrete atoms and deletion must be structural. The weighted formulation represents a field: vectors act as sources whose influence superposes into a potential. Retrieval evaluates that field (or follows its gradient), not a point identity. In this regime, deletion is algebraic (append -v for cancellation), evaluation is sparse/local, and no index rebuild is required.

The paper goes into this in more detail.