Memories in context

Context-dependent associative memories are models that allow the retrieval of different vectorial responses given a same vectorial stimulus, depending on the context presented to the memory. The contextualization is obtained by doing the Kronecker product between two vectorial entries to the associative memory: the key stimulus and the context. These memories are able to display a wide variety of behaviors that range from all the basic operations of the logical calculus (including fuzzy logics) to the selective extraction of features from complex vectorial patterns. In the present contribution, we show that a context-dependent memory matrix stores a large amount of possible virtual associative memories, that awaken in the presence of a context. We show how the vectorial context allows a memory matrix to be representable in terms of its singular-value decomposition. We describe a neural interpretation of the model in which the Kronecker product is performed on the same neurons that sustain the memory. We explored, with numerical experiments, the reliability of chains of contextualized associations. In some cases, random disconnection produces the emergence of oscillatory behaviors of the system. Our results show that associative chains retain their performances for relatively large dimensions. Finally, we analyze the properties of some modules of context-dependent autoassociative memories inserted in recursive nets: the perceptual autoorganization in the presence of ambiguous inputs (e.g. the disambiguation of the Necker's cube figure), the construction of intersection filters, and the feature extraction capabilities.