Gerard J. Rinkus

Gerard J. Rinkus

Quantum superposition says that any physical system simultaneously exists in all of its possible states, the number of which is exponential in the number of entities composing the system. The strength of presence of each possible state in the superposition, i.e., its probability of being observed, is represented by its probability amplitude coefficient. The assumption that these coefficients must be represented physically disjointly from each other, i.e., localistically, is nearly universal in the quantum theory/computing literature. Alternatively, these coefficients can be represented using sparse distributed representations (SDR), wherein each coefficient is represented by small subset of an overall population of units, and the subsets can overlap. Specifically, I consider an SDR model in which the overall population consists of Q WTA clusters, each with K binary units. Each coefficient is represented by a set of Q units, one per cluster. Thus, K^Q coefficients can be represented with KQ units. Thus, the particular world state, X, whose coefficient's representation, R(X), is the set of Q units active at time t has the max probability and the probability of every other state, Y_i, at time t, is measured by R(Y_i)'s intersection with R(X). Thus, R(X) simultaneously represents both the particular state, X, and the probability distribution over all states. Thus, set intersection may be used to classically implement quantum superposition. If algorithms exist for which the time it takes to store (learn) new representations and to find the closest-matching stored representation (probabilistic inference) remains constant as additional representations are stored, this meets the criterion of quantum computing. Such an algorithm has already been described: it achieves this "quantum speed-up" without esoteric hardware, and in fact, on a single-processor, classical (Von Neumann) computer.

Gerard J. Rinkus

Visual cortex's hierarchical, multi-level organization is captured in many biologically inspired computational vision models, the general idea being that progressively larger scale, more complex spatiotemporal features are represented in progressively higher areas. However, most earlier models use localist representations (codes) in each representational field, which we equate with the cortical macrocolumn (mac), at each level. In localism, each represented feature/event (item) is coded by a single unit. Our model, Sparsey, is also hierarchical but crucially, uses sparse distributed coding (SDC) in every mac in all levels. In SDC, each represented item is coded by a small subset of the mac's units. SDCs of different items can overlap and the size of overlap between items can represent their similarity. The difference between localism and SDC is crucial because SDC allows the two essential operations of associative memory, storing a new item and retrieving the best-matching stored item, to be done in fixed time for the life of the model. Since the model's core algorithm, which does both storage and retrieval (inference), makes a single pass over all macs on each time step, the overall model's storage/retrieval operation is also fixed-time, a criterion we consider essential for scalability to huge datasets. A 2010 paper described a nonhierarchical version of this model in the context of purely spatial pattern processing. Here, we elaborate a fully hierarchical model (arbitrary numbers of levels and macs per level), describing novel model principles like progressive critical periods, dynamic modulation of principal cells' activation functions based on a mac-level familiarity measure, representation of multiple simultaneously active hypotheses, a novel method of time warp invariant recognition, and we report results showing learning/recognition of spatiotemporal patterns.