The Operation of Memory Systems in the Brain - Computational Neuroscience: A Comprehensive Approach - page 504

represent spaces with arbitrary topologies, as the topology is represented in the con-
nection strengths [101, 102, 104, 105]. Indeed, it is this that enables many different
charts each with its own topology to be represented in a single continuous attractor
network [8].

16.2.4.3 Continuous attractor networks in two or more dimensions

Some types of spatial representation used by the brain are of spaces that exist in two
or more dimensions. Examples are the two- (or three-) dimensional space represent-
ing where one is looking at in a spatial scene. Another is the two- (or three-) dimen-
sional space representing where one is located. It is possible to extend continuous
attractor networks to operate in higher dimensional spaces than the one-dimensional
spaces considered so far [111, 104]. Indeed, it is also possible to extend the analyses
of how idiothetic inputs could be used to update two-dimensional state spaces, such
as the locations represented by place cells in rats [104] and the location at which
one is looking represented by primate spatial view cells [102, 105]. Interestingly,
the number of terms in the synapses implementing idiothetic update do not need to
increase beyond three (as in Sigma-Pi synapses) even when higher dimensional state
spaces are being considered [104]. Also interestingly, a continuous attractor net-
work can in fact represent the properties of very high dimensional spaces, because
the properties of the spaces are captured by the connections between the neurons
of the continuous attractor, and these connections are of course, as in the world of
discrete attractor networks, capable of representing high dimensional spaces [104].
With these approaches, continuous attractor networks have been developed of the
two-dimensional representation of rat hippocampal place cells with idiothetic update
by movements in the environment [104], and of primate hippocampal spatial view
cells with idiothetic update by eye and head movements [102, 105].

16.2.5 A unified theory of hippocampal memory: mixed continuous

and discrete attractor networks

If the hippocampus is to store and retrieve episodic memories, it may need to asso-
ciate together patterns which have continuous spatial attributes, and other patterns
which represent objects, which are discrete. To address this issue, we have now
shown that attractor networks can store both continuous patterns and discrete pat-
terns, and can thus be used to store for example the location in (continuous, physi-
cal) space where an object (a discrete item) is present (see Figure 16.4 a nd [88]). In
this network, when events are stored that have both discrete (object) and continuous
(spatial) aspects, then the whole place can be retrieved later by the object, and the
object can be retrieved by using the place as a retrieval cue. Such networks are likely
to be present in parts of the brain that receive and combine inputs both from systems
that contain representations of continuous (physical) space, and from brain systems
that contain representations of discrete objects, such as the inferior temporal visual
cortex. One such brain system is the hippocampus, which appears to combine and
store such representations in a mixed attractor network in the CA3 region, which thus