Raphael Ritz

Why spikes? Hebbian learning and retrieval of time-resolved excitation patterns

Hebbian learning allows a network of spiking neurons to store and retrieve spatio-temporal patterns with a time resolution of 1 ms, despite the long postsynaptic and dendritic integration times. To show this, we introduce and analyze a model of spiking neurons, the spike response model, with a realistic distribution of axonal delays and with realistic postsynaptic potentials. Learning is performed by a local Hebbian rule which is based on the synchronism of presynaptic neurotransmitter release and some short-acting postsynaptic process. The time window of this synchronism determines the temporal resolution of pattern retrieval, which can be initiated by applying a short external stimulus pattern. Furthermore, a rate quantization is found in dependence upon the threshold value of the neurons, i.e., in a given time a pattern runs n times as often as learned, where n is a positive integer (n ⩾ 0). We show that all information about the spike pattern is lost if only mean firing rates (temporal average) or ensemble activities (spatial average) are considered. An average over several retrieval runs in order to generate a post-stimulus time histogram may also deteriorate the signal. The full information on a pattern is contained in the spike raster of a single run. Our results stress the importance, and advantage, of coding by spatio-temporal spike patterns instead of firing rates and average ensemble activity. The implications regarding modelling and experimental data analysis are discussed.

Synchronous oscillatory activity in sensory systems: new vistas on mechanisms

The origin and nature, as well as the functional role, of synchronous oscillatory activity in the cortex are among the major unresolved issues in systems neurobiology. Recent advances in understanding the mechanisms underlying oscillations include the description of intrinsically bursting pyramidal cells in striate cortex in vivo and the discovery of inhibitory interneurons that fire spike doublets to induce synchrony. The behavioral consequences of coordinated activity in cortical neurons remain poorly understood.

A biologically motivated and analytically soluble model of collective oscillations in the cortex

A model of an associative network of spiking neurons with stationary states, globally locked oscillations, and weakly locked oscillatory states is presented and analyzed. The network is close to biology in the following sense. First, the neurons spike and our model includes an absolute refractory period after each spike. Second, we consider a distribution of axonal delay times. Finally, we describe synaptic signal transmission by excitatory and inhibitory potentials (EPSP and IPSP) with a realistic shape, that is, through a response kernel. During retrieval of a pattern, all active neurons exhibit periodic spike bursts which may or may not be synchronized (‘locked’) into a coherent oscillation. We derive an analytical condition of locking and calculate the period of collective activity during oscillatory retrieval. In a stationary retrieval state, the overlap assumes a constant value proportional to the mean firing rate of the neurons. It is argued that in a biological network an intermediate scenario of “weak locking” is most likely.

Spontaneous excitations in the visual cortex: stripes, spirals, rings, and collective bursts

As a simple model of the cortical sheet, we study a locally connected net of spiking neurons, Refractoriness, noise, axonal delays, and the time course of excitatory and inhibitory postsynaptic potentials are taken into account explicitly. In addition to a low-activity state and depending on the synaptic efficacy, four different scenarios evolve spontaneously, viz., stripes, spirals, rings, and collective bursts. Our results can be related to experimental observations of drug-induced epilepsy and hallucinations.

Associative Binding and Segregation in a Network of Spiking Neurons

A model of an associative network of spiking neurons (the Spike Response Model) with stationary states, globally locked oscillations, and weakly locked oscillatory states is presented and analyzed. The network is close to biology in the following sense. First, the neuron spikes and our model includes an absolute refractory period after each spike. Second, we consider a distribution of axonal delay times. Finally, we describe synaptic signal transmission by excitatory and inhibitory potentials (EPSP and IPSP) with a realistic shape, that is, through a response kernel. The patterns have been learned by an asymmetric Hebbian rule that can handle a low activity which may vary from pattern to pattern. During retrieval of a pattern all active neurons exhibit periodic spike bursts which may or may not be synchronized ( “locked” ) into a coherent oscillation. We derive an analytical condition of locking and calculate the period of collective activity during oscillatory retrieval. It is argued that in a biological network an intermediate scenario of “weak locking” is most likely. In this regime, we discuss applications to feature linking and pattern segmentation as well as the problem of context sensitive binding that can be solved in a layered structure including feedback. In addition, we address the question of synchronization between the two hemispheres of the brain.

Neural Coding - A Theoretical Vista of Mechanisms, Techniques, and Applications

This paper presents an overview of the capabilities of spiking neurons in processing complex information. We propose a flexible neuron model (the Spike Response Model), that is amenable to both analytic treatment and straightforward numerical simulation, and analyze the dynamics of a large network consisting of these neurons. We also present tools that, given some homogeneity, enable one to analytically treat the dynamical response of a network, a highly nonlinear system. Finally, we evaluate the underlying mechanisms, such as the dependence upon the axonal delays, the local inhibition, structural feedback, and discuss applications to associative feature linking, pattern segmentation, and context-sensitive binding.

A ‘microscopic’ model of collective oscillations in the cortex

The discovery of coherent oscillations in the primary visual cortex of the cat has aroused considerable theoretical interest. Most model networks that try to simulate these collective oscillations use some kind of oscillatory element as the basic unit of the network. It is, however, not clear how these oscillations should be described on a more microscopic level. Here we present a network that is based on a couple of measurable neurobiological quantities: (i) A distribution of axonal delay times for the transmission of spikes, (ii) A postsynaptic response described by realistic excitatory or inhibitory postsynaptic potentials (EPSP or IPSP). (iii) A threshold dynamics for the model neurons that includes refractoriness and noise. For a realistic set of parameters, the network shows collective oscillations only while an external signal is applied. If the parameters are changed significantly, other scenarios result with a behaviour which is qualitatively different in that it shows prolonged oscillations or no oscillations at all.

Correlation Coding in Stochastic Neural Networks

Stimulus-dependent changes have been observed in the correlations between the spike trains of simultaneously-recorded pairs of neurons from the auditory cortex of marmosets even when there was no change in the average firing rates. A simple neural model can reproduce most of the characteristics of these experimental observations based on model neurons having leaky integration and fire-and-reset spikes and with Poisson-distributed, balanced input. The source of the synchrony in the model was common sensory input. The outputs of neurons in the model appear noisy (almost Poisson owing to the stochastic nature of the input signal, but there is nevertheless a strong central peak in the correlation of the output spike trains. The experimental data and this simple model clearly demonstrate how even a noisy-looking spike train can convey basic information about a sensory stimulus in the relative spike timing between neurons.

Poisson-like neuronal firing due to multiple synfire chains in simultaneous action

The irregularity of neuronal firing times is commonly interpreted as being due to noise6. Here, an alternative approach is taken to show that even in a completely deterministic model — without any noise — neuronal firing times might appear random. This can be achieved in an attractor model with spiking neurons where the limit cycles are complex spatio—temporal spiking patterns also called synfire chainsl. Simultaneous activation of several synfire chains can lead to arbitrarily complex-looking spike patterns at the single neuron level. In addition, a learning rule is presented that allows to store general spatio—temporal spiking patterns.

Pattern Segmentation and Feature Linking as Simultaneous Processes in an Associative Network of Spiking Neurons

Feature linking and segmentation of four stationary patterns are shown to be performed as simultaneous processes by a fully connected, auto-associative neural network of spiking neurons. The patterns have been learned through an asymmetric, Hebbian rule that can handle a varying low activity. In this case the total activity of the patterns ranges between 4 and 7%. The underlying model is the ‘spike response model’. Spiking is achieved by an absolute refractory period (1ms) while an inhibitory delay loop prevents continuous firing. Reaching the synapse after some axonal delay each spike evokes an excitatory or inhibitory postsynaptic potential (EPSP or IPSP) with a realistic response at the receiving neuron. Each neuron sums up its input signals linearly and acts as a noisy threshold element for generating a new spike.