arXiv subjects

Royal Skousen

Publications and source records attributed to Royal Skousen.

3 recordsLinked to original sources

arXiv2010

Quantum Analogical Modeling with Homogeneous Pointers

Quantum Analogical Modeling (QAM) works under the assumption that the correct exemplar-based description for a system of behavior minimizes the overall uncertainty of the system. The measure used in QAM differs from the traditional logarithmic measure of uncertainty; instead QAM uses a quadratic measure of disagreement between pairs of exemplars. (This quadratic measure parallels the squaring function holding between the amplitude and the probability for a state function in quantum mechanics.) QAM eliminates all supracontexts (contextual groupings of exemplars) that fail to minimize the number of disagreements. The resulting system thus distinguishes between homogeneous and heterogeneous supracontexts and uses only exemplars in homogeneous supracontexts to predict behavior. This paper revises earlier work on QAM (in 2005) by showing that homogeneity for a supracontext can be most simply determined by discovering whether there are any heterogeneous pointers between any of the supracontext's exemplars. A pointer for a pair of exemplars is heterogeneous whenever those two exemplars are found in different subcontexts of the supracontext and take different outcomes.

quant-ph↗

arXiv2005

Quantum Analogical Modeling: A General Quantum Computing Algorithm for Predicting Language Behavior

This paper proposes a general quantum algorithm that can be applied to any classical computer program. Each computational step is written using reversible operators, but the operators remain classical in that the qubits take on values of only zero and one. This classical restriction on the quantum states allows the copying of qubits, a necessary requirement for doing general classical computation. Parallel processing of the quantum algorithm proceeds because of the superpositioning of qubits, the only aspect of the algorithm that is strictly quantum mechanical. Measurement of the system collapses the superposition, leaving only one state that can be observed. In most instances, the loss of information as a result of measurement would be unacceptable. But the linguistically motivated theory of Analogical Modeling (AM) proposes that the probabilistic nature of language behavior can be accurately modeled in terms of the simultaneous analysis of all possible contexts (referred to as supracontexts) providing one selects a single supracontext from those supracontexts that are homogeneous in behavior (namely, supracontexts that allow no increase in uncertainty). The amplitude for each homogeneous supracontext is proportional to its frequency of occurrence, with the result that the probability of selecting one particular supracontext to predict the behavior of the system is proportional to the square of its frequency.

quant-ph↗

arXiv2000

Analogical Modeling and Quantum Computing

This paper serves as a bridge between quantum computing and analogical modeling (a general theory for predicting categories of behavior in varying contexts). Since its formulation in the early 1980s, analogical modeling has been successfully applied to a variety of problems in language. Several striking similarities between quantum mechanics and analogical modeling have recently been noted: (1) traditional statistics can be derived from a non-statistical basis by assuming data occurrences are accessed through a spin-up state (given two equally probable quantum states, spin-up and spin-down); (2) the probability of predicting a particular outcome is determined by the squaring of an underlying linear measure and is the result of decoherence (which occurs when a quantum system is observed); and (3) a natural measure of certainty (called the agreement) is based on one chance of guessing the right outcome and corresponds to the integrated squaring of Schroedinger's wave equation. Analogical modeling considers all possible combiantions of a given context of n variables, which is classical terms leads to an exponential explosion on the order of 2**n. This paper proposes a quantum computational solution to this exponentiality by applying a cycle of reversible quantum operators to all 2**n possibilities, thus reducing the time and space of analogical modeling to a polynomial order.

quant-ph↗