  We discuss memory models which are based on tensor decompositions using
latent representations of entities and events. We show how episodic memory and
semantic memory can be realized and discuss how new memory traces can be
generated from sensory input: Existing memories are the basis for perception
and new memories are generated via perception. We relate our mathematical
approach to the hippocampal memory indexing theory. We describe the first
detailed mathematical models for the complete processing pipeline from sensory
input and its semantic decoding, i.e., perception, to the formation of episodic
and semantic memories and their declarative semantic decodings. Our main
hypothesis is that perception includes an active semantic decoding process,
which relies on latent representations of entities and predicates, and that
episodic and semantic memories depend on the same decoding process. We
contribute to the debate between the leading memory consolidation theories,
i.e., the standard consolidation theory (SCT) and the multiple trace theory
(MTT). The latter is closely related to the complementary learning systems
(CLS) framework. In particular, we show explicitly how episodic memory can
teach the neocortex to form a semantic memory, which is a core issue in MTT and
CLS.
