 So I'd like to thank, first of all, all of you for staying so late. I think the day was very fruitful in terms of the different talks we had. So now we're going to start the panel related to various questions concerning mathematics and ICT and how mathematics can impact ICT. So maybe I'll start by a question very fast. And then maybe I'll give you, I mean, you can start speaking and maybe animate this panel. The first thing is, as you know, Hawaii has established a close collaboration with the US and we're very happy with that. And the main issue that, and I would like to have your feedback is between, I would say, the long-term research that mathematics require to get into new IDs and I would say the short-term perspective in which industry, especially the ICT industry, is implicated. So what's your advice in terms as far as we are concerned with the math lab here in Paris? How do you see the effort that has to be made with respect to the long-term perspective that the mathematics require in terms of innovation and the short-term applications that the industry is requiring? When you see how industry is evolving, you have new phones nearly every six months to one year. And basically, how do you see this different temporal time scales between, I would say, the fundamentals, the required, I would say, time to evolve and produce new IDs and the applications behind? So I don't know who wants to talk first. I want to ask a question back to you. A question back to you, Mervan, because, yes, you said a new phone every six months or whatever, but in your speech, you said five years to develop a new technology, like for Geo5D and 20 years to use it. So it looked like 25-year cycle. This looks like long-term to me. Very good question. So you're totally right. You're totally right. So within our lab, and I have to explain, we have what we call research-oriented project and what we call product-oriented projects. And these product-oriented projects are more like a supporting effort related to mostly, I would say, not those five years' perspective. So whenever you do research in a company-wise, you have some long-term perspective, of course, and more, I would say, short-term perspective, where you need to produce and help the company in producing some results. So in what I showed, of course, in even 20 years, there's always evolutions of the technologies. You don't just sit down and wait 20 years. So even when I was talking about five years in between, you really have to make the technology evolve. So for example, as you know, you have 4.5G, 4.6G, 4.7G, before the 5G is arriving, okay? So that was my response. I was having a conversation with Stefan a couple of hours before, he was telling something precisely about short-term, long-term, and the impact on training for students that may be relevant in this discussion. My first reaction when you talk about long-term, organizational long-term, is what about the training? You know, train the student, and then he will be or she will be active in research or research industry, whatever, for 30, 40 years. So if the person is well-trained, then you may have long-term success, badly trained and nothing on the contrary. And Stefan was insisting on the importance of carrying on long-term project from the start, I guess, was that correct? Yes, I think that's, and to address your question, Meroin, I think that's one of the biggest challenge of a company that are establishing a research lab, is to be able to have teams that are working long-term, which is very difficult because of the pressure of the everyday life, the pressure coming from the business units. And at the same time, you don't want the researchers to be obviously completely disconnected from the real problem of the company. At the same time, you want them to have time to think and lose time. And this equilibrium is incredibly hard to maintain in a company. There are companies who know how to do that, and there are companies who were never able to do that. And this is part of the culture of a company which has to be acquired. And there are, I mean, many French companies had problems to do that. In, management are trained to handle the tension between marketing, commercial, finance, development. They are not trained very often to understand the tension between research and development. And when they are not, research is getting absorbed by development. So that will be your job, but you probably know it. The difficulty of your job is to maintain that. And that strategy has to be adapted to the culture of the company. We all believe that you need long-term, but at the same time, we also know many failures. For example, you had all these Japanese companies, I'm thinking of Neck. Neck established a completely isolated lab in the US with telling all the researchers, don't worry, you'll be able to publish, you'll be completely independent, you won't be burdened and so on. The day that Neck began to have financial problem, the lab was closed because they looked and it was not sufficiently in terms of production for the Neck business. So all the extremes have been done. The problem is that if you completely isolate the lab from the company, the day there are financial problem, the lab is closed. So this equilibrium is very hard. That's the only thing that I, nothing to add. I always told a couple of years ago, I mean a couple of weeks ago with Gowning that research was about transforming money into knowledge and development was about transforming knowledge into money. So of course, the question is how do you think you can transfer knowledge into money? Okay, so the example which is often given is AT&T with Bell Labs which had amazing results. On the other hand, it's not a fair example because AT&T was in a monopoly and the day the monopoly stopped they killed Bell Labs. So it was not in a usual case. But you do have example like, it seems like Google is able to make it work. They do maintain a research, but there are, yeah and so and then there is, yes, I, it's, for me it's a living body. Research in a company can die at any time or can survive. It's a result of tension. I don't know any good recipes about that. In the case of Bell Labs, they had a few emblematic, charismatic researchers which also at the same time were very aware of the applications and the problems. Take Shandon who of course was the emblem as one was mentioned and at the same time was devising carrying up research that was inspirational and foundational. So he was inspired by the development and at the same time doing the research of course. And the Bell Labs they understood from early on that it was good that they had some people who would be reticent, just no obligation, not in project but so that they could always be consulted by others or be free to involve others in some of their, some of the project, a small number of them and they were completely integrated at some point. Yeah, I would like to comment because Bell Labs is usually chosen as an example but it's really a tricky example because one has to know that AT&T was on a pile of money because of their monopoly. The state forced AT&T to do research to give back to society and indeed it had a feedback. The day AT&T had a cash problem and was transformed into no more monopoly they killed their research. Look what's happening with Microsoft. Microsoft established a completely free with amazing researchers and so on. Microsoft is getting problem, they closed their labs in California. So I'm not so sure that the success of Bell Labs is because they knew but it's because also it was almost a university. They didn't have any problem of money. So when you are in a company which is completely competitive market it's much harder to do it than Bell Labs I think. Yes, of course the audience can watch. Okay, so several years ago I worked for actor Lucent and I contacted with Bell Labs person researchers and in my opinion they do some research they did some research and it's quite independent. It's not very close to product. So sometimes it's not good for business it's barely for company and they can get benefit from the research. And I think for Huawei it's barely in FRC is some kind of things is different because we all think about product even for next generation product maybe this is not this is this generation product and maybe it's a feature of product. So that's a good thing for us and we how to say connect mathematics to product. It's not only mathematics, it's not only product. We connected them together and I think it's good thing because we are here to try to think how to solve problem. So I think that's an important reason for us to survive in a very hard business environment. So it depends on us how can contribute to the product to the future product. Okay. So I think Stefan wanted to ask you then. Yes, I just want to give two quick comments. So I've been with Bellapps for the last five years before I decided to go here. Two observations and then we can stop this topic water and a bridge. First of all, they're pretty decoupled from product units. So actually they don't want to talk to product units product units don't want to talk to them that has been going on for decades now. So that has benefits for research. I mean, if you're looking for well-paid postdoc you can go there, do what you want. That has drawbacks for research. You're working with models and under assumptions that you cannot validate by measurements or by contact to people who can do measurements. That's all I wanted to say. This is my experience from the last five years. When I got here at Huawei, it took colleagues and basically my Chinese friends took them about three weeks to bring me in contact with the people who work exactly in the product line on the field I worked on for the last years and where I have my algorithms which will now go into products. So the company is extremely quick and extremely open for input, even for theoretical work. That was not exactly, but yeah, based on the work portfolio with me. Yes, exactly. Yeah, yep. There was a question behind? Okay. What is the mathematical tool that according to you is the most promising for the type of problems that we need to solve? Maybe we need to meet more specific in the type of problems that we need to solve. But to me at least today there are points of connections between the three, the four talks. So maybe you can come up with some keywords that we need to dig into. And then. I can give some keywords. Well, at least I was impressed. I mean, as far as I'm concerned, I'm impressed by the number of dedicated research which is pushed toward learning. And this is one of my other question. I mean, then we can talk about keywords. Is, I mean, not why, but I have the feeling that as far as application or concern, learning is taking a huge part of our, I would say, applied mathematicians in France. And is it the case, you think? Or is it because of the big data realm, no? We hear about it all the time. It's revolution and so on, but it's still a small fraction of people going into learning. At least that is my understanding of the situation. And putting, setting up the training, the masters in which people learn things that will be useful later in learning in big data and so on, has been a matter of discussion over the past few years. I don't know if Stephen considers that it is satisfactory situation now as far as the training goes on. No, I think like several masters have been created for doing data science and the broader than big data. One is the SACLE and some in Paris and some others, I'm sure. So the training is there and clearly there is not enough people to satisfy the demand from industry. And if you look at, let's say, Google, when they recruit the researchers, the top of the list is indeed machine learning. There is a strong need. There is still not enough trans students. I think to me the good transfer is mostly through PhD students. So PhD student that has done his PhD in the university then goes to Huawei, Google or whatsoever. It's a very, very good way to put some like long-term ideas into companies because they've been trained as PhD students so they know how to think long-term and then they can mix this with the short-term requirements from companies. Apart from that, if I may say what we saw in the talks, most of it are mathematical tools which were not developed specifically for the issues. What is new is the combination but wavelet was done long before people were thinking of machine learning, optimization, gradient flows, all this has been discussed for decades. Entropy has been there for a century. And so it's the particular spirit of combination of all these, the idea of working in very large dimension. I mean, people had this idea for a long time but it remained at theoretical level. Now there is a pressure to have efficient methods in large dimension. It's not really the tools, it's the combinations, the savoir faire and the intuition, like it was extremely interesting. I thought when Stefan was discussing about which group to do now, maybe more groups and so on. Of course, harmonic analysis of groups, people have done this for a long time but not that kind. No, harmonic analysis on groups as a topic, yes, but not that kind of questions, not invariance along groups but people like Valopoulos were combining group theory and the harmonic analysis already long ago. Okay, I'm going to answer to both questions. The first question is that you asked me one, are there many, I agree with Cedric? No, there is not many and there is a reason. The mathematics community is by essence a conservative community. We are working on problems that Fermat's theorem is 300 years. We are still reading papers which were published in the 1950s. So there is a good side. When I put a conservative, it's not in a bad side. Behind this thing, it's rooted in the path. So you can't expect that a community which is still dreaming or was dreaming of the Fermat theorem or the Poincaré conjecture is going from the day one to day two, boom, going to switch on this exciting thing. It's a conservative community which moves slowly. And it's not so bad. It's not so bad. I mean, it has the good side of it and the sometimes problematic aspect. If you look, for me, it's very striking the difference with the US. Right now, in the US, for the first time it has happening for the last two years, a number of students enrolling in mathematics is increasing because of this phenomenon. A lot of people are moving. In France, they are moving much less. But the trend is going on, in particular in statistics, but I think that this is much broader. There are statistics, there is optimization. These are the first two fields that have moved very strongly, but I think there will be many other fields that will move. Where I pretty strongly disagree with Cedric is on the fact that these are just aggregations of tool. I personally, I don't think so. I think that the range of problems that are in front of us are indeed high dimensional problems treated in a different way. Think of turbulence. It's the problem which has moved the least, both in math and in physics. This is the typical high dimensional problems where there is some low dimensional structures embedded in these very high dimensional problems. The math haven't moved. What, from my point of view, we observe is that engineers have come out with algorithms which are able suddenly to deal with these high dimensional problems. I think that there is a lot of new mathematics to be done. In the kind of thing that I was describing, for example, wavelets are well known on these things. Wavelets have been useless until now to improve results on PDE. I mean, a lot of things have been done, but they've not improved anything since the result of 1930 liter with Pele, basically. Now, if you look at what these engineers are doing, they are doing something very, very nonlinear. So the math will have to be worked out, understood, and so on. But for me, it's an opening, mathematically. It's going to be much more than just tools. It's about understanding geometry, finding functional spaces of very different nature that can capture geometry in high dimensions, and so on. There are many topics. It will take time for mathematicians to move, but personally, I think it's going, and of course, I'm completely biased. About the question you asked to express the buy. When you ask a researcher, what do you think is the most important tool? The response is what I'm doing right now, okay? So I'm completely biased, I accept. Still, I believe that the field as a whole is going to bring a lot. Why did I give the example of physics? Is to show that it's touching very fundamental things in these areas. If these algorithms are able to learn, it means that they were somewhere able to project in low dimensions something which is believed to be a very high dimensional object, they captured something at a mathematical level. So I think it's overall deep areas. And the wonderful thing is that a lot of observation comes from engineering. Engineering is very much in advance on math on this area right now. A comment, by the way, about the wavelet story. As you see, of course, there is little woodpelly which goes back to the 30s and so on, but wavelet theory, as developed by Mayor and other people recently, was partly inspired by industry, also, in particular, petrol detection, et cetera. So in this case, also, it was ingenious, our fair turned into mathematical theory, to some extent, it was meeting. So maybe I would like to add something. So computer science is often forgotten in all of our discussions and part of this part of the economy, I have to say something. I don't make a big distinction between CS and math to me it's all like a big blur, but computational thinking is important. Okay, we deal with computers, we deal with lots of data and doing math without a small amount of computational thinking and thinking about algorithms, I think, is a big problem. So training in France is not so good in this, like for algorithms. The important is math, of course, but algorithms are also important and I ask because I'm doing algorithms, but this is a thing to me, like mathematics and computer science in a very broad, broad sense. And of course curvature is the most important of all. And random matrices, of course. So you're raising the question of training, which is a good question. So a lot of my colleagues from Huawei always raise the question of first, why is France so good in mathematics? The main reason. And second is the trend going to be still the case in the next years. As you know, I mean, all other countries in the world are also investing in reforming their education perspective. So what's your thought on the training that we have in France in mathematics? And do you think it's still going to be continuing this way or not? I mean, about the training, I mean, there are two different issues. If a system is able to produce a reasonable amount of people with a little knowledge in math, or is the system able to produce 20 very good researchers every year? And so it's not the same question. And I would say that at the moment I don't fear too much for research at the top level. So each time I see all the recent PhDs, which are so good. And I mean, so it's really quite, still quite impressive. So I really think the system is still adapt for fundamental research and top-level research. We fear more for the more average level in mathematics in France because the programs are not as exigent as in the past. I think there is a good start where new subjects with more probabilities and more statistics, and this is very positive, but also there is a loss in the exigence of the quality and what is approved. So I think we are losing something, maybe not for top-level research. I kind of agree, yes. And it's true that mathematical education is not an easy thing for any country. Any kind of reform which is directed from top and based on pedagogical science mainly is almost short to fail. At least we have many examples of this. And of course the big issue is where to get the good teachers, where to get them motivated and so on. In the past few years, this was our main concern in France. Lack of teachers, of good teachers that we could hire. For two years in a row, it was numbers were crazily bad. Then last year I heard it was not so bad. And next year it's not clear at all. So it's very indicative that it is very sensitive to watch and to monitor here. I would like to go back to a point I think Stefan Malin mentioned before which is the understanding of machine learning. So far it seems to me that, I mean of course we have these fundamental techniques. Stochastic approximation if you want, support vector machines, wavelets to some extent or understanding of Gaussian processes, but everything else like parameterizing these boxes is more or less magic or basically experience. So there's a gap seeing this as a whole. And you mentioned before you said something interesting. Algorithms can provide us with insight like the typical working model theoretical and applied physicists have. Applied guys try to prove the theoretical models of the theoretical physicists and the other way around. So my question to you is, if you now could wish from us, what would you like us to study? Which evidence you need? Which type of results or justifications you need from the algorithmic point of view from the experiments to allow you to establish a systematic on machine learning, on training machine learning? Big question I know, but maybe we can carve a bit on it. To establish a basic answer, so to me what I'm interested in is the problems you face linked with your data. And if you have a problem, it means that there's something to do with it for research. So it's very, very bottom-up. So I believe a lot in bottom-up problems, but maybe my colleagues have a more top-down approach to the bigger scheme. But we mean it's really that. Talk to me about your data, and then we can see what to do. I'd like to say, why we don't understand? We have to realize that the problem that machine learning is attacking are problems that we don't understand either physically or mathematically. Analyzing an image or an audio signal is again by far as difficult as analyzing the property of a turbulence signal which we don't know how to do, either with the standard math tools or physical tools. So the problems that machine learning is attacking are problems which are completely at the frontier of science, or beyond the frontier of science. So what I believe is that the tools is not because people in machine learning are doing a crummy work about analyzing what they are doing, but it is because they are working on incredibly complicated high-dimensional problems on which we have a hard time to understand what are the concepts. At the end, it will boil down to low-dimensions. Somewhere, if you can do estimation, that means that you've been able to structure your problem to bring it to low-dimension, which is ultimately the goal of a mathematical or physical analysis to understand how to attack the problem, to construct a low-dimensional structure out of it. But we just don't know how to do it on these problems right now, which are non-Gaussian problems. So it's not very surprising that we don't know how to explain. So for me, that's what I'm saying. For me, it's a beautiful frontier. For me, it's going to be a meeting of these two points of view by working at the intersection, but I really don't think, because there is a little bit that saying, oh, people in machine learning, they don't care about understanding. I don't think it's true. I just think it's very hard. Everything is very difficult. They're trying, but nobody knows. It's just a frontier of research. I would like to make a comment, even though I'm not answering the question, but making a side comment. The question that Stéphane was asking at some point in the talk, why does it work so well, is also a question that a few years ago, specialists of Monte Carlo Markov chains were asking at some point, the big revolution in algorithms and optimization was Monte Carlo Markov chains. It changed the life of people in physics, in biology, all these things, and we still don't know why they work so well. I remember Percy Diaconis telling me, understanding why MCMC methods are so powerful is one of the biggest things, one of the biggest things in science nowadays. He did himself, by the way, establish some estimates on a crazily simplified model with a crazily bad rate, and so on, so we are so far from it. Of course, the optimistic view as expressed by Stéphane is there's a deep reason up there. We'll have some big mathematical understanding at some point and understand some structure and really understand it, not just witnessing the fact that it always works. Maybe a last question to Stéphane related to your start-up experience that you've been making. I was wondering, was the original ideas you had or I would say innovative ideas which are mathematically oriented because you've been working a lot on wavelets, were they pushed within your start-up, or was it something else that made it? That's why you asked the question. I think there is always this naive idea for a researcher or an entrepreneur to think that the idea he has is the idea that is going to make his start-up be an amazing success. It's like for a researcher, and it never ends up that way. So, of course, we began with a very nice result. We thought we were going to conquer the world without, and on the way we realized this very nice result is not powerful enough, nobody cares about it, and so on, and blah, blah, blah, and we changed. I think what is important is the know-how. We didn't even know how in applied math we had many tools, and the day we found the right problem or right market and with the know-how we had, we could develop a solution that other people didn't have. And the past we had done before was useful for it. So, the short answer is it was not the band-let theorem that we had at the end that went into the chip, but it was the know-how we had to build this thing that allowed us to have a chip more efficient than Samsung, Intel, and so on on this little problem. And in terms of building a team together, the human side? Yeah, and there is the team. But which we do, it's like in a lab. A lab or a group is a group of people, and that's something that you build when doing a for me, building a start-up or building a research group is the same thing. Building a big company has nothing to do, but a start-up of 20 people or research group of 20 people it's the same spirit, it's the same excitations, and so on. When there is. That's definitely a good message. Meaning from the original idea, they didn't work but the team was smart enough to find another application and another also problem to which to apply. And I think, yeah, we'll be finishing right now because I think there's also a bus who has to take the lab. So I'm very happy that we could co-organize with Emmanuel and this workshop and also for all the plenary speakers who took the time to come here. And Cédric also this morning, I think he was a bit of a hassle driving back here and all and the others. We also I mean, a cordially invite you when you have time and now you have a busy schedule to visit us in our lab and also give talks or just have a coffee. We have a nice coffee machine, in fact we have two coffee machines. So I think there is no question, I think we hope you enjoyed also the day and hopefully we'll do it also for next year another workshop all together. Let's thank the speakers.