Richardson's hyperstructures display the characteristics of a number of earlier explanatory concepts in perception and pattern recognition. Questions can be raised about their exact ontological status: Are they truly global constructs? or are they derived from the products of prior local processing? If the former, then what is the mechanism of their direct detection? If the latter, then questions can be asked about the validity of Richardson's attack on so-called "feature theory," which would seem to provide the basis for the extraction and derivation of hyperstructures. A more explicit conception of hyperstructures may be in terms of the "dependence systems" suggested by Rescher & Oppenheim (1955). Richardson suggests that hyperstructures fill a "void" in connectionist systems. It is argued here that there is no such void, and that Richardson's claim stems from his confusion of neural-level and cognitive descriptions, together with an incomplete exposition of the exact ontological status of his hyperstructures.
2. First, the terms "feature", "holistic", "local" and "global" are relative, and any stimulus object will admit of an indefinite number of decompositions and sets of attributes. Accordingly, before there can be any useful discourse on such matters, it must be established, in each and every case, what is to constitute a whole and what are to be regarded as parts and attributes of that whole. In many cases, it is also necessary to state explicitly any background theory and assumptions relating to how the objects in question are composed of their parts. In the absence of this information on hyperstructures, a number of questions about their status are necessary. How exactly are these global configurations to be detected by the visual system? Are they extracted directly from objects and stimuli in motion without the need for prior registration and analysis of their local properties (whatever these may be)? On the other hand, are the putative global properties derived from the products of prior analysis of their local properties or, dare one use the term, "features"? These questions bear on the viability of hyperstructures as genuine candidates for the truly global theory that Richardson and Uttal believe is missing.
3. If hyperstructures are products of, or mere derivations from, the outputs of lower-order analyzers, one may be led to question the truly global status claimed by Richardson. Indeed, if the analysis of local features plays such a crucial role in the detection and construction of hyperstructures, one may also question the validity of Richardson's arguments against local feature theory. On the other hand, if local feature analysis is bypassed and hyperstructures are extracted directly from objects, then, unfashionable as the question is, it must still be asked; how exactly would such a system work? Normally, it would be apposite to ask for a specification of the mechanism that could detect global properties directly, but theorists of global processing have always been reluctant to commit themselves in this way. Richardson is no exception, even going so far as to rule out the relevance of modelling to hyperstructures: "All this can happen without the need for hypothetical computational engines, which may be fine for the idealised world of machine intelligence, but not for the real world of complex animals." (para. 44).
4. In the absence of any clearly specified and testable mechanism for hyperstructures, one has to resort to other methods of trying to invest Richardson's concept with clear meaning. Throughout the paper, he cites examples of models that illustrate some of the principles embodied in hyperstructures, and these include Marr's (1982) theory, Uttal's (1975) autocorrelation model and connectionist systems, but a close scrutiny of these schemes reveals nothing of direct detection of global properties. Marr's construction of the primal sketch begins with a grey-level image from which a rich description of local features is compiled. It is from this local analysis that the higher-order features are then derived. With regard to autocorrelation, Dodwell (1971) points out that any such model must rely on prior processes of contour extraction. Uttal's procedures are carried out on matrices of discrete elements, and Engel, Dougherty and Jones (1973) in their application of autocorrelation to alphabetic character recognition, use a 15 x 15 spatial analysis of their stimuli.
5. Connectionist models of pattern recognition are patently not global analyzers. Arrays of input units sample discrete regions of patterns, and pass their activations to hidden units which in turn respond to combinations of input activation. Global properties such as "symmetry" are clearly derived from the products of activation from discrete input units - see Latimer, Joung and Stevens (1996) for examples. Although not mentioned directly by Richardson, Schema theory (Evans, 1967) is often cited as an holistic alternative to feature theory. However, attempts to program schema theory (e.g. Evans, Hoffman, Arnoult & Zinser, 1968) quickly uncover its feature-analytic origins. Schema are constructed from prior detection of "subschemata". Finally, it should also be noted that the models cited by Schmidhuber (1999) as mechanisms capable of hyperstructure use derivation rather than direct detection of global properties. Clearly, in all the above cases, what is claimed to be direct extraction of global properties is really derivation of such properties from prior local analysis. Indeed, Richardson's Figure 4 depicting "nested-representational hyperstructures" makes this evident.
6. Advocates of direct global detection often try to counter the above arguments in a number of ways. Grey-level images are said to be truly continuous and global. They are not so in machine memory where they reside as discrete levels of grey at discrete locations in the image. It is also argued that autocorrelation can be effected by optical methods which are truly continuous and global. This rejoinder, like the previous one, ignores the relativity of "local" and "global". What may appear to be a continuous, smooth, grey-level surface at one level of magnification, can become a discrete, segmented surface at another level. There can be no case whatsoever for absolute notions of whole and part, local and global. Of course, because of this relativity, theorists may choose to designate certain properties as local or global, and that is fair enough. However, they should also indicate exactly how prior local analysis has contributed to the construction of their global properties, if indeed it has. Richardson can quite legitimately call his hyperstructures global entities, but it seems odd that he attacks feature theory when it provides the whole basis for derivation of his global properties. Yet another common rejoinder to these criticisms of global theory is to propose that prior local analyses are mere fixes necessitated by the use of digital machines in modelling global processing. This is a reasonable assumption to make, but the onus is on those who make it to demonstrate that the prior local analysis plays no significant role or theoretical basis for higher-order processing. It should also be noted that the first level of analysis in the human visual system is unquestionably a rich, interactive, high-resolution and pointillistic registration of stimuli, be they static or moving.
7. Perhaps a more explicit exposition of the concept of hyperstructure could be afforded by the notion of a "dependence system" by Rescher & Oppenheim (1955) - see Latimer & Stevens (1997) for discussion and examples from perception and pattern recognition. Consider for example a set of magnetic needles of equal strength inserted in pieces of cork and floated with all like poles upwards in a basin of water. A magnet of unlike pole, suspended above the floating magnets, results in a pattern of one or more concentric circles of magnets, depending on the number of magnets. Various dependencies exist in this sort of configuration. The distance between magnets depends on their relative strengths and the number of magnets. In this sense, any configuration can be characterized as a dependence system by specifying the various dependence relations in which its constituents or parts must stand.
8. Richardson's point-light examples are particularly germane in this context. Light points in particular locations move to new locations, and, because of their dependence relations, provide a chain of inference and prediction for light points in new locations. For example, Cutting and Proffitt (1981) regard gait perception as spatiotemporal and explicitly interpret their results in terms of dependencies between parts. They suggest that in perceiving a human walker from a dynamic display of lights attached to joints, "we extract information in logical steps that result in the parts of the body being perceived as a system of dynamic nested dependencies. The motions and locations of the hip and shoulder are extracted first, as they are related to the body's deepest center of moment, that within the torso. Each step of information extraction that follows takes the previously described part as the center of moment for the determination of dynamic relations to other parts." (p. 270). Rather than some nebulous global property, perception of gait is conceived of as arising from a serial extraction of explicit, dynamic, dependent local properties.
9. There is one further intriguing issue raised by Richardson. He claims that hyperstructures "may fill a void in connectionist literature." For example, he argues that, "successful connectionist nets 'work' by surreptitiously discovering just such covariation hyperstructures in inputs" (para.52). Certainly, the representations that develop in hidden unit space can be described by sets of rules (Anderson & Diederich, 1996), but Richardson's concern with a void seems to be one of ontology. If that is the case, then just what could the ontological status of hyperstructures in connectionist systems be? One can describe the behaviour of neural nets, clocks, speedometers automobile engines, thermostats etc in terms of rules or even hyperstructures, but what (if anything) is added to these systems by doing so? When one looks at artificial neural networks, one sees only units, connections, activations and "anonymous" weight changes. The reductionist message of connectionism, although not always explicit, is that maybe this is all there is. If one were able to observe the workings of the real neural net (the brain) would Richardson claim there is a void there too? There is, of course, no void in connectionist systems as there is no void in the brain. Richardson appears to be slipping between cognitive and neural descriptions in an ambiguous and potentially confusing manner, which raises again my earlier questions on the exact ontological status of hyperstructures.
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