Multiplicative coding and factorization in vector symbolic models of cognition

This dissertation covers my attempts to confront the challenge and promise of multiplicative representations, and their attendant factorization problems, in the brain. This is grounded in a paradigm for modeling cognition that defines an algebra over high-dimensional vectors and presents a compelling factorization problem. The proposed solution to this problem, a recurrent neural network architecture called Resonator Networks, has several interesting properties that make it uniquely effective on this problem and may provide some principles for designing a new class of neural network models. I show some applications of multiplicative distributed codes for representing visual scenes and suggest how such representations may be a useful tool for unifying symbolic and connectionist theories of intelligence