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8 Dec 2025 Machine Learning Street Talk Pedro Domingos: Tensor Logic Unifies AI Paradigms
“You know, we're not then describing laws of the universe, and and I think tensor logic at least is my best attempt at having a language in order to do both this AI and this type of scientific discovery.”
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- Pedro Domingos
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- 8 Dec 2025
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- Machine Learning Street Talk
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…Increasingly more of a believer in kind of Hofstadter's, you know, concepts. Right? That there are multiple levels of description. And even within a level of description, there may be multiple languages, you know, to describe things at that level. And I think part of the lesson is not only do we observe, like, not only do we kind of observe a particular level. And sure, we try to reduce things and come up with theories at finer grain levels, higher resolution theories, or whatever. But we also observe a certain layer, and we're able to, by whatever sort of miraculous mechanism, to almost pull out of thin air to abduct, a theory at this level. Like, here's thermodynamics. Somehow we came up with that. Right? And even if we learn theories at lower levels or higher resolution theories, actually, most of the time, you don't replace those older ones. It's like within their domain of operation. You know, Newtonian mechanics is still extremely useful for all lots of things that have to do with our scale. Right? Our scale of activity. GR is useful to different scale. Quantum mechanics at different scale. So we we retain all these languages. And I'm hearing that tensor tensor logic is is a great language for a certain, you know, layer of description and for for activities of of AI, but you're not arguing that it's the language to sort of replace all other layers. Right? Like, you still buy into the idea that other languages are different. I'm glad you asked that question. I am absolutely arguing that tensor logic is the language to use in all these layers, and let me give you some evidence towards that. Express relativity in tensor logic, it's tensors and you know, differentials of tensors and whatnot. That's, you know, that tensor logic does that out of the box. Do the same thing with quantum mechanics. Do the same thing with all these others, with all of the different pieces of AI that I know. And why why is that possible and why does tensor logic do that? Again, think this gets at a at a very deep fact about the universe, which you know, complex systems people and physicists have, you know, suspected as well. Which is that the universe has this amazing property without which it would not be comprehensible, that you can have a lot of complexity at 1 level that then organizes itself into a new level at which now a different set of, you know, laws applies, right? And in a way what we do with computers is do that by design, right? But here's the key. What you want is a language in which to express this process, right? The whole process by which multiple levels get created, by which multiple representations get created, including different representations at the same level. Right? For example, right, you know, going back to Herb Simon, you know, people, many people at least and I have believed that the essence of human intelligence is your ability to switch between representations as the problem dictates. And as long as you pick 1 representation you've stuck yourself in the box. But but at that level, tensor logic is a meta representation. It's the way to construct representations. And yeah, you know, a large language model, you know, to take a very salient example, what has a transformer learned, right, when it looks at all that text? Precisely I would say where a lot of its part come from is that it has looked, know, it's it's like, you know, Seb Bubeck says, it's like it has learned this soup of algorithms. There's all these different pieces and different ways of doing things that it has gathered from different places, And it doesn't choose between them. It's the prompting and the fine tuning and more that that then pull out the parts that are better for 1 thing or another. So we absolutely have to do this in AI. I think it also reflects a deeper truth about the universe. I think there are gonna be laws of this. You know, we're not then describing laws of the universe, and and I think tensor logic at least is my best attempt at having a language in order to do both this AI and this type of scientific discovery. I also believe, and I you know, I I discussed that briefly in the paper that tensor logic is not going to be just a good language for AI, it's going to be a good language for science in general for several reasons. , and I you know, I I discussed that briefly in the paper that tensor logic is not going to be just a good language for AI, it's going to be a good language for science in general for several reasons. 1 of them is this, but the other 1 is that if you look at the difference between the equations on the page and and and the resulting program from implementing them, often there's a lot of complication. In tensor logic it's almost, you know, the the tensor equation is an almost symbol for symbol translation of the equation on the page. So now you can just do, you know, science you know, on a different level. Also the log if you look at scientific computing computing, right, it's usually these tensor operations with some logic wrapped around it. Tensor logic does the tensor operations and the logic in 1 language, but more importantly, the logic now becomes learnable. You can now learn the logic as well.…
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