AI at the Edge: Qualcomm AI Research at NeurIPS 2024 with Arash Behboodi - #711

0:00Suppose you want to optimize your antenna within a limited space to get a certain propagation pattern. that's something that you need to go through a simulator, see how it performs, and then iterate around that. And experts usually do that kind of mentally. They know what to exclude and where to start, but still doesn't solve the problem that iteration is quite similar. Therefore, surrogate models for differential equations, they become important exactly for a similar reason.

0:40All right, everyone. Welcome to another episode of the TwiML AI podcast. I am your host, Sam Charrington. Today, I'm joined by Arash Beboody. Arash is Director of Engineering at Qualcomm. Before we get going, be sure to take a moment to hit that subscribe button wherever you're listening to today's show. Arash, welcome back to the podcast. Hi, Sam. Glad to be here. It's great to have you on. It has been a little while. I think we were speaking about ICML 2022 last time we spoke. Wow, it seems like such a long time ago. So much has changed in the world of AI. Why don't we get started by having you share a little bit about what you've been focused on recently in terms of your research?

1:26Yeah, exactly. It's unbelievable how much things have changed during past years. Yeah, well, last time we talked, we talked about inverse problems and all sorts of techniques that we can use for solving them and particularly using generative models and generative priors. And for what we discussed back then, it still continues to be one of our main interests, But the forward process, which is like what we observe, was quite a nice tractable, let's say, linear transformation or something like that for most of the cases. But for a large class of inverse problems, basically, which includes a lot of things that we try to figure out in our day-to-day life, the forward process is a very, very complicated system.

2:18And we use simulators, for example, to simulate various physical phenomena, various activities, and so on and so forth. And having good simulators with certain desirable characteristics is very, very important as well. And if you really want to solve an inverse problem through a really complicated simulator, it's a challenging task. So, you know, we should probably level set on forward and inverse problems. So an inverse problem is when you've got some data about the world and you want to extract the model from that. And forward is when you have a model and you want to kind of project that into real world behavior.

2:59Is that the right way to think about those two? Yeah, I would say so. I would say so. So, you know, very simply, you can look at the, we talk about the function, right? So you have a function that the forward part of that function basically is your forward process. And the backward part is the back. You're applying that function to some data, right. Yeah, I have this kind of mathematical thinking always. So for me, it's just a function, I would say. Okay. Yeah. But yeah, so I've been focusing on that research quite a lot during past years. And, you know, of course, like wireless being one of the main, you know, focuses of Qualcomm.

3:47I've been like really looking into different wireless simulators and the way we simulate wave propagation and those things. So it's been like my focus during past years. What's the intersection between the, or remind us, I think we talked a little bit about this last time, of the intersection between the forward and reverse functions that we talked about and wireless systems. Very, very good point. So, you know, when we're building wireless or wireless systems, starting, let's say, from your antenna design, from the wireless system design, on all sort of parameter tuning, we need to be able to understand how will our algorithms perform, right?

4:27and at the end of the day we're working with in wireless communication we're working with electromagnetic waves and electromagnetic prepropagations so we want to be able to simulate those those phenomena effectively that is the that is the goal now in wireless we have like different class of simulators so if we focus on let's say the more what we call the link level simulation which is about like a point to point communication we have on the one hand On the one end of the spectrum, we have the statistical simulators, which kind of statistically, on average, tells you how the propagation looks like.

5:04And on the other end, you have physically consistent simulators that, based on some ray tracing principles or even solving electromagnetic Maxwell equations, try to give you the exact propagation in the environment. So that's the whole spectrum. And you use that to solve different problems or vet your algorithms. your positioning algorithms, right? Your throughputs, your latency, all sorts of communication metrics that we have. So that is roughly the class of simulators we have, but they have their own challenges, right? So if I list some of these challenges, I can say, of course, statistical simulators, usually they are not physically, spatially consistent, meaning they're just a statistical model.

5:54So it's not like they model some concrete trajectories necessarily or the impact of certain buildings or certain objects in the environment. But they're fast. So you sample from them fast so you can iterate around them. On the other end of the spectrum, ray tracing-based simulators that give you quite detailed propagation information, They generally, of course, first of all, they are based on some mathematical models of physical phenomena, of diffraction, scattering, reflection, all those things. But they are also quite complicated to set up. They're professional. Their company is actually selling those services, professional softwares for that.

6:44And you really have to go into that. and then at the end of the day, you end up with a complicated simulators. What is common between all these simulators is that if you, let's say you want to solve an inverse problem through these simulators, for example, you want to figure out where should I put my access point, my home, to get the best coverage. It's a common problem that many people will do. This is a typical inverse problem. You want to find the optimal location that, given the 3D map, provides the basically best coverage in whatever sense you define. And if you don't have a differentiable model, you just have to find heuristics of iterating or use some sort of Bayesian optimization or those type of methods.

7:26So our focus has been trying to find different operation points within this spectrum. Maybe we can sacrifice some of the accuracies that we have, but we get faster differentiable versions of it. Or maybe by building specialized simulators, you're able to get accurate, but since it's specialized, you already have low complexity for that. How can we inject inductive biases into the simulator? We're already processing 3D space. So how we can leverage that 3D space and simulators of that 3D space in building the simulator. So we had like a range of papers during last years on all these different topics and covering all this.

8:14I should have mentioned that we're going to be focusing our conversation today on the work that you and your colleagues are presenting at the upcoming NeurIPS conference. And one of the activities that you've got planned is a workshop that you helped organize on just this area that we're discussing. There's a lot of overlap there. Data-driven and differentiable simulation surrogates and solvers is the title of the workshop. But it's not just application to communications. It sounds like you're applying these techniques or you're inviting folks to come talk about the broad application of these techniques.

8:57Can you share a little bit about the idea behind this workshop? Yeah. Yeah, so what, you know, the D3S3 workshop, which is the kind of the abbreviation of all these names. So that workshop, the goal was actually to get together, you know, all different people in the machine learning community who are working on similar set of topics. So if I, you know, take a step back and, you know, keeping the discussion we have about wireless in mind, if I take a step back, there are certain problems we're dealing with. We're dealing with a problem of the interreal gap. Basically, we're not accurate to representing reality and how we can leverage data to close the interreal gap.

9:44We have the question of basic accuracy versus complexity, accuracy versus latency trade-off. And then we have the question of differentiability that enables solving all sorts of inverse problems. So a similar set of problems come up in many different areas. And many notable works coming up recently. We have heard of drug discovery and molecular simulations and works around that. We are aware of the work that came, I think, one or two years ago on ForecastNet, which is about weather prediction using neural operators. So that's fully neural operators. So that's one version of that. Then we have Unisim, which was the outstanding iClear24 paper by Sherry Young and colleagues who was actually on your podcast as well.

10:40It's about interactive simulators that can be used for robotics and all sorts of applications. It's a video diffusion-based simulator. And then you have very quite recently a foundation model on basically the earth system, which is about all sorts of climate related behaviors and predict those. So we have all sorts of things. And actually a lot of folks who are co-authors or lead authors in these papers, either are speakers or organizers of the workshop. So we want to bring together different people working on similar topics to be able to discuss about these challenges, how we can address them, what are the challenges we're facing, what are the lessons learned from previous experiences, and things like that.

11:36One thing that I think will be a good segue for a later discussion we'll have is uncertainty. You know, we know that if the simulators are not perfect, how we can characterize their uncertainty and use them in our design process, right? So that's a very, very good, important question. And like discussing about that can be interesting. One question that I wanted to ask is related to this idea of differentiability and differential simulators in the context of this workshop. There's two concepts of differentiability. One is like the differentiability of your machine learning models and equations that allow you to do your gradient updates.

12:22And another is the idea of differential equations and modeling those using machine learning. Um, are you talking about one or both of those, or, uh, you know, how does that, how do those two ideas, I feel like both of those ideas are coming into play and what we're talking about. Um, but maybe elaborate on that for a sec. Yeah, yeah, absolutely. Actually, it's an excellent question because differential equations, they are mathematical models that try to capture certain, you know, physical system if you want. Right. and they're an example of a complicated simulator. You know, if you want to solve, let's say, the exact differential equation that represents a certain dynamics, those are molecular dynamics, it can be quite tricky to solve it for a large set of simulation scenarios.

13:20Meaning you've got some differential equation that has a lot of parameters and you want to map that to some set of data. Exactly. Yeah. Exactly. And just assume that you have to iterate on that. Let's say you have to iterate on some configurations and figure out what is the impact of configuration on the ultimate KPI. Again, let me give you an example of something familiar in the wireless domain again. Suppose that you want to optimize your antenna within the limited space, and you have to figure out where you want to put your antenna to get certain propagation pattern, right? That's something that you need to make an iteration, go through a simulator, see how it performs, and then iterate around that.

14:08And experts usually do that kind of mentally. They know what to exclude and where to start, but still doesn't solve the problem that iteration is quite slow. So therefore, surrogate models for differential equations, it comes in different shape and form. they become important exactly for a similar reason. And you have this kind of a physics-informed neural network is an example of that. You have graph neural network-based physical surrogates with all these equivariant symmetries. Neural operators is another way of parameterizing functions and building surrogate for these differential equations.

14:52So all these topics are very much related to, you know, differentiable simulation there. So that is about differential equation part of it. One thing I want to add on the differentiable simulation, just implementing things on PyTorch or having a, you know, neural network there might not be sufficient for solving an inverse problem. Like very, very, one easy example is that if you just have a step function or a quantizer function, the gradient of that is going to be zero. So when you're back propping toward that, you will not get useful gradients. So you have to be cautious about just implementing your simulator in PyTorch doesn't solve differentiability problems.

15:32So you need to understand, you know, how you, you know, if your gradients are useful and take a look at that. And these are, these are actually quite, quite important problems as well. So two distinct concepts, but you're kind of talking about both of them in this workshop because of the importance and prevalence of differential equations in modeling real world phenomena. Exactly. And so your team or the various teams at Qualcomm had quite a number of papers at this year's NeurIPS. You are co-author on one that we'll dig into, and that one is related to a topic that you just brought up, the idea of uncertainty.

16:15And the paper is called An Information Theoretic Perspective on Conformal Prediction. A ton to unpack there. Let's maybe start with a broad brush overview. What are you looking at with this paper? What's the core question that you're attempting to ask here? I think the starting point for us was we have the framework of conformal prediction, which I explained shortly. We have framework of conformal prediction on the one hand, which provides a qualitative way of characterizing uncertainty. basically instead of a single point it gives you a set of labels that contain your true label, right? It is qualitative on the other hand you have the information theoretic way of characterizing uncertainty based on let's say conditional entropy and entropy and those concepts.

17:10So the question for us was how these two are connected to each other are we talking about two different notions of uncertainty or are they closely related and what we've done in this work, we connected these two concepts through the lens of information theory, and particularly list decoding. So that's roughly the question we had in this paper. And of course, it has consequences that I will talk about later, but that was the starting point. I'd love for you to elaborate a bit on uncertainty from an information theoretic perspective and broadly. Why is it important that we model uncertainty and what is the connection between entropy and uncertainty?

17:56How do you think about the broad space of uncertainty? Of course, we know that for a lot of use cases, it's always good to know that how much uncertainty the model has about the output it's providing. And Particularly, you can have a very common justification of safety, right? You want to make sure that the model is certain in what it's telling you so that you can use it based on that, right? That is really a rough idea. So we can think of this as like if an LLM could say, you know, I'm only 20 % confident about what I just told you, then we can use that to fight things like hallucinations. But we don't have that.

18:44It's very hard to do. And so, you know, the area that you're exploring is how do we get those kinds of uncertainty bounds for different types of models, not necessarily LLMs. Correct. Correct. Exactly. So that's one, that's a good example. So that's like why uncertainty matters. The other thing is like what information theory has to say about uncertainty. So in general, when you look at the original notion of entropy, there are different ways of deriving or introducing notion of entropy in information theory. There are certain just axiomatic version of defining the entropy. And there are other ways that just say, okay, entropy is just expected value of minus logarithm of probability, something like that.

19:48So that's how you find it. When you look at the axiomatic version of entropy, it actually is quite intuitively related to the notion of uncertainty. It basically, let's look at like a binary case. You have just a binary random variable. The axiomatic version, it has something, okay, the entropy is going to be positive. The function I'm looking for is going to be positive. It's going to be bigger than between, you know, it's going to be positive. And then if you have two independent random variables, their entropy is going to be sum of their entropy. And you'll write down those, which was quite intuitive from, you know, the common sense entropy notion.

20:34And if you solve that functional equation, already you can see that if you have the, you know, if you write down those axiom, it kind of gets leading you toward the logarithm function, right? So suddenly you recover the notion of entropy that is defined just like this on the paper, like expected value of minus logarithm. So that is roughly the idea. And then we continue using that as a notion for characterizing different things. For example, if the uncertainty you have about something, knowing another thing is characterized by conditional entropy. Now, interestingly, if you know something and you know that the other thing is just a function of this, you don't have any uncertainty about the new thing knowing the previous one.

21:34And in those cases, the conditional entropy is going to be zero. And so there are all these very nice intuitive behaviors and kind of nice because we can always use the probability outputs of our models to come up with different characterization of uncertainty, whether it's epistemic, aleatoric, and all those things. So that's roughly the connection. Of course, there are a lot of caveats here. Some of the examples I made, it's for discrete random variables, for continuous random variables. Things are more subtle. But yeah, I think we don't want to bore the audience with all these details here.

22:15How does the idea of entropy in information theory relate to the idea of entropy in physics? Like the whole chaos theory aspect of it? Yeah, I think there are connections, what I can say. And there has been very fruitful interaction between a statistical physicist and information theorist in the past. Even there are, I think there are these stories that Shannon, when he wanted to name this notion that was later called entropy, He got the feedback from, I think, von Neumann and some others that this is actually very much related to the national entropy. I might be mistaken, but I remember such anecdotes.

23:02Yeah, the connections are there, but at the end of the day, we can look at this. So there are connections between, let's say, the free energy, free entropy and all those things. So there are connections between that if you look at those concepts and the notion of entropy as we have in information theory. And so conformal prediction. So conformal prediction has an interesting beginning. Of course, the idea goes back to, you know, work of Alexander Wolfkes, a student of Alexander Kolmogorov and like that school. But the underlying idea is, I would like to present it like that, which seems quite intuitive to me.

23:50Suppose that, you know, you go to your market and you buy a classifier, right? You buy your classifier and then you look at the output of your classifier, right? You give images and you get the labels and it gives you some number between zero and one. But, you know, you just bought it. You don't know if you should trust it or you shouldn't trust it. So those numbers doesn't tell you anything. It's just you might want to pick the maximum one, which might be the case. But what you do then, you say, okay, let me actually gather some data, which you call calibration data, which has my samples and two labels there, like my images and my labels.

24:34And then I look at how much the score of my classifier deviates from, let's say, in this case, let's say one, right? You can combine, you can build any score that you want, how much it deviates from one. And you look at your calibration set and you notice that actually for 90 % of my samples in my calibration set, for 90 % of them, I only have, let's say, 0.4 gap between 0.6 and 1, basically. My score is between them. So what you do later on, you know that if you look at the output scores and the scores fall between, let's say, 0.6 and 1, then you call that as your true label. So you know that this is a true label.

25:25And now, if you just have so many samples, in this case, mathematically, you would probably have a 1-1-2 sample that lies between 0.6 and 1. But let's say if that threshold is 0.3, you can have multiple samples that can pass that threshold. In those cases, you will have a set as the output. That's the idea of conformal prediction. Collect calibration data, then try to define some conformity score. And there are a lot of research on how you define this conformity score. And then look that, you know, we'll get some quantile that you choose, right? Let's say 90%. And is the conformity score the threshold that you've set?

26:07So the conformity score is not the threshold you say. The conformity score just shows how conformal your classifier is with respect to the behavior you, you know. So you expect it. But now you want to pick a threshold. So what you do, you say, okay, I've picked 90 % quantile, 90 % of the set. So let's pick 90 % quantile. And then you look at the threshold according to that. You say, okay, for 90 % of my data, that is my conformity scores, right? And you use it like that. Okay. So the interesting thing about conformal prediction is that it says if you randomly pick your calibration data, IID samples, and you follow this procedure, 90%, pick the quantile and compute the threshold like that, actually that 90 % quantile, that 90 % is going to be the probability, approximately the probability that your true label belongs to the set.

27:15So it actually comes with a statistical guarantee. That is the nice thing about conformal prediction. It's an average, if you want, guarantee across all different sampling that you can do, but it's still a very, very nice guarantee. It's basically the more precise expression is that your probability is going to be lower bounded by the quantile and upper bounded by quantile plus one over the number of samples plus one, something like that. So if you have a very large calibration set, basically you get the exact guarantee that it's the 90%. And you can pick that 90%. So that's the design that you can have based on the use case you have.

27:54If you're looking for 99%, this is what you get. So that's roughly the conformal prediction, and it provides a set of outputs labels that you can use for your prediction.

28:10Now, when we looked at this, we said, okay, how this is connected, how we can connect this to information theory? Like, what is the connection between all these entropy notions and this? And then we say, look, look at the output labels of your classifier. as an output of a noisy channel, right? It's just a noisy version of your true label. What you want to do, you want to build a list that contains the correct label. And this is list decoding, basically. And there is like a lot of work already, like from in 50s, there are many works on list decoding and establishing different properties of list decoding.

28:52And what we're interested in is variable size list decoding because we just care for the guarantee that we have. So the list size might change. And using information theoretic inequalities like funnel inequality and data processing inequality and all that, we can connect these two together. On the one hand, we come up with the conditional entropy, which is the uncertainty of the model, if you want. And on the other side, we come up with an expression that contains something related to the expected set size, basically, which is somehow measure of inefficiency of your conformal prediction. And that is the connection.

29:32So it's interesting. So you can basically translate a lot of these inequalities to bounds that connect conformal prediction and entropy. And is the benefit that you're seeking that you can use these inequalities to determine, you know, principled bounds for your conformal prediction problem? Yeah, that's definitely one of the main interests we have and we're pursuing. We're interested to see, like, you know, how tight we can get in terms of bounds. So that's definitely one. But there are other things that caught our eye when we were working on that. One, for example, was what we call conformal training.

30:21The idea is that during training, instead of optimizing cross-entropy, let's try to basically optimize the conformal objective. Right? So there were works that already started. basically they put the whole conformal procedure, conformal prediction procedure in the training loop and optimize basically the set size there. So, and there are all sort of like smoothing operation that needs to happen because there are a lot of non-differentiability there, but they try to optimize those things and that's the conformal training objective. What we did is that, okay, look, actually the bond we obtained from funnels inequality and data processing inequality, in general, they tend to be tighter than just the expected set size.