Where is Noether's principle in machine learning?
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Re: Where is Noether's principle in machine learning?
#2This is one of those links where just seeing the title sets you off, thinking about the implications.
I'm going to have to spend more time digesting the article, but one thing that jumps out at me, and maybe it's answered in the article and I don't understand it, is the role of time. Generally in physics, you're talking about a quantity being conserved over time, and I'm not sure what plays the role of time when you're talking about conserved quantities in machine learning -- is it conserved over training iterations or over inference layers, or what?
edit: now that i've read it again, I just saw that they described in the second paragraph.
I'm now wondering if in something like Sora that can do a kind of physical modeling, if there's some conserved quantity in the neural network that is _directly analagous_ to conserved quantities in physics -- if there is, for example, something that represents momentum, that operates exactly as momentum as it progresses through the layers.
Re: Where is Noether's principle in machine learning?
#3This is one of those links where just seeing the title sets you off, thinking about the implications. I'm going to have to spend more time digesting the article, but one thing that jumps out at me, and maybe it's answered in the article and I don't understand it, is the role of time. Generally in physics, you're talking about a quantity being conserved over time, and I'm not sure what plays the role of time when you'…
Yeah, I've been thinking about similar concepts in a different context. Fascinating.
Regarding the role of time, the idea of a purely conserved quantity is that it is conserved under the conditions of the system (that's why the article frequently references Newton's First Law), so they're generally held "for all time that these symmetries exist in the system".
Specifically on time: the invariant for systems that exhibit continuous time symmetries (i.e. you move a little bit forward or backward in time and the system looks exactly the same) is energy.
Re: Where is Noether's principle in machine learning?
#4how do you direct what the network learns if it all comes from supervised learning training sets?
How do you insert rules that aren't learned into what weights are learned?
Re: Where is Noether's principle in machine learning?
#5How does he create those animations? I'd like to make them as well for myself.
Re: Where is Noether's principle in machine learning?
#6This is one of those links where just seeing the title sets you off, thinking about the implications. I'm going to have to spend more time digesting the article, but one thing that jumps out at me, and maybe it's answered in the article and I don't understand it, is the role of time. Generally in physics, you're talking about a quantity being conserved over time, and I'm not sure what plays the role of time when you'…
Ha, my previous comment was before your new edit mentioning Sora. There is a good reason why the accompanying research report to the Sora demo isn't titled "Awesome Generative Video," but references world models. The interesting feature is how many apparently (approximations to) physical properties emerge (object permanence, linear motion, partially elastic collisions, as well as many of the elements of grammar of film), and which do not (notably material properties of solid and fluids, creation of objects from nothing, etc.)
Re: Where is Noether's principle in machine learning?
#7How does he create those animations? I'd like to make them as well for myself.
They seem to be built with some love by the author. Apparently they have written it in Haxe, judging from the comment in the page source.
Re: Where is Noether's principle in machine learning?
#8This is one of those links where just seeing the title sets you off, thinking about the implications. I'm going to have to spend more time digesting the article, but one thing that jumps out at me, and maybe it's answered in the article and I don't understand it, is the role of time. Generally in physics, you're talking about a quantity being conserved over time, and I'm not sure what plays the role of time when you'…
Yeah, I've been thinking about similar concepts in a different context. Fascinating. Regarding the role of time, the idea of a purely conserved quantity is that it is conserved under the conditions of the system (that's why the article frequently references Newton's First Law), so they're generally held "for all time that these symmetries exist in the system". Specifically on time: the invariant for systems that exhi…
Here's my ELI5 attempt of the time/energy relation:
imagine a spring at rest (not moving)
strike the spring, it's now oscillating
the system now contains energy like a battery
what is energy? it's stored work potential
the battery is storing the energy, which can then be taken out at some future time
the spring is transporting the energy through time
in fact how do we measure time? with clocks. What's a clock? It's an oscillator. The energized spring is the clock. When system energy is zero, what is time even? There's no baseline against which to measure change when nothing is changing
Re: Where is Noether's principle in machine learning?
#9As a complete amateur I was wondering if it could be possible to use that property of light ("to always choose the most optimal route") to solve the traveling salesman problem (and the whole class of those problems as a consequence). Maybe not with an algorithmic approach, but rather some smart implementation of the machine itself.
Re: Where is Noether's principle in machine learning?
#10As a complete amateur I was wondering if it could be possible to use that property of light ("to always choose the most optimal route") to solve the traveling salesman problem (and the whole class of those problems as a consequence). Maybe not with an algorithmic approach, but rather some smart implementation of the machine itself.
This sounds a bit like LIDAR implementations, I assume you mean something similar at a smaller scale, where physical obstacles provide a "path" representation of a problem space?