Physicists Missed These Particle Tracks for Decades (ft. Daniel Whiteson)

Please join my mailing list here 👉 https://briankeating.com/yt to win a meteorite 💥 From the electrifying environment of high-speed particle collisions to the challenge of sifting signals from heaps of experimental noise, you'll hear how Prof Whiteson and his team are pushing boundaries. They discuss bold new algorithms capable of spotting non-standard tracks—think wild trajectories that defy classical expectations and could reveal surprises nature has kept hidden. Practical questions about detector design, efficiency, and even the mathematics of “smooth” particle paths make for a rich, dynamic dialogue. If you’re curious about how physicists ask the universe its most challenging questions, the frustrations and breakthroughs of innovation, and the fascinating interplay between theory and experiment, this episode will take you to the front lines of discovery. Plus, hear how machine learning might help us find not just the next weird particle, but perhaps the next Nobel-worthy revelation. Get ready for a fascinating journey into the impossible! Daniel Whiteson is a physicist whose research spans a wide range of topics at UC Irvine. By day, he works on the ATLAS experiment, one of the major physics collaborations at the Large Hadron Collider, where he contributes to Higgs boson precision measurements and develops advanced techniques in machine learning, data acquisition, and trigger systems. His research group is known for applying machine learning innovations to physics problems, including projects beyond ATLAS—like using approximate symmetries or jet pattern matching. Recently, his team has been focused on machine learning projects to identify unusual particle tracks, always pushing the frontier between physics and data science. Timestamps: 00:00 Revisiting Discovery with New Tools 04:43 Particle Tracking Constraints Explained 06:56 Challenges in Non-Helical Track Detection 10:29 Non-Helical Tracks and Dark QCD 14:38 "Track Reconstruction and Efficiency" 18:43 Quirk Detection and Reconstruction" 23:27 Testing Generalization Beyond Memorization 25:23 Quirk Tracks and Overlap Analysis 30:36 "Smooth Paths and Signal Control" 31:17 "Training Pipeline on Weird Tracks" 35:55 Filtering Standard Model Tracks 38:24 "Challenges in Parameter Optimization" 43:15 "Neural Networks Learn Complex Mappings" 44:38 "Machine Learning for Track Detection" - Join this channel to get access to perks like monthly Office Hours: https://www.youtube.com/channel/UCmXH_moPhfkqCk6S3b9RWuw/join 📚 Get my books: Think Like a Nobel Prize Winner, with productivity tips from 9 Nobel Prize winners: https://a.co/d/03ezQFu Focus Like a Nobel Prize Winner, with life-changing interviews with 9 Nobel Prizewinners: https://a.co/d/hi50U9U My tell-all cosmic memoir Losing the Nobel Prize: http://amzn.to/2sa5UpA The first-ever audiobook from Galileo: Dialogue Concerning the Two Chief World Systems: Ptolemaic and Copernican https://a.co/d/iZPi9Un Follow me to ask questions of my guests: 🏄‍♂️ Twitter: https://twitter.com/DrBrianKeating 🔔 Subscribe https://www.youtube.com/DrBrianKeating?sub_confirmation=1 📝 Join my mailing list; just click here http://briankeating.com/list ✍️ Detailed Blog posts here: https://briankeating.com/blog 🎙️ Listen on audio-only platforms: https://briankeating.com/podcast #universe #podcast #briankeating #intotheimpossible #science #astronomy #cosmology #cosmicmicrowavebackground #intotheimpossible #briankeating Learn more about your ad choices. Visit megaphone.fm/adchoices

• 0:00Speaker 00

  This episode is brought to you by Indeed. You're ready to level up your business, but the pressure to find the right person to make that happen is intense. Indeed sponsored jobs can help carry the load. It boosts your job post to help it reach quality talent fast. Cut through the chaos with Indeed sponsored jobs. Get a $75 sponsored job credit at indeed.com/podcast. Terms and conditions apply. Hiring now? Then this is a job for Indeed sponsored jobs.

• 0:29Speaker 01

  Today, you're in for a special treat, a lecture delivered by UC Irvine professor Daniel White son, who takes us straight to the edge of what we know and then pushes us over the edge. Particles collide at near light speed, detectors light up and data pours in by the petabyte. But what does it all mean? Most of it is noise, but somewhere deep inside is a signal that shouldn't exist unless nature is trying to tell us something new. This is how modern experimental physics works. Ask a precise question, build a machine to listen and let the universe answer. Let's go with the incomparable Daniel White son.

• 1:03Speaker 02

  But today I want to talk to you about a project I've been working on recently about finding weird tracks. All right. So very brief introduction to who I am. I have a sort of broad research program up at UC Irvine. My day job is working on Atlas, so the competitors or friendly collaborators of your CMS colleagues here. We do Higgs precision measurements, machine learning unfolding, trigger data acquisition stuff. But I also have folks in my group who do machine learning for physics who are not on Atlas. And so, for example, we work on applying approximate symmetries or jet parton matching. Today I'll be talking to you about their machine learning tracking projects they've been working on.

• 1:43Speaker 02

  And I have a sideline in astrophysics, so I do some neutron star work and have a project on building a cosmic ray telescope using smartphones, as well as a couple of projects in high energy theory, exploring high dimensional theoretical spaces with machine learning. And at the very end, I'll tell you a little bit about my experience in science communication as well, if we have time. Okay, so today I'm talking about machine learning. And machine learning is everywhere in particle physics. You hear about it everywhere. All the cool people are doing it. It's very powerful and popular. And it's been a big success. And mostly the story of machine learning is in optimization. We have really big data sets.

• 2:25Speaker 02

  We use physics intuition to compactify them to one or two dimensions. We can analyze them effectively. But that's limited because our intuition is limited. And the data never perfectly follows it. So machine learning helps us extract more information from our data. And that's wonderful. And that's fantastic. And I totally prove it and participate in it. But I also hope for something more. I'm hoping that machine learning can do more than just improve our reconstruction of the data. But that it can knock down the walls that have prevented us from making certain kinds of discoveries. That it can let us tap into problems we always thought were impossible. We just sort of put them on the shelf and said, well, nobody's ever going to do that. So let's just not even think about it. Now that we have these new tools, let's go back and look at that shelf of impossible problems

• 3:10Speaker 02

  and see if we can actually crack any of them. Because it'd be awesome if machine learning could do more than just optimize our analysis. If it could make what was once impossible, possible again. And so I want to go back to like the old days of particle physics and think about what discovery used to mean. It used to be you could make a single event discovery. Back when the signals were high and the backgrounds were low, before all the easy stuff was taken, right? You could like see one positron. And then your like data to Nobel Prize ratio was one to one, right? Pretty awesome ratio there. All the good stuff has been used up. And so now we got to make low rate, high background discoveries, which are mostly statistical. So you can't look at one event and say, this was a Higgs or that was a Higgs.

• 3:55Speaker 02

  It's all statistical, which, you know, doesn't mean it's not valid. But it's just sort of a different kind of experience. And the reason we do this is that the new signals are rare, right? And so we need high rate experiments. And when you go from low rate experiments to high rate experiments, you have to upgrade your technology. You can't do tracking the way we used to do tracking with computers. These are computers back in the day, right? Humans doing computing. Where you could like look at the data and say, here's a track, here's a track, here's a track. Because it turns out your brain is really good at that. But they can't keep up with sort of high-rate modern tracking, or high-rate modern data-taking. And so we have to move to a new kind of tracking,

• 4:38Speaker 02

  which allows for high-rate analysis, but comes at a cost. Because tracking is a hard problem. So let's make sure we're talking about the same thing. You produce a bunch of particles. They fly out, you have detector elements. You don't see the whole particle trace, right? Often you look at an event display and you're like, "There's the muon." But what you actually see are individual hits, where the muon has left a blip. And there's this task, tracking, of going back and saying, "Oh, all of these hits were on one particle. And these hits were on a different particle." It's pretty simple for this example. But now imagine you have 1,000 particles, 10,000 hits. How many ways are there to assign 10,000 hits to 1,000 particles, right?

• 5:22Speaker 02

  10,000, choose 1,000 is a big number, right? And so, in principle, the problem is impossible to brute force. And so we have approximate approaches. In order to make this problem accessible, we've made some assumptions, right? So, and that's fine. That's the way you should first do things, right? Every time you start a hard physics problem nobody's ever done before, you assume something spherical, or you take the first order, whatever, right? But let's think beyond that. So, the typical assumptions that are made in tracking are two. Number one, you assume that particles begin at the interaction point. Because most of them do. And most of the particles you're looking for are emitted from the hard interaction.

• 6:05Speaker 02

  And so if you're looking for a set of hits that are a particle, constrain it so that the track has to go through the vertex, dramatic reduction in the number of combinations, right? Very quickly. Much easier problem. And most of the particles do that, so awesome. The other assumption typically made is that tracks move as a helix. Because particles are either neutral, in which case they're invisible anyway, or they're charged under electromagnetism, in which case, in our constant magnetic field, you get a helix. Another huge simplification, right? If you only have to look for helices, then you know how to look for particles, where to look for them. Very important assumptions made for tracking, but these also limit our discoveries.

• 6:50Speaker 02

  If you're not looking for particles that don't come from the hard interaction, you can't find them. If you're not looking for particles that are not helices, you can't find them. Now, there's been a lot of work recognizing that we should look for particles that don't come from the vertex. There's a whole cottage industry of these folks now, and it's great work. And one of my postdocs is working on this. I think it's very creative and lots of possibilities for discovery. You know, there's things that are created later and things that are invisible and then pop up. All sorts of awesome stuff. So clearly, we've recognized that we should dig into these assumptions and figure out ways to avoid making them. Much less attention has been paid to the question of finding non-helical tracks.

• 7:31Speaker 02

  And one reason is that the assumption of helicity of helical track is built into our track-finding algorithm. Typically, the way this works is you find a little stub, a few hits in a line, and then you fit a helix to it so that you can project forward and figure out where your next hit should be. You don't have to consider a hit all the way over there or a hit all the way over here because you know where this track is going. You have an envelope with uncertainties and Kalman filter, and it's very sophisticated and it works really well if you know the parametric form of your track, if you assume it. So track-finding and fitting closely woven together, right? We assume it's a helix. So this algorithm, how could it possibly find non-helical tracks?

• 8:16Speaker 02

  It's woven deeply into this strategy. So, well, you might think, well, let's just put in another parametrization, right? Just plug in something else. I have a helix, plug in a schmelix. Why don't you look for schmelices, right? Okay, that's cool, and we can do that. And I'll show you an example. But I want to do something bigger. I want to find something where I didn't have to come up with a parametrization in advance. I want to be prepared for that crazy weird particle that's in my detector, which if I just showed you the event display, it would look like the positron discovery. Your eyes would be like, oh, look at that. That's something. I don't know what it is, but it's something in there in detector. I want to discover that, find a real surprise.

• 8:56Speaker 02

  So that's the big, hard problem that I think has been seen as impossible, you know, to look for effectively potential single-event discoveries waiting in our data if only you knew which event to look at. But currently, we have no algorithms capable of finding these things. Okay, so usually, right? And this is my fantasy, right? Find something that makes the theorists go, "No, that's not possible. You can't have discovered that. We proved that doesn't exist in the universe." Like, awesome, let's do it. So how do we do this? Well, we piggyback on the good work of other people. So there's a collaboration of folks called Exit Track and other people around the world

• 9:39Speaker 02

  who developed a new way to find tracks using machine learning. For completely separate motivations, they were trying to develop tracking which is good at high pileup environments, where there's lots and lots of particles. Because the traditional method doesn't work really well when you have huge numbers of particles. So they developed a completely new approach, which uses graph networks. So you recognize that your data looks like a graph, your network looks like a graph. It's all very, very cool. And it works. In high pileup environments, they're good at finding tracks. But along the way, they reinvented tracking, and their tracking separates finding and fitting. Their machine learning tracking does not assume a helix. It learns that tracks are helix from the training examples that you give it.

• 10:24Speaker 02

  And it separates the finding and the fitting. It says, "Here's a set of points I think are on a track." Then later, you fit it to a helix. So it's separated these two tasks, which is exactly what we need if we're going to find things that are not helices. All right, so that's the setup. And that's what made me wonder, when I saw these papers, can we use machine learning tracking to sort of generalize track finding? To find things that are unexpected? And then, as a bonus, I think we came up with a way to speed up the track fitting part of it. All right, so first, I'm going to talk to you about generalized track finding. How do you find tracks that are not helices? Then talk about fast and precise fitting of those tracks.

• 11:06Speaker 02

  Okay, so first, you might think, "I like the idea of craziness, but I need an example. Is this even possible? Like, you know, weird discoveries are cool, but give me an example." So there are folks up at UC Davis who came up with this idea that maybe there are particles that don't just have electromagnetic charges, but that are like charged under a dark QCD. So for example, the quark, right? The quark is a dark matter particle. That, it's like a dark analog of a quark, right? But it has a dark analog of QCD. But in dark QCD, the confinement scale and the mass scale have a different relationship. So when you create quarks, and they get macroscopically far apart,

• 11:48Speaker 02

  instead of having a flux tube which then pops new quarks out of that energy, because the quark mass is low, the quark mass is high. And so it can't pop new quarks out of that flux tube. And so they remain separated, and they oscillate macroscopically. So you create them in a pair, and they go like whoa, whoa, whoa, whoa, whoa, whoa, through your detector, right? Crazy, weird trajectories. So that's very cool. It's a good example of something which we cannot find at all. And so we thought it was a good initial test case to work on, right? Don't start with a full problem, start with a baby step. So we generated a bunch of quarks in MadGraph, passed them through a simulated detector.

• 12:31Speaker 02

  And as an aside here, this detector that we use is sort of a toy setup. We just have a bunch of layers of detector, and if a particle passes through it, we say there was a hit. We'd love to do the more realistic study, actually modeling what happens to a quark as it passes through many layers of detectors, and doing that in Jayant. But it's very tricky to modify Jayant in this specific way. And the lore is that there was a student at Berkeley who spent three years working on this, failed, and then left the field. And so, sort of like, people are like, "Oh, it's impossible." But recently, there's a student at Irvine working on importing quirks into Giant for a separate project for Phaser, and he tells me it's going well. So we'll see. Anyway, for this study, we began with a simplified detector, just a bunch of layers.

• 13:16Speaker 02

  And you see that you get lots of different weird kinds of behavior depending on the quirk parameters, of course. So there's this ratio of the mass of the quirks and the confinement scale. If the ratio is correct, you get oscillations on the order of centimeters, which is very cool. Otherwise, you might get oscillations on the order of nanometers, in which case they're invisible, or really, really large, in which case they're invisible. But in this intermediate scale, you get all sorts of really weird tracks you would just never expect from the standard model. So can we find these things? And most of the actual work was done by Max Feig. He's now a postdoc at Fermilab and Chi Yu Shaw at Beijing.

• 13:59Speaker 02

  And we use this machine learning track pipeline. And I won't go into great detail about how it works, but the idea is that you learn to find tracks. You don't assume they're helices. And the way you do this is you take your tracks, which has a bunch of hits in it, and you map it to some abstract latent space. What is this latent space? We don't know. We're going to learn this mapping, which defines the latent space. And we're going to learn a mapping so that hits that are on the same track end up near each other in this latent space, and hits that are not on the same track end up far apart from each other. That sounds cool, but like, how do you come up with this mapping, right? That's the joy of machine learning. You don't have to know how to construct this or write this down or find some analytical solution. You just train it to do that.

• 14:43Speaker 02

  And so that's what this pipeline does. You give a bunch of examples of things that are on the same track and things that are not on the same track. It learns this mapping. So that in the latent space, things that are on the same track are near each other. You can just be like, "Tracking is easy now. These places are all clustered together. Obviously, they're on the same track," right? So it's like saying, "Could you map my hard problem to an easy problem? Thanks." And that's effectively what it does. And you notice, along the way, it never assumes a helical path. It just says, "This set of hits are on a track. This set of hits are on a track." So I'm going to quote the performance of our tracker in terms of efficiency. And technically, I define that as the number of reconstructed tracks divided by the reconstructable

• 15:28Speaker 02

  tracks. Reconstructable, meaning you went through a bunch of layers. Reconstructed, meaning that you are matched to the true, a double majority matched to the truth. Which means the true track, most of its hits are on your reconstructed track, and most of the hits on the reconstructed track are from the true track.

• 15:47Speaker 00

  This episode is brought to you by Indeed. You're ready to level up your business, but the pressure to find the right person to make that happen is intense. Indeed sponsored jobs can help carry the load. It boosts your job post to help it reach quality talent fast. Cut through the chaos with Indeed sponsored jobs. Get a $75 sponsored job credit at indeed.com/podcast. Terms and conditions apply. Hiring now? Then this is a job for Indeed sponsored jobs.

• 16:17Speaker 02

  All right, and we can get into the details of that if somebody has a question. So we started by saying, hey, can we get this pipeline to run at all? Because this is like a research thing. It's not like an app you download on your phone and just works, right? So we got an account at Nurse, we got this thing to run. This step was not easy, I'll be honest. Like just getting this code to run. We got some help from the authors. But first thing we did is like, all right, feed it standard model tracks. Ask it if it can find standard model tracks. Answer is yes. Woo-hoo, all right, first step, right? Then we said, well, let's see how hard this problem is. Let's train it on standard model tracks and then just feed it a bunch of quirks. Maybe it's just good at it, right? Maybe we're underestimating it. Answer is no.

• 17:00Speaker 02

  It sometimes finds quirk tracks, but only when those tracks happen to look exactly like standard model tracks. All right, so it doesn't find any of the interesting quirks. So this tells us the pipeline works and that

• 17:15Speaker 02

  Ah, yes, the fake rate. We'll talk about that at the end. It's very, very low. If you just take like random sets of hits, it almost never chooses those to be tracks.

• 17:24Speaker 03

  What are the examples that is at least 11% for that might change of the examples you chose?

• 17:31Speaker 02

  Yeah.

• 17:34Speaker 02

  So for example, these, right? It's good at finding these. These are cases when the oscillations are not visible because the parameters either give you microscopic oscillations.

• 17:44Speaker 03

  So the 11% is covering the, I see the mid-left.

• 17:51Speaker 02

  Yes, and it fails at this kind of stuff.

• 17:57Speaker 02

  Okay, so the pipeline works, but the quirk problem is hard. If this had just worked, we would have been like, oh, well, standard tracking can find this. This is already a solved problem.

• 18:07Speaker 04

  Daniel may have said this, but as a theorist, I'll have to ask, what is, what are the characteristics of your tracker that you're simulating here?

• 18:16Speaker 02

  Oh, that's an experimental question. We have two configurations, one with eight layers and one with 25 layers, just simple cylinders.

• 18:24Speaker 03

  And each layer does X1 or?

• 18:26Speaker 02

  Each, each layer gives you a space point, X, Y, so effectively X, Y, Z.

• 18:31Speaker 03

  And time, yeah.

• 18:32Speaker 02

  Yeah.

• 18:34Speaker 02

  Other questions?

• 18:35Speaker 05

  So you're training on a just standard model data set, but testing on a quirk data set?

• 18:42Speaker 02

  In this line, yes. Just to see, this is a stand-in for traditional trackers. If something that's good at standard model can find quirks, then the problem is too easy. Right? So this was just to see if the problem was hard enough.

• 18:57Speaker 03

  And not expect it to be bad, so there were any?

• 19:00Speaker 02

  Exactly. We expected it to be bad. It was bad. So that was good.

• 19:05Speaker 02

  And the, the performance here depends a lot on these parameters. In some cases, arrangements of the parameters, you get like most of the tracks look like standard model tracks. In some cases, you get very few of them. So anyway, in the paper, you can see this whole table.

• 19:21Speaker 02

  Then we did the harder thing. We said, "All right, now let's teach it to find quirks. Let's give it a bunch of quirk examples. Can it find them?" Right? This is the thing we were excited about. And the answer is yes. All right, so there really isn't like some built-in assumption about helices in this pipeline. The only thing we had to change was we had to change the assumption that the order of the hits are the order in time, because sometimes quirks go backwards and then go out. So we just had to make a little tweak to the pipeline, but then it can learn them. So we were very excited that this pipeline can learn to associate sets of hits that are not in a helix. But as you said, somebody asked, like, "Okay, well, if you only have one quirk in your detector, then like, how hard is this problem anyway?" So, you know, we're taking baby steps there.

• 20:06Speaker 02

  But here's an example of an event where you have two quirks, and the truth quirk looks like this, and the reconstructed quirk are these dots. So it doesn't find every single hit, right? You see there's some places it intercepts, but it finds a majority of the hits and definitely enough to reconstruct this quirk, to identify this as like something weird in your detector. That's an example. Okay, so then we said, "All right, let's get more realistic. We're going to run this thing on events with, obviously, standard model particles also. So let's train it with standard model particles and quirks in the training data set, and then test it on events that have a mixture, right?

• 20:48Speaker 02

  Because obviously, events are going to have a lot of standard model background. And this efficiency is the quirk efficiency, not the standard model efficiency, because here, we labeled these negatively. We said, "Don't find the standard model tracks." Here's a bunch of examples of what not to find. So we trained it to find these and to ignore these, and then we measured the efficiency on events that had a big mixture, mostly standard model, of course, but measured the efficiency only on quirks. And so even when it's drowning in standard model tracks, it can still find quirks with reasonable efficiency.

• 21:23Speaker 02

  I think that was somebody's question about mixing them. Okay.

• 21:29Speaker 04

  I know I'm not supposed to ask questions like this, but.

• 21:32Speaker 02

  Oh, I love, those are my favorite preface or question.

• 21:34Speaker 04

  What is the, what are the characteristics of the tracks geometrically that it's actually? Do you have any idea what is training, how it's training?

• 21:42Speaker 02

  Oh, like how does it solve this problem?

• 21:45Speaker 04

  Right, I mean with standard model, we have several ideas that we're looking for, as you said, like a helix.

• 21:49Speaker 02

  Yeah.

• 21:49Speaker 04

  We have no idea of the geometry.

• 21:51Speaker 02

  Uh huh.

• 21:52Speaker 04

  And, sorry, are these like pixels with timing or no timing?

• 21:55Speaker 02

  No timing, just 3D space points.

• 21:57Speaker 04

  Just a bunch of points.

• 21:58Speaker 02

  Just a bunch of points.

• 21:59Speaker 04

  That's kind of hard.

• 22:00Speaker 02

  Yeah, it is hard. But, so we did examples with eight layers, an example with 25 layers. Here's an example of a pair of quirks. I'm not showing the standard model tracks just for clarity because they drown you out. But this trajectory was found, and it was able to disentangle these, right? It's like, this is, this is the purple, this is the red, this is the purple, this is the red.

• 22:21Speaker 02

  Because it learned some pattern about how the quirks. What did it learn here? How is it doing it? Every training sample is quirks and standard model in the same detector. But we label the tracks as like quirk or standard model, so find these but don't find these. We never show a quirks without standard model, in the last, in the last layer, line.

• 22:41Speaker 03

  What is the ratio of the, how many events of the standard model versus how many events of the?

• 22:49Speaker 02

  Yeah, great question. I don't know that number, but we used TT bar as the background. And we, I think, overlaid two TT bar events on every, on every quirk.

• 23:00Speaker 03

  So how often does it, the quirk tracks to TT bar events?

• 23:04Speaker 02

  Yeah, almost never. So the fake rate is very, very low.

• 23:09Speaker 04

  I'm sorry, and when you train, you train on like one quirk string tension or something, but is there some?

• 23:16Speaker 02

  I'll talk about that in a minute, yes, exactly. Right, so in the paper, we scan the, these two parameters. There's the confinement scale and the mass. And we measure the efficiency across this whole plane. And in some cases, the efficiency is excellent, in some places it's pretty good, in some cases it's a little lower. These cases are mostly when the two quirks are overlapping on top of each other. And so you can't reconstruct both of them, so your maximum efficiency is 50% anyway, like here.

• 23:51Speaker 04

  So you say train, you train one, each one separately?

• 23:54Speaker 02

  Exactly, and so what I'm doing here is I have, you know, what, 20 examples? These are 20 trackers, each one for a specific quirk parameter. Now, if I'm gonna go to Atlas and say, "I wanna run a new tracking algorithm on the data," they're gonna laugh at me anyway, even if I have a great idea. And then if I say I have 20 tracking algorithms I wanna run, it's never gonna happen. And so we don't wanna develop an individual tracking algorithm for every point. So we are interested in generalizing. Can we develop a single one that can find any kind of quirk? So we did some generalization tests. We said, "What if we train on one point and then test on that point?" Okay, so that's the baseline. But what if we train on everything but this point?

• 24:37Speaker 02

  We have all these points that aren't our target. We train on all the other ones and test on one of these points. What's the efficiency? And so the efficiency, it goes down, but it's not devastating, which tells you that like it's learning something quirky. It's not like just memorizing these tracks or these paths. It's something about the quirkiness of these tracks that it can generalize across these parameters. Then we did another one, similar for a different point, and you see a similar relative behavior. So this was exciting for us because the whole time, like, yeah, quirks, whatever, I'm not actually interested in finding quirks. I wanna find something new and weird. And our hope was to use this as a stepping stone

• 25:20Speaker 02

  to generalize this into finding any kind of weird track.

• 25:26Speaker 02

  All right, so before I get there, let me answer your question in more detail, I think it was about, or somebody's, about the fakes. Because you're gonna run this thing on data, there's lots and lots and lots of tracks in there. How often do you get something that looks like a quirk, but is actually a standard model track? Because you're drowning in standard model tracks. So what I did is I wrote a quirk fitter takes a bunch of points and just like a helix fitter finds the best parameters of quirks that describe those points. And so then you can calculate the chi squared of the quirk hypothesis. What is the distance from those points to the quirk track, the best fit quirk track? And just like you can for the helix. And then you can effectively subtract those two chi squared, it's like a likelihood ratio of your quirk to helix hypothesis.

• 26:10Speaker 02

  So here are standard model tracks and here are quirk tracks. And you see the separation, this is a log scale. So most of the quirk tracks are way over here and the standard model tail falls very, very rapidly. There is some overlap. There are some quirk tracks that don't fit great to the quirk hypothesis because they're missing some of the hits. There are some standard model tracks that do look a little quirky, that like the quirk fitter finds some parameters. It turns out that's when the tracks are almost back to back. Essentially, you have two standard model tracks. If you have a standard model track and you try to fit it to the quirk, it will find, it will assume there was another quirk back to back and that the oscillation length was too small or too big to see.

• 26:54Speaker 02

  So you can almost always find some place in quirk parameter space to describe a standard model track, but then you get these two tracks that are back to back. So if you make the cut here, this is all the standard model tracks, you can remove essentially all of the background. And you know, how efficient you want to be versus how much you want to tolerate background is a question of choice, but these are definitely two separatable populations. So that was studying the background, yes.

• 27:21Speaker 00

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• 27:53Speaker 06

  A basic question going back, so in your event you have lots and lots of hits.

• 27:57Speaker 02

  Yeah.

• 27:57Speaker 06

  You're reconstructing tracks. There's probably lots of hits that aren't assigned to anything. So like, I'm just wondering what, in a normal event, when you hope to assign every hit to something, when you wanna make sure you're getting all the hits, otherwise you just have like a thousand hits that you picked up two tracks and then move them off, that's kind of weird. Do you understand what I'm asking?

• 28:20Speaker 02

  Are you asking whether random hits that are not from quirks get fitted as quirks? Or whether you're using up all the hits?

• 28:27Speaker 06

  Yeah, whether you're using up all the hits, because I could imagine some approach where I'm gonna fit all the standard model things and just look at what's left behind.

• 28:35Speaker 02

  Oh, I see.

• 28:36Speaker 06

  Something like this, or...

• 28:37Speaker 02

  Yeah. There's a lot of...

• 28:39Speaker 06

  Like you wanna get all the particles.

• 28:41Speaker 02

  Right.

• 28:42Speaker 06

  How long, are you picking up every second?

• 28:44Speaker 02

  I don't think you're usually using all the hits, because there's also a lot of noise.

• 28:48Speaker 06

  The in-these are you?

• 28:52Speaker 02

  Yeah, it's an interesting question. In these, we don't have, we did, right, we don't have pileup, but we did add random hits as noise.

• 29:02Speaker 02

  And so I don't, I think you might be suggesting that as a strategy for finding weird tracks, you could just fit all the standard model tracks, remove them, and then consider what's left.

• 29:11Speaker 06

  Right, that's standard.

• 29:12Speaker 02

  Yeah, which I think is a reasonable thing to do. And it's sort of what's happening here, because here I'm fitting all those tracks to the standard model hypothesis also and using that as a way to reject them. But you're suggesting, don't even include them in the track finding, which I think is a reasonable strategy, but we haven't explored that.

• 29:29Speaker 07

  For this quirk feature, do you assume a specific confinement scale?

• 29:35Speaker 02

  No, it fits the best confinement scale.

• 29:38Speaker 07

  Oh.

• 29:39Speaker 02

  Yeah, which is why it always ends up here for standard model tracks. It finds one to effectively make the quirks look like straight lines.

• 29:47Speaker 02

  Okay, so, and then you can calculate like how many quirks you would see, et cetera, et cetera. And the next step is to actually get this in a geant and do realistic studies, sort of proof of principle. And we had a paper out last year. You can go and read up on the details. But that was really just the warm-up, because what we actually want to do is find something weird. Like quirks are interesting, they're not helical, but they're still an idea somebody had. And what I really want to do is find an idea that nobody had, a discovery that's a surprise. And so, how do you describe, number one, how do you find things you don't know if you're what you're looking for? And how do you even define the space of things you might be looking for, so you can like train your network?

• 30:32Speaker 02

  So our goal is to find all possible weird tracks, even unanticipated ones. So I pitched this problem to Levi, Khondren, he's a grad student at UCI. I said, "Here's a hard problem, what do you think about it?" And he said, "Well, let's make some restrictions. You can't be sensitive to anything, because then you could take literally any set of hits and say, you know, I have a magic unicorn that flies through my detector and deposits these hits, and, right, any set of hits could be a hypothesis." So he said, "Let's restrict it to any smooth path, something that has, that's infinitely differentiable, because then you could imagine there's some force that's causing the particle to move that way. And then let's describe the path of the particles in the basis of Fourier modes.

• 31:14Speaker 02

  So you can take any path through space and express it as a sum of Fourier modes at various frequencies." And he discovered this mathematical tool called a Schwartz function, which will guarantee that your path is smooth. So if the amplitude at high frequency falls fast enough, then your path, excuse me, your path is guaranteed to be smooth to satisfy this infinite differentiability condition. So this is called the Schwartz function. I'd never heard of it before. Turns out there's a guy in our math department, he's an expert in them, so that was cool. And then you can generate example Schwartz functions, or tracks with, that satisfy a Schwartz function. And here's one, right, so this one...

• 32:01Speaker 02

  All right, he starts at the vertex and then does this crazy thing, all right? And it's definitely not a quirk, it's not a helix, it's some other weird path. And just as an example of the kind of weird track we're hoping to be able to find. In order to guarantee that the path is infinitely differentiable, that it doesn't have a kink in it, then we limit the amplitude of the high-frequency modes. Because if the high-frequency modes can have very large amplitudes, then you can get crazy behavior. So we don't want to describe any possible function, we want to describe a subset of functions that are smooth, and this is the way that we can sample from the space of smooth. And here's a distribution of the number of hits in a 25-layer detector. If you start with just one mode, like you just pick one frequency, then you get this

• 32:46Speaker 02

  distribution, and as you get up to 25 modes, you start to get some pretty weird tracks that let go in and out and do weird stuff, which is a lot of fun. So we did the same game, we said, well, let's see what happens. So we started out by training our pipeline on the standard model and saying, let's feed it some weird tracks. And so this is the number of Fourier modes up to 25. And you see, it does terribly. Like occasionally, one of these things will happen to look helical enough to be reconstructed, but usually not. So it's a hard enough problem. And then we said, well, let's train it on our tracks. So let's feed it a bunch of weird tracks and see if it can learn the relationship between the hits so that it can reconstruct them.

• 33:29Speaker 02

  And here, the training and testing, these are one-frequency modes, one-frequency modes, but obviously different tracks. We're not giving it exactly the same tracks, just new samples from the same space. And it can do it. So it's not rejecting these tracks, it's rejecting helices mostly, but it's not rejecting these tracks, which is exciting. And then we said, all right, well, let's do it with standard model tracks. So we now are mixing standard model tracks and weird tracks together, training in on that, and measuring the efficiency on the weird tracks. Still pretty good. Important detail here is that now, because standard model tracks in principle are a subset of the weird tracks, we can't label them as "don't find these," because we want to find a generalized track finder.

• 34:14Speaker 02

  So we might use your idea, like first find those, delete those hits, and then run this track finder. But here, we didn't negatively label those tracks.

• 34:28Speaker 02

  Like it could disappear inside? Well, it's continuous, it's continuous. Like a continuous path from the inner layer to the outer layer? It doesn't have to go to the outer layer, no. But it has to start at the interaction point and then follow a smooth trajectory.

• 34:45Speaker 02

  I think I have some examples.

• 34:47Speaker 04

  We can surprise the difference if it goes up as you include more and more modes?

• 34:51Speaker 02

  Yeah. And so as you get more modes, I think it's maybe learning something more general about the problem. But I'll talk about generalization in a minute. I here some examples of tracks that it found. So the green circles are the hits on the reconstructed track. Again, it doesn't find all of them, but you know, it finds this guy. It identifies it, it gets the majority of the hits. And these have TT bar events also, I'm just not showing those.

• 35:21Speaker 02

  Okay, so the question then is, well, you've trained it on a certain set of tracks and you've tested it on other tracks and the efficiency is pretty good. But have you really learned to find any smooth path? That's the big claim. How do you span that whole space? Well, we can't. And one reason that we can't is that there's an infinite number of possible Schwartz functions. Schwartz function is some condition about how quickly the amplitudes fall. A Gaussian satisfies it, but there's an infinite number of them. So you could choose any of them and they each define a different space of smooth tracks. But what we can do is try to sample this space. We can like choose a couple of different functions and see what happens.

• 35:59Speaker 02

  So if we make one choice of Schwartz function. A, for example, and train it and test on that one, we get pretty good efficiency. If we train on the same set and then we test on a different set where we remove the overlap. So we remove all tracks that are in B and in A and only on the B tracks, we get good efficiency, even higher efficiency. Okay, so it's definitely learning to reconstruct tracks that are not represented in its training sample. It's not just learning some efficiencies, some Fourier modes, or memorizing some details about them. It's learning some property of these weird tracks, some smoothness, that it's then using to be able to generalize to other tracks it's not seen before, which was very exciting to me.

• 36:44Speaker 00

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• 37:15Speaker 02

  And again, you have to worry about fakes. Like if you're talking about weird tracks, you're also going to be susceptible to like some garbage, or the thing radiated away, or just looks ugly. And so here, we don't have a hypothesis to fit with, as we do with the quirks, where we can fit to the quirks and compare it to the helix. All we can do is try to fit to a helix. And sometimes, like this thing just does not fit to a helix. You get a terrible chi squared. But sometimes, a weird track will get a pretty reasonable chi squared for the helix hypothesis. So you can't be sensitive to all of them. But you definitely can reject a lot of them, because they don't look... You can reject a lot of the standard model, because they look like standard model tracks.

• 37:58Speaker 02

  So before I move into the next step, questions about... That's essentially what I'm trying to do here, is I'm trying to show how you could try to filter these things out. Effectively, you have to remove stuff that has a bad chi squared in the standard model tracks. That's dangerous, because the performance here, that means cutting this tail.

• 38:17Speaker 02

  And this tail depends a lot on the details. Like, in this simplified environment, most of your standard model tracks fit well to a helix. You go to a more realistic environment, you're gonna get all sorts of crap that's happening. This tail's gonna get worse and worse and worse. So, when we go to a more realistic environment, I think this is gonna get a lot harder. So then, I got interested in this question of fitting. Because essential to removing, to discovering a weird track, is filtering out the weirdest tracks and identifying them. Which means finding the standard model tracks and removing them. This is essentially anomaly detection. In the language of anomaly detection, we typically use an autoencoder, which is a classical approach.

• 38:59Speaker 02

  And in autoencoder, you start from some dataset, which is physical, say for example, hits. And you find a mapping to a latent space, which is lower dimensional. And you train your autoencoder to find some mapping so that it can map to the latent space, and then back, and recover the original data. Right? If you can do that, then you've done some sort of like effective compression. You've found some way to encapsulate your complicated data in a lower dimensional space so that you can expand it back out. Right? That's the principle of anomaly detection. But tracking is essentially already that. Right? We start from a hit space, and then we try to describe that using a lower dimensional parameter space, the helical parameters. Right?

• 39:44Speaker 02

  Essentially, you're saying, "I'm gonna summarize all of these hits with a five-dimensional parameter, five-dimensional helix. And if I've done it correctly, then when I go the other direction, I could predict where the hits were, if I know where the detector layers are." And if I try to fit something which is totally not a helix, I'm gonna get some crazy fit, which when I go back, is not gonna recover my original hits. So, tracking already is in the language of anomaly detection.

• 40:11Speaker 02

  But the problem with tracking is that we know how to go from parameters to hits. If I tell you a helix, I could tell you exactly where that helix goes. I don't know how to go from helix to, I don't know how to go from hits to parameters. If I give you a set of hits, there's no function I can write down that says, "Here are the helical parameters," right? This mapping is unknown.

• 40:35Speaker 02

  And so traditionally, what do we do? Well, we do this horrible scan where you explore this space. You say, "How about this point?" And you map it back to hits and compare the hits. "No, that didn't work." "How about this space?" "No, how about this space?" And you have this optimization problem where you're scanning the parameter space, looking for the point which best describes your hits. And yes, we have optimizers, but they're all terrible. Anybody who has worked on a realistic experiment is always like one guy, usually some Russian dude, whose job it is to like make the track fitter work. And there's so many things in there that you need to tune just right because it's such a pain. And tracking is filled with local minima, right? It's a really hard task and it's slow. If you have to run your optimizer every time and you have to start from different conditions

• 41:19Speaker 02

  just to make sure you minimize, it's a pain. So it's slow, it's unreliable. In addition, it assumes Gaussian hit noise, right? You have, in this parametrization, you're assuming that your hits have a Gaussian distribution.

• 41:35Speaker 02

  And finally, it optimizes for the thing we're not interested in. It optimizes for what is the point of the parameters that brings me closest to my hits. But what we're actually interested in are the parameters. Right, like save easier hits. And the true track is the green line. The fitted track might be this red one because what you're optimizing for is the distance from the fitted track to the hits. Nobody actually cares about the distance between the fitted track and the hits. What you care about are what was the momentum of this electron? Which means what you want to know is what was the curvature? What was the direction? Those are the physical things we're interested in. We don't care about this distance. And one experience from machine learning is make sure you're optimizing for the thing you actually care about.

• 42:20Speaker 02

  Not some proxy, which usually is a good proxy for it, but sometimes isn't, right? Always optimize for the thing you actually care about. So I said, "Well, we don't know this function to go from hits to parameters. What if we just try to learn it?" "Or instead of searching this space here, let's learn this mapping from hits to parameters." There's no search, there's no assumption of Gaussian distributions, and it can optimize for the thing we're actually interested in, which is the parameters. So I gave this task to a machine learning grad student, and he came up with a model which will take as input hits and take as output parameters. Because there is a mapping, right? We don't know it. It might not be easy to express, but it exists.

• 43:03Speaker 02

  Each set of hits defines parameters, right? So you should be able to...

• 43:07Speaker 03

  Which parameters?

• 43:08Speaker 02

  Parameters of the track, the helical parameters.

• 43:12Speaker 03

  The origin?

• 43:13Speaker 02

  Well, there's... One of the parameters includes distance of closest approach.

• 43:18Speaker 03

  So with the origin, right?

• 43:20Speaker 02

  Well, the track is not required to go through the origin.

• 43:24Speaker 03

  Now, the problem is that there is a ball of force scattering around the material effects.

• 43:28Speaker 02

  Absolutely.

• 43:29Speaker 03

  We can take an electron, it looks completely different than the...

• 43:34Speaker 02

  Absolutely. Absolutely, yes.

• 43:36Speaker 03

  So it puts the target in the origin or some other point that I guess you...

• 43:43Speaker 02

  Well, the beauty... Thank you for raising that. The beauty of this is that we don't have to assume, for example, that the hits have a Gaussian distribution. We can include all of that stuff implicitly in the training sample. Give it a bunch of electrons and say, "Here were the true parameters of the electrons, here were the hits," and it'll learn to associate those.

• 44:00Speaker 03

  So with the origin, right? You need to pass the input to the true value, right?

• 44:04Speaker 02

  You need to pass in the true value, absolutely. And you can generate... Well, the five parameters define the helix, right? But that doesn't require it to go through the origin. So wherever you generated your tracks, maybe they all came from the origin, in which case they do pass through it. Or maybe you have a spread of them, is that what you're asking about? How we generated the training sample?

• 44:22Speaker 03

  No, I mean...

• 44:24Speaker 02

  Well, I mean, it's... Material effects will make it not move in a helical path, right? They'll deviate from a perfect helix.

• 44:34Speaker 02

  Yeah, maybe we can talk about it offline, yeah. I think we're having a semantic issue. Anyway, produced a model which learns to map hits to helical parameters. And in the case that the hits actually are Gaussian distributed around the track, it reproduces the performance of least squares fitting. So here's the residual in a couple of the parameters. I'm not showing all of them. They're in the paper. And this is the difference. So you want a peak at 0 and you want to be narrow. So the neural network has the same performance as the least squared. And the least squared, in the case of Gaussian distributed hits, is the best you can do in the terms of minimizing the residual. And so we hope to match it.

• 45:16Speaker 02

  And so in this case, the neural network does match the idealized least squared, which is good. We show that we can learn this mapping. But what if you have a more complicated situation? Let's get that for now. What if you have a more complicated situation? What if your hits do not map, are not Gaussian distributed? What if instead they're skewed from the true path? Or there's an offset, or there's multiple scattering? Now, you can describe that implicitly in your training sample just by adding those deviations to the hits in the training sample. And it will, the neural network will still learn the true parameters. Because it has seen the examples. It says, if your hits are over here, the true track was over there. It will learn that relationship.

• 46:01Speaker 02

  Whereas the least squared, you have to encode directly into the model your exact noise distribution. Here, we only have to encode it implicitly. We can run some complicated simulation or whatever. We can include as many effects as we want. Implicitly in the training sample, the network will learn that. The least squared has to explicitly encode in the chi squared exactly what the noise model is. And of course, this is much, much faster. So it's about 1,000 times faster than searching the parameter space to try to find the best values of the parameter.

• 46:37Speaker 02

  And it works very well as an anomaly detector. So in the case that you have some deviation from Gaussianness, then your neural network is much better at separating non-helical tracks from helical tracks than your least squares fitter. All right. So in conclusion, machine learning tracking is much more flexible. By separating the finding and the fitting, we can do finding of non-helical tracks and we can do fast and precise fitting of the helical tracks. All right. Thanks very much.

• 47:12Speaker 01

  If this fascinating lecture by Daniel White son sparked your interest, don't let your curiosity end there. Watch my full podcast conversation with Daniel about his latest book, Do Aliens Speak Physics? Where we ask what the laws of nature say about life beyond Earth. Don't forget to like this video, comment with your biggest question about particle physics and subscribe for more trips to the edge of the universe and beyond. And don't forget to share it with your friends.

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