Associative memory in networks of spiking neurons.

Here, we develop and investigate a computational model of a network of cortical neurons on the base of biophysically well constrained and tested two-compartmental neurons developed by Pinsky and Rinzel [Pinsky, P. F., & Rinzel, J. (1994). Intrinsic and network rhythmogenesis in a reduced Traub model for CA3 neurons. Journal of Computational Neuroscience, 1, 39-60]. To study associative memory, we connect a pool of cells by a structured connectivity matrix. The connection weights are shaped by simple Hebbian coincidence learning using a set of spatially sparse patterns. We study the neuronal activity processes following an external stimulation of a stored memory. In two series of simulation experiments, we explore the effect of different classes of external input, tonic and flashed stimulation. With tonic stimulation, the addressed memory is an attractor of the network dynamics. The memory is displayed rhythmically, coded by phase-locked bursts or regular spikes. The participating neurons have rhythmic activity in the gamma-frequency range (30-80 Hz). If the input is switched from one memory to another, the network activity can follow this change within one or two gamma cycles. Unlike similar models in the literature, we studied the range of high memory capacity (in the order of 0.1 bit/synapse), comparable to optimally tuned formal associative networks. We explored the robustness of efficient retrieval varying the memory load, the excitation/inhibition parameters, and background activity. A stimulation pulse applied to the identical simulation network can push away ongoing network activity and trigger a phase-locked association event within one gamma period. Unlike as under tonic stimulation, the memories are not attractors. After one association process, the network activity moves to other states. Applying in close succession pulses addressing different memories, one can switch through the space of memory patterns. The readout speed can be increased up to the point where in every gamma cycle another pattern is displayed. With pulsed stimulation. bursts become relevant for coding, their occurrence can be used to discriminate relevant processes from background activity.

Global relationship between anatomical connectivity and activity propagation in the cerebral cortex.

Anatomical connectivity is a prerequisite for cooperative interactions between cortical areas, but it has yet to be demonstrated that association fibre networks determine the macroscopical flow of activity in the cerebral cortex. To test this notion, we constructed a large-scale model of cortical areas whose interconnections were based on published anatomical data from tracing studies. Using this model we simulated the propagation of activity in response to activation of individual cortical areas and compared the resulting topographic activation patterns to electrophysiological observations on the global spread of epileptic activity following intracortical stimulation. Here we show that a neural network with connectivity derived from experimental data reproduces cortical propagation of activity significantly better than networks with different types of neighbourhood-based connectivity or random connections. Our results indicate that association fibres and their relative connection strengths are useful predictors of global topographic activation patterns in the cerebral cortex. This global structure-function relationship may open a door to explicit interpretation of cortical activation data in terms of underlying anatomical connectivity.

Modelling studies on the computational function of fast temporal structure in cortical circuit activity.

The interplay between modelling and experimental studies can support the exploration of the function of neuronal circuits in the cortex. We exemplify such an approach with a study on the role of spike timing and gamma-oscillations in associative memory in strongly connected circuits of cortical neurones. It is demonstrated how associative memory studies on different levels of abstraction can specify the functionality to be expected in real cortical neuronal circuits. In our model overlapping random configurations of sparse cell populations correspond to memory items that are stored by simple Hebbian coincidence learning. This associative memory task will be implemented with biophysically well tested compartmental neurones developed by Pinsky and Rinzel . We ran simulation experiments to study memory recall in two network architectures: one interconnected pool of cells, and two reciprocally connected pools. When recalling a memory by stimulating a spatially overlapping set of cells, the completed pattern is coded by an event of synchronized single spikes occurring after 25-60 ms. These fast associations are performed even at a memory load corresponding to the memory capacity of optimally tuned formal associative networks (>0.1 bit/synapse). With tonic stimulation or feedback loops in the network the neurones fire periodically in the gamma-frequency range (20-80 Hz). With fast changing inputs memory recall can be switched between items within a single gamma cycle. Thus, oscillation is not a primary coding feature necessary for associative memory. However, it accompanies reverberatory feedback providing an improved iterative memory recall completed after a few gamma cycles (60-260 ms). In the bidirectional architecture reverberations do not express in a rigid phase locking between the pools. For small stimulation sets bursting occurred in these cells acting as a supportive mechanism for associative memory.

Dynamical cluster analysis of cortical fMRI activation.

Localized changes in cortical blood oxygenation during voluntary movements were examined with functional magnetic resonance imaging (fMRI) and evaluated with a new dynamical cluster analysis (DCA) method. fMRI was performed during finger movements with eight subjects on a 1.5-T scanner using single-slice echo planar imaging with a 107-ms repetition time. Clustering based on similarity of the detailed signal time courses requires besides the used distance measure no assumptions about spatial location and extension of activation sites or the shape of the expected activation time course. We discuss the basic requirements on a clustering algorithm for fMRI data. It is shown that with respect to easy adjustment of the quantization error and reproducibility of the results DCA outperforms the standard k-means algorithm. In contrast to currently used clustering methods for fMRI, like k-means or fuzzy k-means, DCA extracts the appropriate number and initial shapes of representative signal time courses from data properties during run time. With DCA we simultaneously calculate a two-dimensional projection of cluster centers (MDS) and data points for online visualization of the results. We describe the new DCA method and show for the well-studied motor task that it detects cortical activation loci and provides additional information by discriminating different shapes and phases of hemodynamic responses. Robustness of activity detection is demonstrated with respect to repeated DCA runs and effects of different data preprocessing are shown. As an example of how DCA enables further analysis we examined activation onset times. In areas SMA, M1, and S1 simultaneous and sequential activation (in the given order) was found.

Bayesian retrieval in associative memories with storage errors.

It is well known that for finite-sized networks, onestep retrieval in the autoassociative Willshaw net is a suboptimal way to extract the information stored in the synapses. Iterative retrieval strategies are much better, but have hitherto only had heuristic justification. We show how they emerge naturally from considerations of probabilistic inference under conditions of noisy and partial input and a corrupted weight matrix. We start from the conditional probability distribution over possible patterns for retrieval. This contains all possible information that is available to an observer of the network and the initial input. Since this distribution is over exponentially many patterns, we use it to develop two approximate, but tractable, iterative retrieval methods. One performs maximum likelihood inference to find the single most likely pattern, using the (negative log of the) conditional probability as a Lyapunov function for retrieval. In physics terms, if storage errors are present, then the modified iterative update equations contain an additional antiferromagnetic interaction term and site dependent threshold values. The second method makes a mean field assumption to optimize a tractable estimate of the full conditional probability distribution. This leads to iterative mean field equations which can be interpreted in terms of a network of neurons with sigmoidal responses but with the same interactions and thresholds as in the maximum likelihood update equations. In the absence of storage errors, both models become very similiar to the Willshaw model, where standard retrieval is iterated using a particular form of linear threshold strategy.