The sample complexity of pattern classification with neural networks: the size of the weights is more important than the size of the network

Sample complexity results from computational learning theory, when applied to neural network learning for pattern classification problems, suggest that for good generalization performance the number of training examples should grow at least linearly with the number of adjustable parameters in the network. Results in this paper show that if a large neural network is used for a pattern classification problem and the learning algorithm finds a network with small weights that has small squared error on the training patterns, then the generalization performance depends on the size of the weights rather than the number of weights. For example, consider a two-layer feedforward network of sigmoid units, in which the sum of the magnitudes of the weights associated with each unit is bounded by A and the input dimension is n. We show that the misclassification probability is no more than a certain error estimate (that is related to squared error on the training set) plus A3 √((log n)/m) (ignoring log A and log m factors), where m is the number of training patterns. This may explain the generalization performance of neural networks, particularly when the number of training examples is considerably smaller than the number of weights. It also supports heuristics (such as weight decay and early stopping) that attempt to keep the weights small during training. The proof techniques appear to be useful for the analysis of other pattern classifiers: when the input domain is a totally bounded metric space, we use the same approach to give upper bounds on misclassification probability for classifiers with decision boundaries that are far from the training examples.

Stochastic models for regulatory networks of the genetic toggle switch

Bistability arises within a wide range of biological systems from the λ phage switch in bacteria to cellular signal transduction pathways in mammalian cells. Changes in regulatory mechanisms may result in genetic switching in a bistable system. Recently, more and more experimental evidence in the form of bimodal population distributions indicates that noise plays a very important role in the switching of bistable systems. Although deterministic models have been used for studying the existence of bistability properties under various system conditions, these models cannot realize cell-to-cell fluctuations in genetic switching. However, there is a lag in the development of stochastic models for studying the impact of noise in bistable systems because of the lack of detailed knowledge of biochemical reactions, kinetic rates, and molecular numbers. In this work, we develop a previously undescribed general technique for developing quantitative stochastic models for large-scale genetic regulatory networks by introducing Poisson random variables into deterministic models described by ordinary differential equations. Two stochastic models have been proposed for the genetic toggle switch interfaced with either the SOS signaling pathway or a quorum-sensing signaling pathway, and we have successfully realized experimental results showing bimodal population distributions. Because the introduced stochastic models are based on widely used ordinary differential equation models, the success of this work suggests that this approach is a very promising one for studying noise in large-scale genetic regulatory networks.

Stochastic simulation of chemical reactions in spatially complex media

Discrete stochastic simulations, via techniques such as the Stochastic Simulation Algorithm (SSA) are a powerful tool for understanding the dynamics of chemical kinetics when there are low numbers of certain molecular species. However, an important constraint is the assumption of well-mixedness and homogeneity. In this paper, we show how to use Monte Carlo simulations to estimate an anomalous diffusion parameter that encapsulates the crowdedness of the spatial environment. We then use this parameter to replace the rate constants of bimolecular reactions by a time-dependent power law to produce an SSA valid in cases where anomalous diffusion occurs or the system is not well-mixed (ASSA). Simulations then show that ASSA can successfully predict the temporal dynamics of chemical kinetics in a spatially constrained environment.

Propagation of low power low divergence Gaussian fields in unbiased self-defocusing photorefractive media and their interactions

Many optical networks are limited in speed and processing capability due to the necessity for the optical signal to be converted to an electrical signal and back again. In addition, electronically manipulated interconnects in an otherwise optical network lead to overly complicated systems. Optical spatial solitons are optical beams that propagate without spatial divergence. They are capable of phase dependent interactions, and have therefore been extensively researched as suitable all optical interconnects for over 20 years. However, they require additional external components, initially high voltage power sources were required, several years later, high power background illumination had replaced the high voltage. However, these additional components have always remained as the greatest hurdle in realising the applications of the interactions of spatial optical solitons as all optical interconnects. Recently however, self-focusing was observed in an otherwise self-defocusing photorefractive crystal. This observation raises the possibility of the formation of soliton-like fields in unbiased self-defocusing media, without the need for an applied electrical field or background illumination. This thesis will present an examination of the possibility of the formation of soliton-like low divergence fields in unbiased self-defocusing photorefractive media. The optimal incident beam and photorefractive media parameters for the formation of these fields will be presented, together with an analytical and numerical study of the effect of these parameters. In addition, preliminary examination of the interactions of two of these fields will be presented. In order to complete an analytical examination of the field propagating through the photorefractive medium, the spatial profile of the beam after propagation through the medium was determined. For a low power solution, it was found that an incident Gaussian field maintains its Gaussian profile as it propagates. This allowed the beam at all times to be described by an individual complex beam parameter, while also allowing simple analytical solutions to the appropriate wave equation. An analytical model was developed to describe the effect of the photorefractive medium on the Gaussian beam. Using this model, expressions for the required intensity dependent change in both the real and imaginary components of the refractive index were found. Numerical investigation showed that under certain conditions, a low powered Gaussian field could propagate in self-defocusing photorefractive media with divergence of approximately 0.1 % per metre. An investigation into the parameters of a Ce:BaTiO3 crystal showed that the intensity dependent absorption is wavelength dependent, and can in fact transition to intensity dependent transparency. Thus, with careful wavelength selection, the required intensity dependent change in both the real and imaginary components of the refractive index for the formation of a low divergence Gaussian field are physically realisable. A theoretical model incorporating the dependence of the change in real and imaginary components of the refractive index on propagation distance was developed. Analytical and numerical results from this model are congruent with the results from the previous model, showing low divergence fields with divergence less than 0.003 % over the propagation length of the photorefractive medium. In addition, this approach also confirmed the previously mentioned self-focusing effect of the self-defocusing media, and provided an analogy to a negative index GRIN lens with an intensity dependent focal length. Experimental results supported the findings of the numerical analysis. Two low divergence fields were found to possess the ability to interact in a Ce:BaTiO3 crystal in a soliton-like fashion. The strength of these interactions was found to be dependent on the degree of divergence of the individual beams. This research found that low-divergence fields are possible in unbiased self-defocusing photorefractive media, and that soliton-like interactions between two of these fields are possible. However, in order for these types of fields to be used in future all optical interconnects, the manipulation of these interactions, together with the ability for these fields to guide a second beam at a different wavelength, must be investigated.

Computational approaches for modelling intrinsic noise and delays in genetic regulatory networks

This chapter focuses on the interactions and roles between delays and intrinsic noise effects within cellular pathways and regulatory networks. We address these aspects by focusing on genetic regulatory networks that share a common network motif, namely the negative feedback loop, leading to oscillatory gene expression and protein levels. In this context, we discuss computational simulation algorithms for addressing the interplay of delays and noise within the signaling pathways based on biological data. We address implementational issues associated with efficiency and robustness. In a molecular biology setting we present two case studies of temporal models for the Hes1 gene (Monk, 2003; Hirata et al., 2002), known to act as a molecular clock, and the Her1/Her7 regulatory system controlling the periodic somite segmentation in vertebrate embryos (Giudicelli and Lewis, 2004; Horikawa et al., 2006).

Emergent task-specific object semantics through distributed experience networks

Autonomous development of sensorimotor coordination enables a robot to adapt and change its action choices to interact with the world throughout its lifetime. The Experience Network is a structure that rapidly learns coordination between visual and haptic inputs and motor action. This paper presents methods which handle the high dimensionality of the network state-space which occurs due to the simultaneous detection of multiple sensory features. The methods provide no significant increase in the complexity of the underlying representations and also allow emergent, task-specific, semantic information to inform action selection. Experimental results show rapid learning in a real robot, beginning with no sensorimotor mappings, to a mobile robot capable of wall avoidance and target acquisition.

Evolving noisy oscillatory dynamics in genetic regulatory networks

We introduce a genetic programming (GP) approach for evolving genetic networks that demonstrate desired dynamics when simulated as a discrete stochastic process. Our representation of genetic networks is based on a biochemical reaction model including key elements such as transcription, translation and post-translational modifications. The stochastic, reaction-based GP system is similar but not identical with algorithmic chemistries. We evolved genetic networks with noisy oscillatory dynamics. The results show the practicality of evolving particular dynamics in gene regulatory networks when modelled with intrinsic noise.

Aerial image analysis using spiking neural networks with application to power line corridor monitoring

Trees, shrubs and other vegetation are of continued importance to the environment and our daily life. They provide shade around our roads and houses, offer a habitat for birds and wildlife, and absorb air pollutants. However, vegetation touching power lines is a risk to public safety and the environment, and one of the main causes of power supply problems. Vegetation management, which includes tree trimming and vegetation control, is a significant cost component of the maintenance of electrical infrastructure. For example, Ergon Energy, the Australia’s largest geographic footprint energy distributor, currently spends over $80 million a year inspecting and managing vegetation that encroach on power line assets. Currently, most vegetation management programs for distribution systems are calendar-based ground patrol. However, calendar-based inspection by linesman is labour-intensive, time consuming and expensive. It also results in some zones being trimmed more frequently than needed and others not cut often enough. Moreover, it’s seldom practicable to measure all the plants around power line corridors by field methods. Remote sensing data captured from airborne sensors has great potential in assisting vegetation management in power line corridors. This thesis presented a comprehensive study on using spiking neural networks in a specific image analysis application: power line corridor monitoring. Theoretically, the thesis focuses on a biologically inspired spiking cortical model: pulse coupled neural network (PCNN). The original PCNN model was simplified in order to better analyze the pulse dynamics and control the performance. Some new and effective algorithms were developed based on the proposed spiking cortical model for object detection, image segmentation and invariant feature extraction. The developed algorithms were evaluated in a number of experiments using real image data collected from our flight trails. The experimental results demonstrated the effectiveness and advantages of spiking neural networks in image processing tasks. Operationally, the knowledge gained from this research project offers a good reference to our industry partner (i.e. Ergon Energy) and other energy utilities who wants to improve their vegetation management activities. The novel approaches described in this thesis showed the potential of using the cutting edge sensor technologies and intelligent computing techniques in improve power line corridor monitoring. The lessons learnt from this project are also expected to increase the confidence of energy companies to move from traditional vegetation management strategy to a more automated, accurate and cost-effective solution using aerial remote sensing techniques.

Evolving genetic regulatory networks performing as stochastic switches

Recent studies have shown that small genetic regulatory networks (GRNs) can be evolved in silico displaying certain dynamics in the underlying mathematical model. It is expected that evolutionary approaches can help to gain a better understanding of biological design principles and assist in the engineering of genetic networks. To take the stochastic nature of GRNs into account, our evolutionary approach models GRNs as biochemical reaction networks based on simple enzyme kinetics and simulates them by using Gillespie’s stochastic simulation algorithm (SSA). We have already demonstrated the relevance of considering intrinsic stochasticity by evolving GRNs that show oscillatory dynamics in the SSA but not in the ODE regime. Here, we present and discuss first results in the evolution of GRNs performing as stochastic switches.

An efficient public key management regime for vehicular ad hoc networks (VANETS)

The primary goal of the Vehicular Ad Hoc Network (VANET) is to provide real-time safety-related messages to motorists to enhance road safety. Accessing and disseminating safety-related information through the use of wireless communications technology in VANETs should be secured, as motorists may make critical decisions in dealing with an emergency situation based on the received information. If security concerns are not addressed in developing VANET systems, an adversary can tamper with, or suppress, the unprotected message to mislead motorists to cause traffic accidents and hazards. Current research on secure messaging in VANETs focuses on employing the certificate-based Public Key Infrastructure (PKI) scheme to support message encryption and digital signing. The security overhead of such a scheme, however, creates a transmission delay and introduces a time-consuming verification process to VANET communications. This thesis has proposed a novel public key verification and management approach for VANETs; namely, the Public Key Registry (PKR) regime. Compared to the VANET PKI scheme, this new approach can satisfy necessary security requirements with improved performance and scalability, and at a lower cost by reducing the security overheads of message transmission and eliminating digital certificate deployment and maintenance issues. The proposed PKR regime consists of the required infrastructure components, rules for public key management and verification, and a set of interactions and associated behaviours to meet these rule requirements. This is achieved through a system design as a logic process model with functional specifications. The PKR regime can be used as development guidelines for conforming implementations. An analysis and evaluation of the proposed PKR regime includes security features assessment, analysis of the security overhead of message transmission, transmission latency, processing latency, and scalability of the proposed PKR regime. Compared to certificate-based PKI approaches, the proposed PKR regime can maintain the necessary security requirements, significantly reduce the security overhead by approximately 70%, and improve the performance by 98%. Meanwhile, the result of the scalability evaluation shows that the latency of employing the proposed PKR regime stays much lower at approximately 15 milliseconds, whether operating in a huge or small environment. It is therefore believed that this research will create a new dimension to the provision of secure messaging services in VANETs.