00:00-Introduction 01:00-Part I 03:06-Tradititional approach to science 04:16-Era of AI (new approach) 05:46-Data to Neural Net 13:44-Neural Net to Theory 15:45-Symbolic Regression 21:45-Rediscoverying Newton's Law of gravity 23:40-Part II 25:23-Rise of foundation model paradigm 27:28-Why does this help? 31:06-Polymathic AI 37:52-Simplicity 42:09-Takeaways 42:42-Questions

Another banger from youtube algorithm

It seems like very powerful idea, when AI observes the system, then learns to predict behaviour and then the rules of this predictions are used to delivery math statement. Wish the authors the best luck

I was wondering or missing the concept of Meta-Learning with transformers, especially because most of these physics simulations shown are quite low-dimensional. Put a ton of physics equations into a unifying language format, treat each problem as a gradient step of a transformer, and predict on new problems. In this way, your transformer has learned on other physics problems, and infers maybe the equation/solution to your problem right away. The difference to pre-training is that these tasks or problems are shown each at a time unlike the entire distribution without specification. There has been work to this on causal graphs, and low-dimensional image data of mnist, where the token size is the limitational factor of this approach, I believe.

I came here to read all the insane comments, and I’m not disappointed.

It is precisely what I'm working on for some time now, very well explained in this presentation, nice work! (the idea of pySR is outrageously elegant, I absolutely love it!)

The 'Avada Kedavra' potential of that pointy stick is immense. Brilliant presentation.

It makes intuitive sense that a cat video is better initialization than noise. It's a real measurement of the physical world

Love the definition of simplicity, I found that to be pretty insightful.

Amazing talk, and great Research!

What an amazing fck of presentation. I mean, of course the subject and research is absolutely mind-blowing, but the presentation in itself is soooo crystal clear, I will surely aim for this kind of distilled communication, thank you!!

There are multiple different awesome ideas in this presentations. For example, an idea of having a neural net discovering new physics, or simply of being the better scientist than a human scientist. Such neural nets are on the verge of discovery or maybe in use right now. But I think the symbolic distillation in the multidimensional space is the most intriguing to me and a subject that was worked on as long as the neural networks were here. Using a genetic algorithm but also maybe another (maybe bigger?) neural network is needed for such a symbolic distillation. In a way, yes, the distillation is needed to speed up the inference process, but I can also imagine that the future AI (past the singularity) will not be using symbolic distillation. Simply, it will just create a better single model of reality in its network and such model will be enough to understand the reality around and to make (future) prediction of the behavior of the reality around.

This is SO cool! My first thought was just having incredible speed once the neural net is simplified down. For systems that are heavily used, this is so important

Jesus christ, okay UKposts I will watch this video now stop putting it in my recommendations every damn time

Training LLMs on code doesn't teach them to reason a bit better, it teaches them to reason a LOT better. It makes sense if you think about it: what do you learn when you (a human being) learn to write software? You learn a new way of thinking.

Being able to derive gravity laws from raw data is a cool example. How sensitive is this process to bad data? For example, non-unique samples, imprecise measurements, missing data (poor choice of sample space), irrelevant data, biased data, etc). I would expect any attempt to derive new theories from raw data to have this sort of problem in spades.

The folding analogy looks a lot like convolution. Also, the piecewise continuous construction of functions is used extensively in waveform composition in circuit analysis applications, though the notation is different, using multiplication by the unit step function u(t).

been in the rabbit hole lately so glad this popped up you rock miles!

All i always wanted to hear is in this video ! thanks !

Nice! I interpret this as, “these are the standard models - we can use them to kind of explain why AI is growing so exponentially in languages we can’t even understand, but really - we have no idea what’s going on and this is why to complex for our linear models.”

Amazing lecture!!

Incredible lecture

This is a very nice idea. I hope it will work! It will be very interesting to see new analytical expressions coming out of complicated phenomena.

This is the first exciting concept I’ve heard in the current AI revolution

Very cool visual at 28:12 - where would harmonic analysis fit?

This is a brilliant idea. I hope this goes places

Well not sure this will go anywhere except maybe modify some of our archaic equations for nonlinear terms. The problem is probably related to NP hardness and using more expansive nonlinearity methods to crack certain problems that are more specified. We will always not know what we don't know. Using more general nonlinear models was bound to greatly improve our simulations. The real question for NN is this the MOST ACCURATE or most INSIGHTFUL and BEST of nonlinear methods to do so? Somehow I doubt this, but it's certainly a nice proof of principle and place to venture off further. To put all our faith in it might be a mistake though. We might be looking at long predicted by mathematicians limits to reductionism, and our first method to not overfit billions of parameters will give us an illusion that this is the only way, and we could be looking at a modern version of epicycles. If we want to really go further we need to use such models to not just get better at copying reality, but finding general rules that allow it's consistent creation and persistence through time. Perhaps one way to do this would be to consider physical type symmetries on weights.

There's a paper on Feature Imitating Networks that's gotten a few good applications in medical classification, and subtask induction is a similar line of thought. FINs are usually used to produce low dimensional outputs, but I was thinking about using them for generative surrogate modeling. FINs can help answer the question of how to use neural networks to discover new physics. An idealized approach would turn every step of a coded simulator into something differentiable. It occurs to me that the approach of this talk, and interpretability research generally, is essentially the inverse problem of trying to get neural networks to mimic arbitrary potentially nondifferentiable data workflows.

Awesome explanation

This is some ingenious work

Cool idea! Essentially, we can deduce symbolic, testable scientific theories from deep learning models using things like PySR. Making foundation models (which are trained on a wide variety of phenomena, not necessarily related to the area of application) for specific scientific application gives ANNs an advantage. Simplicity (explainability, legibility) comes from familiarity with a problem area, so we should be training models on lots of diverse examples to help them “get used” to solving these types of problems, even if the examples may seem irrelevant (cat videos & differential equations 🐈) Interesting application of explainable AI 🎉 Congratulations on your research

That notion of pre-trained NN's discovering new mathematical operations and generalizations is so fascinating! It's so difficult to imagine there would be huge conceptual holes in our version of mathematics, but there's no reason why they couldn't exist! They're probably already there in our foundation models, just waiting to be discovered!

This was amazing-- confirms my suspicions.

So am i the only one that going to point out that SORA from OAI is basically a generalization for a 3d engine that might let us preform experiments!

This is actually really important

Great presentation. Its marvelous to see a take on AI from a broad, scientific/mathematical perspective without too much focus on technicalities. Really exited to see how this might improve or add to our understanding of the/(this?:) ) universe.

Briliant ideas

Fantastic. At 55 minutes though, it is suggested that we don't have a simple concept like + built into us. Perhaps not in a blank neural net, but we for example are not born with a blank slate. It is clear that any toddler understands in some way, the concept of 'more' and 'less' even though they lack empirical understanding. With sufficiently robust generalized data sets based on physical principles, information theory as language and perhaps even the nature of emotions, given enough GPUs to sustain large inter-operational neural nets, would this not give rise to something more than the sum of it's parts?

Regarding simplicity: I think that you are missing something important about the addition operation that makes it "simple". We are also familiar with division (the arithmetic operation) and it is also useful, but we would not say that division is "simple" in the same way the addition is simple (or we would say that addition is simpler than division, even though both are "familiar" and "useful").

interesting! was just learning about neural networks, so this is a pretty cool application :)

Fantastic work, I thought we would take AI in this direction and here we have that reality.

Am I confused? It feels like he is explaining the calculus of variation and linear algebra. The elemental functional priors he seems to be talking about are literally the concepts of functions and groups of related functions existing in hierarchial topics like trigonometry grouping sine, cosine, tangent together because they are mutually dependent and reduce the parameter space. Students may ask why we learn both sine and cosine when we could just learn one and use a parameterized offset for the other. The synthesis in seeing how together they can convert a two positions into single time parameter given a fixed length and a pivot point. Similarly, an ellipse can be described by these same two equations with a single parameter, t for position along the curve and the axis lengths. These are all model building concepts from statistics though. Am I missing something? It feels like he is explaining statistical model building. Yes, parsimony is great and admirable in a model. The push for larger and larger model is simply brute forcing and filling out the solution space with so many variables that it would be difficult for an answer to not exist if the idea previously existed in the world. However, they suck at low context situations where they need to make deductive leaps. If I'm talking about fear of a need to "abort", whether the conversation is happening at Kennedy Space Center or in a medical examination room completely change what we are talking about. If I don't tell ChatGPT the context, it may suggest language talking about "T-minus" for one contexts or "weeks" in another. At some level we are simply talking about different methods of representing temporal, spatial, social, economic, etc relationships and how abstracted from the ideas of initiating, terminating, increasing, decreasing, linear, exponential, repetition, regular, irregular, stochastic, or predictable. Whether one uses the term "sine" or "wave-like" or "repeating" is all just representation of the same linguistic concept

I am re-reading once again the book By David Foster Wallace History of Infinity. There he describes the book by Bacon Novum Organum. In book one there is an apt statement that I would like to paste 8. Even the effects already discovered are due to chance and experiment, rather than to the sciences. For our present sciences are nothing more than peculiar arrangements of matters already discovered, and not methods for discovery, or plans for new operations.

At 17:53, he has a plot on the right side, but he seems to attain only an expression in the variables x and y. There is no equation, so how is he even able to make a plot against those 2 variables? If you try plotting some of the given expressions by equating them to a constant (e.g. 2(x+sin(y+1.3))=3 ), you don't get anything that looks like his plot. If there is a 3rd variable (e.g. z, or something like f(x, y)), then the plot should be a 3D plot. Instead, the plot is 2D.

35:21 Good pretrained in some epochs by using Polymathics results does not mean training from scratch has a worse error. It is just a matter of time the good model will have the same quality.

30 mins to say that you can fit simpler models to a neural network data-generating process, and another 30 to say that more training data (even if relegated to what we call “pretraining”) improves performance. ps: things are simple because they are ubiquitous and they are ubiquitous because it’s how the world works (law of conservation of mass and energy, i.e. addition), not because it’s “useful”

This is the reason why I like UKposts

I can't shake the feeling that someone is going to train an AI model on a range of differently scaled phenomena (quantum mechanics, atomic physics, fluid dynamics, macro gravity / chemical / physical dynamics) and accidentally find an aligned theory of everything, and they'll only end up finding it because they noticed some weird behavior in the network while looking for something else. Truly, "the greatest discoveries are typically denoted not by 'Eureka' but by 'Hm, that's funny...' "

I'm going to state the obvious. That is smart. Yes it draws questions about AI explainability regarding deep learning NNs but what this chap is saying is quite brilliant. For me, as long as the conventional approach is combined with the model he is propounding, there should be some excellent science out of that. Then there can be even more science when we start to understand the reasons and mechanisms by which the deep learning neural networks some humans build are doing and are capable of what they are so. Let's not miss the point of what he is saying, at least what I interpret that he is saying... The NN is finding some order through patterns, it really is those patterns that are probably most related to something interesting, ie of scientific interest, then we can sift through the rest of the noise to see if something was missed, let's say we do that if questions are presented that don't have an answer. So all in all, it is a very powerful way of cutting through the fluff. If we then want to scientifically describe the fluff itself, it is now more distinct. I think what this guy is saying is brilliant. Incidentally, I think we ultimately find out that deep learning neural networks come to sensible decisions because the have the fidelity to tap into the innate intelligence structure of reality itself, but that is a next topic, although entirely pertinent.

Wow!

The "folding analogy" is incorrect. That is not how composition works. It works only in this case because of the very specific nature of the "first layer"(in his example).

Slime mold is my favorite way of imagining it

I don't know about all the fancy stuff but as a programmer this makes me 30 to 50% more productive and my daughter, who is a manager, makes her about 10 to 15% more productive.

Yes AI is definitely faster generating random ideas, and is also quicker fitting these random ideas to a data set. It’s a very powerful tool.

I see similarity with physics informed neural network especially with Sparse identification of nonlinear dynamics (SINDy)

I would love to see some breakthrough in Dark Matter regime. There is so much data regarding Dark Matter yet no theory to back it up.

35:16 Yes, doing the model from scratch with traditional machine learning is worse compared to the pre-trained generative network, but only for the *same time frame*, if you give the traditional machine learning approach more *time*, then it can out-perform the pre-trained generative network, while the pre-trained network will just keep on spitting out the same type of results.

The issue is discovering the higher-ordering principle which subsumes a continuum of self singularities and discontinuities. Linear math works well in-between the singularities, but cannot extrapolate through them, in a sense they are like mathematical worm-holes. Attempts to linearize across the discontinuities will fail. A whole harmonically-related series will only be properly understood from the perspective of a higher-ordering principle, similar to the idea of projection from a higher magnitude to a lower dimensional space, or from the idea of negative curvature. The point is the epistemological assumption of a static model is problematic, the real world has static islands which are bounded within areas of great change, and so the basic function changes completely there, that is to say, the dynamics of change themselves change. So to bridge that gap you can’t just ignore it, or flatten it, you have to seek how to remap it in such a manner that it is no longer infinite, but cyclical, as Gauss did with the complex number domain.

Polymathic AI 🤖 is a wonderful idea 💡

Simplicity is the absence of relative complexity.

36:36 becoming more basically intelligent because of understanding spacio temporal connectivity. The flashing faces in peripheral vision illusion it shows us The monsters we create when we lack that.

You might want to think about simplicity in terms of Kolmogorov complexity e.g your NN should try to emit the least complex, in the Kolmogorov sense, syntax tree. Also, I think "+" is simple because it is closed over the field of integers. I think that if your operation takes you from one domain to another its more complicated. In that way you might consider using Category Theory. You could think about penalizing models that "move' further away into other mathematical spaces from a 'base" space.

So if you sought to get what an LLM knows out into some equations we could understand, what could they be like?

This is very trival knowledge if one has an open mind, but its great that it is now formally been empirically proven for those out there that need proofs.

So here we are, you guys seems to be chosen by algorithm for us to meet here. Welcome, for some reason.

Did you see the Lifestyle Trader ad? Proof that money is not just a commodity but logarithmic.

someone so smart, only listenable at 4x

Your Analytic Distillation sounds like an algorithm for Low-Rank Adaptation (LORA). Considering also semantic relationships in latent space (e.g. the vector pointing from Woman to Man added to Queen returns King), I speculate there may be something like a basis/spanning set approximation we could come up with for any arbitrary concept. Like, what if we consider lots of things we consider "good" and "evil" and try to analytically model that? Would it give us insights into morality?

Fine-tune an LLM to interpret neural nets. Iterate and maybe symbolic regression (i.e. language) will help us supercharge LLM training. But hallucinations could be a major issue...

No feasible for UHDLSS Feature Selection.

it's seen it before so it pattern matches and i think it will be useful to scale up and pattern match and have other people pattern match and we can train it generally and scale up and train it generally and fluid simulation and we found matching outperform train it on more data and it does better the title of this video overdelivers

With enough inputs you can make any curve or field match the current data. So it this even science ? I am very skeptical. It will provide very little real insight, when you have inscrutable AI model able to predi t something. It might as well be the oracle of Delphi.

Add some thermodynamic constraints?

Reminds me of a sociology paper with tons of seemingly complex math that, in the end, says something like, "school bullying is exacerbated when it goes unaddressed." So what was all the math for? Credibility.

Is this folding similar to convolution?

the empirical fit part was a bit of a thinker, huh

This has crossed my mind and this is exciting indeed. High dimensionality patterns are often hidden but the fact that they are high dimension makes for the discovery of robust natural laws. We are in need of territory. We no no longer have to rely on empirical, philosophical or mathematical models to create natural laws. Data in high dimensionality can reveal many laws. Exciting times!

For "+," I do think it is simple because I hypothesize that the human brain does have built-in neurons specifically for counting small numbers (usually 5-9 varying between persons), so when you are an infant, you don't actually need to learn to count objects under this number (I suspect that in certain area of the brain, likely hippocampus, there are this amount of special neurons that are served as synaptic placeholders for the visual cortex in object identification. Then, it serves as the starting point to further learn the abstract concept of "+." That is also why "+" is the first mathematical operation that most humans (if not all) learned. If nothing is built-in, I wonder if someone can teach a human multiplication without them knowing addition. This experiment would be highly unethical, tho.

broadly useful algorithms across different systems = mathematics

my man just reinvented the wheel with already existing meta and unsupervised learning. good luck ig

There's a new thing in the market called laser pointer

Problem, reaction, solution -- The Hegelian dialectic! Neural networks create solutions to input vectors or problems, your mind is therefore a reaction to the external world of problems! Thesis (action) is dual to anti-thesis (reaction) creates the converging or syntropic thesis, synthesis -- the time independent Hegelian dialectic. Concepts are dual to percepts -- the mind duality of Immanuel Kant. Vectors (contravariant) are dual to co-vectors (covariant) -- Riemann geometry is dual. Converting measurements or perceptions (vectors) into ideas or conceptions is a syntropic process -- teleological. Your mind is building a "reaction space" from the input or "problem (vector) space" to create a "solution space" and this process is called problem solving or thinking (concepts) -- Hegel. Targets, goals, or objectives are inherently teleological and problem solving is a syntropic process -- duality! "Always two there are" -- Yoda. Syntropy is dual to increasing entropy -- the 4th law of thermodynamics!

38:18 Why is “+” simple? Well, maybe because it is closely related to the concept of counting and “having” things. If I have two apples and I get (add) three more, I can just count the number of apples to verify that I now have five apples. That has got nothing to do with the concept of simplicity. Not sure if I even want to continue watching the whole thing…

Interesting! How could neural network be an empirical finding? It’s not sth tangible that we can see or touch. It’s hard to believe that AI is developing the way fluid dynamics did.

Too little research into optimization and "understanding". We should be able to determine optimal compressed hierarchy. Hypothetically, all knowledge might be first compressed and divided into discrete tokens, say for example nouns, verbs, causation/temporality, and description.

Great

The proof is trivial! Just view the problem as an associative topological space whose elements are fundamental varieties.

Great idea. By the way he sounds like a science-oriented version of Mark Ruffalo

"Science today will be this one: the experimentalist arrives with a data collection unit, the theorist arrives with a Neural network and symbolic regression algorithm, we sit down, we plug in both machines, observe the two machines performing the scientific inquiry for us and then real Understanding comes. We did our super ego duty. The science is done out there for us. And maybe while the scientists sit there they come up with a truly novel idea together but it is pure curiosity, surplus, since the science is already done."

Could these models apply compression to themselves through techniques like quantization, pruning, and knowledge distillation becoming faster and faster and smaller until AGI emerges from a phone sized device which can invent warp drive?

Surely the problem with AI is Fudge In = Fudge Out, so if the Standard Model (and especially attempts to fix it) is full of fudge then fudge will result. I'm not saying the model outline below is correct, but if it is, or something pretty similar, no physics AI would come up with it, even if fed all the accepted (potentially) useful papers, and (filtered, biased, artefact-ridden) data.. -- POLECTRON FIELD: cell: a + & a - particle split by Full Split Energy as a positron+ & electron-. Bonds to 12 neighbours MATTER: p+ / e- = half cell (& a cell as +-+ / -+-)? Polarises field as + & - shells. SPIN: centre polarisation axis LECKY: total absolute charge. MASS: cells/lecky inside particles. INERTIA: field rebalances behind mass with a kick STRONG GRAVITY: field repels mass. DARK ENERGY: voids grow as lecky shrinks cells and is lost to gravity gradients DARK 'MATTER': galactic lecky gradient. Denser field slows acceleration and TIME, thinner field aids acceleration BIG BANG: more proton-antiproton pairs malformed as proton-muon than antiproton-antimuon so hydrogen beat antihydrogen POSITRONIUM: e+p. Muon: ep_e. Proton: pep. Neutron: pep_e. Tau: epep_e. Neutron mass is halfway between muon and tau ANTIMATTER: 1,2 e_p pairs annihilate. 3: proton+anti proton or muon+anti muon. 4: neutron+anti neutron. 5: tau+anti tau WEAK FORCE: unstable atoms form and annihilate e_p pairs. BETA- DECAY: pep_e => pep e. BETA+: pep + new e_p => pep_e p NUCLEAR FORCE: neutron electrons bond to protons. ENTANGLEMENT: correlation broken by interaction? Physical link? BLACK HOLE: atoms cut into neutrons fused as higher mass tau cores (epep). Field rotates. Core annihilates: ep => cell? PHOTON: cell polarisation/lateral shift wave. LONGITUDINAL WAVE: gravitational wave, neutrino: 1 to 3 cell wave DOUBLE SLIT: photon/particle field warps diffract and interfere, guiding the core. Detectors interfere with guides ENTROPY: simplicity. Closed system complexity reduces over time. Uniformly (dis)ordered (hot)/cold field is simplest

If you "symbolize" a neural network you lose it's robustness. It's capacity to come up with reasonable output to unseen input.

How do you avoid p-hacking your data?

Feynman would've loved this age!

Kalle's Ninth Proof of Folding is here.

Dear UKposts algorithm, Please send me more like this With love -O

Serious questions here, isn't his "folding analogy" just superposition of waves? Or I am missing something?

4:35 Era of AI presenter uses stick to point on canvas

What kind of magical language they speak?

Holy shit…the folding is more powerful than he realizes….