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 potentials, 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 it 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.

e tests of the electronic device cover the range from spontaneous activity (3--4 Hz) to stimulus-driven rates (50 Hz). Low transition probabilities can be maintained in all ranges, even though the intrinsic time constants of the device are short (# 100 ms). Synaptic transitions are triggered by elevated presynaptic rates: for low presynaptic rates, there are essentially no transitions. The synaptic device can preserve its memory for years in the absence of stimulation. Stochasticity of learning is a result of the variability of interspike intervals; noise is a feature of the distributed dynamics of the network. The fact Neural Computation 12, 2227--2258 (2000) c # 2000 Massachusetts Institute of Technology 2228 Fusi, Annunziato, Badoni, Salamon, and Amit that the synapse is binary on long timescales solves the stability problem of synaptic efficacies in the absence of stimulation. Yet stochastic learning theory

We study analytically a model of long-term synaptic plasticity where synaptic changes are triggered by presynaptic spikes, postsynaptic spikes, and the time dierences between presynaptic and postsynaptic spikes. The changes due to correlated input and output spikes are quanti- ed by means of a learning window. We show that plasticity can lead to an intrinsic stabilization of the mean ring rate of the postsynaptic neuron. Subtractive normalization of the synaptic weights (summed over all presynaptic inputs converging on a postsynaptic neuron) follows if, in addition, the mean input rates and the mean input correlations are identical at all synapses. If the integral over the learning window is positive, ring-rate stabilization requires a non-Hebbian component, whereas such a component is not needed, if the integral of the learning window is negative. A negative integral corresponds to `anti-Hebbian' learning in a model with slowly varying ring rates. For spike-based learning, a strict distinction between Hebbian and `anti-Hebbian' rules is questionable since learning is driven by correlations on the time scale of the learning window. The correlations between presynaptic and postsynaptic ring are evaluated for a piecewise-linear Poisson model and for a noisy spiking neuron model with refractoriness. While a negative integral over the learning window leads to intrinsic rate stabilization, the positive part of the learning window picks up spatial and temporal correlations in the input.

switching Cognitive behaviour requires complex context-dependent mapping between sensory stimuli and actions. The same stimulus can lead to different behaviours depending on the situation, or the same behaviour may be elicited by different cueing stimuli. Neurons in the primate prefrontal cortex show task-speci®c ®ring activity during working memory delay periods. These neurons provide a neural substrate for mapping stimulus and response in a ¯exible, context- or rule-dependent, fashion. We describe here an integrate-and-®re network model to explain and investigate the different types of working-memory-related neuronal activity observed. The model contains different populations (or pools) of neurons (as found neurophysiologically) in attractor networks which respond in the delay period to the stimulus object, the stimulus position (`sensory pools'), to combinations of the stimulus sensory properties (e.g. the object identity or object location) and the response (`intermediate pools'), and to the response required (left or right) (`premotor pools'). The pools are arranged hierarchically, are linked by associative synaptic connections, and have global inhibition through inhibitory interneurons to implement competition. It is shown that a biasing attentional input to de®ne the current rule applied to the intermediate pools enables the system to select the correct response in what is a biased competition model of attention. The integrate-and-®re model not only produces realistic spiking dynamicals very similar to the neuronal data but also shows how dopamine could weaken and shorten the persistent neuronal activity in the delay period; and allows us to predict more response errors when dopamine is elevated because there

In this article we compare methods for temporal sequence learning (TSL) across the disciplines machine-control, classical conditioning, neuronal models for TSL as well as spiketiming dependent plasticity. This review will briefly introduce the most influential models and focus on two questions: 1) To what degree are reward-based (e.g. TD-learning) and correlation based (hebbian) learning related? and 2) How do the different models correspond to possibly underlying biological mechanisms of synaptic plasticity? We will first compare the different models in an open-loop condition, where behavioral feedback does not alter the learning. Here we observe, that reward-based and correlation based learning are indeed very similar. Machine-control is then used to introduce the problem of closed-loop control (e.g. “actor-critic architectures”). Here the problem of evaluative (“rewards”) versus nonevaluative (“correlations”) feedback from the environment will be discussed showing that both learning approaches are fundamentally different in the closed-loop condition. In trying to answer the second question we will compare neuronal versions of the different learning architectures to the anatomy of the involved brain structures (basal-ganglia, thalamus and

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Carson C. Chow. Calcium time course as a signal for spike-timing–

on. First, There has been little doubt that suppression is due to inhibition from cortical neurons that respond to the suppression can be obtained with masks drifting too rapidly to elicit much of a response in cortex. Second, mask. These neurons would (1) have largely overlapping receptive fields because suppression is elicited from a suppression is immune to hyperpolarization (through visual adaptation) of cortical neurons responding to small central region within the receptive field of the V1 neuron (DeAngelis et al., 1992); (2) be selective for a the mask. Signals mediating suppression might originate in thalamus, rather than in cortex. Thalamic neu- variety of orientations, spatial frequencies, and temporal frequencies because suppression is not selective or rons exhibit some suppression; additional suppression might arise from depression at thalamocortical broadly selective for these attributes (Allison et al., 2001; Bauman and Bonds, 1991; Bonds, 1989; DeAngelis et syna

In timing-based neural codes, neurons have to emit action potentials at precise moments in time. We use a supervised learning paradigm to derive a synaptic update rule that optimizes by gradient ascent the likelihood of postsynaptic firing at one or several desired firing times. We find that the optimal strategy of up- and downregulating synaptic efficacies depends on the relative timing between presynaptic spike arrival and desired postsynaptic firing. If the presynaptic spike arrives before the desired postsynaptic spike timing, our optimal learning rule predicts that the synapse should become potentiated. The dependence of the potentiation on spike timing directly reflects the time course of an excitatory postsynaptic potential. However, our approach gives no unique reason for synaptic depression under reversed spike timing. In fact, the presence and amplitude of depression of synaptic efficacies for reversed spike timing depend on how constraints are implemented in the optimization problem. Two different constraints, control of postsynaptic rates and control of temporal locality, are studied. The relation of our results to spike-timing-dependent plasticity and reinforcement learning is discussed.

What is the 'meaning' of a single spike? Spike-triggered averaging ('reverse correlations') yields the typical input just before a spike. Similarly, cross-correlations describe the probability of firing an output spike given (one additional) presynaptic input spike. In this paper, we analytically calculate reverse and cross-correlations for a spiking neuron model with escape noise. The influence of neuronal parameters (such as the membrane time constant, the noise level, and the mean firing rate) on the form of the correlation function is illustrated. The calculation is done in the framework of a population theory that is reviewed. The relation of the population activity equations to population density methods is discussed. Finally, we indicate the role of cross-correlations in spike-time dependent Hebbian plasticity. 2001 Elsevier Science Ltd. All rights reserved.