The relation between neuronal dynamics and neuronal group dynamics has been explored by a number of different researchers, leading to conclusions rather different from those put forth by Wright, Kydd & Liley (1993). Whereas their attempt at a synthesis of models is ambitious and interesting, the path they trace from linear stochastic dynamics on the millimetric scale to Hopfield-style dynamics on the macroscopic scale is not entirely convincing, and clearly needs more work.
2. First of all, although I have little doubt that asymmetry of connection is the generic case, I am not completely satisfied with the argument presented in favor of this point (Section VI.1). Although it is only presented as a "back of the envelope" calculation, and it is perfectly adequate as such calculations go, a little more comparison of the argument's assumptions (par. 36) with the actual process of neural development would be useful. What effect do cell adhesion molecules (Edelman, 1988) and all the other chemical intricacies of the developing brain have on this sort of probabilistic argument?
3. Granted that asymmetry of connection is prevalent, the point made in Wright et al.'s par. 43, that "average couplings can more appropriately be considered symmetric," is a very interesting one. However, it is a tremendous leap from this observation to the idea that the global dynamics of the brain can be modeled by Hopfield-style spin-glass-type equations. Edelman's theory of neuronal group selection (Edelman, 1988) also deals with symmetric connections between large groups of neurons; it would be nice to know whether the target article's analysis of microscopic dynamics is compatible with Edelman's view of macroscopic dynamics.
4. Putting aside the details of Edelman's neuronal group selection theory, there are clear advantages to an evolutionary view of global brain dynamics. Murre, Phaf and Wolters (1992; Murre, 1992), in their work on CALM networks, have shown that a simulated network of competitively evolving neural clusters can solve a variety of problems involving pattern recognition and unsupervised learning. Others have constructed psychological theories founded on the evolutionary view of the brain (Rosenfield, 1988; Goertzel, 1993). It seems highly unlikely that similar psychological and computer science connections can be drawn with the global Hopfield-type network proposed in the target article (Hopfield & Tank 1986). This is a weak point if one believes that the study of global brain structure should be guided by what the brain DOES as well as by physiological observations.
5. It is pointed out in par. 30 that Hopfield networks bear only a loose resemblance to the actual neural networks in the brain; the authors propose that there is a closer resemblance between Hopfield networks and the (presumably symmetric) network of neuronal groups. But this entire line of argument seems silly because a Hopfield network for which "the minimum at zero is the only energy minimum" is not really a Hopfield network at all. This also overlooks another fact about Hopfield networks: aside from the question of faithfulness to the brain, they have very serious limitations as COMPUTATIONAL ALGORITHMS. The Hopfield network, used as an associative memory, becomes overloaded very quickly; and there is no reliable method to cause it to "dump" old memories to make room for new ones. Christos (1993) has shown that the idea of cycling between periods of learning and forgetting does not work. When used as an optimization scheme, Hopfield networks are a little more successful, but they have an unfortunate tendency to converge to local minima and are therefore not that frequently used in practical neural net applications.
6. In conclusion, the first part of the target article is very strong. It does not give an extensive review of all the different approaches to chaos in EEG's, but it does present a most interesting and competent unification of two approaches to EEG modeling, revealing a degree of commonality underlying the apparent differences. But the second part, on which I have focused here, gives a somewhat muddled and incomplete treatment of the link between microscopic and macroscopic levels of neurodynamics, culminating in the nonconclusions of par. 48-49. There is much food for thought here, but one wishes that the global implications had been a little more carefully worked out.
Christos, G. (1993). Reverse Learning in Hopfield Nets. ms.
Edelman, G. (1988). Neural Darwinism, New York: Basic.
Goertzel, B. (1993). The Evolving Mind. New York: Gordon and Breach.
Gregson, R.A.M. (1994). Thinking About the Unconsidered Chaotic EEG Data: Commentary on Wright on EEG-Chaos. PSYCOLOQUY 5(6) eeg-chaos.2.gregson.
Hopfield, J.J. & Tank, D.W. (1986) Computing with neural circuits: a model. Science 233: 625-633.
Murre, J.M.J., (1992) Precis of: Learning and categorization in modular neural networks PSYCOLOQUY 3(68) categorization.1.murre
Murre, J.M., Phaf, H.R. and Wolters, G. (1992). CALM: Categorizing and Learning Module. Neural Networks, 5, 55-82.
Rosenfield, I. (1988). The Invention of Memory, New York: Basic.
Wright, J.J., Kydd, R.R. and Liley, D.T.J. (1993). EEG Models: Chaotic and Linear. PSYCOLOQUY 4(60) eeg-chaos.1.wright.