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## “Darwinian Evolution is a form of PAC (Machine) Learning”

Changing or increasing functionality of circuits in biological evolution is a form of computational learning. – Leslie Valiant

The title of this post comes from Prof. Leslie Valiant‘s The ACM Alan M. Turing award lecture titled “The Extent and Limitations of Mechanistic Explanations of Nature”.

Prof. Leslie G. Valiant

Click on the image above to watch the lecture

[Image Source: CACM “Beauty and Elegance”]

Short blurb: Though the lecture came out sometime in June-July 2011, and I have shared it (and a paper that it quotes) on every online social network I have presence on, I have no idea why I never blogged about it.

The fact that I have zero training (and epsilon knowledge of) in biology that has not stopped me from being completely fascinated by the contents of the talk and a few papers that he cites in it. I have tried to see the lecture a few times and have also started to read and understand some of the papers he mentions. Infact, the talk has inspired me enough to know more about PAC Learning than the usual Machine Learning graduate course might cover. Knowing more about it is now my “full time side-project” and it is a very exciting side-project to say the least!

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Getting back to the title: One of the motivating questions about this work is the following:

It is widely accepted that Darwinian Evolution has been the driving force for the immense complexity observed in life or how life evolved. In this beautiful 10 minute video Carl Sagan sums up the timeline and the progression:

There is however one problem: While evolution is considered the driving force for such complexity, there isn’t a satisfactory explanation of how 13.75 billion years of it could have been enough. Many have often complained that this reduces it to a little more than an intuitive explanation. Can we understand the underlying mechanism of Evolution (that can in turn give reasonable time bounds)? Valiant makes the case that this underlying mechanism is of computational learning.

There have been a number of computational models that have been based on the general intuitive idea of Darwinian Evolution. Some of these include: Genetic Algorithms/Programming etc. However, people like Valiant amongst others find such methods useful in an engineering sense but unsatisfying w.r.t the question.

In the talk Valiant mentions that this question was asked in Darwin’s day as well. To which Darwin proposed a bound of 300 million years for such evolution to occur. This immediately fell into a problem as Lord Kelvin, one of the leading physicists of the time put the figure of the age of Earth to be 24 million years. Now obviously this was a problem as evolution could not have happened for more than 24 million years according to Kelvin’s estimate. The estimate of the age of the Earth is now much higher. ;-)

The question can be rehashed as: How much time is enough? Can biological circuits evolve in sub-exponential time?

For more I would point out to his paper:

Evolvability: Leslie Valiant (Journal of the ACM – PDF)

Towards the end of the talk he shows a Venn diagram of the type usually seen in complexity theory text books for classes P, NP, BQP etc but with one major difference: These subsets are fact and not unproven:

$Fact: Evolvability \subseteq SQ Learnable \subseteq PAC Learnable$

*SQ or Statistical Query Learning is due to Michael Kearns (1993)

Coda: Valiant claims that the problem of evolution is no more mysterious than the problem of learning. The mechanism that underlies biological evolution is “evolvable target pursuit”, which in turn is the same as “learnable target pursuit”.

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