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David Barber
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Journal Articles
Optimal Spike-Timing-Dependent Plasticity for Precise Action Potential Firing in Supervised Learning
Publisher: Journals Gateway
Neural Computation (2006) 18 (6): 1318–1348.
Published: 01 June 2006
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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.
Journal Articles
Publisher: Journals Gateway
Neural Computation (1998) 10 (8): 2201–2217.
Published: 15 November 1998
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We analyze online gradient descent learning from finite training sets at noninfinitesimal learning rates η. Exact results are obtained for the time-dependent generalization error of a simple model system: a linear network with a large number of weights N , trained on p = α N examples. This allows us to study in detail the effects of finite training set size α on, for example, the optimal choice of learning rate η. We also compare online and offline learning, for respective optimal settings of η at given final learning time. Online learning turns out to be much more robust to input bias and actually outperforms offline learning when such bias is present; for unbiased inputs, online and offline learning perform almost equally well.
Journal Articles
Publisher: Journals Gateway
Neural Computation (1996) 8 (1): 202–214.
Published: 01 January 1996
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The generalization error is a widely used performance measure employed in the analysis of adaptive learning systems. This measure is generally critically dependent on the knowledge that the system is given about the problem it is trying to learn. In this paper we examine to what extent it is necessarily the case that an increase in the knowledge that the system has about the problem will reduce the generalization error. Using the standard definition of the generalization error, we present simple cases for which the intuitive idea of “reducivity”—that more knowledge will improve generalization—does not hold. Under a simple approximation, however, we find conditions to satisfy “reducivity.” Finally, we calculate the effect of a specific constraint on the generalization error of the linear perceptron, in which the signs of the weight components are fixed. This particular restriction results in a significant improvement in generalization performance.