The Operation of Memory Systems in the Brain - Computational Neuroscience: A Comprehensive Approach - page 505

is able to implement episodic memories which typically have a spatial component,
for example where an item such as a key is located.
This network thus shows that in brain regions where the spatial and object pro-
cessing streams are brought together, then a single network can represent and learn
associations between both types of input. Indeed, in brain regions such as the hip-
pocampal system, it is essential that the spatial and object processing streams are
brought together in a single network, for it is only when both types of information
are in the same network that spatial information can be retrieved from object infor-
mation, and vice versa, which is a fundamental property of episodic memory. It may
also be the case that in the prefrontal cortex, attractor networks can store both spa-
tial and discrete (e.g., object-based) types of information in short-term memory (see
below).

16.2.6 The speed of operation of memory networks: the integrate-and-

fire approach

Consider for example a real network whose operation has been described by an au-
toassociative formal model that acquires, with learning, a given attractor structure.
How does the state of the network approach, in real time during a retrieval operation,
one of those attractors? How long does it take? How does the amount of informa-
tion that can be read off the network's activity evolve with time? Also, which of the
potential steady states is indeed a stable state that can be reached asymptotically by
the net? How is the stability of different states modulated by external agents? These
are examples of dynamical properties, which to be studied require the use of models
endowed with some dynamics. An appropriate such model is one which incorporates
integrate-and-fire neurons.
The concept that attractor (autoassociation) networks can operate very rapidly if
implemented with neurons that operate dynamically in continuous time is described
by [82] and [92]. The result described was that the principal factor affecting the
speed of retrieval is the time constant of the synapses between the neurons that form
the attractor ([7, 59, 92, 112]). This was shown analytically by [112], and described
by [92] Appendix 5. If the (inactivation) time constant of AMPA synapses is taken
as 10 ms, then the settling time for a single attractor network is approximately 15-17
ms [7, 59, 92]. A connected series of four such networks (representing for example
four connected cortical areas) each involving recurrent (feedback) processing imple-
mented by the recurrent collateral synaptic connections, takes approximately 4 x 17
ms to propagate from start to finish, retrieving information from each layer as the
propagation proceeds [59, 82]. This speed of operation is sufficiently rapid that such
attractor networks are biologically plausible [82, 92].
The way in which networks with continuous dynamics (such as networks made
of real neurons in the brain, and networks modelled with integrate-and-fire neurons)
can be conceptualized as settling so fast into their attractor states is that spontaneous
activity in the network ensures that some neurons are close to their firing threshold
when the retrieval cue is presented, so that the firing of these neurons is influenced
within 1-2 ms by the retrieval cue. These neurons then influence other neurons