Timeline for What's the point of Hamiltonian mechanics?
Current License: CC BY-SA 4.0
6 events
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| May 16, 2019 at 6:23 | comment | added | jhegedus | free energy and how thermodynamics is derived from simple principles, ergodicity, phase space, entropy and such... I came to the realisation that the existence of Hamiltonian formalism and independence in "ML" has the same underlying reason, namely, reducing the Kolmogorov complexity of the algorithm that describes the "theory" in physics, or the "model" in ML. Also, the prior (in both disciplines) is exponentially getting sparser with the number of independent degrees of freedom. Also, once independence is maximized, it becomes easier to "do" unsupervised learning (I forgot why ... :) ). | |
| May 16, 2019 at 6:17 | comment | added | jhegedus | I came to this conclusion after learning "ML" for many hours, 3 years + 2 or so... and also have a physics PhD, with focus on theoretical condensed matter physics. Funnily ML and cond mat phys fit splendidly smoothly together. Like spin glasses for DNNs and such. So I was wondering why is so extremely big deal that "stuff" has to be independent in "ML" (see graphical models and their friends), nevertheless, the concept of independence is central in ML. Finding independent "coordinate system". It makes it possible to write the entropy as a sum. Then I thought about stat phys, entropy | |
| May 16, 2019 at 6:13 | comment | added | jhegedus | I like that you also bring up the information angle. The story goes much deeper than that. Consider independence. Independent systems. Decoupling. The entropy is additive. The energy is additive. Energy is simple a measure of entropy. The equation of motions are independent. IMHO this goes both ways. Also, I suspect, that this gives meaning to "dimensions". Generalized coordinates. Which take constraints into account. They (can) decouple the energy dependence. So H(x,y)=H(x)+H(y) becomes possible to write. Due to the "concept" that the total energy is the sum of the component energies. | |
| May 2, 2019 at 20:24 | history | edited | user3072048 | CC BY-SA 4.0 |
added 2 characters in body
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| May 2, 2019 at 13:25 | review | Late answers | |||
| May 2, 2019 at 13:48 | |||||
| May 2, 2019 at 13:05 | history | answered | user3072048 | CC BY-SA 4.0 |