Early theories of perception have suggested that the brain interprets its visual input on the basis of an internal model of the world. In the early visual system this model is stored on the backbone of a complex recurrent connectivity structure. I will present evidence for efficient recurrent computation in the primary visual cortex based on data obtained with chronic multisite recordings from anesthetized cats and awake monkeys. We focus on stimuli that are less redundant than oriented bars and gratings and thus better suited to capture aspects of distributed coding. We show that the evoked population responses to shapes and natural scenes, exhibit complex temporal dynamics: information about a briefly presented stimulus can persist for up to one second and can superimpose with subsequent stimuli. Structured visual stimuli are encoded more efficiently compared to scrambled controls and engage the local excitatory-inhibitory rhythms in a differential manner. And most remarkably, repetitive visual experience increases the amount of information conveyed by the local population dynamics over time, by consolidating specific low-dimensional representations of stimulus structure.
Information processing at a conceptual level is considered to be one of the hardest challenges in Cognitive Science. In particular, a number of studies in behavioral research have shown that humans process concepts in a way that is incompatible with traditional frameworks such as classical probability and fuzzy set theory. Recently, this incompatibility has been shown to occur at a deep structural level, and mathematical schemes founded on quantum structures have been proposed as alternative modeling frameworks. The quantum approach allows to faithfully model a number of non-classical deviations observed in experimental data. Moreover, it shows that genuine quantum theoretical notions, such as contextuality, superposition, emergence and entanglement, are interesting epistemic tools to understand and represent hard problems in Artificial Intelligence. In this talk, we identify the limitations of traditional frameworks to handle some important cognitive tasks, introduce the fundamentals of this quantum cognitive approach, and present some remarkable applications.
We present here a novel method for clustering and de-noising high-dimensional, noisy, binary data based on Hopfield networks and minimum probability flow (MPF) learning. In this talk I will discuss both theoretical aspects of MPF as well as applications of themethod to synthetic and neural data. We propose the method as a general technique for de-noising and clustering high-dimensional binary data and compare it to other well-known methods such as k-means clustering, locally-linear embedding and multi-dimensional scaling. We show how the method can be applied to the classical task of finding and extracting recurring spatiotemporal patterns in recorded spiking activity of neuronal populations. In contrast to previously proposed methods, the proposed technique (1) does not seek to classify exactly recurring patterns, but rather approximate versions possibly differing by a certain number of missed, shifted or excess spikes, (2) does not suffer of combinatorial explosion when complexity and size of the patterns considered are increased. Modeling furthermore the sequence of occurring Hopfield memories over the original data as a Markov process, we are able to extract low-dimensional representations of neural population activity on longer time scales. We demonstrate the approach on a data set obtained in rat barrel cortex and show that it is able to extract a remarkably low-dimensional, yet accurate representation of average population activity observed during the experiment.
This is joint work with Christopher Hillar, MSRI and Redwood Center for Theoretical Neuroscience, Berkeley, CA, USA.
The human brain has amazing information processing capacity, which relies on the activity of 80 billion neurons, each of them interacting with thousands of other neurons. However, their collective dynamics and the origin of their information processing capacities remain unknown. A popular hypothesis is that the neural network self-organizes to a critical state, because in models this state showed maximal processing capacities (quantified as information storage and transfer). However, I showed recently that in vivo spike recordings from rats, cats and monkeys indicated consistently a subcritical regime instead of criticality. Moreover, the ‘distance to criticality’ changed from wakefulness to deep sleep. I suggest that the brain changes its distance to criticality depending on needs: In general, it maintaining a variable safety margin to criticality, because criticality comes with the risk of runaway activity (epilepsy), but it reduces the safety margin temporarily when high processing capacities are needed.
The Hopfield network is a well-known model of memory and collective processing in networks of abstract neurons, but it has been dismissed for use in signal processing because of its small pattern capacity, difficulty to train, and lack of practical applications. In the last few years, however, it has been demonstrated that exponential storage is possible for special classes of patterns and network connectivity structures. Over the same time period, advances in training large-scale networks have also appeared. Here, we train Hopfield networks on discretizations of grayscale digital photographs using a learning technique called minimum probability flow (MPF).
After training, we demonstrate that these networks have exponential memory capacity, allowing them to perform state-of-the-art image compression in the high quality regime. Our findings suggest that the local structure of images is remarkably well-modeled by a binary recurrent neural network.
(Joint work with Ram Mehta and Kilian Koepsell).
Most of the brain’s activity occurs in the absence of direct stimuli, leading researchers to talk about the "dark energy" of the brain. This spontaneous activity is not merely an epiphenomenon, but contributes to both mental and behavioural processes. In this talk, I discuss several domains where spontaneous brain activity influences neuronal communication, development, and cognitive outcomes. These domains span human neuroimaging, multicellular recordings, as well as computational simulations of brain activity. Taken together, evidence on the key role of spontaneous activity fosters a new approach to understanding the brain, one that focuses on intrinsic dynamics and revises the classic view of synaptic networks as strict input-output systems. Finally, I highlight some of the fundamental principles that form the pillars for the emerging field of complex brain dynamics.
Ever since patient H.M. - arguably the most famous case study in neuroscience - we know that damages of a specific region of the brain, the hippocampus, causes a loss of memories for recent events while preserving memories of events from the distant past. Declarative memories are therefore only transiently dependent on the hippocampus, and appear to be gradually transferred into cortical networks. This process - termed "systems memory consolidation" - apparently takes place during sleep and is thought to be essential for long-term memory retention. Its cellular or systems level implementation, however, is still far from clear.
In my talk, I will suggest a novel mechanism for the consolidation of memories from hippocampus to cortex. I will posit that the full consolidation process consists of a cascade of small consolidations steps, which gradually increase memory lifetime. In each step, memories are copied from one set of synapses to another by a combination of spike timing-dependent plasticity - a form of synaptic plasticity that is widely found in the brain - and a generic anatomical network motif that is also prominent throughout the nervous system. I will use theoretical arguments and simulations to first illustrate the mechanism in one of these consolidation steps, and then show that a hierarchical iteration of the same principle i) consistent with lesion studies and ii) can lead to power-law forgetting, i.e. to long memory retention times (as already suggested by Roxin and others). I will close by discussing that the same mechanism could also serve for the consolidation of other forms of memory (such as perceptual or motor learning) and as a generic mechanism that simplifies information flow in cortical networks.
The large-scale dynamics of a balanced random network of excitatory and inhibitory integrate-and-fire neurons is the focus of our study. Based on the dynamical equations of the model, a mean field approach was employed to reduce the dimensionality of the network dynamics [1,2]. We analyzed the joint activity dynamics of excitatory and inhibitory populations using a pair of mutually interacting differential equations. In absence of a voltage leak for individual neurons, and for negligible synaptic transmission delay, these equations take the form of Lotka-Volterra equations. These are known for describing predator-prey systems, which correspond to excitatory and inhibitory populations in our case. We tried to find optimal parameters for the non-autonomous differential equations given a dataset from a numerical simulations of a network. Moreover, we attempted to analytically infer the parameters and compare it with the statistical estimates. As a next step, we analyzed the stability of the network considering two bifurcation parameters: “g”, the relative strength of recurrent inhibition, which controls the balance between excitation and inhibition in the network, and “eta”, the intensity of external input to the network. We found out that for a value of “g” that keeps the exact balance between excitation and inhibition, a bifurcation from unstable to stable network dynamics takes place. This bifurcation separates Synchronous Regular (SR) from Asynchronous Irregular (AI) activity of the network, similar to what was found in a previous study on the same network using a Fokker-Planck approach [3]. It has been shown that Lotka-Volterra equations are capable of representing switching dynamics between different states of neural networks [4]. Our analysis represents a first step toward analyzing the dynamics of more complex “networks of networks” that are implicated in various cognitive abilities of the brain. References1. Cardanobile S, Rotter S. Multiplicatively interacting point processes and applications to neural modeling. Journal of Computational Neuroscience 28(2): 267-284, 20102. Cardanobile S, Rotter S. Emergent properties of interacting populations of spiking neurons. Frontiers in Computational Neuroscience 5: 59, 20113. Brunel N. Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. Journal of Computational Neuroscience 8(3): 183-208, 2000Bick C, Rabinovich M. On the occurrence of stable heteroclinic channels in Lotka-Volterra models. Dynamical Systems 25: 97-110, 20104. Bick C, Rabinovich M. On the occurrence of stable heteroclinic channels in Lotka-Volterra models. Dynamical Systems 25: 97-110, 2010 Support by the German Federal Ministry of Education and Research (BMBF; grant 01GQ0420 to BCCN Freiburg) is gratefully acknowledged.
The talk is organized along a correspondence principle between equations, architectures and local algorithms. After a short remark on feedforward neural networks and learning we will focus on recurrent neural nets for state space modeling.
First we will discuss the modeling of open dynamical systems, error correction neural networks, dynamical systems on manifolds and feedback control of observed systems.
Second we will continue with closed dynamical systems. Here we understand the dynamics of interest as a very large system which is only partially observable. The related neural network models have very large state spaces ( dim(state) > 300 ) which creates learning and stability problems. In solving these problems we have to skip several standards of regression theory and develop a new view on uncertainty in forecasting.
Finally, we focus on dynamical systems which are generated by human interaction, e.g. markets. Such systems do not only have a causal mechanics, since they are at least partly generated by utility maximization - even if we do not know the utility function explicitly. Now, the question arises how we can identify and exploit the causal and the utility driven parts of the dynamics.
At Siemens Corporate Technology we have 24 years of experience in research in neural networks, related software development and real-world applications.
Cortical circuits are shaped by a number of different plasticity mechanisms, but it is still unclear how these endow the cortex with useful information processing abilities. Over the last years we have developed recurrent neural network models that self-organize their connectivity under the influence of different plasticity mechanism including spike-timing dependent plasticity and different forms of homoestatic plasticity. These self-organizing recurrent networks (SORNs) can learn about the temporal structure in input time series in an unsupervised fashion and can greatly outperform non-adaptive networks on challenging prediction tasks. Furthermore, these networks can explain a number of features of cortical circuits including the Poisson-like firing of individual neurons, the overall distribution of synaptic connection strength, and the high degree of synaptic turnover and patterns of synaptic fluctuations. In addition, they make testable predictions regarding the distribution of synaptic life times. Finally, they also explain some psychological results on sequence learning in adult subjects. Overall, our results suggest that cortical circuits are shaped by processes of network self-organization through the combined action of multiple forms of neuronal plasticity.
Autonomous robots that can assist humans in situations of daily life have been a long standing vision of robotics, artificial intelligence, and cognitive sciences. A first step towards this goal is to create robots that can learn tasks triggered by environmental context or higher level instruction. However, learning techniques have yet to live up to this promise as only few methods manage to scale to high-dimensional manipulator or humanoid robots. In this talk, we investigate a general framework suitable for learning motor skills in robotics which is based on the principles behind many analytical robotics approaches. It involves generating a representation of motor skills by parameterized motor primitive policies acting as building blocks of movement generation, and a learned task execution module that transforms these movements into motor commands. We discuss learning on three different levels of abstraction, i.e., learning for accurate control is needed to execute, learning of motor primitives is needed to acquire simple movements, and learning of the task-dependent "hyperparameters" of these motor primitives allows learning complex tasks. We discuss task-appropriate learning approaches for imitation learning, model learning and reinforcement learning for robots with many degrees of freedom. Empirical evaluations on a several robot systems illustrate the effectiveness and applicability to learning control on an anthropomorphic robot arm.
In recent years there have been many studies of the possible occurrence of selforganized criticality in neural networks with synaptic plasticity. Most of them have concluded that various form of synaptic adaptation drive the network dynamics far below critical point (Siri 2007), in other words they over-regulate the neural activity. Hence, there should exist an additional mechanism, maintaining the desired level of excitability in neural networks and preventing the dynamical states which are non-reactive to external influences.
Such counter mechanism can be found in a form of adaptation observed in biological neurons, working on the level of the membrane elements. This non-synaptic adjustment, manifested as a change in neuron excitability (Mozzachiodi 2010), is also known as intrinsic plasticity.
We have studied a previously proposed model of intrinsic plasticity (Triesch 2005), and its influence on the dynamical properties of autonomous recurrent neural networks with discrete time rate encoding neurons. The introduction of intrinsic plasticity results in ongoing and self-sustained neural activities with non trivial dynamical states. For large networks, one observes three self-organized distinct phase states. Depending on the specied network parameters, the neural activity exhibits either chaotic, intermittent bursting, or synchronized oscillatory behavior. These results show that non-synaptic adaptation plays an important role in the formation of complex patterns of neural activity.
We investigate information processing in randomly connected recurrent neural networks. It has been shown previously that the computational capabilities of these networks are maximized when the recurrent layer is close to the border between a stable and an unstable dynamics regime, the so called edge of chaos. The reasons, however, for this maximized performance are not completely understood. We adopt an information-theoretical framework and are for the first time able to quantify the computational capabilities between elements of these networks directly as they undergo the phase transition to chaos. Specifically, we present evidence that both information transfer and storage in the recurrent layer peak close to this phase transition, providing an explanation for why guiding the recurrent layer towards the edge of chaos is computationally useful. As a consequence, our work suggests self-organized ways of improving performance in recurrent neural networks, driven by both input data and the learning goal. This is in contrast to other self-organized approaches for adapting the recurrent layer, like intrinsic plasticity, which do not take the learning goal into account.
I will present a framework for Artificial Generla Intelligence inspired by knowledge about the only working prototype: the brain. The neurobiological findings make the directives. I define the main algorithmic modules and give solutions for each subtasks together with the available mathematical (hard) constraints. The main themes are compressed sensing, factor learning, independent process analysis and low dimensional embedding for optimal state representation to be used by a particular RL system that can be integrated with a robust controller. However, the blending of the suggested partial solutions is not a straightforward task. Nevertheless, we started to combine these modules and illustrate their working on a simulated problem. I will discuss the ongoing efforts and the steps needed to complete the integration.
Classical Computer Science approaches to behavioural problems -- such as Reinforcement Learning, control and behaviour planning -- are dominated by Bellman's principles and dynamic programming. However, some fundamental questions are hard to address in this framework: How can planning and decision making be realized on distributed representations? How on hierarchies and mixed (discrete, continuous) representations? How can appropriate representations be learnt? And what is a coherent computational paradigm that solves behavioural problems equally to state estimation and sensor processing problems? Recently there have been a series of papers showing that behavioural problems can be reformulated as a problem of Bayesian inference or Free Energy Minimization in graphical models where actions, states, observations and rewards are equally represented as coupled random variables. The most important implication of this view is that existing Machine Learning methods such as inference on factored and hierarchical representations, likelihood maximization, and unsupervised learning (which were classically associated to sensor processing and learning sensor representations) can now be transferred to the realm of behaviour organization. In this talk I will introduce to the general approach and give examples from our recent work. The focus will be on discussing the concept, its premises and limitations, and relations to other models of goal-directed behaviour.
Human brain function depends on interactions between functionally specialized brain regions. One of the most challenging problems in neuroscience today is the detection of functional networks using techniques like fMRI (functional magnetic resonance imaging). In this talk, I will present some recent developments and dicuss their merits and limitations.
I present a mean-field model of the cortex comprised of interacting populations of excitatory and inhibitory neurons which communicate via chemical (neurotransmitter-controlled) and electrical (gap junction) synapses. The model consists of closed set of stochastic differential equations that describe the spatially-averaged behaviour of the firing rates of neurons. When the soma response is slow relative to dendritic events, the model predicts ultra-slow spatiotemporal oscillations in cortical activity reminiscent of "default" BOLD patterns seen in fMRI. This slow oscillation arises from a subharmonic interaction between Turing (spatial) and Hopf (temporal) symmetry-breaking instabilities. If the soma response to dendritic input is prompt, a gamma-band (~40-Hz) standing-wave instability emerges, entraining the cortex into long- range synchronous oscillations consistent with the cognitive state of the cortex.
The ability to localize the source of a sound plays a vital role for survival and communication in the animal kingdom. While the available timing and loudness cues in this task are often subtle, many species perform it remarkably precise. The underlying neuronal structures have to transmit and represent the auditory information from both ears at high acuity to the centers of sound localization in the brainstem. As part of this pathway the synapses of Held are likely to be specialized for this acuity by their extraordinary size. In my doctorate I investigated whether these synapses accurately transmit the incoming information with respect to its quantity and timing. Further the representation of auditory information was investigated using a recently developed class of nonparametric models, the multilinear models.
We found that action potentials are transmitted faithfully at one type of synapse, the calyx of Held, but not at another type, the endbulbs of Held. To obtain this finding it was necessary to develop a statistical test that can detect the occurrence of failures of transmission under the presence of noise. This method was tested and calibrated using simulated voltage recordings which closely mimicked the real data.
Concerning the timing of synaptic transmission we found that - contrary to previous belief - the delay introduced by synaptic transmission varies as a function of the rate of transmission events at the synapse. Using specialized stimulus paradigms the dynamics of the transmission delay were measured. This allowed us to devise a phenomenological model of the transmission delay which was used to quantify the single spike increases of transmission delay and captured 67\% of the explainable variance. The explainable variance was estimated by simulating the noise induced variability in transmission delay and appropriately correcting the total variance. The changes in transmission delay are large enough to provide constraints for future models of sound localization in following neuronal stages.
Lastly, we investigated the stimulus representation at the calyx of Held, which is useful for modeling the localization of high frequency sounds based on differences in stimulus intensity between the ears. A nonparametric class of models, the multilinear models, was chosen which allows sub-millisecond predictions, flexible regularization, and meaningful interpretation of the parameters. A member of this class, the context model was able to explain 75\% of the explainable variance on average. An important tool in quantifying the model performance is the predictive power whose asymptotic properties were explored formally in some detail. The parameters of the context model also provided some structural insights concerning the sources of inhibition which could be attributed to processes of the inner ear rather than subsequent neuronal interactions.
There is now accumulating evidence that cortical neurons represent sensory input in a sparse format. Such sparse representations are useful because they make explicit the features contained in sensory data, and they facilitate the learning of associations and higher-order statistical relationships at higher levels of analysis. However, the neural mechanisms of sparse coding are not well understood. Here, I will describe a model neural circuit that computes sparse representations efficiently using a network of recurrently connected leaky integrator + threshold units (essentially a Hopfield network that minimizes a weighted combination of reconstruction error and an activity cost function). When applied to video sequences, the resulting sparse codes demonstrate inertial properties that are more regular (i.e., smoother and more predictable) than representations produced by greedy algorithms such as matching pursuit. I will also describe how sparse representations can be factorized into amplitude and phase components, which then allows higher levels of analysis to learn invariances from natural image sequences.
When learning the parameters of a regression model, one may have control over the set of inputs for which one wants to query the corresponding outputs. Depending on the goals, prior knowledge and model some inputs may be more informative than others. Active learning or optimal experimental design deals with the problem of choosing the optimal inputs.
In this talk we present a general adaptive Bayesian method for experimental design which is more flexible and accurate then existing psychophysical methods and which allows more control over the optimisation of free parameters. In particular, it uses weighted marginal conditional entropies and takes into account nuisance parameters. We investigated the efficency of various enhancements useful for psychophysics such as block designs, dynamic termination and application to common experimental designs.
We also briefly discuss the application of the approach as a normative model of human eye movements.
Effective complexity measures the information content of the regularities of an object. It has been introduced by Gell-Mann and Lloyd to avoid some of the disadvantages of Kolmogorov complexity. In these two talks, we report on recent work with Nihat Ay on effective complexity. In the first talk, we give a precise formal definition, and show that incompressible binary strings are effectively simple. Furthermore, we prove the existence of effectively complex strings, and relate effective complexity to Bennett's logical depth and to Kolmogorov minimal sufficient statistic. In the second talk, we apply effective complexity to ergodic processes. In particular, we show that typical realizations of computable ergodic processes are effectively simple.
Complex systems are often irreducibly complex, i.e. the complexity is lost, if they are separated into independently studied sub-systems. The complexity manifests itself in emerging properties of the complex systems, like long-term correlations (memory effects) and non-linear fluctuation behavior. Such behavior is studied by non-linear time series analysis. Taking the control of the human autonomous nervous system as an example, I will show how long-term correlations and phase synchronization measures applied to heartbeat and respiration signals reflect physiologically different states of the whole complex system. I will present techniques for the reliable quantification of these measures in real non-stationary data recordings. Using the Detrended Fluctuation Analysis (DFA) we found that long-range correlations reminiscent to the wake phase are present only during REM (rapid eye movement) sleep, but not during non-REM (light and deep) sleep [1]. We also found that phase synchronization between heartbeat and respiration is enhanced during non-REM and reduced during REM sleep [2]. Studying brain waves from EEG recordings during the sleep phase, we analyze how the spatial and spectral inter-relations within the brain can be quantified. Very recently, we have developed amplitude and frequency phase synchronization techniques, which show interactions between amplitudes and frequencies of the (quasi-periodic) oscillations in different parts of the brain and in different frequency domains. I will also discuss briefly applications to climate data and climate models.[1] Correlated and uncorrelated regions in heart-rate fluctuations during sleep, A. Bunde, S. Havlin, J. W. Kantelhardt, T. Penzel, J.-H. Peter und K. Voigt, Phys. Rev. Lett. 85, 3736 (2000).[2] Experimental evidence for phase synchronization transitions in human cardio-respiratory system, R. Bartsch, J. W. Kantelhardt, T. Penzel und S. Havlin, Phys. Rev. Lett. 98, 054102 (2007).
Joint work with Nilesh V. Kulkarni
Say we have a set of players engaged in a non-cooperative game, with y being a parameter of that game. So the joint behavior of the players, q, is given by the equilibrium of the game specified by y. In other words, q is a function of y. We consider a ''manager'' who controls y but whose utility function U depends on q. So the manager's problem is to find the y whose associated q optimizes U. This problem can be viewed as an extension of mechanism design, to allow bounded rational players, to exploit knowledgeconcerning players not directly affected by y, and to allow arbitrary types of variable y. We introduce a solution to this problem based on using gradient descent to move a fixed point, and illustrate this solution with computer experiments.
This talk shows how three aspects of human behavior that seem irrational are actually rational:
1) I first present recent work on persona games that explains more features of human behavior in the ultimatum game as actually being rational. I also present new work on persona games that has uncovered an unavoidable tradeoff in the Prisoner's Dilemma: The greater the benefit of cooperation, the less robust that cooperation is against noise.
2) Next, experimentally, a major factor determining an individual's happiness is whether their neighbor is wealthier than they are, no matter what their wealth. I present a model in which marginally greater wealth of a neighbor provides information advising you that exploring for a new strategy is likely to make you wealthier. This can explain unhappiness at a neighbor's marginally greater wealth: it is an emotional ''prod'' that causes you to explore for a new strategy, a prod that substitutes for the full computation of whether to explore.
3) Finally, I present a similar model that explains why people are unhappy if their current wealth is less than their recent wealth, no matter what their current wealth.
We review a novel information-theoretic measure of spatiotemporal coordination in a modular robotic system, and use it as a fitness function in evolving the system. This approach exemplifies a new methodology formalizing co-evolution in multi-agent adaptive systems: information-driven self-organization (IDSO). The methodology attempts to link together different aspects of information transfer involved in adaptive systems, and suggests to approximate direct task-specific fitness functions with intrinsic selection pressures. In particular, the information-theoretic measure of coordination employed in this work estimates the generalized correlation entropy K2 and the generalized excess entropy E2 computed over a multivariate time series of actuators' states. The simulated modular robotic system evolved according to the new measure exhibits regular locomotion and performs well in challenging terrains.
The principles of statistical mechanics and information theory play an important role in learning theory. I start by asking a simple question: given a time series, what is the class of models of the past data that are maximally predictive at a fixed model complexity? Predictiveness is measured by the information captured about future data, while complexity is measured by the coding rate. As a family of solutions, one finds Gibbs distributions, in which the trade-off parameter between complexity and predictive power plays the role of a temperature. I show that, in the low temperature regime, the resulting algorithm retrieves sufficient statistics by finding the causal state partition of the past. This algorithm is essentially a Blahut-Arimoto algorithm, and the above problem can be mapped onto rate--distortion theory and the "information bottleneck" method. I show in examples that by studying the resulting rate--distortion curve, one can learn something about the underlying d ata generating process's "causal compressibility". The rate distortion curve can be computed analytically for some processes, which act as extreme cases: periodic processes and i.i.d. processes. Time permitting, I will discuss issues of complexity control that arise due to sampling errors because of finite data sets.
Agents, including robots and animals, change their environment. Therefore, the data that they observe is to varying degrees a consequence of their own actions. The above lays the ground work for studying "interactive learning", a paradigm that asks for optimal sampling strategies in the presence of feedback from the learner. A quantitative approach to interactive learning and adaptive behavior is proposed, integrating model- and decision-making into one theoretical framework. I follow the same simple principles as above by requiring that the observer's world model and action policy should result in maximal predictive power at minimal complexity. A fundamental consequence of the feedback is that the optimal action policy balances exploration and control. Time permitting, I will discuss some simple examples which can be solved analytically and I will talk about integrating reward maximization into this theory.
In visual masking, a target stimulus is reduced in visibility or detectability by a second stimulus (the mask) presented in close spatiotemporal contingency. For more than one century, visual masking has been used to study perceptual timing. It remains an open debate if masking is caused solely by disruptions in bottom up processing of the visual information flow or involves feedback signals from higher visual areas. After the presentation of basic properties and classical as well as more recent experiments of visual masking, I will introduce a project that had taken place in our institute: We used Chinese characters to study the role of object perception in visual masking. I will show a number of recently performed experiments together with some preliminary results which indicate that the masking effects in our paradigm involve top down signals from higher visual areas concerned with object perception. My talk is also intended to provide feedback to the voluntary subjects from our institute who participated in the experiments.
Two information-theoretic frameworks developed for quantifying spatial structure in dynamical systems are reviewed. In the case of microscopic dynamics, the formalism is applied to cellular automata. Even though entropy is conserved when the dynamics is reversible, there are examples in which the “complexity” of the system increases in time resulting in an apparently more random situation. In the case of macroscopic dynamics, we present a set of quantities that can be used for characterising flows of information in the process of pattern formation in spatially extended chemical dynamics. The connection between these concepts and thermodynamics is discussed.
Technical automation often requires to solve pattern recognition problems. For pattern recognition one needs features which clearly describe the patterns involved. As soon as such features are identified, also the following classification task becomes feasible. Unfortunately, there is no theoretically founded method yet for extracting features with which a pattern recognition problem can be solved optimally. The determination of good features is nowadays based on heuristics and experience of the expert. To take a look at nature might be helpful. The visual cortex employs so called "sparse coding" for representing natural images. We show that on images of technical applications this "sparse coding" generates features with which superior pattern recognition performance can be achieved. This is demonstrated with experiments on digit recognition and face finding. The results support the hypotheses that with "sparse coding" nature eventually has found a universal mechanism for generating good features, and that this mechanism can be highly advantageous also in technical applications.
Contemporary research in the neurosciences produces multivariate time series data from various modalities (EEG,MEG,FMRI,NIRS,etc.). In this talk a statistical framework for the analysis of various classes of such data by predictive modelling will be reviewed; in particular state space models will be discussed. Following a suggestion of Wiener, the residuals of the predictions are called "innovations". Parameter fitting and model comparison can be done by maximisation of likelihood, or preferably by minimisation of an information criterion, such as AIC or BIC. Applications to modelling FMRI and EEG time series will be presented; in the case of the EEG, a new approach to the inverse problem of estimating the source currents within brain will be discussed. Finally the topic of time series filtering and decomposition will be addressed, and an alternative to standard methods like Factor Analysis and Independent Component Analysis (ICA) will be presented.
I present a modification of the Predictive Coding Model (PC, Rao & Ballard, 1999) to nonnegative mappings and representations. The new model retains the advantages of PC but claims to be biologically more plausible. Its major limitations yet is the iterative character of the bottom-up mapping (recognition) which is a consequence of the fact, that the bottom-up synaptic weight matrix and the top-down generative mapping are transposes of each other.
I finally present a new promising approach to learning an inverse of the generative mapping in the bottom-up path using biologically plausible mechanisms. In the new model in development top-down predictions are critically involved in neural self organization.
Optimization problems arise in a wide variety of scientific and engineering applications. It is computationally challenging when optimization procedures have to be performed in real time to optimize the performance of dynamical systems. For such applications, classical optimization techniques may not be competent due to the problem dimensionality and stringent requirement on computational time. One very promising approach to dynamic optimization is to apply artificial neural networks. Because of the inherent nature of parallel and distributed information processing in neural networks, the convergence rate of the solution process is not decreasing as the size of the problem increases. Neural networks can be implemented physically in designated hardware such as ASICs where optimization is carried out in a truly parallel and distributed manner. This feature is particularly desirable for dynamic optimization in decentralized decision-making situations.
In this talk, we will present the historic review and the state of the art of neurodynamic optimization models and applications in winners take all, support vector machine learning and robot kinematic control and joint torque optimization. Specifically, starting from the motivation of neurodynamic optimization, we will review various recurrent neural network models for optimization including quite a few developed by the presenter and his associates. Theoretical results about the stability and optimality of the recurrent neurodynamic optimization models will be given along with many illustrative examples and simulation results. It will be shown that many computational problems, such as sorting, routing, winner-take-all and support vector machine learning, can be readily solved by using the neurodynamic optimization models.
The dynamics of neuronal networks can be modeled either by systems of ODE's or by discrete dynamical systems. The former models seem closer to biological reality, while the latter ones can be easier to study. But under which conditions does a discrete model accurately reflect the dynamics of the underlying ODE system? In this talk we will present a class of neuronal networks with both excitatory and inhibitory synapses for which a strict correspondence between ODE dynamics and discrete dynamics can be rigorously proved. We will describe the network architectures and both the ODE and discrete models, state the theorem about the correspondence, sketch the main idea of the proof, and review some results how the discrete dynamics depends on the connectivity of the network. The talk is based on joint work with David Terman, Sungwoo Ahn, and Xueying Wang of the Mathematical Biosciences Institute and Ohio State University.
In our approach of evolutionary robotics we generate recurrent neural network of arbitrary structure to control autonomous robots in different environments performing various tasks. In dynamically changing and partially unknown environments it is hard if not impossible to define error functions for an on-line learning rule. Therefore, in this context, a learning method must be local and unsupervised. Most of today's local and unsupervised learning rules are variations of the Hebbian Learning Rule, including its limitations, or reinforcement techniques.
In the proposed model each neuron is a self-regulating unit, motivated by Ashby's Homeostat, stabilising its activity towards a target value. In the sensorimotor loop, when such a recurrent neural network with self-regulating neurons is controlling a robot, this regulation process is constantly disturbed by external stimuli. In order to compensate for these disturbances, each neuron has two additional internal properties, motivated by receptors and transmitters of biological neurons. The overall behaviour is the result of the interplay of the self-regulating neurons.
In my talk I will present the followed approach of evolutionary robotics, the software framework which I have designed and written in large parts, as well as the neuron model.
The problem of finding clusters in complex networks has been studied by mathematicians, computer scientists and, more recently, by physicists. Many of the existing algorithms partition a network into clear clusters without overlap. We introduce a method to identify the nodes lying "between clusters", allowing for a general measure of the stability of the clusters. Our method can be used with any clustering algorithm. We present several applications on real-world networks using two different clustering algorithms.
Informally learning denotes the ability of a system to improve its (behavioral) performance if necessary. Especially in a complex system this might be very difficult due to complicated interdependencies between the system parameters and its performance. There seems to exist a sever tradeoff between the number of parameters that are adapted (a crude measure of the size of the search space) and the complexity of their interdependencies, as suggested from simulations of recurrent neural networks. To better understand the properties of this learnability tradeoff a more formal description is certainly necessary. Therefore some attempts towards formalizing learnability and related concepts, such as modularity, will be discussed.
Information is an essential and omnipresent resource and has long been suspected as a major factor shaping the emergence of intelligence in animals and as a guideline to construct artificial intelligent systems. In search for fundamental principles guiding the self-organization of neural networks, Linsker (1988) formulated a number of information-theoretic hypotheses. His model (and most of its successors) was purely passive. However, recent work by Touchette and Lloyd (2000) extending early work by Ashby (1953), as well as some work by Polani et al. (2001) has shown that actions can be incorporated into the information-theoretical analysis.
As was found by Klyubin et al. (2004), incorporating actions into an information-theoretic formalization of the perception action-loop of agents has dramatic consequences in terms of self-organization capabilities of the processing system. As opposed to Linsker's model which required some significant pre-structuring of its neural network, this new model makes only minimal assumptions about the information processing architecture. The agent's "embodiment", i.e. the coupling of its sensors and actuators to the environment, is sufficient to give rise to structured pattern detectors driven by optimization principles applied to the information flow in the system.
In the present talk, we will motivate Shannon information as a primary resource of information processing, introduce a model which allows to consider agents purely in terms of information and show how this model gives rise to the aforementioned observations. If there is time, the talk will discuss the use of information-theoretic methods to structure the information processing also in real robot systems.
The investigation of macroscopic brain activity, as encephalographic signals or local field potentials, plays an important role in the neuropsychology and are supposed to reflect the activity of neural populations. Thus in order to understand information processing in the brain, it is necessary to examine the space-time activity of neural populations, whose activity is strongly related to macroscopic experimental data. The presented work examines an Amari-like neural field model and presents the effects of spatial nonlocal interactions in neural populations while involving general synaptic connectivities and axonal transmission delay. The effects of external constant stimulation, random fluctuations and spatiotemporal stimuli are studied. We find space-time instabilities, traveling fronts, stimulus-evoked propagating pulses and noise-retarded phase transitions.
Following the Artificial Life approach to Evolutionary Robotics the goal of Neurocybernetic Machines is to test hypotheses on the possible realization of artificial cognitive systems. In this context a modular neurodynamics approach to cognition is adopted, which should lead to a bottom up development of larger systems with more and more comprehensive abilities. Since the ability to categorize the features and effects of the real world in behavior relevant terms a rich reservoir of attractors is essential. A reasonable complexity measure for the attractor structure of a neuromodule should help to set up rules for an effective coupling of such functionally segregated modules; effective here refers to what may be called an "emergent" neurodynamics. The modular neurodynamics approach is introduced and a topological complexity measure (R. Thom) is discussed.
Following the Artificial Life approach to Evolutionary Robotics the goal of Neurocybernetic Machines is to test hypotheses on the possible realization of artificial cognitive systems. In this context self-organization in the form of synaptic plasticity of neural networks serving as control systems for autonomous mobile robots is an interesting subject to study. We introduce an approach to adaptivity and plasticity of controllers based on homeostatic neurons and discuss its relation to structure evolution of neural controllers.
Contour integration is an important step in the decomposition of a visual scene into distinct objects (figure-ground segmentation). During this process, oriented and aligned edge elements are bound together to form a coherent contour.
Psychophysical experiments revealed that contour integration in macaque monkeys and human observers is both very efficient and astonishingly fast. This high performance challenges computational algorithms of contour integration, and opens the question about the relevant neurophysiological mechanisms underlying this specific part of neural information processing.
Several algorithms for contour integration have been proposed, ranging from probabilistic algorithms with multiplicative, directed interactions up to neural networks with long-ranging additive, undirected horizontal couplings. We investigate these different model classes by requiring that a suitable, neurophysiologically plausible model should not only reproduce the performance of human observers, but also systematic errors made during the integration of contours. Our analysis of these errors predicts that contour integration in the brain is mediated by multiplicative and directed interactions, as opposed to current models employing additive and non-directed interactions.
Cortical dynamics is frequently modeled on the basis of two extreme network architectures: recurrent random networks or feed-forward networks. The first exhibit a variety of states which resemble cortical in-vivo activity in a statistical sense. The latter highlight the potential functional relevance of the precise timing of individual spikes. Here, we show that under realistic conditions both scenarios are compatible and can be incorporated into a single network model.
While synaptic learning mechanisms have always been a core topic of neural computation research, there has been relatively little work on intrinsic learning processes, which change a neuron's excitability. I will present models of intrinsic plasticity that are based on information theoretic principles, and I will discuss the potential synergistic relation between such intrinsic plasticity mechanisms and Hebbian plasticity at a neuron's synapses. I will show how individual neurons and networks of neurons can utilize these ideas for learning sensory representations.
Recurrent neural networks in time series prediction tasks are traditionally trained with a gradient decent based learning algorithm, notably with back-propagation (BP) through time. A major drawback for the biological plausibility of BP is that it is a supervised scheme in which a teacher has to provide a fully specified target answer to the network. Yet, agents in natural environments often receive a summary feed-back about the degree of success or failure only, a view adopted in reinforcement learning schemes.
In this work we show that for simple recurrent networks in prediction tasks for which there is a probability interpretation of the network's output vector, Elman back-propagation can be implemented as a reinforcement learning scheme for which the expected weight updates agree with the ones from traditional Elman BP, using ideas from the AGREL learning scheme (van Ooyen and Roelfsema 2003).
While there are other draw-backs of BP learning schemes, which we are going to discuss, we hope to contribute to making the widely used BP training scheme more acceptable from a biological point of view.
The vertebrate retina is inverted with respect to optical function; light traverses significant scattering tissue before reaching the photoreceptors. Without additional functionality, this architecture would critically hinder scotopic (low-light-level) vision. Here we show that the retina contains living optical fibers, the Müller glial cells, which efficiently guide light through the scattering layers. Measured transmission and scattering properties of Müller cells, both in their natural matrix, and in isolation, indicate the presence of propagating modes. This finding ascribes a new function to glial cells and enables the understanding of the inverted retina as a complete optical system.
Slow Feature Analysis (SFA) is an algorithm for extracting slowly varying features from a quickly varying signal. We have shown in network simulations on 1-dimensional stimuli that visual invariances to shift, scaling, illumination and other transformations can be learned in an unsupervised fashion based on SFA [1].
More recently we have applied SFA to image sequences generated from natural images using a range of spatial transformations. The resulting units share many properties with complex and hypercomplex cells of early visual areas [2]. All are responsive to Gabor stimuli with phase invariance, some show sharpened or widened orientation or frequency tuning, secondary response lobes, end-stopping, or selectivity for direction of motion. These results indicate that slowness may be an important principle of self-organization in the visual cortex.[1] Wiskott, L. and Sejnowski, T.J. (2002). Slow Feature Analysis: Unsupervised Learning of Invariances. Neural Computation, 14(4):715-770. http://itb1.biologie.hu-berlin.de/~wiskott/Abstracts/WisSej2002.html [2] Berkes, P. and Wiskott, L. (2005). Slow feature analysis yields a rich repertoire of complex cell properties. Journal of Vision, (accepted). http://itb1.biologie.hu-berlin.de/~wiskott/Abstracts/BerkWisk2005c.html
We suggest a method for suppression of synchrony in a globally coupled oscillator network, based on the time-delayed feedback via the mean field. Having in mind possible applications for suppression of pathological rhythms in neural ensembles, we present numerical results for different models of coupled bursting neurons. A theory is developed based on the consideration of the synchronization transition as a Hopf bifurcation.
Complex brain functions are not simply the sum of modular information processing but arise from a continuous interaction of densely connected brain structures. We investigate the structural and functional characteristics of brain networks based on anatomical, electrophysiological and imaging data. These studies provide evidence of a consistent, but non-trivial coupling of structure, function and plasticity of the brain. I will show examples of how this coupling can be used to understand the network mechanisms that generate functional observables and, vice versa, to characterize the anatomy that underlies such mechanisms. References:- Passingham R.E., Stephan K.E., Kötter R. (2002) The anatomical basis of functional localization in the cortex. Nature Rev. Neurosci. 3: 606-616. - Stone J.V., Kötter R. (2002) Making connections about brain connectivity. Trends Cogn. Sci. 6: 327-328. - Kötter R., Stephan K.E. (2003) Network participation indices: Characterizing component roles for information processing in neural networks. Neural Networks 16: 1261-1275. - Kötter R. (2004) Online retrieval, processing, and visualization of primate connectivity data from the CoCoMac database. Neuroinformatics 2: 127-144. - Sporns O. & Kötter R. (2004) Motifs in brain networks. PLoS Biol. 2: 1910-1918.
Increasing noise in nonlinear systems far from equilibrium may induce a more ordered state compared with the case without noise. Our interest is devoted to excitable systems which model a wide class of dynamical behavior in biophysics and chemistry. We formulate a noisy FitzHugh-Nagumo dynamics and discuss the dynamic output by stochastic measures as the stationary spike generation rates, the spike diffusion coefficient and the power spectrum. The analysis shows that deterministic bistable and excitable dynamics converts into stochastic oscillating systems with a high value of the oscillations for non-vanishing noise. As an application we investigate the temporal behaviour of a cluster of inositol-(1,4,5)-triphosphate receptor (IP3R)-I channels. We obtain the spectrum of the calcium signal within a cluster. We compare these results with stochastic simulations and obtain an intermediate number of channels per cluster for optimal signalling periodicity. We also study a cluster of N globally coupled FitzHugh-Nagumo systems and find a rather complex sequence of transitions if noise induced oscillations are generated. These numeric findings were completed by a bifurcation analysis of the dynamics of relevant cumulants which qualitatively agrees well with the simulations.Literature:B. Lindner, J. Garcia-Ojalvo, A. Neiman, and L. Schimansky-Geier, Phys. Report 392, 321-424 (2004).B. Lindner and L. Schimansky-Geier, Phys. Rev E 61, 6103-6110 (2000)B. Lindner, L. Schimansky-Geier, and A. Longtin Phys. Rev. E 66, 031916 (2002).L. Meinhold and L. Schimansky-Geier, Phys. Rev. E 66, 050901 (2002).M. Zaks, X. Sailer, L. SChimansky-Geier, and A. Neiman, Noise Induced Complexity: From Sub- to Superthreshold Oscillations in Coupled Excitable Systems, submitted 2004.
Sensitization means an increasing responsiveness after stimulation and represents a rather ubiquitous biological principle relevant for adaptation and mal-adaptation. We are interested in the basic mechanisms of sensitisation which underly longterm neuronal activity changes under normal and pathological conditions. For that, we recently have explored the dynamics of intrinsic oscillatory neurons engaged in positive feedback loops. The feedback loop becomes activated when a neuron spikes with the result of further excitation. The dynamics depend on the intrinsic properties of the respective neuron (including applied current or temperature range), the "synaptic" or "sensitization" strength, the associated time constant and external factors such as added noise. Dependent on the parameter region we find different periodic and chaotic spiking patterns with stable feedback behavior. As result of the chaotic dynamics of the model, the parametric range for stable spiking patterns is remarkably large. Implications for neurophysiology as well as pathological conditions will be discussed.
Huber MT, Braun HA, Krieg JC (2004): Recurrent affective disorders: nonlinear and stochastic models of disease dynamics. International Journal of Bifurcation and Chaos 14:635-652. Sainz-Trapaga M, Masoller C, Braun HA and Huber MT (2004): Influence of time-delayed feedback in the firing patterns of thermally sensitive neurons. Physical Reviews E 70:031904. Braun HA, Schäfer K, Voigt K and Huber MT (2003): Temperature encoding in peripheral cold receptors: oscillations, resonances, chaos and noise. In: Nonlinear dynamics and the spatiotemporal principles in biology. Nova Acta Leopoldina NF Bd. 88. Nr. 332.Huber MT, Braun HA, Krieg JC (2003): On episode sensitization in recurrent affective disorders: the role of noise. Neuropsychopharmacology 28: S13 -S20.Huber MT, Braun HA, Krieg JC (2001): Impact of episode sensitization on the course of recurrent affective disorders. Journal of Psychiatric Research 35: 49 - 57.
Transition to (complete) synchronization in extended systems can occur via two different scenarios One corresponds to multiplicative noise transition and is described by a Kardar-Parisi-Zhang equation with a repulsive wall.
A second scenario is that of directed percolation. The problem can also be mapped onto (non-equilibrium) wetting transitions. A finite-amplitude Lyapunov analysis helps understanding the macrosocpic behaviour.
Experimental and theoretical evidence suggests that the development of orientation preference maps (OPMs) constitutes an activity-dependent self-organization process. The formation of OPMs in the visual cortex can be modelled by dynamic field equations [1,2]. Key features of such models strongly depend on the symmetries of the dynamics [2]. We presented a new class of Gaussian random maps which allows to study the consequences of shift-twist symmetry (STS), a fundamental symmetry of visual cortical circuitry [3], on the layout of orientation maps. This symmetry mathematically describes that the position of stimuli in the visual field and the preferred orientation of visual cortical neurons ought to be represented in a common coordinate system. Here we use this approach to identify signatures of this new symmetry which are accessible to experimental testing. We find that STS predicts a locking of the layout of the OPM to the retinotopic map. We calculate the joint probability density of the relative orientation preference of separate columns, as a function of their relative distance and direction. We find that this distribution exhibits a characteristic cloverleaf-like shape. The theoretical predictions are compared to OPMs obtained from tupaia and galago visual cortex. [1] Swindale, N.V. Network, 7:161 (1996) [2] Wolf & Geisel, Nature (1998) 395:73 [3] Bressloff, Cowan, Golubitsky, Thomas, Wiener, Phil.Trans.R.Soc.London.B (2001) 356:299
Motion of an extended boundary can be measured locally by neurons only orthogonal to its orientation (aperture problem) while this ambiguity is resolved for localized image features, such as corners or nonocclusion junctions. The integration of local motion signals sampled along the outline of a moving form reveals the object velocity. We propose a new model of V1-MT feedforward and feedback processing in which localized V1 motion signals are integrated along the feedforward path by model MT cells. Top-down feedback from MT cells in turn emphasizes model V1 motion activities of matching velocity by excitatory modulation and thus realizes an attentional gating mechanism. The model dynamics implement a guided filling-in process to disambiguate motion signals through biased on-center, off-surround competition.
Our model makes predictions concerning the time course of cells in area MT and V1 and the disambiguation process of activity patterns in these areas and serves as a means to link physiological mechanisms with perceptual behavior. We further demonstrate that our model also successfully processes natural image sequences.
In this talk I will also present some recent extensions and results obtained with our model.
Some recent results for Hodgkin-Huxley neurons with stochastic input will be described, including those obtained by both analytical and simulation methods. Theorems on network activity where the dynamics of single neurons are given will also be discussed.
Recent experiments have studied waves of electrical activity propagating in various brain regions. Neural field models provide a mathematical framework for the theoretical description of this type of activity.
In the mean-firing-rate approach, the activity of a continuously distributed neural network is modeled by an integral equation for the mean membrane potential. We discuss traveling wave solutions of this equation, and how they are influenced by the distance-dependent axonal propagation delay.
Pulse-coupled oscillators constitute a paradigmatic class of dynamical systems interacting on networks because they model a variety of biological systems including flashing fireflies and chirping crickets as well as pacemaker cells of the heart and neural networks. Synchronization is one of the most simple and most prevailing kinds of collective dynamics on such networks. Here we demonstrate, how breaking different symmetries of the network dynamics affects collective synchronization, often leading to the breaking of synchrony.
Globally coupled, symmetric networks without interaction delays attract every random initial condition towards the completely synchronous state. However, we show that the presence of delays or structured network connectivity lead to completely different phenomena: exponentially many periodic attractors, attracting yet unstable periodic orbits, long chaotic transients, and the coexistence of irregular, asynchronous with regular, synchronous dynamics. Furthermore, we investigate the speed of synchronization in structured networks using random matrix theory. Although, as might be expected, the speed of synchronization increases with increasing coupling strengths, it stays finite even for infinitely strong interactions. The source of this speed limit is determined by the connectivity structure of the network.
Which conditions are necessary and sufficient for the brain's generation of a visible percept under natural viewing conditions?
We might take as a necessary requirement the presence of a physical pattern of light striking the retina. The activation of retinal neurons will cause a cascade of activity coursing its way through the visual system which can then be registered by the brain, and ultimately contribute to perception. But is this sort of automatic sensory response a sufficient condition for a stimulus to be perceived? This question is underscored by the variety of visual suppression phenomena, in which normally visible targets are rendered completely invisible. We developed a paradigm that permits a host of salient and attended patterns to suddenly disappear from view, and remain invisible for up to several seconds and investigated it with psychophysical methods in humans and monkeys (Wilke et al., 2003).
In addition, multielectrode recordings were performed in the visual cortex (V1, V2 and V4) of awake and reporting/fixating monkeys under visual stimulation leading to perceptual suppression. We found that whereas the early visual cortex plays an important role in the detection of congruent vs. incongruent visual stimulation, the changes in neuronal firing rate according to stimulus visibility are rather subtle in comparison with a physical stimulus removal.
I will discuss the geographical spread of infectious diseases in a modern world in which humans travel on all scales. As an appetizer I will present a model for the geographical spread of the Severe Acute Respiratory Syndrome (SARS) on the entire civil aviation network and show that this network can be employed to identity endangered regions of future epidemics.
I will show that scale free dispersal is linked to a class of random walks known as Levy flights which leads to a description in terms of fractional reaction-dispersal equations which exhibit dynamics vastly different from ordinary reaction diffusion systems.
The accelerating progress in hard and software technology, and the decreasing production costs open new opportunities, and at the same time arise new conceptual and methodological demands on an interface between the real and artificial intelligence. The individual is differentiated from the statistical averages, and stands with all his/her particularities, capabilities and deficits, more and more at the focus of the technological developments. On the other hand, conditioned by the desire of being able to control diverse components, such as multimedia applications, environmental conditions (e.g., light and sound in a room) and external devices, a general technology is requested.
In order to fulfill these two contradictory requirements, a concept for a flexible and adaptive brain computer interface (ABCI) is developed and technically implemented. Our studies concentrate on the development of a methodology which can enable the configuration and realization of a subject specific interface. Based on the advanced neurobiological and psychophysiological findings on the role and generation mechanisms of the slow cortical potentials (SP), and in consultation with experienced researchers in the field, an SP-based interface is constructed as a sample application. It is successfully used for self-regulation of brain activity by means of multimedia feedback.
Non-negative Matrix Factorization (NMF) for its restriction of computation to positive vectors and components appears to be biologically plausible. In my talk I will argue that NMF even may serve as an example of how a recurrent neural network which employs spike-timing dependent neural plasticity and synaptic adaptation might work. Resulting problems and directions for their solution will be presented.
The time course of forgetting is known since Ebbinghaus' classical studies in the late 19th century and has been confirmed hundreds of times. In contrast to many relaxation processes in physics the time course is not exponential but more of the form of a power law. Many formulas have been suggested to describe the time course of forgetting, but no theory exists to predict any of them.
In this talk I will present a neuronal net as a tool to study the dynamics of memory. The equivalence between this net and diffusion processes is explained, and then new developments in the domain of kinetics are applied to this memory model, resulting in the well-known forgetting curves of Ebbinghaus and his followers.
A neural network is presented which is based on a columnar interconnection architecture. Motivated by neuroanatomical and neurophysiological findings we model a cortical macrocolumn as a collection of inhibitorily coupled minicolumns, which themselves consist of randomly interconnected spiking neurons. A stability analysis of the system's dynamical equations shows that minicolumns can act as monolithic functional units for purposes of critical, fast decisions and learning. Oscillating inhibition (in the gamma frequency range) leads to a phase-coupled population rate code and high sensitivity to small imbalances in minicolumn inputs. If afferent fibers to the minicolumns are subject to Hebbian plasticity, minicolumns self-organize their receptive fields to become classifiers for the input patterns.
The presentation will include the analytical treatment of the dynamics along with bifurcation diagrams and various computer simulations.
Pharmacologically isolated GABAergic interneurons in the mouse visual cortex display highly irregular spike times (coefficient of variation ? 1) in response to DC de-polarization. This is in marked contrast to cortical pyramidal cells. We used non-linear time series analysis methods to distinguish between the presence of non-linear deterministic processes or the amplification of sub threshold noise giving rise to the observed dynamics. No evidence for non-linear deterministic processes was found. This leaves a high sensibility of the interneuronal spike initiation process for membrane potential noise as the most likely explanation for the high CV. We propose that this intrinsically irregular spiking of an important subpopulation of cortical neurons contributes to the overall irregularity of cortical activity.
Recurrent Neural Networks are powerful, biologically inspired models for computations on time varying input signals. Due to their high-dimensionality it is difficult to utilize their power for information processing. In this talk a new framework will be presented that allows to investigate the computational capabilities inherent in large, randomly connected networks. Using this framework a link between the network dynamics and its computational capabilities is found.
The results illustrate the idea that dynamical systems support computations optimally if they operate at the "Edge of Chaos", a notation which can be formally defined in networks of McCulloch-Pitts neurons. This allows to analyse how the dynamics of such networks depends on the parameters controlling the connectivity distribution. In particular the critical boundary is calculated where the dynamics changes from ordered to chaotic.
Neural activity can be measured by different experimental techniques, as single cell measurements on a microscopic spatial scale (~0.05-0.2 mm) or local field potentials at a mesoscopic spatial scale of some millimeters. As these different spatial scales exhibit different neural mechanisms, most neural models focus to a single scale. The presented talk discusses the stability of mesoscopic activity in synaptically coupled neural fields subject to propagation delays. Since concrete synaptic connectivities are unknown in most neural areas, the work derives stability conditions for arbitrary homogeneous connectivities. The application to gamma-distributed connectivity kernels reveal a novel condition for stationary Turing instabilities.
One of the most intriguing problems in brain research is the high interpersonal variability of the human cortical folding. In this talk, a sequence of image analysis procedures applied to magnetic resonance imaging data will be presented that may help to shed some light on this problem. The aim of these procedures is to extract a generic model of the human cortical folding and to infer rules that govern the formation of cortical folds.
Convolution is one of the most common operations in image processing. For a nervous system to perform such an operation on a topographic map, e.g. to blur a sensory representation of the visual field, would require an extensive network of local cells where each cell connects with all others. Based on experimental findings on two large-field visual interneurons of the fly, I will show by realistic compartmental modeling that a linear dendro-dendritic electrical coupling has the capability to perform this operation.
We will first give an overview on how we have applied differential geometry to study human vision and to improve computer-vision algorithms. Key questions are: what differential invariants should be used to describe image structure; what kind and what amount of information do these invariants encode? We will show that if the visual input is regarded as a hypersurface, the curved regions of that hypersurface determine the input uniquely although a representation by curvature is sparse. We believe that these questions can be well understood based on the concept of intrinsic dimension that refers to the number of locally used degrees of freedom.
Evolutionary robotics in the context of recurrent neural networks seems to be a promising approach to demonstrate and test the relevance of complex internal dynamics of neural systems for nonlinear control problems. An evolutionary algorithm, called ENS^3 (evolution of neural systems by stochastic synthesis), has been successfully applied for behavior control of divers robot platforms and tasks.
The ENS^3 algorithm is applied to networks of standard additive neurons with sigmoidal transfer function and it is designed to generate recurrent architectures allowing complex dynamics. In this talk experiments of the following domain are presented: robust behavior control, sensor fusion and environment representation for differential wheel driven robots; obstacle avoidance controller for an omni-directional robot platform; sensor and behavior fusion in the domain of RoboCup Middle Size League; evolution of morphology and neuro-controller for a biped walking machine; co-evolution experiments in the micro.adam / micro.eva art project of Julius Popp.
Rule extraction (RE) from a recurrent neural network (RNN) is a process of finding a computational machine "as equivalent as possible" to the underlying RNN. RNNs are in principle Turing machine equivalent, but RE typically extracts state machines. A survey of existing RE techniques will be presented and evaluated in this talk.
Combining "additive" and "multiplicative" harmonic analysis to reconstructing trees from binary sequence data presuming a simple probalistic model for sequence evolution.
Neural maps can be taken as biologically inspired vector quantizers including the concept of neighborhood cooperativeness in standard vector quantization. Two important models are self-organizing maps (SOM) and neural gas (NG). Besides the standard error, the squared reconstruction error, several other parameters exist to assess the properties of a map. One of these is the so-called magnification of a map which relates the data probability density to the weight vector density achieved after learning. In the talk we consider different ways to control the magnification in SOM and NG. Starting from well-known and extended control approaches for SOM we transfer these ideas to the NG. We show that the approaches are similar but not identic. Moreover we emphasize the fact that the NG results are valid for any data dimension whereas in the SOM case the results only hold for the one-dimensional case.
Overt behavior is always based on a direct link between sensory and motor surfaces. Moreover, behavior is typically adjusted to the perceived environment, a current "task" setting, and to longer term goals. These two boundary conditions of behavior are emphasized in the "embodied cognition" approach to cognition. This talk introduces the concepts of dynamic field theory, in which simple cognitive properties such as decision making and working memory emerge from a mathematical description of behavior that remains close to sensori-motor processes. Models and related experiments in movement preparation, the development of action planning and spatial memory will be reviewed.
In recent years support vector machines (SVM's) became one of the most successful learning algorithms. In this talk I will present an overview of some recent developments in the theory of these algorithms including:- the role of the kernel and its approximation properties- asymptotic theory of SVM's- some lower bounds on the number of support vectors- incorporating knowledge in nu-SVM'sFinally, I will squetch some interesting open questions.
In physics and biophysics we often deal with many-body systems with components that interact with each other and are subjected to fluctuations. We will discuss a mean-field approach to describe systems of this kind. This approach leads to a one-particle description of many-body systems in terms of nonlinear Fokker-Planck equations.
We will discuss two applications of this mean-field approach: a) multistable stochastic networks and b) networks that exhibit both flexibility and a small amount of variability. Both applications may play an important role for complex motor control systems of humans and animals (as realizations of neural task-related circuitries). For example, horses are believed to have a multistable motor control system (for a given speed they can walk in two different fashions: pace and trot). Flexible and accurate movements are in particular required in sport exercises.
The assembly hypothesis suggests that information processing in the cortex is mediated by groups of neurons by their coordinated spiking activity. Thus, the unitary events analysis (Grün et al (2002)) was designed to detect the presence of conspicuous spike coincidences in multiple single unit recordings and to evaluate their statistical significance. The method assumes spike trains as Poisson processes to realize the null-hypothesis of independent processes leading to a parametric significance estimation. Since experimental data often violates the assumption of an Poisson processes I will present you a non-parametric significance test based on the method of combined shuffling and resampling ('CSR'; Pipa & Grün (2002)). The CSR method considers the original temporal structure of the experimental spike trains and do not assume a special underlying spike train generating stochastic process.
In order to quantify the degree of coupling between stochastic processes with discrete state space, a new quantity called transfer entropy was introduced by T. Schreiber (2000). Recently, this concept has been carried over to continuous processes. Based on information theory, transfer entropy gives the amount of information which is transmitted from one process to the other. In contrast to mutual information any information which is travelling within the driven process through time is excluded. Thus, transfer entropy measures the effective information transmission from the driving system to the driven system. For bidirectional coupled systems the transfered information in each coupling direction can be calculated.
Transitions from neuronal single-spike discharges to impulse groups, i.e. tonic-to-bursting bifurcations, are of particular physiological and pathophysiological relevance for major autonomous and cognitive functions. Experimental recordings have shown that such transitions are often associated with distinct irregularities of the firing patterns as we have seen, for example, in peripheral cold receptors and hypothalamic neurons (Braun et al. Pflügers Arch 386:1-9, 1980; Dewald et al. J Thermal Biol 24: 339-345, 1999). Recently developed methods for the detection of unstable periodic orbits (UPOs) indicate that the irregular firing is not only caused by stochastic components ("noise") but partly results from "deterministic chaos" (e.g. Braun et al. J Comp Neurosci 7: 17-32, 1999).
For a better understanding of these neuronal pattern generators we use a Hodgkin-Huxley type computer model which consists of a minimal set of ionic conductances for spike-generation and subthreshold oscillations (Braun et al., Int J Bifurc & Chaos 8: 881-889, 1998). With addition of noise it successfully mimicks the experimentally observed impulse patterns and their stimulus dependent modifications including the occurrence of UPOs. Moreover, simulation runs without noise clearly exhibited a broad range of deterministic chaos at tonic-to-bursting bifurcations (W Braun et al., Phys Rev E 62: 6352-6360, 2000; Feudel et al., Chaos 10: 231-239). These chaotic dynamics can be seen as the result of "critical" interactions between the two oscillatory subsystems, i.e. the subthreshold oscillations and the spike-generating processes (Braun et al. Neurocomputing 32: 51-59, 2000). However, in "noisy" simulations the unstable regime seems to be considerably extended towards the deterministically regular spiking range (Braun et al. Biosystems 62: 99, 112, 2001) which eventually allows the anticipation of tonic-to-bursting bifurcations and their control.
Given some function f(x), a solution g of the functional equation g(g(x))=f(x) is called an iterative root of f. This functional equation can be mapped to the topology of a neural network which is consequently able to find approximate solutions for g. Algebraic methods struggle with this problem even on simple functions, try g(g(x))=x2+1 for example. Applications range from embedding discrete time data into continuous time models to the modelling of certain industrial processes.
Since Emmi Noether we know that many fundamental laws of nature can take the form of functional equations. Many of these can be translated into the structure of neural networks, too. These networks then embody the corresponding theory and may have the inherent capability to model respective systems from a very limited set of training examples. Their generalization capability within the appropriate domain should go beyond that of traditional artificial neural networks because they are not "universal approximators" anymore but will take the specified laws of nature in account for their predictions.
In the primary stages of the visual system, different areas are devoted to the processing of different stimulus features like orientation, color, or movement. During perception, these features will be grouped together to form representations of "objects". Psychophysical experiments revealed that the spatial as well as the temporal context of visual stimuli play an important role in this grouping process. By driving the visual system to its spatial and temporal limits, it is even possible to induce erroneous groupings.
The dynamics of this complex grouping process involving a whole hierarchy of processing stages in the brain can be captured by a structurally simple cortical model consisting of an excitatory and an inhibitory neuronal layer. Both layers are coupled reciprocally, and receive input from the model retina, where the same stimuli being used in the masking experiments are shown. The visibility and the grouping of specific stimulus features is determined by the duration of a transient activation in the neuronal layer. The dynamics of the network reveals possible mechanisms underlying the experimentally observed phenomena, while its simple structure allows for an analytical treatment and fit of parameters.
Classification is an essential operation for data analysis tasks: either an unsupervised natural grouping of data items is desired in order to identify potential similarities, or a supervised active class separation is required for prediction problems or decision making. Two well-known and biologically plausible algorithms are the supervised Learning Vector Quantization (LVQ) and the unsupervised Self-Organizing Maps (SOM) proposed by Kohonen.
In the talk, we focus on perspectives of transfering paradigms of self organization to the field of compositionality and structured data.
Extensions of LVQ are discussed: structure can be taken into account by implementing an adaptive metric. Here, we present an intuitive method which involves relevance factors. This additional structure can be used for an efficient rule extraction scheme. Turning prototypes into rules leads to easier data interpretation and constitutes a step towards a hybrid system.
Finally, a brief glance will be thrown at ongoing work about an alternative method for unsupervised learning: incorporating the idea of recurrent and recursive nets into SOM, the data structure is stored in the dynamics itself. This is a new approach to sequence processing and to the treatment of graph structures integrating several techniques like TKM, Recursive SOM, and SOM-SD.
The talk introduces a constructive learning algorithm for the supervised training of recurrent neural networks, which is characterized by two properties: (1) a large "echo state" recurrent neural network is used as a "reservoir" of complex dynamics; this network is not changed by learning; (2) only the weights of connections from the echo state network are learnt. The basic mathematical idea is sketched, and a number of theoretical and application-oriented examples are given. The theoretical examples demonstrate a number of novel phenomena in recurrent networks; for instance, the training of short-term memories with large memory spans (100 time step delayed recalls are easily obtained), the training of infinite-duration memories (input-switchable multistate attractors), or the training of arbitrary periodic sequences (n-point attractor learning). The application-oriented examples mostly come from robotics and include the training of motor-controller modules and of event detectors for robots.
Classical selforganisation effects like pattern formation and phase transitions were observed in the human brain. The neural field model proposed by Wilson and Cowan (1973) allows a mathematical description for some of this phenomena, which might play an important role for the understanding of the human brain activity.
We study the dynamics of two-dimensional neural fields of activator-inhibitor-type and consider three types of external stimulation: homogeneous and stationary fields, homogeneous and oscillatory fields and localised excitation. Numerical simulations of the basic equations show interesting behaviors for the neural response, such as spatio-temporal pattern formation, frequency demultiplication, and travelling waves.
We will deal with the connection of symbolic and subsymbolic systems. The focus lies on the question of how is it possible to process symbolic data with neural networks. In so doing we examine the in principle capability of representing and learning symbolic data with various neural architectures which constitute partially dynamic approaches: discrete time partially recurrent neural networks as a simple and well established model for processing sequences, and advanced generalizations for processing tree structured data. Methods like holographic reduced representation, binary spatter codes, recursive autoassiociative memory, and folding networks share the in principle dynamics of how symbolic data are processed, whereas they differ in the specific training methods. We consider the following questions: Which are the representational capabilities of the architectures? Are the involved problems learnable in an appropriate sense? Are they efficiently learnable?
The analysis of neuronal responses to noisy input is a daunting task even for severely abstracted model neurons such as the leaky integrate-and-fire neuron. At best, time-consuming numerical methods can be employed, but often results can only be obtained via simulations. This hinders both a deeper understanding of the parameter dependence of the neuronal dynamics under study, and complicates, e.g., fits to experimental data. I will present escape noise approximations to integrate-and-fire neuronal dynamics, which lead to closed form expressions for the interspike-interval density of the neurons response, and discuss applications of these models to noisy neuronal dynamics.
If the cortex is an associative memory, strongly connected cell assemblies will form when neurons in different cortical areas are frequently active at the same time. The cortical distributions of these assemblies must be a consequence of where in the cortex correlated neuronal activity occurred during learning. An assembly can be considered a functional unit exhibiting activity states such as full activation (ignition) after appropriate sensory stimulation (possibly related to perception) and continuous reverberation of excitation within the assembly (a putative memory process). This has implications for cortical topographies and activity dynamics of cell assemblies representing words. Cortical topographies of assemblies should be related to aspects of the meaning of the words they represent, and physiological signs of cell assembly ignition should be followed by possible indicators of reverberation. The following postulates are discussed in detail: (1) assemblies representing phonological word forms are strongly lateralized and distributed over perisylvian cortices; (2) assemblies representing highly abstract words, such as grammatical function words, are also strongly lateralized and restricted to these perisylvian regions; (3) assemblies representing concrete content words include additional neurons in both hemispheres; (4) assemblies representing words referring to visual stimuli include neurons in visual cortices; (5) assemblies representing words referring to actions include neurons in motor cortices. Two main sources of evidence are used for evaluating these proposals: (a) imaging studies aiming at localizing word processing in the brain, based on stimulus-triggered event-related potentials (ERP), positron emission tomography (PET) and functional magnetic resonance imaging (fMRI), and (b) studies of the temporal dynamics of fast activity changes in the brain, as revealed by high-frequency responses recorded in the electroencephalogram (EEG) and magnetoencephalogram (MEG). These data provide evidence for processing differences between words and matched meaningless pseudowords, and between word classes such as concrete content and abstract function words, and words evoking visual or motor associations. There is evidence for early word class-specific spreading of neuronal activity and for equally specific high-frequency responses occurring later. These results support a neurobiological model of language in the Hebbian tradition. Competing large-scale neuronal theories of language are discussed in the light of the summarized data. Finally, neurobiological perspectives on the problem of serial order of words in syntactic strings are addressed.
Die primäre Sehrinde in höheren Tieren wie Katzen und Affen ist die erste Stufe der Bildverarbeitung im Gehirn. Aus diesem Grunde findet man in der Sehrinde Gruppen von Nervenzellen, die sich oftmals so verhalten, als ob sie auf lokale Bildelemente ansprechen. Beispiele sind "neuronale Detektoren" für Kanten, Farbkontrast, Disparität, Bewegung und Texturen. Experimente haben gezeigt, dass die Antworteigenschaften von Nervenzellen in der Sehrinde bzgl. äußere Reize und die Stärke der Verbindungen zwischen zwei Nervenzellen innerhalb der Sehrinde auch in erwachsenen Tieren nicht konstant sind, sondern sich auf unterschiedlichen Zeitskalen (einige Millisekunden bis einige Stunden) verändern können. Daraus folgt, dass sich die Repräsentation visueller Information im Gehirn ebenfalls auf dieser Zeitskala verändert. Was könnte der Grund dafür sein? In meinem Vortrag möchte ich zeigen, dass eine Reihe der beobachteten Phänomene das Prinzip der optimalen Kodierung von Information erklärt werden können. Als Beispiele dienen mir die Phänomene Kontrast-Adaption, dynamische Kodierung und die aktivitätsabhängige Entstehung rezeptiver Felder während der Entwicklung der Sehrinde.
I will review new results from our laboratory relating compositions of visual scenes to signals in visual cortex and to cortical circuit models in order to understand neural mechanisms of perceptual feature grouping. It starts from the hypothesis that synchronization and decoupling of cortical gamma-activities (35-90 Hz) define the relations among visual objects. Here we concentrate on synchronization related to two basic visual situations, (1.) static retinal stimulation during ocular fixation, and (2.) transient stimulation during sudden luminance modulations or shifts in object position. For testing the synchronization hypothesis we investigated signal correlations of multiple micro-electrode recordings in visual cortex areas V1 and V2 of behaving monkeys. Static retinal stimuli induce gamma-activities that are loosely phase-coupled among neighboring neural populations of an object's cortical representation. This can explain why synchronization, measured by spectral coherence, is restricted to few millimeters cortex.
Such patches of gamma-synchronization become decoupled across representation of an object's contour, and therby can code figure-ground segregation. Transient stimuli evoke synchronized volleys of stimulus-locked activities that are typically non-rhythmic and include low frequency components in addition to those in the gamma-range. It is argued why stimulus-induced and stimulus-locked phase-coupled activations are both appropriate for supporting perceptual feature grouping. Clues for basic neural mechanisms participating in feature grouping are provided by our biologically motivated simulations of synchronization in cortical structures. (1.) Local populations generate gamma-oscillations via feedback inhibition during states of static retinal stimulation. (2.) Bidirectional facilitatory connections serve for phase-coupling among neighboring neural populations. (3.) Spike transmission delays, increasing with cortical distance, can explain the restriction of gamma-coherence to patches of few millimeters cortex. (4.) The size of synchronization patches in one visual area (e.g., V1) can define the size of classical receptive fields at the consecutive level of visual processing (V2) if Hebbian learning is operative. This may explain the increase in receptive field size at consecutive levels of visual processing. In conclusion, our results and those of others are supportive for the hypothesis that phase-coupled gamma-signals can code feature grouping and object continuity. However, convincing experimental proofs showing directly the dependence of perceptual grouping on cortical phase-coupling are still lacking.
KEY WORDS: Visual cortex, Synchronization, Gamma activity, Visual coding, Perceptual grouping, Figure-ground segregation
Anhand welcher Merkmale erkennt das Hörsystem Schall? - Topologische Karten in verschiedenen Kernen der Hörbahn könnten solche Merkmale anzeigen. Der Colliculus inferior (CI) des Mittelhirns ist das erste integrierende Zentrum der Hörbahn, seine Karten sind die Bausteine für Karten komplexer Schallmerkmale in höheren Verarbeitungsebenen. Die Karten des CI erfassen jedoch zunächst charakteristische Parameter neuronaler Antworten wie Ansprechschwellen, Latenz, Tuningbreite, Stellen maximaler Empfindlichkeit oder maximalen Synchronisationsgrades zwischen Reiz und Antwort - der Bezug zu den zugrundeliegenden Parametern des Schalls ist nicht durchgängig geklärt. Der Vortrag stellt ein Modell vor, das die physiologischen Karten auf einen Basissatz von Schallmerkmalen zurückführt.