030730 – Synaptic plasticity (Hebbian learning)

030730 – Synaptic plasticity in the brain

On average, whatever that might mean, each neuron in the brain is connected to about 10,000 other neurons via synapses.  “The human nervous system is able to perform complex visual tasks in time intervals as short as 150 milliseconds.  The pathway from the retina to higher areas in neocortex alone which a visual stimuli [sic] is processed consists of about 10 ‘processing stages’.  (Thomas Nachtschlager, December 1998.  “Networks of Spiking Neurons: A New Generation of Neural Network Models” http://www.cis.tugraz.at/igi/tnatschl/online/3rd_gen_eng/3rd_gen_eng.html).  “Experimental results indicate that some biological neural systems … use the exact timing of individual spikes,” that is, “the firing rate alone does not carry all the relevant information.”  That certainly makes sense in a system that has to deal with race conditions.

“Each cubic millimeter of cortical tissue contains about 105 neurons. This impressive number suggests that a description of neuronal dynamics in terms of an averaged population activity is more appropriate than a description on the single-neuron level. Furthermore, the cerebral cortex is huge. More precisely, the unfolded cerebral cortex of humans covers a surface of 2200-2400 cm2, but its thickness amounts on average to only 2.5-3.0 mm2. If we do not look too closely, the cerebral cortex can hence be treated as a continuous two-dimensional sheet of neurons.” (Wolfram Gerstner & Werner M. Kistler.  Spiking Neuron Models: Single Neurons, Populations, Plasticity. Cambridge University Press, 2002. Chap. 9.)

“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.”

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