วีดีโอ

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While this might be pedantic, the symmetries shown are not symmetries because the object has to be exactly the same. Putting colors and the F on the hexagon prevents the rotations from being symmetric. You have to literally get the same object that you started with. Any differences will prevent the transformation from being a mathematical symmetry. X = TX. E.g., the symmetries of a transformation are it's fixed points. The set of all transformations that leave an object fixed is the set of symmetries. Typically one ignores any labels to keep track of the "fixed points" and one can consider the colors as labels of the vertices but the F is not rotationally symmetric. If one considers the F as simply a sort of "compass" that tells one the rotation or mirror then it is ok. But one has to understand the color and the symbol are not part of the object under consideration. The idea of the symmetries is rather symbol in that if an object is invariant under certain transformations then one cannot tell the difference between it and any possible other symmetric state it is in. The group of symmetries helps one understand the possible states it is in and the structure that may exist in the way the object can move around in these "symmetric states". One may wonder why it matters if the object is exactly the same in each symmetry. It matters because the object may not be actually identical but is "perceived to be" when one ignores certain features. Hence in actuality there is some differences but if you can't tell the difference in some scenario you can still count the possible differences using the symmetries. E.g., imagine a square with painted sides. If you project the square onto the wall the colored sides are all black and you cannot tell the differences. You know the symmetries which is D4. But if the square does have colored sides you know that D4 counts the possible ways that those colors could be hidden. That is, there are no symmetries of the colored square but D4 symmetries of the non-colored one. This tells you that there are D4 possibilities(and what they could be) of that the non-colored square could represent. You then may be able to use this to further understand the square in a larger context. So understanding symmetries is a way to understand something about the innate structure of the object ignoring any "attached details" (as the details can only be attached in a specific away according to the symmetries). E.g., they are non-essential modifications while symmetries are concerned with essential modifications. If an object as the same symmetry group as another it is likely the same or "isomorphic" to it.

Insanity squared

nice talk and handsome speaker :)

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These two talks (Sophia Sanborn and Michael Bronstein on geometric deep learning) complement each other regarding symmetry of the convolution operator. [ th-cam.com/video/w6Pw4MOzMuo/w-d-xo.htmlsi=NAZq0xXlcBlD07FW ]

Incorporate constructor theory

Thanks for posting!

This works connects quite strongly across fields. There seems to be some work to be done with toroidal harmonic groups?

It is very likley theat the reason the same patterns show up is because of the machinery of NN's which involve matrices(inner product spaces), integrals, etc. These are simply the generalized basis functions for NN's. E.g., similar to how a box will shape the energy it contains within it and limit it to a fixed set of discrete frequencies or the same with a vibrating string. The machine of NN's is effectively using the same fundamental mathematics that has always been used. It's in the type of mathematics we use that unifies everything we do. The question is if there are other types of "mathematics" that exist that are completely different. It seems our mathematics is universal rather than anything in particular that uses it. That it shows up biologically is, IMO, what proves our mathematics is complete and general. Of course once one realizes that our mathematics was created by biological machines it really isn't that much of a leap(hence mathematics is simply an emergence of us and "us" is biological).

He named after ilya

Interestingly the picture at 21:25 looks like the same patterns you see with cymatics. They also match that of the probability distribution clouds of atomic orbitals of an electron. The wikipedia page for atomic orbitals has a nice picture.

A really fantastic talk. Thank you.

This is great! Been thinking about this a lot so it's very validating as well. Thanks for the talk and upload

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OMG i love this kind of topic

Very interesting. Nature has it's invariants. Even on atomic scale. I wonder where this will lead.

Здравствуйте. Эйнштейн создал, теорию относительности но сам не ссылался на проделанный опыт Майкельсона Морли для подтверждения своей теории. Но при этом у него, мечта была, чтобы такой же опыт проделать в поезде или самолёте. Просьба. Помощь найти, кто захочет стать автором изобретения. В Китае на предприятии по выпуску Волоконно-оптических гироскопов, возможно договориться. Производить устройство ГИБРИД гироскопы. Эти устройства будут использоваться в качестве учебного пособия в школах, высших учебных заведениях. Также ВОЗМОЖНО будет с помощью «гибрид гироскопа» сделать научные открытия; в астрономии, астрофизики, космологии, высшей теоретической физики, …

thanks this was very interesting

those bananas hit

1:22 you know it absolutely wouldn't hurt to remind the public that the table on a right is a russian chemist Dmitri Mendeleev creation.

Fantastic video thank you

While his thesis has some merits it fails when comparing human beings with AI. The most important error is that we don’t share a ground truth or from a semiotic perspective a referent. Whatever the representation is flawed if it’s pointing to something different or is not grounded in the same thing. AI is grounded on its training data not reality. Eg: science fiction, social media, Internet sources are all biased, subjective and not necessarily grounded in reality.

There's a PNAS paper observing how almost all neural nets learn the same manifold. techxplore.com/news/2024-03-replica-theory-deep-neural-networks.pdf

25min video on looking at how a DNN represents that of a 4F system, i mean it is actually how they were designed.... what has this team done except for checking the math works? oh yeah in mice brain we see similar patterns to the "Gabor filters" lol

I've been thinking about fourier-like components in neural networks and now I see this talk. Amazing, didn't expect it to participate in such a meaningful way

AMAZING

Such an interesting topic and a great presentation!

This was a great presentation. One of the best i have seen in a long time.

There is enough evidence for not having converging learning already in AI. Internal representations in the latent space via high dimensional embeddings are not compatible even within models of the same family. Let alone making any links with the human brain which are highly speculative anyway and not supported by science.

Very interesting. Thanks for sharing.

Very interesting, bringing system 1/2 to synapses 🎉

He said Timber not timbre 😢, I jest, great presentation

Great presentation