Notes and thoughts from Terence Tao’s AI Talk
“The Potential for AI in Science and Mathematics”
Watch the talk on YouTube: https://youtu.be/_sTDSO74D8Q
If you’ve never heard of Terence Tao, he is considered “one of the greatest living mathematicians.” Recently, he gave a talk on “The Potential for AI in Science and Mathematics” and shared his thoughts on AI and its possible applications in science and mathematics. Although I didn’t understand the mathematics part of his talk, his opinions on AI were very inspiring. I decided to take some notes from the talk and share my thoughts on them.
Quoted text is from Terence Tao; the rest are my comments. Any errors, typos, or omissions are solely my responsibility.
…what AI basically is, in non-technical terms, it’s a guessing machine…the way it does it is actually quite mundane mathematically. You just take up your your input and you encode every word or whatever as as a number, you multiply these numbers by weights, and you combine them and maybe you truncate them, and then you multiply by weights again, and combine them and you do this a couple hundred times or something…it's actually mathematically rather boring. How you find the weights that that's a bit more interesting…
Large Language Models (LLMs) work like Terence described. Take ChatGPT as an example: it’s a machine that tries to “guess” the next possible word based on your input. After a new word is generated, it’s appended to the original input as the new input, and the process repeats. So, ChatGPT isn’t actually “answering” your question; it’s “completing” your input. Since your input is a question, it generates text that seems like an “answer”.
Some people dismiss LLMs because of this, saying, “It’s just predicting the next word.” However, as Geoffrey Hinton once argued, predicting the next word is never easy. If you’ve ever given a talk in your second language, you might have felt like you were “predicting the next word.” To do it well, you had to understand your topic and your audience, which is never easy. We could better understand AI if we try not to mystify certain internal processes within the human brain.
…it's not magic, but it can accelerate all kinds of things. Maybe an analogy I like to give is that imagine in this world that flight had not been invented. We just had cars and trucks and ships, just land and sea based travel. Then someone at some point invents the jet engine. Initially these engines are very small and and and just toys. They don't do anything. But they get bigger and bigger and more powerful. Eventually they can enable travel that's 10 times faster than the fastest land based vehicle. But you still have to invent the plane, right? You can't just strap a engine onto a car and expect good results. That is not a good idea. You have to change the way you you think of transportation. You have to design new safety protocols, new instrumentation, [you need] new ways to understand the laws of physics. But it's still not magic. It's not like a star ship transporter. It still obeys the laws of physics, but does it at a different scale.
AI doesn’t have to be true magic. Even if AI could only accelerate existing technology by 10 times, it would completely transform society. Cars are not magic either; they are just faster than walking. Yet because of cars, we had to redesign roads and cities. People were able to live in the suburbs and work in the city. Cars changed the world and our lifestyle by “simply” being faster.
We’re used to computer tools - email, search engines, programming languages, etc. - being fussy and uncreative, but also reliable and predictable. But now we have Large Language Models such as ChatGPT, that can understand natural language requests, and generate endless creative text and image outputs - but without reliability, predictability, or accuracy.
Yes, AI is already creative.
…normally when a program or technology produces something bad, you can kind of tell it's bad. It just doesn't look like the real thing. But AI by design, you know, these weights are chosen specifically so that the answers resemble correct answers as much as possible. So even when they're wrong, they look very very convincing. That's a dangerous combination if we are using existing senses of how to detect when something looks good and looks bad…
I think we’ve all noticed that even when we tell ChatGPT it was wrong, it often generates another incorrect answer with a very confident tone. 🤖
…it's the same as if you invent the jet engine, you can quickly mock up some sort of flying vehicle out of it, but with decades before you would get to a state where it's really safe for the general public. On the other hand, air travel is the safest travel today, despite sort of being an obviously dangerous technology. These problems will be solved and they are solvable. But you have to actually think about safety. You can't just sort of assume it’s going to happen…
How can we use a tool that is powerful, but unreliable? For applications where mistakes can cause real harm (e.g., medicine, financial decisions, personal advice and therapy), one must be cautious, despite the great potential benefits. But there are more promising use cases if the downside of producing an incorrect answer is low (e.g., if one wants to generate background images for slides). In particular, in situations where the Al output can be independently verified, there are many promising applications, both in the sciences and in mathematics. For instance, Al is just beginning to be used to generate potential candidates for new materials in materials science (e.g., new superconductors), or potential candidates for drugs to treat diseases. These candidates can be tested by synthesizing them and performing physical tests or clinical trials. These are expensive, so the potential savings of Al in isolating a small pool of promising candidates is large.
…to give another analogy: current science is is like we have these taps of water that produce a certain amount of drinking water, but there's a certain limit as how much output these taps can produce. And suddenly we have this big fire hose that can turn out 10 times 100 times as much liquid, but not in drinkable form. But if you have a filtration unit that allows you to filter out the undrinkable part, then suddenly you actually have a huge spot of drinking water. That's sort of what I see science and mathematics coming to.
…there are many sciences where the bottleneck is finding good candidates to solve problems…maybe you are in drug design and you want to find a drug for a certain disease. You have to synthesize it, you have to first come up with a drug either from nature or by modifying existing drugs. Then you have to synthesize it, you have to trial it, phase one trials, phase two trials, there's a multi-year process of Trials…if there was a way to cut down on the number of candidates. So what you could do is that you could use AI. They're already using AI to to model proteins now…you can find promising candidates for drugs using AI for various diseases, but then you still have the clinical trials afterwards. So you still have the gold standard of scientific validation, but instead of having test 100 candidates maybe you just have to test 10 before you find one that works. The same for many other Sciences. Material Science is another area where there's going to be a big win.
Another promising use case of Al in science is to accelerate modeling, such as climate modeling, as existing models can be used to validate the Al ones. Traditionally, a climate model for our planet can take months of supercomputer time to generate a single simulation of (say) the next twenty years, at a 10km resolution. While this is already valuable, these single simulations cannot accurately capture outlier ‘once-a-century’ extreme weather events, and are not fine scale enough to make tailored predictions for individual communities. AI technologies (such as physics-informed neural networks) can "downscale" a low resolution climate model to a high resolution one, or create new climate simulations at rates tens of thousands times faster than traditional supercomputers.
…AI in principle can shortcut [modeling] quite a lot, because what AI can do is that if you have lots of data of existing simulations, you know, painfully acquired through all these supercomputers, AI can train on all these models and find plausible best fits for predicting what the outcome should be based on inputs that haven't been seen in the in the data. In the area of climate simulation there's already a big success. You can successfully recover the accuracy of traditional supercomputer simulation in a matter of hours, in instead of months. The acceleration is really really remarkable…
A particularly promising use case for Al is in mathematics:
- Little downside to producing incorrect proofs of mathematical theorems
- Proofs can be independently verified by proof assistants
- Training Al to improve their mathematical reasoning may be of use in broader tasks
Fireside chat part:
…things that humans find hard AI can find easy, and things that humans find easy AI finds hard. So this is a fascinating space. I think one thing that AI research is teaching us actually is not so much artificial intelligence, but human stupidity. For example, speaking language conversationally like a human was considered a pinnacle of of intelligence, because the other animals can't do this. But what these AI tools do is that they're predicting the next word to say. They produce some string of of text and each string of text they just find what is the most likely word to come next. It's basically a fancy version of of just pressing the autocomplete button on your phone over and over again, which normally produces rubbish, but passes certain point it actually becomes reasonably coherent. So one thing we realize is like the way I'm talking to you right now is just basically I'm coming up the next word to say. I'm improvising. And that's what these these tools do, they improvise. They make good guesses as to what comes next. So there are certain mathematical arguments which seem complicated to humans but are kind of natural, like each step is a logical thing to do from the previous steps. It could be many steps but in those context AI does very well. But whereas if you ask it to solve a numerical problem like the arithmetic problem, it's guessing, because there's too many different possible outcomes…
…one thing about AI models right now is that if you want to train a neural network for your own specific problem, you have to collect your data, you have to figure out what correct model to use, there's no off-the-shelf thing that you can just - there are, but almost certainly will give you rubbish. If you had sort of standardized models for different sciences, and standards and guidelines: here are some recommended choices for hyper parameters and here are some standard data sets you can use to train on. And if there are some central repositories for these sort of things, that could certainly help. Having open source models that people can build on. Having competitions, actually I think is is a very important aspect. A lot of innovation has been driven by specific challenges, you know, ‘can you get the success rate of this image recognition benchmark above this percentage?’ Then you can actually really quantitatively see what technologies are actually moving the needle forward and which ones are just vaporware. The current a models are really energy intensive and computing intensive, we're going to need research to to find more lightweight models that can actually fit on like a computer that can actually be put in a lab…
…in the past five 10 years, I I've learned that what we think of as hard for humans is often easy for mathematics. In the '90s we thought Chess was the pinnacle of human activity, and then AI solved that - not this AI but more traditional AI - that was a trick. It was brutal force. Go is what humans can do uniquely, then those are different techniques that basically solved Go. Image detection at one point was hard, voice recognition, translation, one by one these things have all fallen. And it was creating poetry and art was considered like one of the last things that AI would do, and it was one of the first [things] that the AI models could mimic at least. So I think our conception of what's difficult actually needs calibration, I mean the problem is that we've only had one working model of intelligence until very recently. Now we maybe have one and a half.
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