THE WORLD QUESTION CENTER 2006 — Page 10

For many theoretical neuroscientists, it all started twenty five years ago, when John Hopfield made us realize that a network of neurons could operate as an attractor network, driven to optimize an overall energy function which could be designed to accomplish object recognition or memory completion. Then came Geoff Hinton's Boltzmann machine — again, the brain was seen as an optimizing machine that could solve complex probabilistic inferences. Yet both proposals were frameworks rather than laws. Each individual network realization still required the set-up of thousands of ad-hoc connection weights.

Very recently, however, Karl Friston, from UCL in London, has presented two extraordinarily ambitious and demanding papers in which he presents "a theory of cortical responses".  Friston's theory rests on a single, amazingly compact premise: the brain optimizes a free energy function. This function measures how closely the brain's internal representation of the world approximates the true state of the real world. From this simple postulate, Friston spins off an enormous variety of predictions: the multiple layers of cortex, the hierarchical organization of cortical areas, their reciprocal connection with distinct feedforward and feedback properties, the existence of adaptation and repetition suppression… even the type of learning rule — Hebb's rule, or the more sophisticated spike-timing dependent plasticity — can be deduced, no longer postulated, from this single overarching law.

The theory fits easily within what has become a major area of research — the Bayesian Brain, or the extent to which brains perform optimal inferences and take optimal decisions based on the rules of probabilistic logic. Alex Pouget, for instance, recently showed how neurons might encode probability distributions of parameters of the outside world, a mechanism that could be usefully harnessed by Fristonian optimization. And the physiologist Mike Shadlen has discovered that some neurons closely approximate the log-likelihood ratio in favor of a motor decision, a key element of Bayesian decision making. My colleagues and I have shown that the resulting random-walk decision process nicely accounts for the duration of a central decision stage, present in all human cognitive tasks, which might correspond to the slow, serial phase in which we consciously commit to a single decision. During non-conscious processing, my proposal is that we also perform Bayesian accumulation of evidence, but without attaining the final commitment stage. Thus, Bayesian theory is bringing us increasingly closer to the holy grail of neuroscience — a theory of consciousness.

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But I have now changed my mind. Talents, tastes and temperaments play fundamental roles. But they alone don't fully explain the differences. It is a fourth T that most decisively shapes the distinctive structure of male — female differences. That T is Tails — the tails of these statistical distributions. Females are much of a muchness, clustering round the mean. But, among males, the variance — the difference between the most and the least, the best and the worst — can be vast. So males are almost bound to be over-represented both at the bottom and at the top. I think of this as 'more dumbbells but more Nobels'.

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Let's look at those causes. The legacy of natural selection is twofold: mean differences in the 3 Ts and males generally being more variable; these two features hold for most sex differences in our species and, as Darwin noted, greater male variance is ubiquitous across the entire animal kingdom. As to the facts of statistical distribution, they are three-fold … and watch what happens at the end of the right tail: first, for overlapping bell-curves, even with only a small difference in the means, the ratios become more inflated as one goes further out along the tail; second, where there's greater variance, there's likely to be a dumbbells-and-Nobels effect; and third, when one group has both greater mean and greater variance, that group becomes even more over-represented at the far end of the right tail.

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