Wulfram Gerstner

Spiking Neuron Models

Note: book Reference LCN-BOOK-2002-001 URL: http://diwww.epfl.ch/~gerstner/BUCH.html Record created on 2006-12-12, modified on 2017-05-12

Noninvasive brain-actuated control of a mobile robot by human EEG

Brain activity recorded noninvasively is sufficient to control a mobile robot if advanced robotics is used in combination with asynchronous electroencephalogram (EEG) analysis and machine learning techniques. Until now brain-actuated control has mainly relied on implanted electrodes, since EEG-based systems have been considered too slow for controlling rapid and complex sequences of movements. We show that two human subjects successfully moved a robot between several rooms by mental control only, using an EEG-based brain-machine interface that recognized three mental states. Mental control was comparable to manual control on the same task with a performance ratio of 0.74.

Phenomenological models of synaptic plasticity based on spike timing

Synaptic plasticity is considered to be the biological substrate of learning and memory. In this document we review phenomenological models of short-term and long-term synaptic plasticity, in particular spike-timing dependent plasticity (STDP). The aim of the document is to provide a framework for classifying and evaluating different models of plasticity. We focus on phenomenological synaptic models that are compatible with integrate-and-fire type neuron models where each neuron is described by a small number of variables. This implies that synaptic update rules for short-term or long-term plasticity can only depend on spike timing and, potentially, on membrane potential, as well as on the value of the synaptic weight, or on low-pass filtered (temporally averaged) versions of the above variables. We examine the ability of the models to account for experimental data and to fulfill expectations derived from theoretical considerations. We further discuss their relations to teacher-based rules (supervised learning) and reward-based rules (reinforcement learning). All models discussed in this paper are suitable for large-scale network simulations.

Triplets of spikes in a model of spike timing-dependent plasticity.

Classical experiments on spike timing-dependent plasticity (STDP) use a protocol based on pairs of presynaptic and postsynaptic spikes repeated at a given frequency to induce synaptic potentiation or depression. Therefore, standard STDP models have expressed the weight change as a function of pairs of presynaptic and postsynaptic spike. Unfortunately, those paired-based STDP models cannot account for the dependence on the repetition frequency of the pairs of spike. Moreover, those STDP models cannot reproduce recent triplet and quadruplet experiments. Here, we examine a triplet rule (i.e., a rule which considers sets of three spikes, i.e., two pre and one post or one pre and two post) and compare it to classical pair-based STDP learning rules. With such a triplet rule, it is possible to fit experimental data from visual cortical slices as well as from hippocampal cultures. Moreover, when assuming stochastic spike trains, the triplet learning rule can be mapped to a Bienenstock–Cooper–Munro learning rule.

Connectivity reflects coding: a model of voltage-based STDP with homeostasis

Electrophysiological connectivity patterns in cortex often have a few strong connections, which are sometimes bidirectional, among a lot of weak connections. To explain these connectivity patterns, we created a model of spike timing–dependent plasticity (STDP) in which synaptic changes depend on presynaptic spike arrival and the postsynaptic membrane potential, filtered with two different time constants. Our model describes several nonlinear effects that are observed in STDP experiments, as well as the voltage dependence of plasticity. We found that, in a simulated recurrent network of spiking neurons, our plasticity rule led not only to development of localized receptive fields but also to connectivity patterns that reflect the neural code. For temporal coding procedures with spatio-temporal input correlations, strong connections were predominantly unidirectional, whereas they were bidirectional under rate-coded input with spatial correlations only. Thus, variable connectivity patterns in the brain could reflect different coding principles across brain areas; moreover, our simulations suggested that plasticity is fast.

Population Dynamics of Spiking Neurons: Fast Transients, Asynchronous States, and Locking

An integral equation describing the time evolution of the population activity in a homogeneous pool of spiking neurons of the integrate-and-fire type is discussed. It is analytically shown that transients from a state of incoherent firing can be immediate. The stability of incoherent firing is analyzed in terms of the noise level and transmission delay, and a bifurcation diagram is derived. The response of a population of noisy integrate-and-fire neurons to an input current of small amplitude is calculated and characterized by a linear filter L. The stability of perfectly synchronized locked solutions is analyzed.

Mathematical Formulations of Hebbian Learning

Abstract. Several formulations of correlation-based Hebbian learning are reviewed. On the presynaptic side, activity is described either by a firing rate or by presynaptic spike arrival. The state of the postsynaptic neuron can be described by its membrane potential, its firing rate, or the timing of backpropagating action potentials (BPAPs). It is shown that all of the above formulations can be derived from the point of view of an expansion. In the absence of BPAPs, it is natural to correlate presynaptic spikes with the postsynaptic membrane potential. Time windows of spike-time-dependent plasticity arise naturally if the timing of postsynaptic spikes is available at the site of the synapse, as is the case in the presence of BPAPs. With an appropriate choice of parameters, Hebbian synaptic plasticity has intrinsic normalization properties that stabilizes postsynaptic firing rates and leads to subtractive weight normalization.

Reduction of the hodgkin-huxley equations to a single-variable threshold model

It is generally believed that a neuron is a threshold element that fires when some variable u reaches a threshold. Here we pursue the question of whether this picture can be justified and study the four-dimensional neuron model of Hodgkin and Huxley as a concrete example. The model is approximated by a response kernel expansion in terms of a single variable, the membrane voltage. The first-order term is linear in the input and its kernel has the typical form of an elementary postsynaptic potential. Higher-order kernels take care of nonlinear interactions between input spikes. In contrast to the standard Volterra expansion, the kernels depend on the firing time of the most recent output spike. In particular, a zero-order kernel that describes the shape of the spike and the typical after-potential is included. Our model neuron fires if the membrane voltage, given by the truncated response kernel expansion, crosses a threshold. The threshold model is tested on a spike train generated by the Hodgkin-Huxley model with a stochastic input current. We find that the threshold model predicts 90 percent of the spikes correctly. Our results show that, to good approximation, the description of a neuron as a threshold element can indeed be justified.

Inhibitory plasticity balances excitation and inhibition in sensory pathways and memory networks.

Plasticity at inhibitory synapses maintains balanced excitatory and inhibitory synaptic inputs at cortical neurons. Cortical neurons receive balanced excitatory and inhibitory synaptic currents. Such a balance could be established and maintained in an experience-dependent manner by synaptic plasticity at inhibitory synapses. We show that this mechanism provides an explanation for the sparse firing patterns observed in response to natural stimuli and fits well with a recently observed interaction of excitatory and inhibitory receptive field plasticity. The introduction of inhibitory plasticity in suitable recurrent networks provides a homeostatic mechanism that leads to asynchronous irregular network states. Further, it can accommodate synaptic memories with activity patterns that become indiscernible from the background state but can be reactivated by external stimuli. Our results suggest an essential role of inhibitory plasticity in the formation and maintenance of functional cortical circuitry.

Spatial cognition and neuro-mimetic navigation: a model of hippocampal place cell activity

Abstract. A computational model of hippocampal activity during spatial cognition and navigation tasks is presented. The spatial representation in our model of the rat hippocampus is built on-line during exploration via two processing streams. An allothetic vision-based representation is built by unsupervised Hebbian learning extracting spatio-temporal properties of the environment from visual input. An idiothetic representation is learned based on internal movement-related information provided by path integration. On the level of the hippocampus, allothetic and idiothetic representations are integrated to yield a stable representation of the environment by a population of localized overlapping CA3-CA1 place fields. The hippocampal spatial representation is used as a basis for goal-oriented spatial behavior. We focus on the neural pathway connecting the hippocampus to the nucleus accumbens. Place cells drive a population of locomotor action neurons in the nucleus accumbens. Reward-based learning is applied to map place cell activity into action cell activity. The ensemble action cell activity provides navigational maps to support spatial behavior. We present experimental results obtained with a mobile Khepera robot.