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Institute
Machine learning (ML) techniques have evolved rapidly in recent years and have shown impressive capabilities in feature extraction, pattern recognition, and causal inference. There has been an increasing attention to applying ML to medical applications, such as medical diagnosis, drug discovery, personalized medicine, and numerous other medical problems. ML-based methods have the advantage of processing vast amounts of data.
With an ever increasing amount of medical data collection and large, inter-subject variability in the medical data, automated data processing pipelines are very much desirable since it is laborious, expensive, and error-prone to rely solely on human processing. ML methods have the potential to uncover interesting patterns, unravel correlations between complex features, learn patient-specific representations, and make accurate predictions. Motivated by these promising aspects, in this thesis, I present studies where I have implemented deep neural networks for the early diagnosis of epilepsy based on electroencephalography (EEG) data and brain tumor detection based on magnetic resonance spectroscopy (MRS) data.
In the project for early diagnosis of epilepsy, we are dealing with one of the most common neurological disorders, epilepsy, which is characterized by recurrent unprovoked seizures. It can be triggered by a variety of initial brain injuries and manifests itself after a time window which is called the latent period. During this period, a cascade of structural and functional brain alterations takes place leading to an increased seizure susceptibility.
The development and extension of brain tissue capable of generating spontaneous seizures is defined as epileptogenesis (EPG).
Detecting the presence of EPG provides a precious opportunity for targeted early medical interventions and, thus, can slow down or even halt the disease progression. In order to study brain signals in this latent window, animal epilepsy models are used to provide valuable data as it is extremely difficult to obtain this data from human patients. The aim of this study is to discover biomarkers of EPG using animal models and then to find the equivalent and counterparts in human patients' data. However, the EEG features for EPG are not well-understood and there is not a sufficiently large amount of annotated data for ML-based algorithms. To approach this problem, firstly, I utilized the timestamp information of the recorded EEG from an animal epilepsy model where epilepsy is induced by an electrical stimulation. The timestamp serves as a form of weak supervision, i.e., before and after the stimulation. Secondly, I implemented a deep residual neural network and trained it with a binary classification task to distinguish the EEG signals from these two phases. After obtaining a high discriminative ability on the binary classification task, I proposed to divide further the time span after the stimulation for a three-class classification, aiming to detect possible stages of the progression of the latent EPG phase. I have shown that the model can distinguish EEG signals at different stages of EPG with high accuracy and generalization ability. I have also demonstrated that some of the learned features from the network are clinically relevant.
In the task of detecting brain tumors based on MRS data, I first proposed to apply a deep neural network on the MRS data collected from over 400 patients for a binary classification task. To combat the challenge of noisy labeling, I developed a distillation step to filter out relatively ``cleanly'' labeled samples. A mixing-based data augmentation method was also implemented to expand the size of the training set. All the experiments were designed to be conducted with a leave-patient-out scheme to ensure the generalization ability of the model. Averaged across all leave-patient-out cross-validation sets, the proposed method performed on par with human neuroradiologists, while outperforming other baseline methods. I have demonstrated the distillation effect on the MNIST data set with manually-introduced label noise as well as providing visualization of the input influences on the final classification through a class activation map method.
Moreover, I have proposed to aggregate information at the subject level, which could provide more information and insights. This is inspired by the concept of multiple instance learning, where instance-level labels are not required and which is more tolerant to noisy labeling. I have proposed to generate data bags consisting of instances from each patient and also proposed two modules to ensure permutation invariance, i.e., an attention module and a pooling module. I have compared the performance of the network in different cases, i.e., with and without permutation-invariant modules, with and without data augmentation, single-instance-based and multiple-instance-based learning and have shown that neural networks equipped with the proposed attention or pooling modules can outperform human experts.
The brain is a large complex system which is remarkably good at maintaining stability under a wide range of input patterns and intensities. In addition, such a stable dynamical state is able to sustain essential functions, including the encoding of information about the external environment and storing memories. In order to succeed in these challenging tasks, neural circuits rely on a variety of plasticity mechanisms that act as self-organizational rules and regulate their dynamics. Based on toy models of self-organized criticality, this stable state has been proposed to be a phase transition point, poised between distinct types of unhealthy dynamics, in what has become known as the critical brain hypothesis. It is not yet known, however, if and how self-organization could drive biological neural networks towards a critical state while maintaining or improving their learning and memory functions.
Here, we investigate the emergence of criticality signatures in the form of neuronal avalanches due to self-organizational plasticity rules in a recurrent neural network. We show that power-law distributions of events, widely observed in experiments, arise from a combination of biologically inspired synaptic and homeostatic plasticity but are highly dependent on the external drive. Additionally, we describe how learning abilities and fading memory emerge and are improved by the same self-organizational processes. We finally propose an application of these enhanced functions, focusing on sequence and simple language learning tasks.
Taken together, our results suggest that the same self-organizational processes can be responsible for improving the brain’s spatio-temporal learning abilities and memory capacity while also giving rise to criticality signatures under particular input conditions, thus proposing a novel link between such abilities and neuronal avalanches. Although criticality was not verified, the detailed study of self-organization towards critical dynamics further elucidates its potential emergence and functions in the brain.
Understanding the dynamics of recurrent neural networks is crucial for explaining how the brain processes information. In the neocortex, a range of different plasticity mechanisms are shaping recurrent networks into effective information processing circuits that learn appropriate representations for time-varying sensory stimuli. However, it has been difficult to mimic these abilities in artificial neural models. In the present thesis, we introduce several recurrent network models of threshold units that combine spike timing dependent plasticity with homeostatic plasticity mechanisms like intrinsic plasticity or synaptic normalization. We investigate how these different forms of plasticity shape the dynamics and computational properties of recurrent networks. The networks receive input sequences composed of different symbols and learn the structure embedded in these sequences in an unsupervised manner. Information is encoded in the form of trajectories through a high-dimensional state space reminiscent of recent biological findings on cortical coding. We find that these self-organizing plastic networks are able to represent and "understand" the spatio-temporal patterns in their inputs while maintaining their dynamics in a healthy regime suitable for learning. The emergent properties are not easily predictable on the basis of the individual plasticity mechanisms at work. Our results underscore the importance of studying the interaction of different forms of plasticity on network behavior.
Cryo-electron tomography (CET) is a unique technique to visualize biological objects under near-to-native conditions at near-atomic resolution. CET provides three-dimensional (3D) snapshots of the cellular proteome, in which the spatial relations between macromolecular complexes in their near native cellular context can be explored. Due to the limitation of the electron dose applicable on biological samples, the achievable resolution of a tomogram is restricted to a few nanometers, higher resolution can be achieved by averaging of structures occurring in multiples. For this purpose, computational techniques such as template matching, sub-tomogram averaging and classification are essential for a meaningful processing of CET data.
This thesis introduces the techniques of template matching and sub-tomogram averaging and their applications on real biological data sets. Subsequently, the problem of reference bias, which restricts the applicability of those techniques, is addressed. Two methods that estimate the reference bias in Fourier and real space are demonstrated. The real space method, which we have named the “M-free” score, provides a reliable estimation of the reference bias, which gives access to the reliability of the template matching or sub-tomogram averaging process. Thus, the “M-free” score makes those approaches more applicable to structural biology. Furthermore, a classification algorithm based on Neural Networks (NN) called “KerDenSOM3D” is introduced, which is implemented in 3D and compensates for the missing-wedge. This approach helps extracting different structural states of macromolecular complexes or increasing the class purity of data sets by eliminating outliers. A comprehensive comparison with other classification methods shows superior performance of KerDenSOM3D.
At present, there is a huge lag between the artificial and the biological information processing systems in terms of their capability to learn. This lag could be certainly reduced by gaining more insight into the higher functions of the brain like learning and memory. For instance, primate visual cortex is thought to provide the long-term memory for the visual objects acquired by experience. The visual cortex handles effortlessly arbitrary complex objects by decomposing them rapidly into constituent components of much lower complexity along hierarchically organized visual pathways. How this processing architecture self-organizes into a memory domain that employs such compositional object representation by learning from experience remains to a large extent a riddle. The study presented here approaches this question by proposing a functional model of a self-organizing hierarchical memory network. The model is based on hypothetical neuronal mechanisms involved in cortical processing and adaptation. The network architecture comprises two consecutive layers of distributed, recurrently interconnected modules. Each module is identified with a localized cortical cluster of fine-scale excitatory subnetworks. A single module performs competitive unsupervised learning on the incoming afferent signals to form a suitable representation of the locally accessible input space. The network employs an operating scheme where ongoing processing is made of discrete successive fragments termed decision cycles, presumably identifiable with the fast gamma rhythms observed in the cortex. The cycles are synchronized across the distributed modules that produce highly sparse activity within each cycle by instantiating a local winner-take-all-like operation. Equipped with adaptive mechanisms of bidirectional synaptic plasticity and homeostatic activity regulation, the network is exposed to natural face images of different persons. The images are presented incrementally one per cycle to the lower network layer as a set of Gabor filter responses extracted from local facial landmarks. The images are presented without any person identity labels. In the course of unsupervised learning, the network creates simultaneously vocabularies of reusable local face appearance elements, captures relations between the elements by linking associatively those parts that encode the same face identity, develops the higher-order identity symbols for the memorized compositions and projects this information back onto the vocabularies in generative manner. This learning corresponds to the simultaneous formation of bottom-up, lateral and top-down synaptic connectivity within and between the network layers. In the mature connectivity state, the network holds thus full compositional description of the experienced faces in form of sparse memory traces that reside in the feed-forward and recurrent connectivity. Due to the generative nature of the established representation, the network is able to recreate the full compositional description of a memorized face in terms of all its constituent parts given only its higher-order identity symbol or a subset of its parts. In the test phase, the network successfully proves its ability to recognize identity and gender of the persons from alternative face views not shown before. An intriguing feature of the emerging memory network is its ability to self-generate activity spontaneously in absence of the external stimuli. In this sleep-like off-line mode, the network shows a self-sustaining replay of the memory content formed during the previous learning. Remarkably, the recognition performance is tremendously boosted after this off-line memory reprocessing. The performance boost is articulated stronger on those face views that deviate more from the original view shown during the learning. This indicates that the off-line memory reprocessing during the sleep-like state specifically improves the generalization capability of the memory network. The positive effect turns out to be surprisingly independent of synapse-specific plasticity, relying completely on the synapse-unspecific, homeostatic activity regulation across the memory network. The developed network demonstrates thus functionality not shown by any previous neuronal modeling approach. It forms and maintains a memory domain for compositional, generative object representation in unsupervised manner through experience with natural visual images, using both on- ("wake") and off-line ("sleep") learning regimes. This functionality offers a promising departure point for further studies, aiming for deeper insight into the learning mechanisms employed by the brain and their consequent implementation in the artificial adaptive systems for solving complex tasks not tractable so far.
Neurons are cells with a highly complex morphology; their dendritic arbor spans up to thousands of micrometers. This extended arbor poses a challenge for the logistics of neuronal processes: mRNA, proteins, and organelles have to be transported to dendrites, hundreds of micrometers away from the soma. This thesis aims to calculate the minimum number of proteins needed to populate the dendritic trees for different scenarios.
In chapter 2, I analyzed the ability of different mechanisms to populate the dendritic arbor. I started from the solution of the diffusion equation in Sec. 2.1, then I included the contribution of active transport in Sec. 2.2 and showed how it could have either the effect of increasing the effective diffusion coefficient or of introducing a bias in the diffusion process. In Sec. 2.3 I studied the spatial distribution of locally synthesized protein, accordingly with actively and passively transported mRNA. In Sec. 2.5, I derived the boundary condition for branches showing a qualitatively different behavior of surface and cytoplasmic proteins induced by the medium’s dimensionality in which they diffuse.
In chapter 3, I introduced the concept of protein requirement, defined as the minimum number of proteins that the neuron needs to produce to provide at least one protein to each micrometer of the dendritic arbor. In Sec. 3.1, I derived the protein requirement for diffusive proteins for somatic translation and constant translation in the dendritic arbor. In Sec. 3.2, I analyzed numerically the protein requirement in the case of actively transported protein synthesized in the soma, and, in Sec. 3.3, in the case of actively transported proteins synthesized in the dendritic arbor. In Sec. 3.4, I analyzed the protein requirement of protein synthesized in the dendrite accordingly with the distribution of mRNA described in Sec. 3.3 and 3.2. In Sec. 3.5, I derived the protein requirement for a single branch and purely diffusive proteins.
In chapter 4, I analyzed the relation between the radii of the three afferent dendrites in a branch, their length, and the diffusion length of a protein. In Sec. 4.1 I derived the optimal ratio between the radii of the daughter dendrites that minimizes the protein requirement. In Sec. 4.3 I introduced the 3/2− Rall Rule and in Sec. 4.5 its generalization. Finally, I used those rules to estimate the fraction of proteins diffusing away from and toward the soma.
In chapter 5, I analyzed the radii distribution for three categories of neurons: cultured hippocampal neurons in Sec. 5.1, stomatogastric ganglia neuron in Sec. 5.2, and 3DEM reconstructed prefrontal pyramidal neurons in Sec. 5.3. For each of these three classes, I analyzed the distribution of radii, Rall exponents, and the probability ratio. For most of them, I found that the probability of a protein diffusing away from the soma is higher for surface proteins than for cytoplasmic ones. I quantified this with a parameter called surface bias.
In Chapter 6, I analyzed the fluorescent ratio imaged by our collaborators Anne-Sophie Hafner, for a surface protein, GFP::Nlg, and a soluble one, GFP, in cultured hippocampal neurons, and I compared the fluorescent ratio with the probability ratio obtained in 5.1, finding that they are in good agreement.
In chapter 7, I compared the real dendritic morphologies imaged by one of our collaborators Ali Karimi with the optimal branching rule obtained in Sec. 4.1 and I calculated the cost for not having optimal branching radii.
Finally, in Chapter 8, I used the knowledge of the branching statistics gathered in 5.3 to simulate the protein profile on three different classes of neurons: pyramidal neurons, granule neuron, and Purkinje neurons. I compared the protein profile for surface and cytoplasmic neurons for each morphology for two different values of the diffusion length: λ = 109µm and λ = 473µm, both for optimized radii and symmetrical radii. I showed how the radii optimization reduces the protein requirement of a factor 10 4 for pyramidal neurons.
A framework for the analysis and visualization of multielectrode spike trains / von Ovidiu F. Jurjut
(2009)
The brain is a highly distributed system of constantly interacting neurons. Understanding how it gives rise to our subjective experiences and perceptions depends largely on understanding the neuronal mechanisms of information processing. These mechanisms are still poorly understood and a matter of ongoing debate remains the timescale on which the coding process evolves. Recently, multielectrode recordings of neuronal activity have begun to contribute substantially to elucidating how information coding is implemented in brain circuits. Unfortunately, analysis and interpretation of multielectrode data is often difficult because of their complexity and large volume. Here we propose a framework that enables the efficient analysis and visualization of multielectrode spiking data. First, using self-organizing maps, we identified reoccurring multi-neuronal spike patterns that evolve on various timescales. Second, we developed a color-based visualization technique for these patterns. They were mapped onto a three-dimensional color space based on their reciprocal similarities, i.e., similar patterns were assigned similar colors. This innovative representation enables a quick and comprehensive inspection of spiking data and provides a qualitative description of pattern distribution across entire datasets. Third, we quantified the observed pattern expression motifs and we investigated their contribution to the encoding of stimulus-related information. An emphasis was on the timescale on which patterns evolve, covering the temporal scales from synchrony up to mean firing rate. Using our multi-neuronal analysis framework, we investigated data recorded from the primary visual cortex of anesthetized cats. We found that cortical responses to dynamic stimuli are best described as successions of multi-neuronal activation patterns, i.e., trajectories in a multidimensional pattern space. Patterns that encode stimulus-specific information are not confined to a single timescale but can span a broad range of timescales, which are tightly related to the temporal dynamics of the stimuli. Therefore, the strict separation between synchrony and mean firing rate is somewhat artificial as these two represent only extreme cases of a continuum of timescales that are expressed in cortical dynamics. Results also indicate that timescales consistent with the time constants of neuronal membranes and fast synaptic transmission (~10-20 ms) appear to play a particularly salient role in coding, as patterns evolving on these timescales seem to be involved in the representation of stimuli with both slow and fast temporal dynamics.
In the human brain, the incoming light to the retina is transformed into meaningful representations that allow us to interact with the world. In a similar vein, the RGB pixel values are transformed by a deep neural network (DNN) into meaningful representations relevant to solving a computer vision task it was trained for. Therefore, in my research, I aim to reveal insights into the visual representations in the human visual cortex and DNNs solving vision tasks.
In the previous decade, DNNs have emerged as the state-of-the-art models for predicting neural responses in the human and monkey visual cortex. Research has shown that training on a task related to a brain region’s function leads to better predictivity than a randomly initialized network. Based on this observation, we proposed that we can use DNNs trained on different computer vision tasks to identify functional mapping of the human visual cortex.
To validate our proposed idea, we first investigate a brain region occipital place area (OPA) using DNNs trained on scene parsing task and scene classification task. From the previous investigations about OPA’s functions, we knew that it encodes navigational affordances that require spatial information about the scene. Therefore, we hypothesized that OPA’s representation should be closer to a scene parsing model than a scene classification model as the scene parsing task explicitly requires spatial information about the scene. Our results showed that scene parsing models had representation closer to OPA than scene classification models thus validating our approach.
We then selected multiple DNNs performing a wide range of computer vision tasks ranging from low-level tasks such as edge detection, 3D tasks such as surface normals, and semantic tasks such as semantic segmentation. We compared the representations of these DNNs with all the regions in the visual cortex, thus revealing the functional representations of different regions of the visual cortex. Our results highly converged with previous investigations of these brain regions validating the feasibility of the proposed approach in finding functional representations of the human brain. Our results also provided new insights into underinvestigated brain regions that can serve as starting hypotheses and promote further investigation into those brain regions.
We applied the same approach to find representational insights about the DNNs. A DNN usually consists of multiple layers with each layer performing a computation leading to the final layer that performs prediction for a given task. Training on different tasks could lead to very different representations. Therefore, we first investigate at which stage does the representation in DNNs trained on different tasks starts to differ. We further investigate if the DNNs trained on similar tasks lead to similar representations and on dissimilar tasks lead to more dissimilar representations. We selected the same set of DNNs used in the previous work that were trained on the Taskonomy dataset on a diverse range of 2D, 3D and semantic tasks. Then, given a DNN trained on a particular task, we compared the representation of multiple layers to corresponding layers in other DNNs. From this analysis, we aimed to reveal where in the network architecture task-specific representation is prominent. We found that task specificity increases as we go deeper into the DNN architecture and similar tasks start to cluster in groups. We found that the grouping we found using representational similarity was highly correlated with grouping based on transfer learning thus creating an interesting application of the approach to model selection in transfer learning.
During previous works, several new measures were introduced to compare DNN representations. So, we identified the commonalities in different measures and unified different measures into a single framework referred to as duality diagram similarity. This work opens up new possibilities for similarity measures to understand DNN representations. While demonstrating a much higher correlation with transfer learning than previous state-of-the-art measures we extend it to understanding layer-wise representations of models trained on the Imagenet and Places dataset using different tasks and demonstrate its applicability to layer selection for transfer learning.
In all the previous works, we used the task-specific DNN representations to understand the representations in the human visual cortex and other DNNs. We were able to interpret our findings in terms of computer vision tasks such as edge detection, semantic segmentation, depth estimation, etc. however we were not able to map the representations to human interpretable concepts. Therefore in our most recent work, we developed a new method that associates individual artificial neurons with human interpretable concepts.
Overall, the works in this thesis revealed new insights into the representation of the visual cortex and DNNs...
Navigating a complex environment is assumed to require stable cortical representations of environmental stimuli. Previous experimental studies, however, show substantial ongoing remodeling at the level of synaptic connections, even under behaviorally and environmentally stable conditions. It remains unclear, how these changes affect sensory representations on the level of neuronal populations during basal conditions and how learning influences these dynamics.
Our approach is a joint effort between the analysis of experimental data and theory. We analyze chronic neuronal population activity data – acquired by out collaborators in Mainz – to describe population activity dynamics during basal dynamics and during learning (fear conditioning). The data analysis is complemented by the analysis of a circuit model investigating the link between a neural network’s activity and changes in its underlying structure.
Using chronic two-photon imaging data recorded in awake mouse auditory cortex, we reproduce previous findings that responses of neuronal populations to short complex sounds typically cluster into a near discrete set of possible responses. This means that different stimuli evoke basically the same response and are thus grouped together into one of a small set of possible response modes. The near discrete set of response modes can be utilized as a sensitive and robust means to detect and track changes in population activity over time. Doing so we find that sound representations are subject to a significant ongoing remodeling across the time span of days under basal conditions. Auditory cued fear conditioning introduces a bias into these ongoing dynamics, resulting in a differential generalization both on the level of neuronal populations and on the behavioral level. This means that sounds that are perceived similar to the conditioned stimulus (CS+) show an increased co-mapping to the same response mode the CS+ is mapped to. This differential generalization is also observed in animal behavior, where sounds similar to the CS+ result in the same freezing behavior as the CS+, whereas dissimilar sounds do not. These observations could provide a potential mechanism of stimulus generalization, which is one of the most common phenomena associated with post-traumatic stress disorder, on the level of neuronal populations.
To investigate how the aforementioned changes in neuronal population activity are linked to changes in the underlying synaptic connectivity, we devised a circuit model of excitatory and inhibitory neurons. We studied this firing rate model to investigate the effect of gradual changes in the network’s connectivity on its activity. Apart from an input dominated uni-stable regime (one response per stimulus independent of the network) and a network dominated uni-stable regime (one response per network independent of the stimulus), we also find a multi-stable regime for strong recurrent connectivity and a high ratio of inhibition to excitation. In this regime the model reproduces properties of neural population activity in mouse auditory cortex, including sparse activity, a broad distribution of firing rates, and clustering of stimuli into a near discrete set of response modes. This clustering in the multi-stable regime means that, not only can identical stimuli evoke different responses, depending on the network’s initial condition, but different stimuli can also evoke the same response.
Applying gradual drift to the network connectivity we find periods of stable responses, interrupted by abrupt transitions altering the stimulus response mapping. We study the mechanism underlying these transitions by analyzing changes in the fixed points of this network model, employing a method to numerically find all the fixed points of the system. We find that such abrupt transitions typically cannot be explained by the mere displacement of existing fixed points, but involve qualitative changes in the fixed point structure in the vicinity of the response trajectory. We conclude that gradual synaptic drift can lead to abrupt transitions in stimulus responses and that qualitative changes in the network’s fixed point topology underlie such transitions.
In summary we find that cortical networks display ongoing representational drift under basal conditions that is biased towards a differential generalization during fear conditioning. A circuit model is able to reproduce key characteristics of auditory cortex, including a clustering of stimulus responses into a near discrete set of response modes. Implementing synaptic drift into this model leads to periods of stable responses interrupted by abrupt transitions towards new responses.
Die vorgelegte Dissertation behandelt den Einfluss homöostatischer Adaption auf die Informationsverarbeitung und Lenrprozesse in neuronalen Systemen. Der Begriff Homöostase bezeichnet die Fähigkeit eines dynamischen Systems, bestimmte interne Variablen durch Regelmechanismen in einem dynamischen Gleichgewicht zu halten. Ein klassisches Beispiel neuronaler Homöostase ist die dynamische Skalierung synaptischer Gewichte, wodurch die Aktivität bzw. Feuerrate einzelner Neuronen im zeitlichen Mittel konstant bleibt. Bei den von uns betrachteten Modellen handelt es sich um eine duale Form der neuronalen Homöostase. Das bedeutet, dass für jedes Neuron zwei interne Parameter an eine intrinsische Variable wie die bereits erwähnte mittlere Aktivität oder das Membranpotential gekoppelt werden. Eine Besonderheit dieser dualen Adaption ist die Tatsache, dass dadurch nicht nur das zeitliche Mittel einer dynamischen Variable, sondern auch die zeitliche Varianz, also die stärke der Fluktuation um den Mittelwert, kontrolliert werden kann. In dieser Arbeit werden zwei neuronale Systeme betrachtet, in der dieser Aspekt zum Tragen kommt.
Das erste behandelte System ist ein sogennantes Echo State Netzwerk, welches unter die Kategorie der rekurrenten Netzwerke fällt. Rekurrente neuronale Netzwerke haben im Allgemeinen die Eigenschaft, dass eine Population von Neuronen synaptische Verbindungen besitzt, die auf die Population selbst projizieren, also rückkoppeln. Rekurrente Netzwerke können somit als autonome (falls keinerlei zusätzliche externe synaptische Verbindungen existieren) oder nicht-autonome dynamische Systeme betrachtet werden, die durch die genannte Rückkopplung komplexe dynamische Eigenschaften besitzen. Abhängig von der Struktur der rekurrenten synaptischen Verbindungen kann beispielsweise Information aus externem Input über einen längeren Zeitraum gespeichert werden. Ebenso können dynamische Fixpunkte oder auch periodische bzw. chaotische Aktivitätsmuster entstehen. Diese dynamische Vielseitigkeit findet sich auch in den im Gehirn omnipräsenten rekurrenten Netzwerken und dient hier z.B. der Verarbeitung sensorischer Information oder der Ausführung von motorischen Bewegungsmustern. Das von uns betrachtete Echo State Netzwerk zeichnet sich dadurch aus, dass rekurrente synaptische Verbindungen zufällig generiert werden und keiner synaptischen Plastizität unterliegen. Verändert werden im Zuge eines Lernprozesses nur Verbindungen, die von diesem sogenannten dynamischen Reservoir auf Output-Neuronen projizieren. Trotz der Tatsache, dass dies den Lernvorgang stark vereinfacht, ist die Fähigkeit des Reservoirs zur Verarbeitung zeitabhängiger Inputs stark von der statistischen Verteilung abhängig, die für die Generierung der rekurrenten Verbindungen verwendet wird. Insbesondere die Varianz bzw. die Skalierung der Gewichte ist hierbei von großer Bedeutung. Ein Maß für diese Skalierung ist der Spektralradius der rekurrenten Gewichtsmatrix.
In vorangegangenen theoretischen Arbeiten wurde gezeigt, dass für das betrachtete System ein Spektralradius nahe unterhalb des kritischen Wertes von 1 zu einer guten Performance führt. Oberhalb dieses Wertes kommt es im autonomen Fall zu chaotischem dynamischen Verhalten, welches sich negativ auf die Informationsverarbeitung auswirkt. Der von uns eingeführte und als Flow Control bezeichnete duale Adaptionsmechanismus zielt nun darauf ab, über eine Skalierung der synaptischen Gewichte den Spektralradius auf den gewünschten Zielwert zu regulieren. Essentiell ist hierbei, dass die verwendete Adaptionsdynamik im Sinne der biologischen Plausibilität nur auf lokale Größen zurückgreift. Dies geschieht im Falle von Flow Control über eine Regulation der im Membranpotential der Zelle auftretenden Fluktuationen. Bei der Evaluierung der Effektivität von Flow Control zeigte sich, dass der Spektralradius sehr präzise kontrolliert werden kann, falls die Aktivitäten der Neuronen in der rekurrenten Population nur schwach korreliert sind. Korrelationen können beispielsweise durch einen zwischen den Neuronen stark synchronisierten externen Input induziert werden, der sich dementsprechend negativ auf die Präzision des Adaptionsmechanismus auswirkt.
Beim Testen des Netzwerks in einem Lernszenario wirkte sich dieser Effekt aber nicht negativ auf die Performance aus: Die optimale Performance wurde unabhängig von der stärke des korrelierten Inputs für einen Spektralradius erreicht, der leicht unter dem kritischen Wert von 1 lag. Dies führt uns zu der Schlussfolgerung, dass Flow Control unabhängig von der Stärke der externen Stimulation in der Lage ist, rekurrente Netze in einen für die Informationsverarbeitung optimalen Arbeitsbereich einzuregeln.
Bei dem zweiten betrachteten Modell handelt es sich um ein Neuronenmodell mit zwei Kompartimenten, welche der spezifischen Anatomie von Pyramidenneuronen im Kortex nachempfunden ist. Während ein basales Kompartiment synaptischen Input zusammenfasst, der in Dendriten nahe des Zellkerns auftritt, repräsentiert das zweite apikale Kompartiment die im Kortex anzutreffende komplexe dendritische Baumstruktur. In früheren Experimenten konnte gezeigt werden, dass eine zeitlich korrelierte Stimulation sowohl im basalen als auch apikalen Kompartiment eine deutlich höhere neuronale Aktivität hervorrufen kann als durch Stimulation nur einer der beiden Kompartimente möglich ist. In unserem Modell können wir zeigen, dass dieser Effekt der Koinzidenz-Detektion es erlaubt, den Input im apikalen Kompartiment als Lernsignal für synaptische Plastizität im basalen Kompartiment zu nutzen. Duale Homöostase kommt auch hier zum Tragen, da diese in beiden Kompartimenten sicherstellt, dass sich der synaptische Input hinsichtlich des zeitlichen Mittels und der Varianz in einem für den Lernprozess benötigten Bereich befindet. Anhand eines Lernszenarios, das aus einer linearen binären Klassifikation besteht, können wir zeigen, dass sich das beschriebene Framework für biologisch plausibles überwachtes Lernen eignet.
Die beiden betrachteten Modelle zeigen beispielhaft die Relevanz dualer Homöostase im Hinblick auf zwei Aspekte. Das ist zum einen die Regulation rekurrenter neuronaler Netze in einen dynamischen Zustand, der für Informationsverarbeitung optimal ist. Der Effekt der Adaption zeigt sich hier also im Verhalten des Netzwerks als Ganzes. Zum anderen kann duale Homöostase, wie im zweiten Modell gezeigt, auch für Plastizitäts- und Lernprozesse auf der Ebene einzelner Neuronen von Bedeutung sein. Während neuronale Homöostase im klassischen Sinn darauf beschränkt ist, Teile des Systems möglichst präzise auf einen gewünschten Mittelwert zu regulieren, konnten wir Anhand der diskutierten Modelle also darlegen, dass eine Kontrolle des Ausmaßes von Fluktuationen ebenfalls Einfluss auf die Funktionalität neuronaler Systeme haben kann.