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

Simultaneous identification, tracking control and disturbance rejection of uncertain nonlinear dynamics systems: A unified neural approach

Previous works of traditional zeroing neural networks (or termed Zhang neural networks, ZNN) show great success for solving specific time-variant problems of known systems in an ideal environment. However, it is still a challenging issue for the ZNN to effectively solve time-variant problems for uncertain systems without the prior knowledge. Simultaneously, the involvement of external disturbances in the neural network model makes it even hard for time-variant problem solving due to the intensively computational burden and low accuracy. In this paper, a unified neural approach of simultaneous identification, tracking control and disturbance rejection in the framework of the ZNN is proposed to address the time-variant tracking control of uncertain nonlinear dynamics systems (UNDS). The neural network model derived by the proposed approach captures hidden relations between inputs and outputs of the UNDS. The proposed model shows outstanding tracking performance even under the influences of uncertainties and disturbances. Then, the continuous-time model is discretized via Euler forward formula (EFF). The corresponding discrete algorithm and block diagram are also presented for the convenience of implementation. Theoretical analyses on the convergence property and discretization accuracy are presented to verify the performance of the neural network model. Finally, numerical studies, robot applications, performance comparisons and tests demonstrate the effectiveness and advantages of the proposed neural network model for the time-variant tracking control of UNDS

A Dynamical System Approach to modeling Mental Exploration

The hippocampal-entorhinal complex plays an essential role within the brain in spatial navigation, mapping a spatial path onto a sequence of cells that reaction potentials. During rest or sleep, these sequences are replayed in either reverse or forward temporal order; in some cases, novel sequences occur that may represent paths not yet taken, but connecting contiguous spatial locations. These sequences potentially play a role in the planning of future paths. In particular, mental exploration is needed to discover short-cuts or plan alternative routes. Hopeld proposed a two-dimensional planar attractor network as a substrate for the mental exploration. He extended the concept of a line attractor used for the ocular-motor apparatus, to a planar attractor that can memorize any spatial path and then recall this path in memory. Such a planar attractor contains an infinite number of fixed points for the dynamics, each fixed point corresponding to a spatial location. For symmetric connections in the network, the dynamics generally admits a Lyapunov energy function L. Movement through different fixed points is possible because of the continuous attractor structure. In this model, a key role is played by the evolution of a localized activation of the network, a "bump", that moves across this neural sheet that topographically represents space. For this to occur, the history of paths already taken is imprinted on the synaptic couplings between the neurons. Yet attractor dynamics would seem to preclude the bump from moving; hence, a mechanism that destabilizes the bump is required. The mechanism to destabilize such an activity bump and move it to other locations of the network involves an adaptation current that provides a form of delayed inhibition. Both a spin-glass and a graded-response approach are applied to investigating the dynamics of mental exploration mathematically. Simplifying the neural network proposed by Hopfield to a spin glass, I study the problem of recalling temporal sequences and explore an alternative proposal, that relies on storing the correlation of network activity across time, adding a sequence transition term to the classical instantaneous correlation term during the learning of the synaptic "adaptation current" is interpreted as a local field that can destabilize the equilibrium causing the bump to move. We can also combine the adaptation and transition term to show how the dynamics of exploration is affected. To obtain goal-directed searching, I introduce a weak external field associated with a rewarded location. We show how the bump trajectory then follows a suitable path to get to the target. For networks of graded-response neurons with weak external stimulation, amplitude equations known from pattern formation studies in bio-chemico- physical systems are developed. This allows me to predict the modes of network activity that can be selected by an external stimulus and how these modes evolve. Using perturbation theory and coarse graining, the dynamical equations for the evolution of the system are reduced from many sets of nonlinear integro-dierential equations for each neuron to a single macroscopic equation. This equation, in particular close to the transition to pattern formation, takes the form of the Landau Ginzburg equation. The parameters for the connections between the neurons are shown to be related to the parameters of the Landau-Ginzburg equation that governs the bump of activity. The role of adaptation within this approximation is studied, which leads to the discovery that the macroscopic dynamical equation for the system has the same structure of the coupled equations used to describe the propagation of the electrical activity within one single neuron as given by the Fitzhugh-Nagumo equations

Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network

Because of their effectiveness in broad practical applications, LSTM networks have received a wealth of coverage in scientific journals, technical blogs, and implementation guides. However, in most articles, the inference formulas for the LSTM network and its parent, RNN, are stated axiomatically, while the training formulas are omitted altogether. In addition, the technique of "unrolling" an RNN is routinely presented without justification throughout the literature. The goal of this paper is to explain the essential RNN and LSTM fundamentals in a single document. Drawing from concepts in signal processing, we formally derive the canonical RNN formulation from differential equations. We then propose and prove a precise statement, which yields the RNN unrolling technique. We also review the difficulties with training the standard RNN and address them by transforming the RNN into the "Vanilla LSTM" network through a series of logical arguments. We provide all equations pertaining to the LSTM system together with detailed descriptions of its constituent entities. Albeit unconventional, our choice of notation and the method for presenting the LSTM system emphasizes ease of understanding. As part of the analysis, we identify new opportunities to enrich the LSTM system and incorporate these extensions into the Vanilla LSTM network, producing the most general LSTM variant to date. The target reader has already been exposed to RNNs and LSTM networks through numerous available resources and is open to an alternative pedagogical approach. A Machine Learning practitioner seeking guidance for implementing our new augmented LSTM model in software for experimentation and research will find the insights and derivations in this tutorial valuable as well.Comment: 43 pages, 10 figures, 78 reference

Theory and applications of artificial neural networks

In this thesis some fundamental theoretical problems about artificial neural networks and their application in communication and control systems are discussed. We consider the convergence properties of the Back-Propagation algorithm which is widely used for training of artificial neural networks, and two stepsize variation techniques are proposed to accelerate convergence. Simulation results demonstrate significant improvement over conventional Back-Propagation algorithms. We also discuss the relationship between generalization performance of artificial neural networks and their structure and representation strategy. It is shown that the structure of the network which represent a priori knowledge of the environment has a strong influence on generalization performance. A Theorem about the number of hidden units and the capacity of self-association MLP (Multi-Layer Perceptron) type network is also given in the thesis. In the application part of the thesis, we discuss the feasibility of using artificial neural networks for nonlinear system identification. Some advantages and disadvantages of this approach are analyzed. The thesis continues with a study of artificial neural networks applied to communication channel equalization and the problem of call access control in broadband ATM (Asynchronous Transfer Mode) communication networks. A final chapter provides overall conclusions and suggestions for further work

Neurocomputational Methods for Autonomous Cognitive Control

Artificial Intelligence can be divided between symbolic and sub-symbolic methods, with neural networks making up a majority of the latter. Symbolic systems have the advantage when capabilities such as deduction and planning are required, while sub-symbolic ones are preferable for tasks requiring skills such as perception and generalization. One of the domains in which neural approaches tend to fare poorly is cognitive control: maintaining short-term memory, inhibiting distractions, and shifting attention. Our own biological neural networks are more than capable of these sorts of executive functions, but artificial neural networks struggle with them. This work explores the gap between the cognitive control that is possible with both symbolic AI systems and biological neural networks, but not with artificial neural networks. To do so, I identify a set of general-purpose, regional-level functions and interactions that are useful for cognitive control in large-scale neural architectures. My approach has three main pillars: a region-and-pathway architecture inspired by the human cerebral cortex and biologically-plausible Hebbian learning, neural regions that each serve as an attractor network able to learn sequences, and neural regions that not only learn to exchange information but also to modulate the functions of other regions. The resultant networks have behaviors based on their own memory contents rather than exclusively on their structure. Because they learn not just memories of the environment but also procedures for tasks, it is possible to "program" these neural networks with the desired behaviors. This research makes four primary contributions. First, the extension of Hopfield-like attractor networks from processing only fixed-point attractors to processing sequential ones. This is accomplished via the introduction of temporally asymmetric weights to Hopfield-like networks, a novel technique that I developed. Second, the combination of several such networks to create models capable of autonomously directing their own performance of cognitive control tasks. By learning procedural memories for a task they can perform in ways that match those of human subjects in key respects. Third, the extension of this approach to spatial domains, binding together visuospatial data to perform a complex memory task at the same level observed in humans and a comparable symbolic model. Finally, these new memories and learning procedures are integrated so that models can respond to feedback from the environment. This enables them to improve as they gain experience by refining their own internal representations of their instructions. These results establish that the use of regional networks, sequential attractor dynamics, and gated connections provide an effective way to accomplish the difficult task of neurally-based cognitive control

Dynamics analysis and applications of neural networks

Ph.DDOCTOR OF PHILOSOPH

The hardware implementation of an artificial neural network using stochastic pulse rate encoding principles

In this thesis the development of a hardware artificial neuron device and artificial neural network using stochastic pulse rate encoding principles is considered. After a review of neural network architectures and algorithmic approaches suitable for hardware implementation, a critical review of hardware techniques which have been considered in analogue and digital systems is presented. New results are presented demonstrating the potential of two learning schemes which adapt by the use of a single reinforcement signal. The techniques for computation using stochastic pulse rate encoding are presented and extended with new novel circuits relevant to the hardware implementation of an artificial neural network. The generation of random numbers is the key to the encoding of data into the stochastic pulse rate domain. The formation of random numbers and multiple random bit sequences from a single PRBS generator have been investigated. Two techniques, Simulated Annealing and Genetic Algorithms, have been applied successfully to the problem of optimising the configuration of a PRBS random number generator for the formation of multiple random bit sequences and hence random numbers. A complete hardware design for an artificial neuron using stochastic pulse rate encoded signals has been described, designed, simulated, fabricated and tested before configuration of the device into a network to perform simple test problems. The implementation has shown that the processing elements of the artificial neuron are small and simple, but that there can be a significant overhead for the encoding of information into the stochastic pulse rate domain. The stochastic artificial neuron has the capability of on-line weight adaption. The implementation of reinforcement schemes using the stochastic neuron as a basic element are discussed