Dr. Peter beim Graben

Dr. Peter beim Graben
DFG Heisenberg Fellow for Computational Neurolinguistics
Institut für deutsche Sprache und Linguistik
Humboldt-Universität zu Berlin
Dorotheenstraße 24
D - 10117 Berlin
Room 3.312
Phone: +49 (0)30 2093-9632
Fax: +49 (0)30 2093-9729

Berlin School of Mind and Brain
Bernstein Center for Computational Neuroscience Berlin

E-mail: pbghu
Peter in Rome

A. Computational Neurolinguistics

dopnegEvent-related Brain Potentials (ERP) are commonly regarded to be tiny impulse responses in the electroencephalogram (EEG) generated by neural networks that are time-locked to the perception or processing of stimuli and blended by the spontaneous EEG that reflects the ongoing, continuous activity of the brain. In language processing, unexpected sentence continuations, such as semantic anomalies or syntactic garden paths, elicit characteristic ERP responses, such as the N400 and P600 for semantic and syntactic processing problems, respectively (REF, REF, REF, REF, REF, REF).

The plot shows ERP waves obtained from the Symbolic Resonance Analysis (SRA) at a posterior electode site for processing unlicensed negative polarity items. The SRA reveals an early and a late subcomponent of the reanalysis P600 that are not observable by means of voltage averages (REF).

qunat parsing
Transients in symbolic dynamics represent computational processes. We have utilized this finding for the construction of (context-free) grammar recognizers as Nonlinear Dynamical Automata (
REF, REF). The corresponding phase space representation allows for determining processing costs such as parsing entropy which has been related to language processing ERPs. We have described processes of diagnosis and reanalysis by a bifurcation-like tuning of the system’s control parameter. Additionally, the autonomous parsing dynamics has been augmented by an interactive counterpart (REF, REF).

The Figure shows the temporal evolution of parsing states (from top to bottom) for an interactive NDA with diagnosis and repair steps (indicated by "*"). One  interaction where a new input is scanned from the environment into working memory is indicated by "o" (REF).

You may see an NDA animation by clicking at the image.

fock space parser

Symbolic structures such as linguistic phrase structure trees can be represented through tensor products in Fock spaces. We use finite- and infinite-dimensional Fock space representations to model syntactic language processing in neural networks (
REF, REF) and neural field theories (REF, REF, REF, REF), respectively. Such models are able to describe language-related brain potentials by trajectories exploring functionally different regions in phase space during their transient evolution.

The plot depicts a snapshot sequence of a Fock space parser represented by spherical harmonics. The transient dynamics is governed by nonlinear order parameter equations (REF, REF).

You may see an animation by clicking at the image.

pragmatic information
The concept of "pragmatic information" has been introduced by stating three desiderata: i) Pragmatic information assesses the impact of a message upon its receiver. ii) In the limits of non-interpretable "novelty" and complete "confirmation", the pragmatic information vanishes. iii) Novelty and confirmation behave as Fourier-pairs of complementary operators in quantum mechanics; pragmatic information should hence exhibit some non-classical properties. We have shown how these requirements can be naturally fulfilled within the framework of the dynamic semantics of Bayesian belief models (REF).

The Figure illustrates the property ii) above, the non-monotonic dependence of pragmatic information on novelty (randomness) and confirmation. This is also characteristic for measures of complexity (REF).

B. Computational Neuroscience

ERP data are given as large ensembles of short nonstationary (transient) and noisy time series. Symbolic dynamics of ERPs describes intertrial coherence of polarity deflections by running cylinder entropies and related measures. We have provided heuristics for symbolic encoding of ERP data, such as the median encoding (REF), the half-wave encoding (REF; REF; REF) and the stochastic resonance analysis (SRA) based on the findings of threshold stochastic resonance (REF). Especially the SRA allows to discriminate ERPs for conditions where voltage averaging fails (REF, REF, REF, REF). Most recently, we have developed a recurrence domain segmentation method (REF, REF).

The Figure shows a 3-symbol encoding of a noisy signal exhibiting stochastic resonance at the extrema of the signal.

li networkA leaky integrator (LI) unit is the most simple model neuron described by an ordinary differential equation (REF). We have shown that at least two recurrently connected LI units may form nonlinear neural oscillators possessing limit cycles, which are known, e.g., in thalamo-cortical pathways (REF). We studied networks of coupled LI units in order to model global properties of the EEG (REF, REF). Moreover, we are also investigating the issue of contextual emergence in neural networks (REF, REF).

The Figure shows simulated EEG power spectra obtained from recurrent network of 20, 100, 200, 500, and 1000 LI units whose synaptic connections were randomly drawn such that 80% excitatory and 20% inhibitory synapses have been created. The spectra are computed for the oscillatory phase transition where super-cycles emerge in the network's topology.

neural fieldVery large networks of LI units can be described by a continuum approximation (REF). Starting from the LI equation the sum over the nodes connected with one unit has to be replaced by an integral transformation of a neural field quantity, where the continuous parameter now indicates the position of a unit in the network. Correspondingly, the synaptic weights turn into a kernel function. In addition, for large networks, the propagation velocity of neural activation has to be taken into account. We discuss the solvability and invertibility of neural field equations for general synaptic kernels (REF, REF, REF, REF) and their applicability to computational psycholinguistics (REF, REF) and cognitive science in general (REF).

The Figure should just illustrate the continuum limit starting from a discrete neural network and approaching a continuous neural tissue.

C. Philosophy

comp projectors
The usefulness of symbolic dynamics rests on finding “good partitions” of the phase space, e.g. by construction of generating partitions which allow to approximate individual points in phase space by sustained measurements of coarse-graining devices. This is not possible for “misplaced” partitions where an intrinsic grain remains which makes certain states epistemically unaccessible. We have demonstrated the emergence of quantum-like properties such as complementary observables and contextual topologies (REF, REF).

The Figure shows the possibility of complementary projectors in a chaotic dynamical system. As in algebraic quantum theory, two observables A, B are complementary if no eigenstate of A is eigenstate of B and vice versa. In statistical mechanics, an eigenstate of an observable A can be identified with a phase space domain R where A assumes a constant value making all individual states in R epistemically indistinguishable.

DescartesThe concept of contextual emergence (REF, REF) has been proposed as a non-reductive relation between different levels of description of physical and other systems where the lower level description comprises necessary but not sufficient conditions for the higher level description. These are supplied by contingent contexts obeying particular stability conditions. We have shown that Chalmers' definition of "neural correlates of consciousness" (NCCs) can be complemented in terms of contextual emergence where the sufficient conditions are provided by contextually given "phenomenal families" partitioning the neural phase space (REF). Other examples for contextual emergence are syntactic language processing (REF), the evolutionary formation of categories (REF) macrostates in neural networks (REF, REF), or the contextual emergence of intentionality (REF). Moreover, the usefulness of quantum approaches for cognitive science ("Quantum Cognition"), could be related to incompatible coarse-grainings resulting from bounded rationality (REF, REF).

The Figure illustrates Descartes' "organ metaphor of the mind" (left) mounted together with a brain synchronization map (right). Both portraits together make up the "vase versus faces" ambiguity (REF).

Neural Fields
, 2014. Read Preface.

Special theme issue “Brain Dynamics” of Bulletin of Mathematical Biology 73(2), 2011. Read Editorial.

Cognitive Neurodynamics
Special theme issue “Language Dynamics” of Cognitive Neurodynamics 3(4), 2009. Read Editorial.

Cognitive Neurodynamics
Special theme issue “Brain Waves” of Cognitive Neurodynamics 2(2), 2008. Read Editorial.

Lectures in Supercomputational Neuroscience
Lectures in Supercomputational Neuroscience,  2008. Read Chapt. 1 "Foundations of neurophysics".

Chaos and Complexity Letters
Special theme issue "Advanced Methods of Electrophysiological Signal Analysis and Symbol Grounding? Dynamical Systems Approaches to Language" of Chaos and Complexity Letters 2(2/3), 2007. Read Editorial.

Special theme issue “Pragmatic Information” of  Mind and Matter 4(2), 2006. Read Editorial.

IJBC cover
Special theme issue on “Cognition and Complex Brain Dynamics” of the International Journal of Bifurcation and Chaos, 14(2), 2004. Read Editorial.