arXiv subjects
Publications and source records attributed to Paul J. Werbos.
Inspired by previous studies and pioneers of the field, we present new results on an extensive EPR-Bell experiment using photons generated by parametric down conversion, where one of the photons is deliberately phase-shifted. Our experiments show some surprising results for particular angles of this phase shift.
This paper showed how a simple lumped parameter model of a circuit can yield correct quantum mechanical predictions of its behavior, even when there is quantum entanglement between components of that circuit. It addresses an important example, the circuit of the original Bell's Theorem experiments for ideal polarizers. Correct predictions emerge from two alternative simple but time-symmetric models based on classical Markov Random Field across space time. Exact agreement here does not violate Bell's Theorem itself, because the interplay between initial and final outcomes in these calculations does not fall within the CHSH definition of time forwards causality. Both models raise interesting questions for future research. The final section discusses several possible directions for following up on these results, both in lumped system modeling and in more general approaches. The final section proposed a new experiment with three-photon entanglement which could tell us which is true, local realistic MRF models and time-symmetric physics, or conventional predictions assuming the usual collapse of the wave function. The appendix worked out what the conventional predictions would be for the proposed experiment, and also gives a simple master equation version of the collapse assumption which does not involve metaphysical observers. Section A.4 gives the prediction for the new models.
This paper provides new stability results for Action-Dependent Heuristic Dynamic Programming (ADHDP), using a control algorithm that iteratively improves an internal model of the external world in the autonomous system based on its continuous interaction with the environment. We extend previous results by ADHDP control to the case of general multi-layer neural networks with deep learning across all layers. In particular, we show that the introduced control approach is uniformly ultimately bounded (UUB) under specific conditions on the learning rates, without explicit constraints on the temporal discount factor. We demonstrate the benefit of our results to the control of linear and nonlinear systems, including the cart-pole balancing problem. Our results show significantly improved learning and control performance as compared to the state-of-art.
The most powerful form of quantum learning system possible would somehow learn the parameters W of a quantum system f(X, W), for f representing the largest, most powerful set of possible input-output relations. This paper addresses the issue of how to enlarge the set represented by f, by using a new formulation of time-symmetric physics to model analog quantum computers based on spin and by exploring possible sources of backwards-time free energy so as to address problems of decoherence and dissipation.
A previous paper demonstrated that two local, realistic models based on Markov Random Fields (MRF) across space time do replicate the correct, tested predictions of quantum mechanics for simple Bell Theorem experiments. This paper demonstrates a third such model, MRF3, which is more plausible physically, making contact with the physics of polarizers. It shows how to translate that type of model into an equivalent quantum mechanical model, which requires an augmentation to the usual measurement operator now used to represent polarizers in such experiments. The validity of that augmentation may be testable in experiments involving three or four photons, with relevance to quantum computing and communication.
This paper begins by reviewing the general form of the Glauber-Sudarshan P mapping, a cornerstone of coherence theory in quantum optics, which defines a two-way mapping between ensembles of states S of any classical Hamiltonian field theory and a subset of the allowed density matrices ρ in the corresponding canonical bosonic quantum field theory (QFT). It has been proven that Tr(Hρ)=E(S), where E is the classical energy and H is the normal form Hamiltonian. The new result of this paper is that ensembles of S of definite energy E map into density matrices which are mixes of eigenstates of eigenvalue zero of N(H-E,H-E) where N represents the normal product. This raises interesting questions and opportunities for future research, including questions about the relation between canonical QFT and QFT in the Feynman path formulation. In the Appendix, a corresponding Boltzmann distribution is shown, using a dual version of the P mapping, for the case of statistically compressible dynamical systems.
Classical adaptive control proves total-system stability for control of linear plants, but only for plants meeting very restrictive assumptions. Approximate Dynamic Programming (ADP) has the potential, in principle, to ensure stability without such tight restrictions. It also offers nonlinear and neural extensions for optimal control, with empirically supported links to what is seen in the brain. However, the relevant ADP methods in use today -- TD, HDP, DHP, GDHP -- and the Galerkin-based versions of these all have serious limitations when used here as parallel distributed real-time learning systems; either they do not possess quadratic unconditional stability (to be defined) or they lead to incorrect results in the stochastic case. (ADAC or Q-learning designs do not help.) After explaining these conclusions, this paper describes new ADP designs which overcome these limitations. It also addresses the Generalized Moving Target problem, a common family of static optimization problems, and describes a way to stabilize large-scale economic equilibrium models, such as the old long-term energy model of DOE.
The underlying dynamics (\partialtψ=iHψ) of quantum electrodynamics are symmetric with respect to time (T and CPT), but traditional calculations and designs in electronics and electromagnetics impose an observer formalism or causality constraints which assume a gross asymmetry between forwards time and backwards time. In 2008, I published a paper in the International Journal of Theoretical Physics (see arXiv:0801.1234) which describes how to construct physics based on the dynamics alone, without these extraneous assumptions. It pointed out that this changes certain predictions of physics in a testable way, and that evidence from experiment favors the new and simpler versions of quantum theory. This disclosure follows up on that paper, by describing methods for circuit design based on the new physics. It provides a striking example - how to design a quantum separator (QS), which separates out the eigenfunctions which supply ordinary time-forwards free energy from the time-inverted eigenfunctions, when the QS is connected to bidirectional power supplies now under development in several places.
Brain-Like Stochastic Search (BLiSS) refers to this task: given a family of utility functions U(u,A), where u is a vector of parameters or task descriptors, maximize or minimize U with respect to u, using networks (Option Nets) which input A and learn to generate good options u stochastically. This paper discusses why this is crucial to brain-like intelligence (an area funded by NSF) and to many applications, and discusses various possibilities for network design and training. The appendix discusses recent research, relations to work on stochastic optimization in operations research, and relations to engineering-based approaches to understanding neocortex.
At present, there exists no physically plausible example of a quantum field theory for which the existence of solutions has been proven mathematically. The Clay Mathematics Institute has offered a prize for proving existence for a class of Yang-Mills theories defined by Jaffe and Witten. This paper proposes a multi-stage strategy for proving existence for a quantum version of the "'tHooft Polyakov" (tP) field theory, and argues that this theory, while not renormalizable or physically plausible as it stands, opens up a clear path to a physically plausible well-defined theory. The key initial challenge is to first prove stability for a classical version of this theory, in the spirit of Walter Strauss. The stability results of Bogomolnyi for classical PDE systems are widely cited as a foundation of string theory, but they leave key questions unaddressed, and may even call for small modifications of the tP model itself. This paper calls attention to the questions which require more attention, and proposes some partial possible answers. It also specifies a new numerical method to check for stability for the usual "hedgehog" types of solution, a method which may have broader potential uses for any ODE problems where accuracy in derivatives is as important as accuracy in function values.
Mathematical tools related to coherence theory and classical-quantum equivalence, due to Wigner and Glauber, are essential to modern, practical and empirical understanding of electromagnetics in areas like quantum optics and nanoelectronics. This paper specifies how an extension of these same tools (especially Glauber's "Q" mapping) can be applied to strong nuclear forces as well, and provides a "bottom-up" approach to axiomatic unification of physics, grounded in empirical reality (dice included). The Q hypothesis also has implications for quantum measurement and quantum information technology. The basic hypothesis is that density matrices across all of quantum field theory can be "decoded" or mapped usefully into probability distributions for "classical" fields, by using a generalization of Glauber's Q mapping, which does the same for electromagnetics.
The classic "Bell's Theorem" of Clauser, Holt, Shimony and Horne tells us that we must give up at least one of: (1) objective reality (aka "hidden variables"); (2) locality; or (3) time-forwards macroscopic statistics (aka "causality"). The orthodox Copenhagen version of physics gives up the first. The many-worlds theory of Everett and Wheeler gives up the second. The backwards-time theory of physics (BTP) gives up the third. Contrary to conventional wisdom, empirical evidence strongly favors Everett-Wheeler over orthodox Copenhagen. BTP has two major variations -- a many-worlds version, and a neoclassical version of partial differential equations (PDE) in the spirit of Einstein. Section 2 discusses quantum measurement according to BTP, focusing on how we represent condensed matter objects like polarizers in a Bell's Theorem experiment or in tests of Hawking's cosmology. The Backwards Time Telegraph, though speculative, is discussed.
Many have argued that research on grand unification or local realistic physics will not be truly relevant until it makes predictions verified by experiment, different from the prediction of prior theory (the standard model). This paper proposes a new strategy (and candidate Lagrangians) for such models; that strategy in turn calls for reconsideration of Schwinger's magnetic model of matter. High priority should be given to experiments which fully confirm or deny recent scattering calculations which suggest the presence of van der Waals effects in low energy p-p and pi-pi scattering, consistent with Schwinger's model and inconsistent with QCD as we know it (with a mass gap). I briefly discuss other evidence, which does not yet rule out Schwinger's theory. A recent analysis of hadron masses also seems more consistent with the Schwinger model than with QCD.
Cellular Simultaneous Recurrent Neural Network (SRN) has been shown to be a function approximator more powerful than the MLP. This means that the complexity of MLP would be prohibitively large for some problems while SRN could realize the desired mapping with acceptable computational constraints. The speed of training of complex recurrent networks is crucial to their successful application. Present work improves the previous results by training the network with extended Kalman filter (EKF). We implemented a generic Cellular SRN and applied it for solving two challenging problems: 2D maze navigation and a subset of the connectedness problem. The speed of convergence has been improved by several orders of magnitude in comparison with the earlier results in the case of maze navigation, and superior generalization has been demonstrated in the case of connectedness. The implications of this improvements are discussed.
Since the 1960s I proposed that we could understand and replicate the highest level of intelligence seen in the brain, by building ever more capable and general systems for adaptive dynamic programming (ADP), which is like reinforcement learning but based on approximating the Bellman equation and allowing the controller to know its utility function. Growing empirical evidence on the brain supports this approach. Adaptive critic systems now meet tough engineering challenges and provide a kind of first-generation model of the brain. Lewis, Prokhorov and myself have early second-generation work. Mammal brains possess three core capabilities, creativity/imagination and ways to manage spatial and temporal complexity, even beyond the second generation. This paper reviews previous progress, and describes new tools and approaches to overcome the spatial complexity gap.
This paper suggests that traditional fermi-bose quantum field theories (QFT) in 3+1-D, like the standard model of physics, may often be exactly equivalent to the limiting case of a family of bosonic QFT (BQFT) which generate soliton solutions and are "finite." They are "finite" in the sense of being well-defined mathematically even without regularization or renormalization, though the coupling coefficients would of course be so large that we must use nonperturbative methods for the analysis. Proof of this would open the door to a completely finite, well-defined unification of physics without a need to postulate additional unobserved dimensions of space-time. Axiomatic existence of the BQFT is discussed. Possible relevance to empirical QCD is noted briefly at the end.
Traditional discussions of the Second Law of Thermodynamics studied the limits of very specific types of devices, such as heat engines, chemical reactions, and molecules channeled by valves. Allahverdyan and Nieuwenhuizen (cond-mat/0110422) have come the closest to proving a more general form of the Second Law, applicable to field effect devices -- but recently (cond-mat/0408537) they have observed counterexamples and loopholes. This paper discusses recent field effect nanotechnologies which might permit a more substantial counterexample. Efforts were made to disprove the possibility of extracting electricity from ambient heat, from another perspective -- but these efforts led only to a new result on the equivalence of classical and quantum statistics, which may be important to the backwards-time interpretation of quantum mechanics.
This paper proposes an approach to framing and answering fundamental questions about consciousness. It argues that many of the more theoretical debates about consciousness, such as debates about "when does it begin?", are misplaced and meaningless, in part because "consciousness" as a word has many valid and interesting definitions, and in part because consciousness qua mind or intelligence (the main focus here)is a matter of degree or level, not a binary variable. It proposes that new mathematical work related to functional neural network designs -- designs so functional that they can be used in engineering -- is essential to a functional understanding of intelligence as such, and outlines some key mathematics as of 1999, citing earlier work for more details. Quantum theory is relevant, but not in the simple ways proposed in more popular philosophies.