  In this paper we propose a generalization of the Kontsevich--Soibelman
conjecture on the degeneration of Hochschild-to-cyclic spectral sequence for
smooth and compact DG category. Our conjecture states identical vanishing of a
certain map between bi-additive invariants of arbitrary small DG categories
over a field of characteristic zero.
  We show that this generalized conjecture follows from the
Kontsevich--Soibelman conjecture and the so--called conjecture on smooth
categorical compactification.
