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Hi Olivier,

It's nice to follow your blog. It reminds me of our long discussions...
Physics and learning theory, as someone coming the physics community and now working in learning theory the connection of these two fields is a very interesting question.
In principle I think you are right when you are saying physics and learning theory are similar, since physics basically tries to infer natural laws from measurements. However I see two main differences.

First a more direct comparison. In physics we want to infer a law, that is a differential equation, and not only a function. However one could argue that we would like to learn the solution (a function) to the differential equation for all possible initial conditions. The problem I see here is that there are probably a lot of
initial conditions (so to say the differential equation is a very good compression algorithm). A second difference is that measurements are usually not
stochastic but deterministic.
The second difference is the level of abstract thinking needed to infer physical laws (which is done by humans). As an example take Newtons gravitational law. To infer that an apple falling from a tree follows the same law as the earth going around the sun requires a very high level of abstract thinking. I don't see how you can build this into a traditional statistical learning framework.

Nevertheless this should not prevent research into this direction. I remember
that there exists a book like "Physics from Fisher information". But the book
seems not to be appreciated very much, see the review of R. F. Streater on his homepage.

Olivier Bousquet

Hi Matthias,

Nice to hear from you and thanks for the comment.

You are right about the differences you mention, but my feeling is that there should be a way to place learning theory at a higher level (possibly forgetting the statistical aspect). What I mean is that we could think of learning theory as a theory of how to build theories from observations (not just functions).
It is clear that we are far from being able to account for the thinking that led to Newton's gravitational law, but it would be nice to set this as some sort of long-term goal of the development of the theory.

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