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November 21, 2019

CATEGORY: Blog [back]
TOPIC: Will A.I. Take Over Physicists' Jobs? More on Max Tegmark at the 6th FQXi Meeting [refresh]
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Blogger George Musser wrote on Oct. 17, 2019 @ 17:28 GMT
Max Tegmark
Imagine you could feed the data of the world into a computer and have it extract the laws of physics for you. At the recent Foundational Questions Institute meeting, in Tuscany, FQXi director Max Tegmark described two machine systems he and his grad students have built to do exactly that. One recovers algebraic formulas drawn from textbook physics problems; the other reconstructs the unknown forces buffeting particles. He plans to turn his systems loose on data that have eluded human understanding, trawling for new laws of nature like a drug company screening thousands of compounds for new drugs.“It would be cool if we could one day discover unknown formulas,” Tegmark told me in a coffee break.

“One day” may already be here. Three theorists recently used a neural network to discover a relation between topological properties of knots, with possible applications to quantum field theory and string theory (V. Jejjala, A. Kar & O. Parrikar arXiv:1902.05547 (2019)). Machine learning has analyzed particle collider data , quantum many-body wavefunctions, and much besides. At the FQXi meeting, Andrew Briggs, a quantum physicist at Oxford, presented an A.I. lab assistant that decides how best to measure quantum effects (D. T. Lennon et al, arXiv:1810.10042 (2018)).  The benefits are two-way: not only can A.I. crack physics problems, physics ideas are making neural networks more transparent in their workings.

Still, as impressive as these machines are, when you get into the details, you realize they aren’t going to take over anytime soon. At the risk of stroking physicists’ egos, physics is hard—fundamentally hard—and it flummoxes machines, too. Even something as simple as a pendulum or the moon’s orbit is a lesson in humility. Physics takes a lot of lateral thinking, and that makes it creative, messy, and human. For now, of the jobs least likely to be automated, physics ranks up there with podiatry. (Check the numbers for yourself, at the Will Robots Take My Job? site.)

Survival of the Fittest

Fitting an algebraic formula to data is known as symbolic regression. It’s like the better-known technique of linear regression, but instead of computing just the coefficients in a formula—the slope and intercept of a line—symbolic regression gives you the formula itself. The trouble is that there are infinitely many possible formulas, data are noisy, and any attempt to extract general rules from data faces the philosophical problem of induction: whatever formula you settle on may not hold more broadly.

Searching a big and amorphous space of possibilities is just what evolution does. Organisms can assume an infinity of possible forms, only some of which will thrive in an environment. Evolution finds them by letting a thousand flowers bloom and 999 of them wither. Inspired by nature, computer scientists developed the first automated symbolic regression systems in the 1980s. The computer treats algebraic expressions as if they were DNA. Seeded with a random population of expressions, none of which is especially good at reproducing the data, it merges, mutates, and culls them to refine its guesses.

As three pioneers of the field, John Koza, Martin Keane, and Matthew Streeter, wrote in Scientific American in 2003, evolutionary computation comes up with solutions as inventive as any human’s, or more so. Genetic-based symbolic regression has fit formulas to data in fluid dynamics, structural engineering, and finance. A decade ago, Josh Bongard, Hod Lipson, and Michael Schmidt developed a widely used package, Eureqa. They used to make it available for free, but now charge for it—as well they might, considering how popular it is at oil companies and hedge funds. Fortunately, you can still do a 30-day trial. It’s fun to watch algebraic expressions spawn and radiate in a mathematical Cambrian explosion.

But the algorithm still requires additional principles to narrow the search. You don’t want it to come up with just any formula; you want a concise one. Physics, almost by definition, seeks simplicity within complexity; its goal is to say the most with the least. So the algorithm judges candidate formulas by both exactness and compactness. Eureqa occasionally replaces complicated algebraic terms with a constant value. It also looks for symmetries—whether adding or multiplying by a constant leaves the answer unchanged. That is trickier, because the symmetry transformation produces a value that might not be present in the data set. To make an educated guess at hypothetical values, the software fits a polynomial to the data, in effect performing a virtual experiment.

Feynman in a Box

Tegmark and his MIT graduate student Silviu-Marian Udrescu take a different approach they call “A.I. Feynman” (arXiv:1905.11481 (2019)). Instead of juggling multiple possibilities and gradually refining them, their system follows a step-by-step procedure toward a single solution. If the genetic algorithm is like a community of scientists, each putting forward a particular solution and battling it out in the marketplace of ideas, A.I. Feynman is like an individual human methodically cranking through the problem.

It works by gradually eliminating independent variables from the problem.  “It uses a series of physics ideas… to iteratively transform this hard problem into one or more simpler problems with fewer variables, until it can just crush the whole thing,” Tegmark told the FQXi meeting. It starts by looking for dimensionless combinations of variables, a technique particularly beloved of fluid dynamicists. It tries obvious answers such as simple polynomials and trigonometric functions, so the algorithm has an element of trial and error, like a human. Then it looks for symmetries, using a mini neural network instead of a polynomial fit. Tegmark said: “We train a neural network first to be able to approximate pretty accurately the function.… That gives you the great advantage that now you can generate more data than you were given. You can actually start making little experiments.” The system tries holding one variable constant, then another, to see whether they can be separated.

Credit: Max Tegmark
Udrescu and Tegmark tested their system on 100 formulas from the Feynman Lectures. For each, they generated 100,000 data points and specified the physical units of the variables. The system recovered all 100 formulas, whereas Eureqa got only 71. They also tried 20 bonus problems drawn from textbooks that strike fear into the hearts of physics students, such as Goldstein’s on classical mechanics or Jackson's on electromagnetism. The system got 18; the competition, three.

To be fair, Eureqa is not the only genetic symbolic-regression system out there, and Udrescu and Tegmark did not evaluate them all. Comparing machine systems is notoriously fraught. All require a good deal of preparation and interpretation on your part. You have to specify the palette of functions that the system will mix and match—polynomials, sines, exponentials, and so on—as well as parameters governing the search strategy. When I gave Eureqa a parabola with a touch of noise, it offered x2 only as one entry in a list of possible answers, leaving the final choice to the user. (I wasn’t able to test A.I. Feynman because Udrescu and Tegmark haven’t released their code yet.) This human element needs to be considered when evaluating systems. A tool is only so good as its wielder.

Sorry to report, but symbolic regression is of no use to students doing homework. It does induction: start from data, and infer a formula. Physics problem sets are exercises in deduction: start from a general law of physics and derive a formula for some specified conditions. (Maybe more homework problems should be induction—that might be one use for the software.) As contrived as homework can be, it captures something of how physics typically works. Theorists come up with some physical picture, derive some equations, and see whether they fit the data. Even a wrong picture will do—indeed, one might argue that genuine novelty can arise only through an error. Kepler did not produce his namesake laws purely by crunching raw astronomical data; he relied on physical intuitions, such as occult ideas about magnetism. Once physicists have a law, they can fill in a new picture.

Or at least that is how physics has been done traditionally. Does it seems so human only because that is all it could be, when humans do it?

Making a Difference Equation

A formula describes data, but what if you want to explain data? If you give symbolic regression the position of a well-hit baseball at different moments in time, it will (if you get it to work) tell you the ball follows a parabola. To get at the underlying laws of motion and gravity takes more.

Since the ’80s physicists and machine-learning researchers have developed numerous techniques to model motion, as long as it is basically Newtonian, depending only on the objects’ positions and velocities and on the forces they exert on one another. If the objects are buffeted by random noise, the machine does its best to ignore that. Its output is typically a difference equation, which gives the position at one time given its position at earlier time intervals. This equation treats an object’s path as a series of jumps, but you can infer the continuous trajectory that connects them, thereby translating the difference equation into a differential equation, as the laws of physics are commonly expressed.

Eureqa attacks the problem using genetic methods and can even tell an experimentalist what data would help it to decide among models. It seeds its search not with random guesses but with solutions to easier problems, so that it builds on previously acquired knowledge. That speeds up the search by a factor of five.

Other systems avail themselves of newer innovations in machine learning. Steven Brunton, Nathan Kutz, Joshua Proctor, and Samuel Rudy of the Univeristy of Washington rely on a principle of sparsity: that the resulting equations contain only a few of the many conceivable algebraic terms. That unlocks all sorts of powerful mathematical techniques, and the team has recovered equations not only of Newtonian mechanics but also of diffusion and fluid dynamics. FQXi'ers Lydía del Rio and Renato Renner, along with Raban Iten, Tony Metger, and Henrik Wilming at ETH Zurich, feed their data into a neural network in which they have deliberately engineered a bottleneck, forcing it to create a parsimonious representation (arXiv:1807.10300 (2018)).

Pinball Wizard

Tegmark and his MIT grad student Tailin Wu hew closely to the methods of a paper-and-pencil theorist (Phys. Rev. E 100, 033311 (2019)). Like earlier researchers, they assume the equations should be simple, which, for them, means scrutinizing the numerical coefficients and exponents. If they can replace a real number by an integer or rational number without unduly degrading the model fit, they do. Tegmark told the FQXi meeting, “If you see that the network says, ‘Oh, we should have 1.99999,’ obviously it’s trying to tell you that it’s 2.” In less-obvious situations, they choose whatever rational number minimizes the total number of bits needed to specify the numerator, the denominator, and the error that the substitution produces.



Tegmark and Wu’s main innovation is a strategy of divide-and-conquer. Physicists may dream of a theory of everything, but in practice they have a theory of this and a theory of that. They don’t try to take in everything at once; they ignore friction or air resistance to determine the underlying law, then study those complications separately. “Instead of looking for a single neural network or theory that predicts everything, we ask, Can we come up with a lot of different theories that can specialize in different aspects of the world?” Tegmark said.

Credit Max Tegmark
Accordingly, their system consists of several neural networks, each covering some range of input variables. A master network decides which applies where. Tegmark and Wu train all these networks together. Each specialist network fits data in its own domain, and the master network shifts the domain boundaries to minimize the overall error. If the error remains stubbornly high, the system splits a domain in two. Further tweaking ensures the models dovetail at their boundaries. Tegmark and Wu do not entirely give up on a theory of everything. Their system compares the models it finds to see whether they are instances of the same model—for instance, a gravitational force law differing only in the strength of gravity.

Tegmark tested the system on what looked like a pinball ricocheting around an invisible pinball machine, bouncing off bumpers and deflecting around magnets. The machine had to guess the dynamics purely from the ball’s path. You can see this demonstrated in Tegmarks’ talk, about 4 mins into the YouTube video above. Tegmark and Wu tried out 40 of these mystery worlds and compared their system to a “baseline” neural network that tried to fit the whole venue with a single complicated model. For 36 worlds, the A.I. physicist did much better—its error was a billionth as large.

Think Different

All these algorithms are modeled on human techniques and suppositions, but is that what we really need? Some researchers have argued that the biggest problems in science, such as unification of physics and the nature of consciousness, thwart us because our style of reasoning is mismatched to them. For those problems, we want a machine whose style is orthogonal to ours.

A computer that works like us, only faster, will help at the margins, but seems unlikely to achieve any real breakthrough. For one thing, we may well have mined out the simple formulas by now. Undiscovered patterns in the world might not be encapsulated so neatly. For another, extracting equations from data is a hard problem. Indeed, it is NP-hard: the runtime scales up exponentially with problem size. (Headline: “It’s official: Physics is hard.”) A computer has to make simplifications and approximations no less than we do. If it inherits ours, it will get stuck just where we do.

But if it can make different simplifications and approximations, it can burrow into reaches of theory space that are closed off to us. Machine-learning researchers have achieved some of their greatest successes by minimizing prior assumptions—by letting the machine discover the structure of the world on its own. In so doing, it comes up with solutions that no human would, and that seem downright baffling. Conversely, it might stumble on problems we find easy. As Barbara Tversky’s First Law of Cognition goes, there are no benefits without costs.

What goes on inside neural networks can seldom be written as a simple set of rules. Tegmark introduced his systems as an antidote to this inscrutability, but his methods presuppose that an elementary expression underlies the data, such as Newton’s laws. That won’t help you classify dog breeds or recognize faces, which defy simple description. On these tasks, the inscrutability of neural networks is a feature, not a bug. They are powerful precisely because they develop a distributed rather than a compact representation. And that is what we may need on some problems in science. Perhaps the machines will help the most when they are their most inscrutable.

Credit: Bart Selman
At the previous FQXi meeting in Banff, back in 2016, Bart Selman gave an example of how machines can grasp concepts we can’t. He had worked on computer proofs of the Erdös discrepancy conjecture in mathematics. In 2014 a machine filled in an essential step with a proof of 10 billion steps. Its chain of logic was too long for any human to follow, and that’s the point. The computer has its ways, and we have ours. To those who think the machine did not achieve any genuine understanding—that it was merely brute-forcing the problem—Selman pointed out that a brute-force search would have required 10349 steps. Although Terence Tao soon scored one for humanity with a pithier argument, he cited the computer proof as guidance. If this is any precedent, the hardest problems will take humans and machines side by side.

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Robert H McEachern wrote on Oct. 17, 2019 @ 17:50 GMT
"At the risk of stroking physicists’ egos, physics is hard"

But every other science is even harder. So what does that say about the egos?

Rob McEachern

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Roger Granet replied on Oct. 18, 2019 @ 03:13 GMT
Well put!

Physics is hard, but biochemistry (my area), other sciences and many fields are hard. Psychology and human interactions (learning how we can live together in peace) are probably the hardest of all. But, physicists do seem to be uniquely proud about themselves.

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Robert H McEachern replied on Oct. 18, 2019 @ 14:49 GMT
They are proud, because they have solved some problems, which are "fundamental". But they ought to reflect upon the fact, that the reason they have been so successful at solving such problems, is not because they are the "best and brightest", but because "fundamental" problems are also "elementary" problems; understanding "elementary particles" being analogous to understanding gained in "elementary school", not "high school", college or "graduate school".

Rob McEachern

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Steve Dufourny wrote on Oct. 20, 2019 @ 12:20 GMT
Hi Mr Musser,this article is very interesting.Max Tegmark speaks about an important point,this AI will imply a big global problem for the manual jobs.Of course we cannot stop the evolution and I am not against this AI,but I beleive strongly that this parameter must be taken into account in the high spheres of power.That is why I spoke about these global solutions to create jobs and too to solve...

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Steve Dufourny replied on Oct. 21, 2019 @ 09:22 GMT
An other point very important considering this nature.Ecology is so important,I like to multiplicate the plants.I have several inventions ,like a system with the composting,imagine a fairly large trapezium of compost and insert a metal serpentine pipe, we had a thermophilic phase of hot water.

The bacterias and fungis work in complementarity for us ,we can after take this compost and mix it with different argils to create an argilo humic complex very relevant for the plants

the oligo elements,the mineral salts,this and that are fixed and the plants grow very well and their natural resistance is optimised furthermore

I have tested many species,varieties in the compost pure ,the results are ok and very relevant

I beleive that the composting at big global scale is important,we can too take the CH4 methan in closed system

The nature shows these universal truths about the complementarity after all,we loose our ecosystems and we cannot live without them,the humanity,this Earth and all its Lifes d be better with a global consciousness understanding this and implanting a real harmonised global garden for all these Lifes evolving at all scales.

A Town like New york must have plants,flowers,trees everywhere even on the walls and with this compost

we can balance all this with the harmosisation of interactions furthermore with this vegetal multiplication,the animals interactions are correlated too

even in space ,it is the secret to colonize the solar system with the good technological methods too

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Steve Dufourny replied on Oct. 23, 2019 @ 16:15 GMT
FQXI you too I need your help, come all too we have a work to do there seriously with sciences and conciousness.Alone we are nothing, a time for all ,we must save this planet sphere Earth.

The most difficult will be to unite,I try too on FQXi and on Facebook mainly,I have found wonderful general thinkers.We recognize quickly the false universal altruists with their Vanity finding problems where the solutions are simple.An other parameter is that several are going to tell that we are crazy,they are just unconscious simply and vanitious or even maybe jealous,so these persons cannot be in this universal team.We can do it and I d say even we must do it Before the add of several chaotical exponentials for us and the future generations of this Beautiful blue sphere.

The medias,the televisions,the labs,centers of researchs,the universities,....all these systems can help and many relevant generalists work there,Alone I cannot do all ,I need help.But a sure thing I will not stop lol

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Steve Dufourny replied on Oct. 25, 2019 @ 10:10 GMT
Today we speak about vanity and testosterones ,very important points to take into account,read well lol,let s speak seriously and with determinism,I spoke about the Vanity and the hormons ,mainly the testosterons.

All our global problems are mainly due to this,considering the majority ,the problems are implied by men,not the women,we are governed by men,who? create the arms ? who like to show his power ?the men,who destroy and kill in syria or yemen? men .who violoate the Children mainly? men,who like to buy big cars and show a materialism to disgust the others by power?the men mainly.and many examples exist.

we are still Youngs at this universal scale considering the evolution and the testosterons ,hormons and the correlated Vanity explain all our global problems mainly.Let s give the keys in the hands of women,this planet will be better simply

ahaha I have the solution ,we cut the two small spheroids of men under the belt lol and hop spherical solution :....irritated dear all vanitiousmahaha logic you are governed by your testosterons and this Vanity correlated and these two small spheroids ahah

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Lorraine Ford wrote on Oct. 21, 2019 @ 22:54 GMT
With the “A.I. Feynman” software, Silviu-Marian Udrescu and Max Tegmark have systematised procedures for obtaining relationships that might connect sets of data points that are input to the software. Udrescu and Tegmark: 1) encoded the minimum necessary steps to do this (these coded steps are the “A.I. Feynman” software); 2) encoded the data points and input the code to the software; and 3) interpreted the coded output.

However there are plenty of people, seemingly even Tegmark himself, who don’t really understand what “coded representation” means. These people take a very, very superficial view of things (e.g. a Turing Test view), and deceive themselves that the running of software could represent a machine “grasp[ing] concepts” and/or “achiev[ing] … genuine understanding” of what the code represents.

……………………….

But is understanding the world just a matter of finding all the underlying relationships, the type of relationships that physics represents with equations? Well, no. It’s the continual number jumps (hidden away in the delta symbols in the equations) that are actually driving the system: the relationships can’t drive the system because they can’t precisely specify the number jumps for the variables. Clearly, number jumps cause the numbers for the other variables to change due to relationship. But apart from that, the system does not specify the number jumps, and these number jumps can only be represented algorithmically.

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Eckard Blumschein wrote on Oct. 23, 2019 @ 17:37 GMT
Isn't symmetry simply closely related to redundancy even if physicist may tend to ignore it as a reason behind too artificial descriptions of nature?

Incidentally, how many of a steadily growing population of the world will become redundant? How much of nature is redundant? Do we need AI as to answer such questions?

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Georgina Woodward wrote on Oct. 27, 2019 @ 23:11 GMT
I've watched the video of Max Tegmark's talk. It is really interesting to find out about the 'physics for AI project' and its success. Congratulations to those involved.

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My Domino wrote on Oct. 28, 2019 @ 04:08 GMT
I always like your article because you have provide every time informative post..Thanks!

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Steve Dufourny wrote on Oct. 31, 2019 @ 18:52 GMT
About qubits and quantum computing, to reach these qubits and quantum computing,we must consider foundamental objects dear thinkers,if not you cannot explain it,that must converge with our universal objects….

An other very very important point,if the photons are not the main essence of our universe like primordial information ,so there are problems and never these methods shall explain the quantum computing.The searchers must consider first of all what are these foundamental objects and secondly what is the primordial essence of infornations.

In fact they can utilise all the maths and methods that they want,never they shall reach it ,the same for the quantum gravitation in fact,we need to insert new parameters and foundamentals.

In fact in resume ,the bosonic modes are not sufficient,like our electromagnetism and photonic effects…..

So in conclusion the quantum informations are more than we can imagine simply,they loose their time in trying with these methods.

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