Learning theory is about the process of induction, that is the process of building theories or models from observations.
Most of what physicits do is actually induction about natural phenomena. So one may wonder whether there can be some relationship between Physics and Learning Theory.
One could argue that Physics is using induction in a particular setting, while Learning Theory is studying induction in general, so they cannot really be compared.
But here are some surprising connections:
- In quantum physics Bell's inequality provides a test for the existence of "hidden variables" that explain entanglement. This inequality is based on a statistical reasoning.
- Some physicists study the connection between Bayes formula for updating probabilities and the collapse of the wave function when measurements of a quantum system are made (see e.g. the work of Christopher Fuchs). There are even "Bayesian" and "non-Bayesian" physicists, just like the Machine Learning people !
- Even further, Lucien Hardy tries to rethink the way physics theories are built up. His starting point is that the work of any physicist is to accumulate and correlate data. He thus develops physics theories as theories for how data should be handled ! (see e.g. http://arxiv.org/PS_cache/gr-qc/pdf/0509/0509120.pdf)