Neural Networks as Quantum Field Theories (NNGP, NKT, QFT, NNFT) 

I am actually working in this field of quantum complex networks and once you go down the rabbit hole of this, with quantum tensor networks being the explanation of many-body entanglement, percolation being a feature of quantum networks that display similarities to classical Kuramoto-style synchronization of oscillators as well as the way in which Lagrangians can be used to give a sum-over-histories description of entanglement then you truly never see the world the same way again. Renormalization group theory has also a history in use in complex networks so the mathematical fuel is there and the phenomenology of quantum and network emergent adaptive behaviors' is an increasing field of study.

Fascinating to see this come out now.

Thank you for sharing your interest and ideas regarding this paper. Really, thank you!

Servus aus Linz! Amazing what the youtube algorithm keeps dishing me up; fascinating

This was a great video! I eprosnally enjoyed the formatting, and the subject matter was super interesting! Great content :)

Thanks for the video and links, I hadn’t heard of this connection

one of the amazing applications of the concept of artificial neural networks

What an amazing connection. I dont know much about neural nets but i do know about qft, excited to see whether this idea gets explored further

Really interesting, would love to see more stuff like this. Maybe something on Reinforcement Learning with path ntegrals? Such as MPPI could be interesting too, as an AI scientist with a cs background it's great to get some explanation of the maths

Great video

what do you think the minimal needed background for making some sense of this is?

Question about initial conditions weights in the NN: isn't it the case that with very large layers in the billions or trillions of nodes, the initial weights don't matter so much, given that you are not sampling a small number of weights from a very large probability space, you are pretty much taking all the values of weights up to a trillion, or something? It's obviously not that simple, but I'm wondering whether the influence of the specific sample of initial condition weights decreases as the total number of nodes increases? In other words, the larger the number of nodes, the larger the entropy of the initial weights whatever they are. And the larger the initial entropy, the more likely that the training will eventually land on a very similar result in the end. Whereas if you have low entropy small selection of initial weights, the less freedom the training has to explore all the probability space. Do you think there's something there?

Loved the video! It's a really interesting concept. This is a bit of a naysayer thing to do, but I took some notes on my skepticism of deep meaningful connections between NNs and QFTs. These are things I'm typing out so that I can concretely be proven wrong, or see how they're addressed in papers! 1. If you start at a Gaussian theory, that is fine, but the interesting things in ML should happen far away from this Gaussian theory. Conversely, for using NNs to get at near-Gaussian theories, it seems unlikely that there is any deep understanding/advancement to be made in terms of NNs that doesn't already look better in terms of perturbative QFT or lattice QFT. 2. About gradient descent, it seems like steps not being continuous is a good thing in ML. Right, stochastic gradient descent makes sure that we aren't actually just flowing downhill. I'm not sure what the graph looks like in a real NN (meaning: if we're doing MNIST with a dense NN and we're in the middle of training, what does f(t)=Error( theta(t0) - (t-t0) grad(Error(theta(t0))) ) look like, on the scale of a good step size h? Is it smooth or are we already skipping a lot of maxima and minima?) 3. The gradient descent flow theta'(t)=-grad Error(theta(t)) doesn't have interesting symplectic structure, does it? So the tools of dynamics from classical and quantum mechanics don't directly apply. 4. In QFTs, we can do Feynman diagrams in the position space representation, and the interesting thing is propagators between different points labeled by space. If we're not labeling nodes in the NN by position (so if it's densely connected or, like a human neuron, branches out into many arbitrary dendrites) then any propagator will be much less well-behaved and much less useful. This goes out the window for CNNs though. 5. What you say at 35:30 sounds like a really great way to describe quantum field theories to someone who knows machine learning well and is used to working in these large parameter spaces. So forming this pedagogy and dictionary is nice, but there's the notion of "conservation of difficulty" (Terence Tao "Generalised solutions") where it doesn't seem like translating between a QFT and an NN exploits any essential features. Perturbative QFT exploits being near gaussianity and translation invariance. Renormalization exploit how your theory can be specified given only several free parameters even though it may look initially like there are infinitely many free parameters. But I thought the beauty of large NNs is that they exploit having an enormous number of free parameters which are all important, rather than being set by a few mass scales! I don't know though, maybe after building the dictionary then other concepts like those from gauge theories could be applied to NNs to great effect.

I don't understand any of the terms or the math. Help.

As someone who is a complete layman but finds both neural networks and field theory interesting it is unfortunate that the RU-vid algorithm keeps showing me videos about the potential overlap of these subjects since I am never going to understand any of it. 😆 It’s like having rabies and being thirsty but not being able to swallow while someone keeps presenting you with a tall cool glass of ice water with a garnish of lemon. 😝

woah Matthew D. Schwartz? Is that the QFT book schwartz?

You can also use techniques from quantum field theory to compute the capacity of a NN layer. See my NeuriPS talk on the subject ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-ZT0yZ-wFIaE.html

미치겠다 로저 펜로즈가 좋아하겠네

Why is Gaussian special here? Bell curve shows up in everything everywhere.

The math here is completely out of my league and I'm just a humble CS student, but I have to ask, what the hell does delta raised to the power of delta could even mean conceptually at (1.11) and (4.20)? I understand "(d^3)r" being a shortcut for dxdydz but "(d^d)x" is some next level math wizardry

This feels like it has metaphysical implications

determine is pronounced like Determinante without the ante

This can all be understood within the lens of Modal Homotopy Type Theory EDIT: When I say understood, I more so mean explained.