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Claus Metzner

Claus Metzner appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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Quantitative MethodsNeurons and CognitionArtificial Intelligencecond-mat.softInformation TheoryMachine Learningmath.IT

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Published work

13 published item(s)

preprint2026arXiv

Are cortical microcircuits optimized for information flux? -- A simulation-based reverse engineering study

A sufficiently large information flux in recurrent neural networks, quantified by the mutual information between successive network states, is considered a prerequisite for rich information processing capabilities. This raises the question of whether biological neural networks, such as cortical microcolumns, may be structurally organized to enhance information flux. To investigate this possibility, we study a simplified model of the cortical layer 5 architecture, in which a densely and strongly interconnected core population is embedded within a larger supporting network. Surprisingly, we find that the embedding network exerts a pronounced flux-enhancing effect on the core dynamics. Systematic reverse-engineering analyses reveal that the embedding network provides two key contributions: first, it generates effective biases that shift core neurons into a higher-entropy operating regime; second, it supplies stochastic fluctuations that prevent the network from becoming trapped in simple fixed-point or oscillatory attractors through the mechanism of Recurrence Resonance. We further show that the information flux can be increased even beyond the biologically embedded case by applying individually optimized biases to the core neurons, and that these biases can emerge from a simple self-organization principle. Our findings are relevant both for the functional interpretation of biological neural circuits and for the design of artificial recurrent systems such as reservoir computers.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

Extracting continuous sleep depth from EEG data without machine learning

The human sleep-cycle has been divided into discrete sleep stages that can be recognized in electroencephalographic (EEG) and other bio-signals by trained specialists or machine learning systems. It is however unclear whether these human-defined stages can be re-discovered with unsupervised methods of data analysis, using only a minimal amount of generic pre-processing. Based on EEG data, recorded overnight from sleeping human subjects, we investigate the degree of clustering of the sleep stages using the General Discrimination Value as a quantitative measure of class separability. Virtually no clustering is found in the raw data, even after transforming the EEG signals of each thirty-second epoch from the time domain into the more informative frequency domain. However, a Principal Component Analysis (PCA) of these epoch-wise frequency spectra reveals that the sleep stages separate significantly better in the low-dimensional sub-space of certain PCA components. In particular the component $C_1(t)$ can serve as a robust, continuous 'master variable' that encodes the depth of sleep and therefore correlates strongly with the 'hypnogram', a common plot of the discrete sleep stages over time. Moreover, $C_1(t)$ shows persistent trends during extended time periods where the sleep stage is constant, suggesting that sleep may be better understood as a continuum. These intriguing properties of $C_1(t)$ are not only relevant for understanding brain dynamics during sleep, but might also be exploited in low-cost single-channel sleep tracking devices for private and clinical use.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Classification at the Accuracy Limit -- Facing the Problem of Data Ambiguity

Data classification, the process of analyzing data and organizing it into categories, is a fundamental computing problem of natural and artificial information processing systems. Ideally, the performance of classifier models would be evaluated using unambiguous data sets, where the 'correct' assignment of category labels to the input data vectors is unequivocal. In real-world problems, however, a significant fraction of actually occurring data vectors will be located in a boundary zone between or outside of all categories, so that perfect classification cannot even in principle be achieved. We derive the theoretical limit for classification accuracy that arises from the overlap of data categories. By using a surrogate data generation model with adjustable statistical properties, we show that sufficiently powerful classifiers based on completely different principles, such as perceptrons and Bayesian models, all perform at this universal accuracy limit. Remarkably, the accuracy limit is not affected by applying non-linear transformations to the data, even if these transformations are non-reversible and drastically reduce the information content of the input data. We compare emerging data embeddings produced by supervised and unsupervised training, using MNIST and human EEG recordings during sleep. We find that categories are not only well separated in the final layers of classifiers trained with back-propagation, but to a smaller degree also after unsupervised dimensionality reduction. This suggests that human-defined categories, such as hand-written digits or sleep stages, can indeed be considered as 'natural kinds'.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Neural Network based Successor Representations of Space and Language

How does the mind organize thoughts? The hippocampal-entorhinal complex is thought to support domain-general representation and processing of structural knowledge of arbitrary state, feature and concept spaces. In particular, it enables the formation of cognitive maps, and navigation on these maps, thereby broadly contributing to cognition. It has been proposed that the concept of multi-scale successor representations provides an explanation of the underlying computations performed by place and grid cells. Here, we present a neural network based approach to learn such representations, and its application to different scenarios: a spatial exploration task based on supervised learning, a spatial navigation task based on reinforcement learning, and a non-spatial task where linguistic constructions have to be inferred by observing sample sentences. In all scenarios, the neural network correctly learns and approximates the underlying structure by building successor representations. Furthermore, the resulting neural firing patterns are strikingly similar to experimentally observed place and grid cell firing patterns. We conclude that cognitive maps and neural network-based successor representations of structured knowledge provide a promising way to overcome some of the short comings of deep learning towards artificial general intelligence.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Predictive coding and stochastic resonance as fundamental principles of auditory perception

How is information processed in the brain during perception? Mechanistic insight is achieved only when experiments are employed to test formal or computational models. In analogy to lesion studies, phantom perception may serve as a vehicle to understand the fundamental processing principles underlying auditory perception. With a special focus on tinnitus -- as the prime example of auditory phantom perception -- we review recent work at the intersection of artificial intelligence, psychology, and neuroscience. In particular, we discuss why everyone with tinnitus suffers from hearing loss, but not everyone with hearing loss suffers from tinnitus. We argue that the increase of sensory precision due to Bayesian inference could be caused by intrinsic neural noise and lead to a prediction error in the cerebral cortex. Hence, two fundamental processing principles - being ubiquitous in the brain - provide the most explanatory power for the emergence of tinnitus: predictive coding as a top-down, and stochastic resonance as a complementary bottom-up mechanism. We conclude that both principles play a crucial role in healthy auditory perception.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

A statistical method for analyzing and comparing spatiotemporal cortical activation patterns

We present a new statistical method to analyze multichannel steady-state local field potentials (LFP) recorded within different sensory cortices of different rodent species. Our spatiotemporal multi-dimensional cluster statistics (MCS) method enables statistical analyzing and comparing clusters of data points in n-dimensional space. We demonstrate that using this approach stimulus-specific attractor-like spatiotemporal activity patterns can be detected and be significantly different from each other during stimulation with long-lasting stimuli. Our method may be applied to other types of multichannel neuronal data, like EEG, MEG or spiking responses and used for the development of new read-out algorithms of brain activity and by that opens new perspectives for the development of brain-computer interfaces.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Stochastic resonance controlled upregulation of internal noise after hearing loss as a putative correlate of tinnitus-related neuronal hyperactivity

Subjective tinnitus (ST) is generally assumed to be a consequence of hearing loss (HL). In animal studies acoustic trauma can lead to behavioral signs of ST, in human studies ST patients without increased hearing thresholds were found to suffer from so called hidden HL. Additionally, ST is correlated with pathologically increased spontaneous firing rates and neuronal hyperactivity (NH) along the auditory pathway. Homeostatic plasticity (HP) has been proposed as a compensation mechanism leading to the development of NH, arguing that after HL initially decreased mean firing rates of neurons are subsequently restored by increased spontaneous rates. However all HP models fundamentally lack explanatory power since the function of keeping mean firing rate constant remains elusive as does the benefit this might have in terms of information processing. Furthermore the neural circuitry being able to perform the comparison of preferred with actual mean firing rate remains unclear. Here we propose an entirely new interpretation of ST related development of NH in terms of information theory. We suggest that stochastic resonance (SR) plays a key role in short- and long-term plasticity within the auditory system and is the ultimate cause of NH and ST. SR has been found ubiquitous in neuroscience and refers to the phenomenon that sub-threshold, unperceivable signals can be transmitted by adding noise to sensor input. We argue that after HL, SR serves to lift signals above the increased hearing threshold, hence subsequently decreasing thresholds again. The increased amount of internal noise is the correlate of the NH, which finally leads to the development of ST, due to neuronal plasticity along the auditory pathway. We demonstrate the plausibility of our hypothesis by using a computational model and provide exemplarily findings of human and animal studies that are consistent with our model.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Adaptive stochastic resonance based on output autocorrelations

Successful detection of weak signals is a universal challenge for numerous technical and biological systems and crucially limits signal transduction and transmission. Stochastic resonance (SR) has been identified to have the potential to tackle this problem, namely to enable non-linear systems to detect small, otherwise sub-threshold signals by means of added non-zero noise. This has been demonstrated within a wide range of systems in physical, technological and biological contexts. Based on its ubiquitous importance, numerous theoretical and technical approaches aim at an optimization of signal transduction based on SR. Several quantities like mutual information, signal-to-noise-ratio, or the cross-correlation between input stimulus and resulting detector response have been used to determine optimal noise intensities for SR. The fundamental shortcoming with all these measures is that knowledge of the signal to be detected is required to compute them. This dilemma prevents the use of adaptive SR procedures in any application where the signal to be detected is unknown. We here show that the autocorrelation function (AC) of the detector response fundamentally overcomes this drawback. For a simplified model system, the equivalence of the output AC with the measures mentioned above is proven analytically. In addition, we test our approach numerically for a variety of systems comprising different input signals and different types of detectors. The results indicate a strong similarity between mutual information and output AC in terms of the optimal noise intensity for SR. Hence, using the output AC to adaptively vary the amount of added noise in order to maximize information transmission via SR might be a fundamental processing principle in nature, in particular within neural systems which could be implemented in future technical applications.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Bayesian inference of time varying parameters in autoregressive processes

In the autoregressive process of first order AR(1), a homogeneous correlated time series $u_t$ is recursively constructed as $u_t = q\; u_{t-1} + σ\;ε_t$, using random Gaussian deviates $ε_t$ and fixed values for the correlation coefficient $q$ and for the noise amplitude $σ$. To model temporally heterogeneous time series, the coefficients $q_t$ and $σ_t$ can be regarded as time-dependend variables by themselves, leading to the time-varying autoregressive processes TVAR(1). We assume here that the time series $u_t$ is known and attempt to infer the temporal evolution of the 'superstatistical' parameters $q_t$ and $σ_t$. We present a sequential Bayesian method of inference, which is conceptually related to the Hidden Markov model, but takes into account the direct statistical dependence of successively measured variables $u_t$. The method requires almost no prior knowledge about the temporal dynamics of $q_t$ and $σ_t$ and can handle gradual and abrupt changes of these superparameters simultaneously. We compare our method with a Maximum Likelihood estimate based on a sliding window and show that it is superior for a wide range of window sizes.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

1D analysis of 2D isotropic random walks

Many stochastic systems in physics and biology are investigated by recording the two-dimensional (2D) positions of a moving test particle in regular time intervals. The resulting sample trajectories are then used to induce the properties of the underlying stochastic process. Often, it can be assumed a priori that the underlying discrete-time random walk model is independent from absolute position (homogeneity), direction (isotropy) and time (stationarity), as well as ergodic. In this article we first review some common statistical methods for analyzing 2D trajectories, based on quantities with built-in rotational invariance. We then discuss an alternative approach in which the two-dimensional trajectories are reduced to one dimension by projection onto an arbitrary axis and rotational averaging. Each step of the resulting 1D trajectory is further factorized into sign and magnitude. The statistical properties of the signs and magnitudes are mathematically related to those of the step lengths and turning angles of the original 2D trajectories, demonstrating that no essential information is lost by this data reduction. The resulting binary sequence of signs lends itself for a pattern counting analysis, revealing temporal properties of the random process that are not easily deduced from conventional measures such as the velocity autocorrelation function. In order to highlight this simplified 1D description, we apply it to a 2D random walk with restricted turning angles (RTA model), defined by a finite-variance distribution $p(L)$ of step length and a narrow turning angle distribution $p(ϕ)$, assuming that the lengths and directions of the steps are independent.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

Scaling properties of correlated random walks

Many stochastic time series can be modelled by discrete random walks in which a step of random sign but constant length $δx$ is performed after each time interval $δt$. In correlated discrete time random walks (CDTRWs), the probability $q$ for two successive steps having the same sign is unequal 1/2. The resulting probability distribution $P(Δx,Δt)$ that a displacement $Δx$ is observed after a lagtime $Δt$ is known analytically for arbitrary persistence parameters $q$. In this short note we show how a CDTRW with parameters $[δt, δx, q]$ can be mapped onto another CDTRW with rescaled parameters $[δt/s, δx\cdot g(q,s), q^{\prime}(q,s)]$, for arbitrary scaling parameters $s$, so that both walks have the same displacement distributions $P(Δx,Δt)$ on long time scales. The nonlinear scaling functions $g(q,s)$ and $q^{\prime}(q,s)$ and derived explicitely. This scaling method can be used to model time series measured at discrete sample intervals $δt$ but actually corresponding to continuum processes with variations occuring on a much shorter time scale $δt/s$.

0 citations0 reviewsNo code linkedOpen access
preprint2011arXiv

Poresizes in random line networks

Many natural fibrous networks with fiber diameters much smaller than the average poresize can be described as three-dimensional (3D) random line networks. We consider here a `Mikado' model for such systems, consisting of straight line segments of equal length, distributed homogeneously and isotropically in space. First, we derive analytically the probability density distribution $p(r_{no})$ for the `nearest obstacle distance' $r_{no}$ between a randomly chosen test point within the network pores and its closest neighboring point on a line segment. Second, we show that in the limit where the line segments are much longer than the typical pore size, $p(r_{no})$ becomes a Rayleigh distribution. The single parameter $σ$ of this Rayleigh distribution represents the most probable nearest obstacle distance and can be expressed in terms of the total line length per unit volume. Finally, we show by numerical simulations that $σ$ differs only by a constant factor from the intuitive notion of average `pore size', defined by finding the maximum sphere that fits into each pore and then averaging over the radii of these spheres.

0 citations0 reviewsNo code linkedOpen access
preprint2011arXiv

Reconstructing fiber networks from confocal image stacks

We present a numerically efficient method to reconstruct a disordered network of thin biopolymers, such as collagen gels, from three-dimensional (3D) image stacks recorded with a confocal microscope. Our method is based on a template matching algorithm that simultaneously performs a binarization and skeletonization of the network. The size and intensity pattern of the template is automatically adapted to the input data so that the method is scale invariant and generic. Furthermore, the template matching threshold is iteratively optimized to ensure that the final skeletonized network obeys a universal property of voxelized random line networks, namely, solid-phase voxels have most likely three solid-phase neighbors in a $3\times3$ neighborhood. This optimization criterion makes our method free of user-defined parameters and the output exceptionally robust against imaging noise.

0 citations0 reviewsNo code linkedOpen access