Solving constraint-satisfaction problems with distributed neocortical-like neuronal networks

Finding actions that satisfy the constraints imposed by both external inputs and internal representations is central to decision making. We demonstrate that some important classes of constraint satisfaction problems (CSPs) can be solved by networks composed of homogeneous cooperative-competitive modules that have connectivity similar to motifs observed in the superficial layers of neocortex. The winner-take-all modules are sparsely coupled by programming neurons that embed the constraints onto the otherwise homogeneous modular computational substrate. We show rules that embed any instance of the CSPs planar four-color graph coloring, maximum independent set, and Sudoku on this substrate, and provide mathematical proofs that guarantee these graph coloring problems will convergence to a solution. The network is composed of non-saturating linear threshold neurons. Their lack of right saturation allows the overall network to explore the problem space driven through the unstable dynamics generated by recurrent excitation. The direction of exploration is steered by the constraint neurons. While many problems can be solved using only linear inhibitory constraints, network performance on hard problems benefits significantly when these negative constraints are implemented by non-linear multiplicative inhibition. Overall, our results demonstrate the importance of instability rather than stability in network computation, and also offer insight into the computational role of dual inhibitory mechanisms in neural circuits.Comment: Accepted manuscript, in press, Neural Computation (2018

Learning as a Nonlinear Line of Attraction for Pattern Association, Classification and Recognition

Development of a mathematical model for learning a nonlinear line of attraction is presented in this dissertation, in contrast to the conventional recurrent neural network model in which the memory is stored in an attractive fixed point at discrete location in state space. A nonlinear line of attraction is the encapsulation of attractive fixed points scattered in state space as an attractive nonlinear line, describing patterns with similar characteristics as a family of patterns. It is usually of prime imperative to guarantee the convergence of the dynamics of the recurrent network for associative learning and recall. We propose to alter this picture. That is, if the brain remembers by converging to the state representing familiar patterns, it should also diverge from such states when presented by an unknown encoded representation of a visual image. The conception of the dynamics of the nonlinear line attractor network to operate between stable and unstable states is the second contribution in this dissertation research. These criteria can be used to circumvent the plasticity-stability dilemma by using the unstable state as an indicator to create a new line for an unfamiliar pattern. This novel learning strategy utilizes stability (convergence) and instability (divergence) criteria of the designed dynamics to induce self-organizing behavior. The self-organizing behavior of the nonlinear line attractor model can manifest complex dynamics in an unsupervised manner. The third contribution of this dissertation is the introduction of the concept of manifold of color perception. The fourth contribution of this dissertation is the development of a nonlinear dimensionality reduction technique by embedding a set of related observations into a low-dimensional space utilizing the result attained by the learned memory matrices of the nonlinear line attractor network. Development of a system for affective states computation is also presented in this dissertation. This system is capable of extracting the user\u27s mental state in real time using a low cost computer. It is successfully interfaced with an advanced learning environment for human-computer interaction

Cortical free association dynamics: distinct phases of a latching network

A Potts associative memory network has been proposed as a simplified model of macroscopic cortical dynamics, in which each Potts unit stands for a patch of cortex, which can be activated in one of S local attractor states. The internal neuronal dynamics of the patch is not described by the model, rather it is subsumed into an effective description in terms of graded Potts units, with adaptation effects both specific to each attractor state and generic to the patch. If each unit, or patch, receives effective (tensor) connections from C other units, the network has been shown to be able to store a large number p of global patterns, or network attractors, each with a fraction a of the units active, where the critical load p_c scales roughly like p_c ~ (C S^2)/(a ln(1/a)) (if the patterns are randomly correlated). Interestingly, after retrieving an externally cued attractor, the network can continue jumping, or latching, from attractor to attractor, driven by adaptation effects. The occurrence and duration of latching dynamics is found through simulations to depend critically on the strength of local attractor states, expressed in the Potts model by a parameter w. Here we describe with simulations and then analytically the boundaries between distinct phases of no latching, of transient and sustained latching, deriving a phase diagram in the plane w-T, where T parametrizes thermal noise effects. Implications for real cortical dynamics are briefly reviewed in the conclusions

Neural Networks With Asynchronous Control.

Neural network studies have previously focused on monolithic structures. The brain has a bicameral nature, however, and so it is natural to expect that bicameral structures will perform better. This dissertation offers an approach to the development of such bicameral structures. The companion neural structure takes advantage of the global and subset characteristics of the stored memories. Specifically we propose the use of an asynchronous controller C that implies the following update of a probe vector x by the connection matrix T: x\sp\prime = sgn (C(x, TX)). For a VLSI-implemented neural network the controller block can be easily placed in the feedback loop. In a network running asynchronously, the updating of the probe generally offers a choice among several components. If the right components are not updated the network may converge to an incorrect stable point. The proposed asynchronous controller together with the basic neural net forms a bicameral network that can be programmed in various ways to exploit global and local characteristics of stored memory. Several methods to do this are proposed. In one of the methods the update choices are based on bit frequencies. In another method handles are appended to the memories to improve retrieval. The new methods have been analyzed and their performance studies it is shown that there is a marked improvement in performance. This is illustrated by means of simulations. The use of an asynchronous controller allows the implementation of conditional rules that occur frequently in AI applications. It is shown that a neural network that uses conditional rules can solve problems in natural language understanding. The introduction of the asynchronous controller may be viewed as a first step in the development of truly bicameral structures that may be seen as the next generation of neural computers

Metaheuristic design of feedforward neural networks: a review of two decades of research

Over the past two decades, the feedforward neural network (FNN) optimization has been a key interest among the researchers and practitioners of multiple disciplines. The FNN optimization is often viewed from the various perspectives: the optimization of weights, network architecture, activation nodes, learning parameters, learning environment, etc. Researchers adopted such different viewpoints mainly to improve the FNN's generalization ability. The gradient-descent algorithm such as backpropagation has been widely applied to optimize the FNNs. Its success is evident from the FNN's application to numerous real-world problems. However, due to the limitations of the gradient-based optimization methods, the metaheuristic algorithms including the evolutionary algorithms, swarm intelligence, etc., are still being widely explored by the researchers aiming to obtain generalized FNN for a given problem. This article attempts to summarize a broad spectrum of FNN optimization methodologies including conventional and metaheuristic approaches. This article also tries to connect various research directions emerged out of the FNN optimization practices, such as evolving neural network (NN), cooperative coevolution NN, complex-valued NN, deep learning, extreme learning machine, quantum NN, etc. Additionally, it provides interesting research challenges for future research to cope-up with the present information processing era

A Theory of Cortical Neural Processing.

This dissertation puts forth an original theory of cortical neural processing that is unique in its view of the interplay of chaotic and stable oscillatory neurodynamics and is meant to stimulate new ideas in artificial neural network modeling. Our theory is the first to suggest two new purposes for chaotic neurodynamics: (i) as a natural means of representing the uncertainty in the outcome of performed tasks, such as memory retrieval or classification, and (ii) as an automatic way of producing an economic representation of distributed information. We developed new models, to better understand how the cerebral cortex processes information, which led to our theory. Common to these models is a neuron interaction function that alternates between excitatory and inhibitory neighborhoods. Our theory allows characteristics of the input environment to influence the structural development of the cortex. We view low intensity chaotic activity as the a priori uncertain base condition of the cortex, resulting from the interaction of a multitude of stronger potential responses. Data, distinguishing one response from many others, drives bifurcations back toward the direction of less complex (stable) behavior. Stability appears as temporary bubble-like clusters within the boundaries of cortical columns and begins to propagate through frequency sensitive and non-specific neurons. But this is limited by destabilizing long-path connections. An original model of the post-natal development of ocular dominance columns in the striate cortex is presented and compared to autoradiographic images from the literature with good matching results. Finally, experiments are shown to favor computed update order over traditional approaches for better performance of the pattern completion process

Hypersonic Vehicle Trajectory Optimization and Control

Two classes of neural networks have been developed for the study of hypersonic vehicle trajectory optimization and control. The first one is called an 'adaptive critic'. The uniqueness and main features of this approach are that: (1) they need no external training; (2) they allow variability of initial conditions; and (3) they can serve as feedback control. This is used to solve a 'free final time' two-point boundary value problem that maximizes the mass at the rocket burn-out while satisfying the pre-specified burn-out conditions in velocity, flightpath angle, and altitude. The second neural network is a recurrent network. An interesting feature of this network formulation is that when its inputs are the coefficients of the dynamics and control matrices, the network outputs are the Kalman sequences (with a quadratic cost function); the same network is also used for identifying the coefficients of the dynamics and control matrices. Consequently, we can use it to control a system whose parameters are uncertain. Numerical results are presented which illustrate the potential of these methods