A geometric Newton method for Oja's vector field

Newton's method for solving the matrix equation $F(X)\equiv AX-XX^TAX=0$ runs up against the fact that its zeros are not isolated. This is due to a symmetry of $F$ by the action of the orthogonal group. We show how differential-geometric techniques can be exploited to remove this symmetry and obtain a ``geometric'' Newton algorithm that finds the zeros of $F$. The geometric Newton method does not suffer from the degeneracy issue that stands in the way of the original Newton method

Born to learn: The inspiration, progress, and future of evolved plastic artificial neural networks

Biological plastic neural networks are systems of extraordinary computational capabilities shaped by evolution, development, and lifetime learning. The interplay of these elements leads to the emergence of adaptive behavior and intelligence. Inspired by such intricate natural phenomena, Evolved Plastic Artificial Neural Networks (EPANNs) use simulated evolution in-silico to breed plastic neural networks with a large variety of dynamics, architectures, and plasticity rules: these artificial systems are composed of inputs, outputs, and plastic components that change in response to experiences in an environment. These systems may autonomously discover novel adaptive algorithms, and lead to hypotheses on the emergence of biological adaptation. EPANNs have seen considerable progress over the last two decades. Current scientific and technological advances in artificial neural networks are now setting the conditions for radically new approaches and results. In particular, the limitations of hand-designed networks could be overcome by more flexible and innovative solutions. This paper brings together a variety of inspiring ideas that define the field of EPANNs. The main methods and results are reviewed. Finally, new opportunities and developments are presented

The computational magic of the ventral stream: sketch of a theory (and why some deep architectures work).

This paper explores the theoretical consequences of a simple assumption: the computational goal of the feedforward path in the ventral stream -- from V1, V2, V4 and to IT -- is to discount image transformations, after learning them during development

Single Biological Neurons as Temporally Precise Spatio-Temporal Pattern Recognizers

This PhD thesis is focused on the central idea that single neurons in the brain should be regarded as temporally precise and highly complex spatio-temporal pattern recognizers. This is opposed to the prevalent view of biological neurons as simple and mainly spatial pattern recognizers by most neuroscientists today. In this thesis, I will attempt to demonstrate that this is an important distinction, predominantly because the above-mentioned computational properties of single neurons have far-reaching implications with respect to the various brain circuits that neurons compose, and on how information is encoded by neuronal activity in the brain. Namely, that these particular "low-level" details at the single neuron level have substantial system-wide ramifications. In the introduction we will highlight the main components that comprise a neural microcircuit that can perform useful computations and illustrate the inter-dependence of these components from a system perspective. In chapter 1 we discuss the great complexity of the spatio-temporal input-output relationship of cortical neurons that are the result of morphological structure and biophysical properties of the neuron. In chapter 2 we demonstrate that single neurons can generate temporally precise output patterns in response to specific spatio-temporal input patterns with a very simple biologically plausible learning rule. In chapter 3, we use the differentiable deep network analog of a realistic cortical neuron as a tool to approximate the gradient of the output of the neuron with respect to its input and use this capability in an attempt to teach the neuron to perform nonlinear XOR operation. In chapter 4 we expand chapter 3 to describe extension of our ideas to neuronal networks composed of many realistic biological spiking neurons that represent either small microcircuits or entire brain regions

Coding and learning of chemosensor array patterns in a neurodynamic model of the olfactory system

Arrays of broadly-selective chemical sensors, also known as electronic noses, have been developed during the past two decades as a low-cost and high-throughput alternative to analytical instruments for the measurement of odorant chemicals. Signal processing in these gas-sensor arrays has been traditionally performed by means of statistical and neural pattern recognition techniques. The objective of this dissertation is to develop new computational models to process gas sensor array signals inspired by coding and learning mechanisms of the biological olfactory system. We have used a neurodynamic model of the olfactory system, the KIII, to develop and demonstrate four odor processing computational functions: robust recovery of overlapping patterns, contrast enhancement, background suppression, and novelty detection. First, a coding mechanism based on the synchrony of neural oscillations is used to extract information from the associative memory of the KIII model. This temporal code allows the KIII to recall overlapping patterns in a robust manner. Second, a new learning rule that combines Hebbian and anti-Hebbian terms is proposed. This learning rule is shown to achieve contrast enhancement on gas-sensor array patterns. Third, a new local learning mechanism based on habituation is proposed to perform odor background suppression. Combining the Hebbian/anti-Hebbian rule and the local habituation mechanism, the KIII is able to suppress the response to continuously presented odors, facilitating the detection of the new ones. Finally, a new learning mechanism based on anti-Hebbian learning is proposed to perform novelty detection. This learning mechanism allows the KIII to detect the introduction of new odors even in the presence of strong backgrounds. The four computational models are characterized with synthetic data and validated on gas sensor array patterns obtained from an e-nose prototype developed for this purpose

Unsupervised space-time learning in primary visual cortex

The mammalian visual system is an incredibly complex computation device, capable of performing the various tasks of seeing: navigation, pattern and object recognition, motor coordination, trajectory extrapolation, among others. Decades of research has shown that experience-dependent plasticity of cortical circuitry underlies the impressive ability to rapidly learn many of these tasks and to adjust as required. One particular thread of investigation has focused on unsupervised learning, wherein changes to the visual environment lead to corresponding changes in cortical circuits. The most prominent example of unsupervised learning is ocular dominance plasticity, caused by visual deprivation to one eye and leading to a dramatic re-wiring of cortex. Other examples tend to make more subtle changes to the visual environment through passive exposure to novel visual stimuli. Here, we use one such unsupervised paradigm, sequence learning, to study experience-dependent plasticity in the mouse visual system. Through a combination of theory and experiment, we argue that the mammalian visual system is an unsupervised learning device. Beginning with a mathematical exploration of unsupervised learning in biology, engineering, and machine learning, we seek a more precise expression of our fundamental hypothesis. We draw connections between information theory, efficient coding, and common unsupervised learning algorithms such as Hebbian plasticity and principal component analysis. Efficient coding suggests a simple rule for transmitting information in the nervous system: use more spikes to encode unexpected information, and fewer spikes to encode expected information. Therefore, expectation violations ought to produce prediction errors, or brief periods of heightened firing when an unexpected event occurs. Meanwhile, modern unsupervised learning algorithms show how such expectations can be learned. Next, we review data from decades of visual neuroscience research, highlighting the computational principles and synaptic plasticity processes that support biological learning and seeing. By tracking the flow of visual information from the retina to thalamus and primary visual cortex, we discuss how the principle of efficient coding is evident in neural activity. One common example is predictive coding in the retina, where ganglion cells with canonical center-surround receptive fields compute a prediction error, sending spikes to the central nervous system only in response to locally-unpredictable visual stimuli. This behavior can be learned through simple Hebbian plasticity mechanisms. Similar models explain much of the activity of neurons in primary visual cortex, but we also discuss ways in which the theory fails to capture the rich biological complexity. Finally, we present novel experimental results from physiological investigations of the mouse primary visual cortex. We trained mice by passively exposing them to complex spatiotemporal patterns of light: rapidly-flashed sequences of images. We find evidence that visual cortex learns these sequences in a manner consistent with efficient coding, such that unexpected stimuli tend to elicit more firing than expected ones. Overall, we observe dramatic changes in evoked neural activity across days of passive exposure. Neural responses to the first, unexpected sequence element increase with days of training while responses at other, expected time points either decrease or stay the same. Furthermore, substituting an unexpected element for an expected one or omitting an expected element both cause brief bursts of increased firing. Our results therefore provide evidence for unsupervised learning and efficient coding in the mouse visual system, especially because unexpected events drive prediction errors. Overall, our analysis suggests novel experiments, which could be performed in the near future, and provides a useful framework to understand visual perception and learning

Homeostatische Plastizität - algorithmische und klinische Konsequenzen

Plasticity supports the remarkable adaptability and robustness of cortical processing. It allows the brain to learn and remember patterns in the sensory world, to refine motor control, to predict and obtain reward, or to recover function after injury. Behind this great flexibility hide a range of plasticity mechanisms, affecting different aspects of neuronal communication. However, little is known about the precise computational roles of some of these mechanisms. Here, we show that the interaction between spike-timing dependent plasticity (STDP), intrinsic plasticity and synaptic scaling enables neurons to learn efficient representations of their inputs. In the context of reward-dependent learning, the same mechanisms allow a neural network to solve a working memory task. Moreover, although we make no any apriori assumptions on the encoding used for representing inputs, the network activity resembles that of brain regions known to be associated with working memory, suggesting that reward-dependent learning may be a central force in working memory development. Lastly, we investigated some of the clinical implications of synaptic scaling and showed that, paradoxically, there are situations in which the very mechanisms that normally are required to preserve the balance of the system, may act as a destabilizing factor and lead to seizures. Our model offers a novel explanation for the increased incidence of seizures following chronic inflammation.Das menschliche Gehirn ist in der Lage sich an dramatische Veränderungen der Umgebung anzupassen. Hinter der Anpassungsfähigkeit des Gehirns stecken verschiedenste ernmechanismen. Einige dieser Mechanismen sind bereits relativ gut erforscht, wahrend bei anderen noch kaum bekannt ist, welche Rolle sie innerhalb der Informationsverarbeitungsprozesse im Gehirn spielen. Hier, soll gezeigt werden, dass das Zusammenspiel von Spike-Timing Dependent Plasticity' (STDP) mit zwei weiteren Prozessen, Synaptic Scaling' und Intrinsic Plasticity' (IP), es Nervenzellen ermöglicht Information effizient zu kodieren. Die gleichen Mechanismen führen dazu, dass ein Netzwerk aus Neuronen in der Lage ist, ein Arbeitsgedächtnis' für vergangene Stimuli zu entwickeln. Durch die Kombination von belohnungsabhängigem STDP und homöostatischen Mechanismen lernt das Netzwerk, die Stimulus-Repräsentationen für mehrere Zeitschritte verfügbar zu halten. Obwohl in unserem Modell-Design keinerlei. Informationen über die bevorzugte Art der Kodierung enthalten sind, finden wir nach Ende des Trainings neuronale Repräsentationen, die denjenigen aus vielen Arbeitsgedächtnis-Experimenten gleichen. Unser Modell zeigt, dass solche Repräsentationen durch Lernen enstehen können und dass Reward-abhängige Prozesse eine zentrale Kraft bei der Entwicklung des Arbeitsgedächtnisses spielen können. Abschliessend werden klinische Konsequenzen einiger Lern-Prozesse untersucht. Wir konnten zeigen, dass der selbe Mechanismus, der normalerweise die Aktivität im Gehirn in Balance hält, in speziellen Situationen auch zu Destabilisierung führen und epileptische Anfälle auslösen kann. Das hier vorgestellte Modell liefert eine neuartige Erklärung zur Entstehung von epileptischen Anfällen bei chronischen Entzündungen

Exploring Temporal Computation in Neuronal Systems

This thesis presents two approaches to identifying computational properties of networks of neurons. The first of these involves a bottom-up approach through detailed modelling of neuronal properties, while the second is a top-down approach using principal component analysis that quantifies the behaviour of neurons in complex networks from measurements. An object-oriented modelling tool has been developed that is fast, flexible, and easy to use. A graphical user interface allows the user to manipulate neurons, synapses, and currents visually on the screen during prototyping. Subsequently, a systematic study of the model can be processed in batch mode, for example to tune it to a particular behaviour. Small invertebrate neuronal circuits have been considered where the neuronal outputs can be related to the behaviour of the animal. The fundamental problem faced by experimental neurobiologists is that only one state variable per neuron is readily accessible, i.e. the membrane potential at the cell body. A neuron contains a vast number of state variables, but these are generally all hidden. The modelling tool enables one to "record" from hidden state variables and to manipulate inaccessible parameters of the real neurons. The tool has been evaluated through an investigation involving a leech heart model. Significant findings include non-spiking oscillations, and the modelling has suggested further experimental work involving the real system. The modelling tool provided close to real-time performance in this application which indicates its potential for its interactive use in an experimental environment, including dynamic voltage-clamp. The top-down approach uses principal component analysis to quantify a trace of neuronal activity during a time interval. During this interval, the feedback loops within the neuron and through the neuronal network will affect the output of the neuron. Thus, the resulting measure of the neuronal output will indirectly include the states of "hidden" compartments away from the cell soma and other inaccessible state variables, like channel states. Although the technique offer no promise for tracing these hidden state variables, it will enable us to include them in quantifying the outputs of a neuron. Further, the technique serves as an "objective critic" that display the largest sources of variance over the data set. Therefore, one avoids testing successively and explicitly through a large set of possible features. This also makes the measure low-dimensional and easy to analyse further. Application of the Karhunen-Loeve transform to the crayfish swimmeret showed that the principal components represented features like spike count, burst width, burst concentration, and burst latency. The burst latency proved to be significantly modulated. Principal component analysis was also performed on the membrane potential after having removed the action potentials with a low pass filter. The membrane potential deviations did not correlate with those of the spikes from the same neuron. This demonstrates the point that the membrane potential at the cell body does not solely determine the spiking pattern, but other (unobservable) state variables influence the spiking dynamics. Recently developed imaging techniques show possibilities in terms of measuring the spatial distribution of the membrane potential and ion concentrations throughout a cell, as well as the temporal interaction between these state variables. These imaging techniques are of potential value for validating theoretical models of a more complex kind for the study of which the object-oriented modelling tool could be readily applied. This work has shown that the Karhunen-Loeve transform can be used to quantify the relative coupling strength between two outputs. The coupling strength is estimated at the level of behaviour and relative to normal background activity in the system. This compares to the absolute estimate that at the level of individual synapses measures the coupling strength between two cells. The techniques above enables the effective coupling between two cells to be measured, where the coupling may occur through several pathways and through several cells. These results suggest that the long range intersegmental coupling is not much weaker than short range intrasegmental coupling and that the coupling performs phase locking only

Image database retrieval using neural networks

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The broad objective of this work has been to achieve retrieval of images from large unconstrained databases using image content. The problem is typified by the need to locate a target image within a database where no numerical indexing terms exist. Here, retrieval is based on important features within in an image and uses sample images or user sketches to specify a query. A typical query might be framed as "Find all images similar to this one", for example. The aim of this work has been to show how neural networks can provide a practical, flexible and robust solution to this problem. A neural network is basically an adaptive information filter which can be used to extract the salient characteristics of a data set during a training phase. The transformation learnt by the network can map the images into compact indices which support very rapid fuzzy matching of images across the database. This learning process optimises the performance of the code with respect to the contents of the database. We assess the applicability of several neural network architectures and learning rules for a practical coding scheme and investigate how the system parameters affect the performance of the system. We introduce a novel learning law which has a number of advantages over existing paradigms. In-depth mathematical analysis and extensive empirical tests are used to corroborate the arguments presented throughout. This thesis aims to show the nature of the image retrieval problem, how current research trends attempt to tackle it and how neural networks can offer us a real alternative to conventional approaches