Interconnections of Quantum, Machine and Human Learning.

In earlier work, this author has explained the robustness of nonlinear multilayer machine learning algorithms in terms of an intrinsic chaos of the logistic map. Moreover we have connected that dynamics to a spectral concentration which occurs in bounded-to-free quantum transitions. From these, one may formulate a fundamental irreversibility common to both machine and quantum learning. Second, in recent work this author has treated both the Bell and Zeno paradoxes of quantum measurement theory. Deep unresolved issues are exposed and analyzed. A fundamental new theorem on quantum mechanical reversibility is presented. From such viewpoint, one may see more deeply the issue of decoherence in any quantum computing architecture. Third, in our examinations of human learning, we compared actual human decision processes against those of several A.I. learning schemes. We were struck by the repeated tendency of humans to go to great lengths to avoid a choice that includes a contradiction. That will be contrasted with quantum learning, which permits, at least probabilistically, contradictory conclusions. Introduction and Overview This paper is comprised of 8 sections, the first being this one. The organization, as implied by the paper’s title, is to look at certain interconnections of quantum, machine, and human learning, taken two at a time. Sections 2 and 3 begin with certain interconnections of quantum and machine learning. Sections 4 and 5 look at certain interconnections of human and machine learning. Sections 6 and 7 consider potential interconnections of human and quantum learning. Section 8 is a short summary. The References are selective and reflect only this authors investigations and thoughts, also a few directly related papers in order to give some perspective. A brief overview is as follows. Section 2 presents a connection this author found some years ago between the machine learning algorithms such as Backpropagation or other nonlinear multilayer perception architectures, and certain quantum transitions. The link is the discrete logistic map of dynamical systems theory. Section 3 looks at some issues the author has considered for a long time, in quantum measurement theory, as they may relate to the grand Copyright c © 2007, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. goal of quantum computing. Quantum computing investigations are normally developed in analogy with digital computing paradigms but with qubits replacing bits. By use of qubits one can in theory often show that an exponential time digital algorithm becomes polynomial time on a quantum computer. But in practice, that is, in the very few quantum computing hardwares that have actually been built to date, it is very difficult to maintain a quantum memory state for more than a very short time. This problem of decoherence is very much related to longstanding issues in quantum measurement theory. Turning to human versus (classical, e.g., digital) machine learning, Section 4 reviews our earlier work which compared certain A.I. learning schemes with actual human learning experiences on the same data set. Then Section 5 compares our method of generalization, which we called backprediction, to recent studies of learning based upon Boolean concepts and Boolean complexity. Essentially, we will claim that there are a number of additional factors that importantly affect the learning behavior of humans. Finally Sections 6 and 7 consider, in somewhat speculative fashion, some contrasts and comparisons of human and quantum learning. One of these is our finding in our human learning studies that humans will go to great lengths to avoid a choice that involves a contradiction. Quantum mechanics on the other hand has no such limitation, the most famous example being Schrodinger’s cat which is both dead and alive. We also consider briefly the issues of human and quantum consciousness. It is apparent that none of the investigations which we describe in this paper are finished. Indeed, as corollary we may say that we have here just scratched the surface of these various two-way and three-way interconnections. The paper may thus be viewed as exploratory. Hopefully, further investigations, study, and thought will follow. Interconnection of Machine and Quantum Learning In earlier work (Gustafson 1990, Gustafson 1997a,b, Gustafson 1998a,b,c, Gustafson and Sartoris 1998, Gustafson 2002b) this author has connected the convergence properties of nonlinear multilayer machine learning algorithms to the dynamics of the logistic map of dynamical systems theory. In particular, it was shown how an intrinsic ergodic chaos, which occurs when learning gain becomes large enough, can explain the robustness of these algorithms in practice. The basic connection can be established from the three maps: the sigmoid map f ′(x) = βf(x)(1− f(x)); the weight update map ∆w`j = ηf (net)(t` − o`)oj ; and the discrete logistic map