Much of our understanding of human thinking is based on probabilistic models. This innovative book by Jerome R. Busemeyer and Peter D. Bruza argues that, actually, the underlying mathematical structures from quantum theory provide a much better account of human thinking than traditional models. They introduce the foundations for modelling probabilistic-dynamic systems using two aspects of quantum theory. The first, 'contextuality', is a way to understand interference effects found with inferences and decisions under conditions of uncertainty. The second, 'quantum entanglement', allows cognitive phenomena to be modeled in non-reductionist ways. Employing these principles drawn from quantum theory allows us to view human cognition and decision in a totally new light. Introducing the basic principles in an easy-to-follow way, this book does not assume a physics background or a quantum brain and comes complete with a tutorial and fully worked-out applications in important areas of cognition and decision.

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Quantum Models of Cognition and Decision

Metaheuristic design of feedforward neural networks

In recent years the Probabilistic Neural Network (PPN) has been used in a large number of applications due to its simplicity and efficiency. PNN assigns the test data to the class with maximum likelihood compared with other classes. Likelihood of the test data to each training data is computed in the pattern layer through a kernel density estimation using a simple Bayesian rule. The kernel is usually a standard probability distribution function such as a Gaussian function. A spread parameter is used as a global parameter which determines the width of the kernel. The Bayesian rule in the pattern layer estimates the conditional probability of each class given an input vector without considering any probable local densities or heterogeneity in the training data. In this paper, an enhanced and generalized PNN (EPNN) is presented using local decision circles (LDCs) to overcome the aforementioned shortcoming and improve its robustness to noise in the data. Local decision circles enable EPNN to incorporate local information and non-homogeneity existing in the training population. The circle has a radius which limits the contribution of the local decision. In the conventional PNN the spread parameter can be optimized for maximum classification accuracy. In the proposed EPNN two parameters, the spread parameter and the radius of local decision circles, are optimized to maximize the performance of the model. Accuracy and robustness of EPNN are compared with PNN using three different benchmark classification problems, iris data, diabetic data, and breast cancer data, and five different ratios of training data to testing data: 90:10, 80:20, 70:30, 60:40, and 50:50. EPNN provided the most accurate results consistently for all ratios. Robustness of PNN and EPNN is investigated using different values of signal to noise ratio (SNR). Accuracy of EPNN is consistently higher than accuracy of PNN at different levels of SNR and for all ratios of training data to testing data.

Enhanced probabilistic neural network with local decision circles: A robust classifier

http://audition.ens.fr/dp/pdfs/pressnitzer-2006-bistable_AV_Authors_Manuscript.pdf

Temporal dynamics of auditory and visual bistability reveal common principles of perceptual organization

What are quantum fluctuations

A Learning Network Based on Qubit-Like Neuron Model.

We describe the results of computer simulations of the dynamical behavior of a neural network model based on BP learning incorporated with stochastic resonance (SR neural network). This model is effective in solving the XOR problem, as reported in our previous work. This network is a small scale network for practical engineering. In this study, therefore we apply 4 bits parity problem and investigate learning abilities in the enhanced network to establish our SR method. From the results of experiments, we see the learning abilities of our network is improve more than the limited abilities of the traditional BP learning network. We also observe the stochastic resonance in our network.

Stochastic resonance neural network and its performance

This paper presents a Cellular Automaton CA model designed for possible implementation by the reaction and diffusion of DNA strands. The proposed CA works asynchronously, whereby each cell undergoes its transitions independently from other cells and at random times. The state of a cell changes in a cyclic manner, rather than according to an any-to-any mapping. The transition rules are designed as totalistic, i.e., the next state of a cell is determined only by the number of states in the neighborhood of the cell, not by their relative positions. Universal circuit elements are designed for the CA as well as wires and crossings to connect them, which implies that the CA is Turing-complete.

Universal Totalistic Asynchonous Cellular Automaton and Its Possible Implementation byźDNA

This paper presents Quaternionic Bidirectional Auto-Associative Memory (QBAAM) that is an associative memory network storing patterns with multiple levels. A part of neurons in the network are quaternionic neurons, where their states are encoded by quaternion, which is a four-dimensional hypercomplex number system. These neurons can represent three kinds of discretized phases, i.e., three-dimensional multilevel values. The rest of neurons are conventional (real-valued) neurons. QBAAM is expected to have a rich representation ability by employing quaternionic neurons, as well as to have fewer spurious patterns in the network by a combination of real-valued and quaternionic neurons. The experimental results show that high robustness of noisy inputs is achieved by QBAAM, as compared with Quaternionic Hopfield Associative Memory where all neurons in the network are quaternionic neurons.

On the performance of Quaternionic Bidirectional Auto-Associative Memory

In reinforcement learning, it is necessary to introduce a process of trial and error called an exploration. As a generator for exploration, it seems to be familiar to use the uniform pseudorandom number generator. However, it is known that chaotic source also provides a random-like sequence as like as stochastic source. In this research, we propose an application of the random-like feature of deterministic chaos for a generator of the exploration. As a result, we find that the deterministic chaotic generator for the exploration based on the logistic map gives better performances than the stochastic random exploration generator in a nonstationary shortcut maze problem. In order to understand why the exploration generator based on the logistic map shows the better result, we investigate the learning structures obtained from the two exploration generators.

Nobuyuki Matsui

Papers

A Learning Network Based on Qubit-Like Neuron Model.

Stochastic resonance neural network and its performance

Universal Totalistic Asynchonous Cellular Automaton and Its Possible Implementation byźDNA

On the performance of Quaternionic Bidirectional Auto-Associative Memory

Effects of Chaotic Exploration on Reinforcement Maze Learning