Biomedical Engineering Reference
In-Depth Information
In fact, the majority of synapses in the mammalian neocortex originate from
cortical neurons. In particular, lateral connections from superficial pyramids tend
to be characterized by recurrent excitation with other pyramids (about 80 % of the
total), while only about 20 % of the synaptic connections are with inhibitory intra-
columnar interneurons (Nicoll and Blakemore 1993 ). It is well known that recurrent
excitation in neural networks can implement many interesting functions, like finite-
state automata, associative memories, or spatiotemporal pattern formation
(McCulloch and Pitts 1943 ; Cohen and Grossberg 1983 ; Hopfield 1984 ; Morasso
et al. 1998 ). On the other hand, inhibitory synaptic connections are an important
part of the intrinsic circuitry of the neocortex, serving to modulate the propagation
of sensory information.
More specifically, the inhibitory local field is expressed by a simple “leaky
integrator.” The recurrent lateral connections are excitatory and approximately
symmetric, as in Hopfield networks, thus making sure that the map is stable, i.e.,
has an attractor dynamics. We also assume that the pattern of lateral connectivity is
acquired through a process of babbling and self-organization, thus encoding the
dimensionality and topology of the sensorimotor space represented by the map. The
distribution of activity throughout the map via the lateral connections is normalized
by a mechanism of gating inhibition that takes into account, for each macro-neuron,
the average activity of its neighbors (Reggia et al. 1992 ; Morasso et al. 1998 ).
Finally, the input field, broadcasted to the map by another map or by thalamo-
cortical projections, is channeled to a limited population of macro-neurons via a
mechanism of shunting interaction that induces a cluster of activity in the neural
population around the neuron that resonates with the input field.
The equilibrium states of this network architecture are characterized by clusters
of activation in register with the peak of the external field, i.e., a population code
matching the external input field. After a shift of the input field, corresponding to
the selection of a new target, the combination of symmetric recurrent excitation,
gating inhibition, and shunting interaction induces in the map an attractor dynamics
characterized as follows: first, a diffusion process (which initially flattens the
population code, spreading the activity pattern over a large part of the network)
and, then, a re-sharpening process around the target. The combination of the two
processes can be described as a moving hill, namely, the propagation of the
population code towards the new target.
Suppose now to instantiate two cortical maps, with the same network dynamics
but with different dimensionality and connectivity: for example, a map for
representing hand position and the other for representing arm configuration
(in the case of arm motor control) or a map for representing speech sounds and
the other for representing configurations of the vocal tract (in the case of speech
motor control). Both cases are characterized by a high degree of redundancy, and
thus the latter map will have a larger number of units and a more complex
connectivity than the former one. We may suppose that during a process of self-
supervising learning or Piagetian circular reaction (Kuperstein 1991 ), it was possi-
ble to acquire two sets of topology-representing intra-connections for the two maps
and, at the same time, a set of interconnection between the maps. As a consequence
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