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Cortical Integration: Possible Solutions to the Binding and Linking Problems in Perception, Reasoning and Long Term Memory

Nick Bostrom

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The problem of cortical integration is described and various proposed solutions, including grandmother cells, cell assemblies, feed-forward structures, RAAM and synchronization, are reviewed. One method, involving complex attractors, that has received little attention in the literature, is explained and developed. I call this binding through annexation. A simulation study is then presented which suggests ways in which complex attractors could underlie our capacity to reason. The paper ends with a discussion of the efficiency and biological plausibility of the proposals as integration mechanisms for different regions and functions of the brain.


1. The problem of cortical integration

If sensory input and memory mechanisms lead to spatially distinct neural representations in the brain, these representations must somehow come to interact in order to bring about an appropriate behavioral output. The problem of cortical integration is how such a constructive interaction can take place.

One straightforward solution would be if the earlier representations converged on more abstract representations, determining which of these abstract representations should be activated; that representation, in turn, causing the adequate motor response. These abstract representations could be either individual cells or assemblies of cells. If they were individual cells, and if the representations were what we shall call transparent, i.e. possessing a readily identifiable representational content, then we would have a vindication of an extreme form of the so called "grandmother-cell hypothesis": there would be a specific cell for each possible situation the subject could ever be in. In this extreme form, the grandmother-cell hypothesis is obviously absurd: already the well-formed English sentences of less than 15 words with clearly distinct meanings outnumber the total of neurons in the brain [1]. The explosion of combinatorial possibilities makes it impossible to reserve one nerve cell, much less a cell assembly, for every conceivable input configuration that needs to be distinguished.

So it is necessary to have compositional representations: individual neurons must be enrolled to serve in combination with many different sets of other neurons as constituents of compositional representations. Somehow these individual neurons must interact, for instance by projecting onto the same down-stream neurons. This type of arrangement we will call integration through convergence and will be discussed in section 2.

A major disadvantage with convergence as an integration mechanism is its lack of flexibility. Since the functional significance of a node in a homogenous feed-forward network is wholly dependent on its position in the connection matrix, it is not easy to extract its representational content, examine it, and put it back in a modified form. This rigidity makes it unsuitable as a way of integrating those representations that will undergo frequent and drastic change, like the transitory combinations used in abstract reasoning. These cry out for more flexible a more flexible approach.

It is sometimes useful to distinguish two cases here. If the representations to be integrated, or held together, are within the same cortical area, we talk of the need of linking them together. If they are in different areas, we speak instead of binding. Thus the problem of cortical integration splits into the linking problem and the binding problem. Sometimes, in the literature, "binding" is also used in a broad sense to refer indiscriminately to all forms of cortical integration, but I we shall try to keep the terms distinct in this paper.

2. Integration through convergence

2.1 Grandmother cells and cell assemblies
Because of its rigidity, binding by convergence is almost certainly not the whole story of cortical integration. This does not mean, however, that it doesn't occur and play an important part. On the contrary, there is evidence, if not literally for grandmother cells, then at least for cell assemblies, and hence individual neurons, that respond selectively to faces, hands and similar items. Some cells in the visual cortex of a monkey, for example, respond exclusively when the animal is presented with monkey hands and star-like shapes; other cells show selectivity for faces. (No such specificity has been observed for unfamiliar objects or novel scenes.) Furthermore, it is well documented that in the early stages of visual processing there are successive layers of cells acting as feature extractors for edges, corners, moving edges etc. At the other extreme, there are reports that increased activity in individual cells antecedes specific motor actions in a regular manner Sakai&Miyashita(1991). It thus appears that convergence plays a prominent part in both early sensory processing and late motoric sequencing.

Less is known about what happens in between. A reasonable guess is that insofar as the activity of individual cells significantly correlates with a particular act of reasoning or with the entertaining of a certain concept, it does so only by virtue of being a member of a cell assembly that correlates similarly but more significantly. The reason is that a single cell would not have the requisite robustness in a such a noisy system as the CNS. A representation in early visual processing may or may not be robust: if it fails on some occasions, it would only cause an unnoticeable error of the size of a pixel in the visual field, a blur that would probably disappear completely after later abstraction and interpretation. But if you were thinking "I wish run to away from yonder wolf", and the neuron representing the concept "run away from" inadvertently flipped, changing the thought to "I wish to greet yonder wolf.", then you would be in trouble.

If it is not a single neuron by itself, then it must be a group of neurons; and if the representation must be kept active, then the neuronal activity must persist, presumably in the same neuronal group. Therefore Amit(1995) has a strong case when he argues that the reverberating attractor is an ubiquitous building block in cortex. Sustained attention to a thought or percept indicates that a group of neurons is engaged in continuous firing. The best way to accomplish such attention is through mutual feedback. Even for periods shorter than one second, it seems necessary for a neuron to have steady support from excitatory inputs if its activity is not to wane. Thus a reverberating attractor, a state of self-sustained activity in a group of interconnected neurons, serves to sustain the information contained in the active representation until it has served its purpose in the present computation and can be dropped. The dance moves on to another site; the attractor remains, slumbering in the synaptic efficacies, awaiting the next occasion when it will be called upon like an organ pipe to contribute its designated note to the cognitive concerto.

The Attractor also has several other features that makes it an intuitively likely correlate to the Concept, but we can't go into that here. In any case, however useful it may be in every other respect, the unstructured attractor does not solve the problem of cortical integration. As has often been pointed out, understanding the sentence "John loves Mary", for example, cannot consist simply in a special attractor representing "John", and one representing "loves", and one for "Mary", being activated; for then there would be nothing to distinguish this sentence from "Mary loves John." which consists of the same words and the understanding of which presumably involves the same concepts.

2.2 Integration through opaque feed-forward structures
The paradigmatic neural network is the three-layered feed-forward structure, trained with the back-propagation algorithm. Such an architecture exhibits generalization, graceful degeneration, and it is efficient as a classifier or feature extractor in many natural settings. Feed-forward structures abound in the brain, especially in sensory processing. It is not wholly clear how learning takes place: there is no known mechanism for back-propagation of error messages in the brain. Possibly, a great deal is genetically predetermined; but since perceptual skills have to be learned, there must also be some mechanism for modifying synaptic weights in these feed-forward structures capable of leading to greatly improved performance.

The properties of feed-forward structures and the location of their biological implementations are well-known and need not be further explained here. What needs to be clarified is rather the taxonomic issue of how these structures relate to other means of cortical integration. We may informally distinguish between two sorts of representations: transparent and opaque. A transparent representation is one that is readily given an interpretation in a natural language. For example, if there were a node that was activated only in the presence of a pink elephant, then that node could be said to represent (the notion of) a pink elephant; if a node responds to a moving edge in a certain part of the visual field, then that is what the node represents. For an opaquerepresentation, it is not possible to single out a definite denotation or meaning and explain it with a short expression in a natural language. If a three-layered network is trained to perform some discrimination task, it sometimes happens that the nodes in the hidden layer correspond to readily identifiable features, but often they don't, and in that case we say that they are opaque representations: they correspond to some holistic feature of the input which could be expressed in English only as an enumeration of the inputs that would elicit it, or as some complicated sort of weighed sum of different properties for which we have predicates.

We can now see that binding by grandmother cells is only a special case of convergence-integration in a feed-forward structure: the case where the representations are transparent. The sense in which a grandmother cell or cell assembly is a mechanism of integration is the same as the sense in which any hidden or output node in a feed-forward structure is an integration mechanism: its activity reflects complex relations between the activity of nodes in earlier layers.




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