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10.5 Summary

Correlation-based learning is, as a whole, often called Hebbian learning. The Hebb rule (10.2) is a special case of a local learning rule because it only depends on pre- and postsynaptic firing rates and the present state wij of the synapse, i.e., information that is easily `available' at the location of the synapse.

Recent experiments have shown that the relative timing of pre- and postsynaptic spikes critically determines the amplitude and even the direction of changes of the synaptic efficacy. In order to account for these effects, learning rules on the level of individual spikes are formulated with a learning window that consists of two parts: If the presynaptic spike arrives before a postsynaptic output spike, the synaptic change is positive. If the timing is the other way round, the synaptic change is negative (Zhang et al., 1998; Markram et al., 1997; Bi and Poo, 1998,1999; Debanne et al., 1998). For some synapses, the learning window is reversed (Bell et al., 1997b), for others it contains only a single component (Egger et al., 1999).

Hebbian learning is considered to be a major principle of neuronal organization during development. The first modeling studies of cortical organization development (Willshaw and von der Malsburg, 1976; Swindale, 1982) have incited a long line of research, e.g., Linsker (1986b); Obermayer et al. (1992); Linsker (1986a); Kohonen (1984); Miller et al. (1989); MacKay and Miller (1990); Linsker (1986c). Most of these models use in some way or another an unsupervised correlation-based learning rule similar to the general Hebb rule of Eq. (10.2); see Erwin et al. (1995) for a recent review.


Correlation-based learning can be traced back to Aristoteles 10.2 and has been discussed extensively by James (1890) who formulated a learning principle on the level of `brain processes' rather than neurons:

When two elementary brain-processes have been active together or in immediate succession, one of them, on re-occurring, tends to propagate its excitement into the other.
A chapter of James' book is reprinted in volume 1 of Anderson and Rosenfeld's collection on Neurocomputing (Anderson and Rosenfeld, 1988). More than 50 years later, Hebb's book (Hebb, 1949) of which two interesting sections are reprinted in the collection of Anderson and Rosenfeld (1988) was published. The historical context of Hebb's postulate is discussed in the review of Sejnowski (1999). In the reprint volume of Anderson and Rosenfeld (1988), articles of Grossberg (1976) and Bienenstock et al. (1982) illustrate the use of the rate-based learning rules discussed in Section 10.2. Kohonen's book gives an overview of some mathematical results for several generic rate-based learning rules (Kohonen, 1984).

For reviews on (hippocampal) LTP, see the book of Byrne and Berry (1989), in particular the articles of Sejnowski and Tesauro (1989) and Brown et al. (1989). Cerebellar LTD has been reviewed by Daniel et al. (1996,1998) and Linden and Connor (1995). Further references and a classification of different forms of LTP and LTD can be found in the nice review of Bliss and Collingridge (1993). For the relation of LTP and LTD, consult Artola and Singer (1993). A modern and highly recommendable review with a focus on recent results, in particular on spike-time dependent plasticity has been written by Bi and Poo (2001). The theoretical context of spike-time dependent plasticity has been discussed by Abbott (2000).

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Gerstner and Kistler
Spiking Neuron Models. Single Neurons, Populations, Plasticity
Cambridge University Press, 2002

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