Spiking model neurons can be set up to respond selectively to specific spatio-temporal spike patterns by optimization of their input weights. It is unknown, however, if existing synaptic plasticity mechanisms can achieve this temporal mode of neuronal coding and computation. Here it is shown that changes of synaptic efficacies which tend to balance excitatory and inhibitory synaptic inputs can make neurons sensitive to particular input spike patterns. Simulations demonstrate that a combination of Hebbian mechanisms, hetero-synaptic plasticity and synaptic scaling is sufficient for self-organizing sensitivity for spatio-temporal spike patterns that repeat in the input. In networks inclusion of hetero-synaptic plasticity that depends on the pre-synaptic neurons leads to specialization and faithful representation of pattern sequences by a group of target neurons. Pattern detection is robust against a range of distortions and noise. The proposed combination of Hebbian mechanisms, hetero-synaptic plasticity and synaptic scaling is found to protect the memories for specific patterns from being overwritten by ongoing learning during extended periods when the patterns are not present. This suggests a novel explanation for the long term robustness of memory traces despite ongoing activity with substantial synaptic plasticity. Taken together, our results promote the plausibility of precise temporal coding in the brain.

When probed with complex stimuli that extend beyond their classical receptive field, neurons in primary visual cortex display complex and non-linear response characteristics. Sparse coding models reproduce some of the observed contextual effects, but still fail to provide a satisfactory explanation in terms of realistic neural structures and cortical mechanisms, since the connection scheme they propose consists only of interactions among neurons with overlapping input fields. Here we propose an extended generative model for visual scenes that includes spatial dependencies among different features. We derive a neurophysiologically realistic inference scheme under the constraint that neurons have direct access only to local image information. The scheme can be interpreted as a network in primary visual cortex where two neural populations are organized in different layers within orientation hypercolumns that are connected by local, short-range and long-range recurrent interactions. When trained with natural images, the model predicts a connectivity structure linking neurons with similar orientation preferences matching the typical patterns found for long-ranging horizontal axons and feedback projections in visual cortex. Subjected to contextual stimuli typically used in empirical studies, our model replicates several hallmark effects of contextual processing and predicts characteristic differences for surround modulation between the two model populations. In summary, our model provides a novel framework for contextual processing in the visual system proposing a well-defined functional role for horizontal axons and feedback projections.

This paper presents a fully implantable neural recording system for the simultaneous recording of 128 channels. The electrocorticography (ECoG) signals are sensed with 128 gold electrodes embedded in a 10 µm thick polyimide foil. The signals are picked up by eight amplifier array ICs and digitized with a resolution of 16 bit at 10 kHz. The digitized measurement data is processed in a reconfigurable digital ASIC, which is fabricated in a 0.35 µm CMOS technology and occupies an area of 2.8×2.8mm2. After data reduction, the measurement data is fed into a transceiver IC, which transmits the data with up to 495 kbit/s to a base station, using an RF loop antenna on a flexible PCB. The power consumption of 84mW is delivered via inductive coupling from the base station.

Recent extensions of the Perceptron, as e.g. the Tempotron, suggest that this theoretical concept is highly relevant also for understanding networks of spiking neurons in the brain. It is not known, however, how the computational power of the Perceptron and of its variants might be accomplished by the plasticity mechanisms of real synapses. Here we prove that spike-timing-dependent plasticity having an anti-Hebbian form for excitatory synapses as well as a spike-timing-dependent plasticity of Hebbian shape for inhibitory synapses are sufficient for realizing the original Perceptron Learning Rule if the respective plasticity mechanisms act in concert with the hyperpolarisation of the post-synaptic neurons. We also show that with these simple yet biologically realistic dynamics Tempotrons are efficiently learned. The proposed mechanism might underly the acquisition of mappings of spatio-temporal activity patterns in one area of the brain onto other spatio-temporal spike patterns in another region and of long term memories in cortex. Our results underline that learning processes in realistic networks of spiking neurons depend crucially on the interactions of synaptic plasticity mechanisms with the dynamics of participating neurons.

For processing and segmenting visual scenes, the brain is required to combine a multitude of features and sensory channels. It is neither known if these complex tasks involve optimal integration of information, nor according to which objectives computations might be performed. Here, we investigate if optimal inference can explain contour integration in human subjects. We performed experiments where observers detected contours of curvilinearly aligned edge configurations embedded into randomly oriented distractors. The key feature of our framework is to use a generative process for creating the contours, for which it is possible to derive a class of ideal detection models. This allowed us to compare human detection for contours with different statistical properties to the corresponding ideal detection models for the same stimuli. We then subjected the detection models to realistic constraints and required them to reproduce human decisions for every stimulus as well as possible. By independently varying the four model parameters, we identify a single detection model which quantitatively captures all correlations of human decision behaviour for more than 2000 stimuli from 42 contour ensembles with greatly varying statistical properties. This model reveals specific interactions between edges closely matching independent findings from physiology and psychophysics. These interactions imply a statistics of contours for which edge stimuli are indeed optimally integrated by the visual system, with the objective of inferring the presence of contours in cluttered scenes. The recurrent algorithm of our model makes testable predictions about the temporal dynamics of neuronal populations engaged in contour integration, and it suggests a strong directionality of the underlying functional anatomy.

When stimulated with complex action potential sequences synapses exhibit spike timing-dependent plasticity (STDP) with attenuated and enhanced pre- and postsynaptic contributions to long-term synaptic modifications. In order to investigate the functional consequences of these contribution dynamics (CD) we propose a minimal model formulated in terms of differential equations. We find that our model reproduces a wide range of experimental results with a small number of biophysically interpretable parameters. The model allows to investigate the susceptibility of STDP to arbitrary time courses of pre- and postsynaptic activities, i.e. its nonlinear filter properties. We demonstrate this for the simple example of small periodic modulations of pre- and postsynaptic firing rates for which our model can be solved. It predicts synaptic strengthening for synchronous rate modulations. For low baseline rates modifications are dominant in the theta frequency range, a result which underlines the well known relevance of theta activities in hippocampus and cortex for learning. We also find emphasis of low baseline spike rates and suppression for high baseline rates. The latter suggests a mechanism of network activity regulation inherent in STDP. Furthermore, our novel formulation provides a general framework for investigating the joint dynamics of neuronal activity and the CD of STDP in both spike-based as well as rate-based neuronal network models.

The speed and reliability of mammalian perception indicate that cortical computations can rely on very few action potentials per involved neuron. Together with the stochasticity of single-spike events in cortex, this appears to imply that large populations of redundant neurons are needed for rapid computations with action potentials. Here we demonstrate that very fast and precise computations can be realized also in small networks of stochastically spiking neurons. We present a generative network model for which we derive biologically plausible algorithms that perform spike-by-spike updates of the neuron's internal states and adaptation of its synaptic weights from maximizing the likelihood of the observed spike patterns. Paradigmatic computational tasks demonstrate the online performance and learning efficiency of our framework. The potential relevance of our approach as a model for cortical computation is discussed.

Here we derive optimal gain functions for minimum mean square re(cid:173) construction from neural rate responses subjected to Poisson noise. The shape of these functions strongly depends on the length T of the time window within which spikes are counted in order to estimate the under(cid:173) lying firing rate. A phase transition towards pure binary encoding occurs if the maximum mean spike count becomes smaller than approximately three provided the minimum firing rate is zero. For a particular function class, we were able to prove the existence of a second-order phase tran(cid:173) sition analytically. The critical decoding time window length obtained from the analytical derivation is in precise agreement with the numerical results. We conclude that under most circumstances relevant to informa(cid:173) tion processing in the brain, rate coding can be better ascribed to a binary (low-entropy) code than to the other extreme of rich analog coding. 1 Optimal neuronal gain functions for short decoding time windows The use of action potentials (spikes) as a means of communication is the striking feature of neurons in the central nervous system. Since the discovery by Adrian [1] that action poten(cid:173) tials are generated by sensory neurons with a frequency that is substantially determined by the stimulus, the idea of rate coding has become a prevalent paradigm in neuroscience [2]. In particular, today the coding properties of many neurons from various areas in the cortex have been characterized by tuning curves, which describe the average firing rate response as a function of certain stimulus parameters. This way of description is closely related to the idea of analog coding, which constitutes the basis for many neural network models. Reliablv inference from the observed number of spikes about the underlying firing rate of a neuronal response, however, requires a sufficiently long time interval, while integration times of neurons in vivo [3] as well as reaction times of humans or animals when per(cid:173) forming classification tasks [4, 5] are known to be rather short. Therefore, it is important to understand, how neural rate coding is affected by a limited time window available for decoding. While rate codes are usually characterized by tuning functions relating the intensity of the ,f *http://www.neuro.urn-bremen.dermbethge neuronal response to a particular stimulus parameter, the question, how relevant the idea of analog coding actually is does not depend on the particular entity represented by a neuron. Instead it suffices to determine the shape of the gain function, which displays the mean fir(cid:173) ing rate as a function of the actual analog signal to be sent to subsequent neurons. Here we seek for optimal gain functions that minimize the minimum average squared reconstruction error for a uniform source signal transmitted through a Poisson channel as a function of the maximum mean number of spikes. In formal terms, the issue is to optimally encode a real random variable x in the number of pulses emitted by a neuron within a certain time window. Thereby, x stands for the intended analog output of the neuron that shall be signaled to subsequent neurons. The latter, however, can only observe a number of spikes k integrated within a time interval of length T. The statistical dependency between x and k is specified by the assumption of Poisson noise p(kIJL(x)) = (JL~))k exp{-JL(X)} ,

Efficient coding has been proposed as a first principle explaining neuronal response properties in the central nervous system. The shape of optimal codes, however, strongly depends on the natural limitations of the particular physical system. Here we investigate how optimal neuronal encoding strategies are influenced by the finite number of neurons N (place constraint), the limited decoding time window length T (time constraint), the maximum neuronal firing rate f(max) (power constraint), and the maximal average rate (f)(max) (energy constraint). While Fisher information provides a general lower bound for the mean squared error of unbiased signal reconstruction, its use to characterize the coding precision is limited. Analyzing simple examples, we illustrate some typical pitfalls and thereby show that Fisher information provides a valid measure for the precision of a code only if the dynamic range (f(min)T, f(max)T) is sufficiently large. In particular, we demonstrate that the optimal width of gaussian tuning curves depends on the available decoding time T. Within the broader class of unimodal tuning functions, it turns out that the shape of a Fisher-optimal coding scheme is not unique. We solve this ambiguity by taking the minimum mean square error into account, which leads to flat tuning curves. The tuning width, however, remains to be determined by energy constraints rather than by the principle of efficient coding.

A recent study of cat visual cortex reported abrupt changes in the positions of the receptive fields of adjacent neurons whose preferred orientations strongly differed (Das & Gilbert, 1997). Using a simple cortical model, we show that this covariation of discontinuities in maps of orientation preference and local distortions in maps of visual space reflects collective effects of the lateral cortical feedback.

Transmission across neocortical synapses depends on the frequency of presynaptic activity (Thomson & Deuchars, 1994). Interpyramidal synapses in layer V exhibit fast depression of synaptic transmission, while other types of synapses exhibit facilitation of transmission. To study the role of dynamic synapses in network computation, we propose a unified phenomenological model that allows computation of the postsynaptic current generated by both types of synapses when driven by an arbitrary pattern of action potential (AP) activity in a presynaptic population. Using this formalism, we analyze different regimes of synaptic transmission and demonstrate that dynamic synapses transmit different aspects of the presynaptic activity depending on the average presynaptic frequency. The model also allows for derivation of mean-field equations, which govern the activity of large, interconnected networks. We show that the dynamics of synaptic transmission results in complex sets of regular and irregular regimes of network activity.

We present a method for the unsupervised segmentation of data streams originating from different unknown sources that alternate in time. We use an architecture consisting of competing neural networks. Memory is included to resolve ambiguities of input-output relations. To obtain maximal specialization, the competition is adiabatically increased during training. Our method achieves almost perfect identification and segmentation in the case of switching chaotic dynamics where input manifolds overlap and input-output relations are ambiguous. Only a small dataset is needed for the training procedure. Applications to time series from complex systems demonstrate the potential relevance of our approach for time series analysis and short-term prediction.

It is shown that a topographic product P, first introduced in nonlinear dynamics, is an appropriate measure of the preservation or violation of neighborhood relations. It is sensitive to large-scale violations of the neighborhood ordering, but does not account for neighborhood ordering distortions caused by varying areal magnification factors. A vanishing value of the topographic product indicates a perfect neighborhood preservation; negative (positive) values indicate a too small (too large) output space dimensionality. In a simple example of maps from a 2D input space onto 1D, 2D, and 3D output spaces, it is demonstrated how the topographic product picks the correct output space dimensionality. In a second example, 19D speech data are mapped onto various output spaces and it is found that a 3D output space (instead of 2D) seems to be optimally suited to the data. This is an agreement with a recent speech recognition experiment on the same data set.