The Synthesis of Arbitrary Stable Dynamics in Non-linear Neural Networks II: Feedback and Universality

We wish to construct a realization theory of stable neural networks and use this theory to model the variety of stable dynamics apparent in natural data. Such a theory should have numerous applications to constructing specific artificial neural networks with desired dynamical behavior. The networks used in this theory should have well understood dynamics yet be as diverse as possible to capture natural diversity. In this article, I describe a parameterized family of higher order, gradient-like neural networks which have known arbitrary equilibria with unstable manifolds of known specified dimension. Moreover, any system with hyperbolic dynamics is conjugate to one of these systems in a neighborhood of the equilibrium points. Prior work on how to synthesize attractors using dynamical systems theory, optimization, or direct parametric. fits to known stable systems, is either non-constructive, lacks generality, or has unspecified attracting equilibria. More specifically, We construct a parameterized family of gradient-like neural networks with a simple feedback rule which will generate equilibrium points with a set of unstable manifolds of specified dimension. Strict Lyapunov functions and nested periodic orbits are obtained for these systems and used as a method of synthesis to generate a large family of systems with the same local dynamics. This work is applied to show how one can interpolate finite sets of data, on nested periodic orbits.

The Sensor Network Workbench: Towards Functional Specification, Verification and Deployment of Constrained Distributed Systems

As the commoditization of sensing, actuation and communication hardware increases, so does the potential for dynamically tasked sense and respond networked systems (i.e., Sensor Networks or SNs) to replace existing disjoint and inflexible special-purpose deployments (closed-circuit security video, anti-theft sensors, etc.). While various solutions have emerged to many individual SN-centric challenges (e.g., power management, communication protocols, role assignment), perhaps the largest remaining obstacle to widespread SN deployment is that those who wish to deploy, utilize, and maintain a programmable Sensor Network lack the programming and systems expertise to do so. The contributions of this thesis centers on the design, development and deployment of the SN Workbench (snBench). snBench embodies an accessible, modular programming platform coupled with a flexible and extensible run-time system that, together, support the entire life-cycle of distributed sensory services. As it is impossible to find a one-size-fits-all programming interface, this work advocates the use of tiered layers of abstraction that enable a variety of high-level, domain specific languages to be compiled to a common (thin-waist) tasking language; this common tasking language is statically verified and can be subsequently re-translated, if needed, for execution on a wide variety of hardware platforms. snBench provides: (1) a common sensory tasking language (Instruction Set Architecture) powerful enough to express complex SN services, yet simple enough to be executed by highly constrained resources with soft, real-time constraints, (2) a prototype high-level language (and corresponding compiler) to illustrate the utility of the common tasking language and the tiered programming approach in this domain, (3) an execution environment and a run-time support infrastructure that abstract a collection of heterogeneous resources into a single virtual Sensor Network, tasked via this common tasking language, and (4) novel formal methods (i.e., static analysis techniques) that verify safety properties and infer implicit resource constraints to facilitate resource allocation for new services. This thesis presents these components in detail, as well as two specific case-studies: the use of snBench to integrate physical and wireless network security, and the use of snBench as the foundation for semester-long student projects in a graduate-level Software Engineering course.

Construction of Neural Network Classification Expert Systems Using Switching Theory Algorithms

A new family of neural network architectures is presented. This family of architectures solves the problem of constructing and training minimal neural network classification expert systems by using switching theory. The primary insight that leads to the use of switching theory is that the problem of minimizing the number of rules and the number of IF statements (antecedents) per rule in a neural network expert system can be recast into the problem of minimizing the number of digital gates and the number of connections between digital gates in a Very Large Scale Integrated (VLSI) circuit. The rules that the neural network generates to perform a task are readily extractable from the network's weights and topology. Analysis and simulations on the Mushroom database illustrate the system's performance.