Lightning Talks
This is a modal window.
Das Video konnte nicht geladen werden, da entweder ein Server- oder Netzwerkfehler auftrat oder das Format nicht unterstützt wird.
Formale Metadaten
| Titel |
| |
| Serientitel | ||
| Anzahl der Teile | 11 | |
| Autor | ||
| Mitwirkende | ||
| Lizenz | Keine Open-Access-Lizenz: Es gilt deutsches Urheberrecht. Der Film darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | |
| Identifikatoren | 10.5446/69292 (DOI) | |
| Herausgeber | ||
| Erscheinungsjahr | ||
| Sprache |
Inhaltliche Metadaten
| Fachgebiet | ||
| Genre | ||
| Abstract |
|
2
3
6
8
00:00
Elektronisches ForumFormation <Mathematik>MultiplikationsoperatorComputeranimationBesprechung/InterviewVorlesung/Konferenz
00:42
Elektronisches ForumTorusSingle Sign-OnEreignishorizontKonfiguration <Informatik>Luenberger-BeobachterRechter WinkelMAPTouchscreenRoutingBitOrdnung <Mathematik>AdditionYouTubeVorlesung/KonferenzBesprechung/Interview
02:19
MAPUnrundheitSchlüsselverwaltungKontrollstrukturInformationRechenschieberBitVorlesung/KonferenzBesprechung/Interview
03:17
Elektronisches ForumRegulärer Ausdruck <Textverarbeitung>ErwartungswertEinfügungsdämpfungFunktion <Mathematik>DruckverlaufSystemidentifikationPlastikkartePrognoseverfahrenKoroutineInformationElektronischer ProgrammführerBitrateMAPMultiplikationsoperatorParametersystemPunktDruckverlaufNumerische MathematikRechenschieberSchätzfunktionSoftwaretestPlastikkarteProzess <Informatik>BitrateVollständigkeitVorlesung/KonferenzBesprechung/InterviewComputeranimation
06:34
DigitalisierungTreiber <Programm>EinfügungsdämpfungPunktAutomatische HandlungsplanungPhysikalisches SystemDatenmissbrauchMultiplikationsoperatorParametersystemVorlesung/KonferenzBesprechung/Interview
08:47
Elektronisches ForumProzess <Informatik>VererbungshierarchieRelativitätstheorieVerkehrsinformationSpiegelung <Mathematik>BitAusnahmebehandlungMultiplikationsoperatorBridge <Kommunikationstechnik>Basis <Mathematik>Lokales MinimumStatistikGradientKlasse <Mathematik>EreignishorizontStatistische HypotheseLesezeichen <Internet>RechenschieberBesprechung/InterviewVorlesung/Konferenz
12:16
PunktFolge <Mathematik>Lokales MinimumExponentialabbildungFunktionalLokales MinimumRelativitätstheorieAlgorithmische ProgrammierspracheStellenringBitratePunktSchnittmengeGüte der AnpassungQuick-SortDifferenteRechenschieberKonstanteStandardabweichungKontextbezogenes SystemTermSchätzfunktionMultiplikationsoperatorGebundener ZustandComputeranimation
13:33
Elektronisches ForumBitSupercomputerWissenschaftliches RechnenProgrammierumgebungBeweistheorieNotebook-ComputerBesprechung/InterviewVorlesung/Konferenz
14:04
TopologieElektronisches ForumGraphikprozessorKnotenmengeBefehlsprozessorParallelrechnerVerteilter SpeicherProgrammierungMathematisches ModellOffene MengeProgrammierumgebungHochleistungsrechnenWissenschaftliches RechnenSupercomputerSoftwareAlgorithmusVirtuelle MaschinePunktBitrateNichtlinearer OperatorFrequenzProgrammierparadigmaMultiplikationsoperatorMessage-PassingDifferenteMAPProgrammierungPhysikalisches SystemTermTransformation <Mathematik>ResultanteBitPetaflopsGraphikprozessorComputerComputerarchitekturCoprozessorParallelrechnerHardwareMixed RealityKontextbezogenes SystemHalbleiterspeicherSpeicherabzugInterface <Schaltung>PerspektiveVorlesung/KonferenzBesprechung/InterviewComputeranimation
18:46
MaßstabSprachsyntheseDifferenteMAPRechenschieberVorlesung/KonferenzBesprechung/Interview
19:26
Turing-TestDean-ZahlTuring-TestCASE <Informatik>E-MailInternetworkingRechenschieberProtokoll <Datenverarbeitungssystem>Dean-ZahlARPANetVorlesung/KonferenzComputeranimation
21:34
MultiplikationsoperatorRechter WinkelCASE <Informatik>Vorlesung/KonferenzBesprechung/Interview
22:12
ComputerKomponente <Software>InformationRechenwerkGerichtete MengeAuflösbare GruppePhysikalisches SystemKategorie <Mathematik>Verteilte ProgrammierungRechnernetzTelekommunikationDatenerfassungWiderspruchsfreiheitWort <Informatik>VektorrechnungDivisionMinkowski-MetrikDesign by ContractAbstraktionsebeneCompilerGruppenoperationSystemprogrammierungProgrammierungRechenschieberExogene VariableMathematisches ModellWiderspruchsfreiheitSchnittmengeStrategisches SpielIdentitätsverwaltungAlgorithmusEinflussgrößeRelativitätstheorieNP-hartes ProblemMetropolitan area networkGleitendes MittelWort <Informatik>Automatische HandlungsplanungGruppenoperationAbstimmung <Frequenz>PlotterForcingLie-GruppeGüte der AnpassungFormation <Mathematik>ATMMedianwertBesprechung/InterviewVorlesung/KonferenzXML
26:01
MAPAlgebraisches ModellRichtungVorlesung/KonferenzBesprechung/Interview
26:34
Elektronisches ForumAlgebraisches ModellGruppenoperationSelbstrepräsentationUnendlichkeitRechenschieberAlgebraisches ModellWort <Informatik>Familie <Mathematik>GrenzschichtablösungPhysikalismusLineare DarstellungMathematikGenerator <Informatik>Einfache GruppeEinfache GenauigkeitZweiElementare ZahlentheorieProjektive EbeneFinitismusWeb-Seitet-TestTheoremKontextbezogenes SystemEndliche einfache GruppeComputerspielGruppenoperationLineare AlgebraLineares GleichungssystemAngewandte MathematikWürfelLinearisierungPhysikalisches SystemSporadische GruppeMatrizenrechnungVorlesung/KonferenzBesprechung/InterviewComputeranimation
29:38
Elektronisches ForumEntscheidungsmodellMultiplikationsoperatorFisher-InformationInternetworkingRechenschieberPhysikalisches SystemRouterEinfach zusammenhängender RaumTrajektorie <Kinematik>SoftwareBitFinitismusInformationsspeicherungKontrollstrukturFaserbündelKanalkapazitätHalbleiterspeicherOrbit <Mathematik>MatrizenrechnungRoutingVorlesung/KonferenzBesprechung/Interview
31:25
InformationMultiplikationsoperatorComputerspielBesprechung/InterviewVorlesung/Konferenz
32:01
Turing-TestKontextbezogenes SystemInformationFokalpunktProzess <Informatik>Fakultät <Mathematik>Numerische MathematikSelbst organisierendes SystemVorlesung/KonferenzBesprechung/InterviewComputeranimation
32:47
FokalpunktNumerische MathematikTheoretische InformatikAutonomes SystemComputerspielFakultät <Mathematik>Selbst organisierendes SystemMessage-PassingVorlesung/KonferenzBesprechung/Interview
34:18
Elektronisches ForumWort <Informatik>Nichtlineares GleichungssystemNeuronales NetzAuflösung <Mathematik>Physikalisches SystemAutomatische HandlungsplanungVorlesung/KonferenzBesprechung/Interview
34:50
MereologieLineare AbbildungRechnernetzGewicht <Ausgleichsrechnung>KreisbogenBlockchiffreNichtlineares GleichungssystemDomain <Netzwerk>SystemprogrammierungComputerKryptologieMathematikBoolesche AlgebraPolynomZahlenbereichEin-AusgabeFunktion <Mathematik>Mathematikgeschichte <Fach>InformatikAuflösung <Mathematik>Domain <Netzwerk>ComputerNichtlineares GleichungssystemAlgorithmusLineares GleichungssystemKryptosystemFunktion <Mathematik>Radikal <Mathematik>CASE <Informatik>ChiffrierungKontextbezogenes SystemMultiplikationsoperatorEin-AusgabeFunktionalOrtsoperatorPhysikalische TheorieBitSchlüsselverwaltungMinimalgradMatrizenrechnungBoolesche AlgebraNichtlineares SystemMathematikKlasse <Mathematik>Komplex <Algebra>Transformation <Mathematik>Ordnung <Mathematik>Lineare AbbildungArithmetischer AusdruckVollständigkeitNeuronales NetzSoftwareentwicklerGewicht <Ausgleichsrechnung>Lineare GleichungKontrollstrukturSoftwareWellenpaketDatenstrukturLinearisierungBasis <Mathematik>Potenz <Mathematik>Numerische MathematikFlächeninhaltResultanteNichtlinearer OperatorVektorraump-BlockPhysikalisches SystemChiffrePolynomErfüllbarkeitsproblemVorlesung/KonferenzBesprechung/InterviewComputeranimation
39:50
KontrollstrukturQuick-SortVorlesung/KonferenzBesprechung/Interview
40:40
Elektronisches ForumFormation <Mathematik>Vorlesung/KonferenzComputeranimation
Transkript: Englisch(automatisch erzeugt)
00:31
Lovely introduction. It is always a pleasure to come to the HLF. This is actually my fifth time back in Heidelberg, but I would just start before I introduce
00:42
the event with a very, let's say, interesting observation for all of the young researchers in the audience, because no doubt you will be sitting here seeing all of these fantastic lectures that we will have this week from our very distinguished speakers and thinking, I would like to be on that stage.
01:00
That is the idea. We want to inspire you. One option is to reach the pinnacle of your subject like our laureates and win or be awarded one of these fantastic prizes. Option two is my route, do YouTube stuff. You may end up also on the stage with all of these brilliant laureates.
01:23
I have the pleasure of once again moderating the lightning talk event. I say pleasure. It's also a bit of a challenge, but a fun one. We are going to have nine speakers. They will each have three minutes to talk. There will be a timer on the screen.
01:42
I am saying this for the audience's benefit and also for all of the speakers. You will have a timer, so please try and stick to the three minutes. You will possibly, if you're running over, see me slowly creeping on stage. Apologies in advance if I have to cut you off, but we want to make sure we get through everybody.
02:01
The other thing you need to know is this is a fun new edition. I decided this year that the order of speakers was only determined this morning, so the speakers themselves do not know in which order you will be called to the stage. Please listen very carefully for your name.
02:22
I will announce you, invite you up onto the stage. You will need to stand here so that these microphones can pick you up. Otherwise, you will be able to see the timer, see your slides. You'll have three minutes. We'll all give you a lovely round of applause, and then I will introduce the second speaker. It's going to be very quick fire.
02:41
Questions of course, coffee break afterwards, because three minutes is already short enough. I think they are probably all of the key bits of information. So, let's start by introducing our first speaker. So, our first speaker is Raj Reddy, and he will be talking about eliminating COVID lockdowns.
03:06
And I thought when I saw this title, I'm very intrigued to hear what you say, Raj, but when I heard this title, I did think if we had this in 2020, this would now actually be HLF 12, as we could have prevented the lockdown. But Raj, I will pass over to you whenever you are ready.
03:23
Good morning. So, I don't know how many of you have been through two pandemics, probably none of us. You know, the last well-documented pandemic was the Spanish flu, about 100 years ago. The number of people that died at that time was 50 million.
03:45
We don't know exact number of people that died in the recent pandemic. The estimates are between 10 and 15 million. In the United States alone, we exceeded a million people that died.
04:03
So pandemics are a serious thing. So we say, we don't know how to handle these pandemics. So what did we do last time? Countries locked down, everything was shut down completely. And India and China, for example, did this in a major way, where they locked down whole
04:25
cities or whole country, and this caused great, great upheaval. The reason is most people have to go to another place for a job.
04:42
And if you can't move about, then you don't have a job. And a lot of people, especially the poor people, are affected by this. I don't know if my slide is that good. So we are certainly going to have another pandemic in 10 to 20 years, not 100 years.
05:05
And this is, you know, again being predicted. We don't know when. I think we should be prepared. I think we have the technology, and it requires each of us to having a smartwatch,
05:21
a watch that measures your vitals, temperature, heart rate, blood pressure, and so on. And given these parameters, you can actually predict whose temperature is going up slowly, it takes about a day, you can very quickly predict who may be
05:43
infected and who may not be. And even if you're infected, sometimes all this don't go forward. But if you simply say, we're only going to lock down the people that are infected, that means it requires all of us to wear a watch, smartwatch, and it's like a passport.
06:05
If you want to move about, you need to have this watch. And it should have measured your data for at least a day. For example, when I was in Paris coming back, they said, you have to have your vaccinated test within 24 hours.
06:21
I had to run around and to find and said, what happens if I don't pass? So I think we are at a point in time where if the society decides, we ought to have everybody providing a smartwatch.
06:41
How does this happen? And most of us will say, I don't want you to monitor my parameters, my privacy, this and the other. But on the other hand, if I want to go drive a car or get on a plane, I'm happy to have a driver's license or a passport. So I think it is possible for us to do that, to require people to have a smartwatch,
07:06
if you want to move about. And we should do that. The question is, how much does it cost? The cost is 10% of the loss in GDP this last time. We had our $25 trillion economy in the US, we lost about 10 to 15%,
07:28
about $2 trillion, 2 to 3 trillion. It is possible to have, give everybody a free watch. And this is, I'm assuming it is possible, people are thinking rationally
07:44
and they will actually require it. So I think we would be able to get to a point where everyone gets, it's like digital infrastructure, like we have roads and water, supply systems, hygiene and so on.
08:01
And this is a digital infrastructure. We must require everyone to have a watch, just like you require them to have a driver's license. And I think if we do that and say you can't move, then you're stuck.
08:20
So I think we can lock down only the people that are infected, but if you are showing symptoms of the infection, if you don't have the infection, or you have the infection but not the symptoms, some people will go down. And I think we can tolerate that within the R0 going down,
08:41
not to zero, but below one. Thank you. Thank you very much. Okay, our second randomly selected speaker is Raghu Varadhan, who will be talking about reflections on a research career.
09:04
And I was very appreciative. Let's say I found this very interesting, that Raghu was the only speaker who emailed me to ask how they should prepare for this event. So I was greatly appreciated. So Raghu, if you can come up to the lectern.
09:21
Fabulous, so there's a clicker there if you need it. And I will leave it to you. Stop watching. What's the time?
09:56
I want to begin with a little bit about how I got to where I am.
10:03
I was born very late, 20 years after my parents got married. So I was a favorite of all relatives. And I went through school, skipped grades, graduated early.
10:20
At that time, the job market was frozen in India and there was no jobs, except in government. And for that, I had to take an exam and had a minimum age requirement, which I did not satisfy. So I had to wait for two or three years even to apply for a government job. So the only job that was open was research.
10:43
So I applied for and I got a job to do research at the Indian Statistical Institute. No idea what was expected of me. There were no classes. I was just given a desk and asked to produce something.
11:00
I got very depressed and spent most of my time playing bridge. My father used to play bridge at a club when I was growing up. I used to go with him and watch him play and that's how I learned how to play bridge. So my first year of graduate school, this is actually playing bridge.
11:20
Then a couple of my friends came to me and said, why are you wasting your time? Let's work on some problem. So we started, created our own problem, worked on it, successful at it. And after a while, I realized I really enjoyed doing what I was doing and that's how I got into research.
11:41
So I earned my PhD. One of my reviewers of my PhD thesis was Karmagora and he gave a very positive report. On that basis, I got a job and moved to NYU as a postdoc. There I had Donsker and Marquez
12:04
suggesting problems to me and we worked on it and got into it. There are some slides. Large deviations. These slides explains what large deviations is about.
12:24
You get an upper bound, you get a lower bound. The point is the rate at which probably it is decay for a set. If you call the decay constant C of A, C of A union B is the minimum C A and C B.
12:42
So in some sense, the local rate of decay determines the global rate. To determine the local rate, upper bound we just estimate by taking the integral of a function and reproducing it and then using an estimated probability.
13:03
But on the other hand, to get a lower bound is hard. What you do is you look at a different set of assumptions that gives you a good lower bound and you use relative entropy to control one in terms of the other. So this is sort of a standard procedure
13:22
and you can apply it to various contexts. And I think my time is up. Thank you.
13:42
Possibly the fastest click-through of a proof we've ever seen. Okay, so our next speaker will be Jack Dongara who will be talking about today's high-performance computing environment for scientific computing. And in my quick bit of research ahead of this talk, I discovered the world's fastest supercomputer
14:01
can outpace 100,000 laptops simultaneously. Which may have just stolen your thunder, I don't know, but I found that interesting. Jack, over to you. Very good. Thank you very much for that kind introduction. I'd like to talk about high-performance computing with respect to scientific computing.
14:21
So we're talking about supercomputers here. And I just want to give you a feel for what we face today. I'm interested in designing software and algorithms for these machines. So today's systems are highly parallel. They have distributed memory. They use a programming paradigm of the message passing interface, MPI,
14:41
plus something called OpenMP. So MPI is used between the nodes and OpenMP is used within a node. A node of this machine, so the fastest machine today that submitted a benchmark result is a machine at Oak Ridge National Laboratory
15:00
in Tennessee. It's a Department of Energy laboratory and that machine is called Frontier and it has a peak performance of two exaflops. So two exaflops is two times 10 to the 18 floating point operations per second. And an operation is an add or a multiply. And in this context,
15:20
I'm talking about 64-bit operands for those operations. So this machine has 8.8 million cores. So if you're going to program this machine, you have to orchestrate that level of parallelism. It consumes about 30 megawatts. So megawatts, if I use a megawatt at my house
15:42
in East Tennessee for one year, I'll get a bill for a million dollars. So that's a megawatt year. So this machine is 30 megawatts. So it's consuming about 30 million dollars a year just in terms of its electric usage. And this machine cost about 600 million dollars
16:01
just to put that into perspective. The price of electricity here in Germany is about four times that of East Tennessee. So quite a bit of difference. And one of the big concerns about running a computer center here in Germany. Let's see, what else can I say? This machine is composed of nodes. Each node is based on an AMD processor,
16:21
64 cores, plus four AMD GPUs. And that all goes to put together to give that peak performance of two exaflops. These machines are heterogeneous today. So they're based in terms of commodity processors.
16:41
So think of x86 architecture together with some accelerator to boost performance. And that boost of performance comes from GPUs today. Think Nvidia, Intel, AMD, those are the producers of those GPUs today. So it's a heterogeneous mix that we have to deal with.
17:03
And if you take a look at the machines, the most expensive thing to do on a computer like this is to communicate. So data movement is very expensive. The machine is over provisioned for floating point operations. So floating point is almost free in this computer. It's moving the data from one place to another
17:22
to carry out those operations that we pay for. And if we think about algorithms, the conventional wisdom is if I have two algorithms that are roughly doing the same thing, and one algorithm takes more operations, then I would choose the one that takes fewer operations.
17:41
But that's not true today. It's not true because of data movement. So we wanna get an algorithm which moves the least amount of data, and that's the one that would provide us with the highest level of performance. And finally, we have floating point arithmetic. So scientific computing traditionally is done
18:01
with 32 and 64-bit operands, but today with AI machine learning transformers, we see hardware being produced which is at a much lower rate. So we have 32-bit, 16-bit, eight-bit, even four-bit floating point operations. Those four bits are there for transformers.
18:22
They can get by with a lot less precision, and the rate of execution goes up as we go through that. So one of the challenges in terms of scientific computing is to try to utilize that hardware that's there really for the machine learning capabilities, try to use that in our scientific computing
18:40
to get additional performance. So thank you for your attention. It's good to see that even Laureates fired a three-minute speech, very difficult, as many of us as young researchers have experienced.
19:01
Okay, so our fourth speaker is Martin Hellman. So where is Martin? There he is. Martin, if you wanna come up on stage. So my note here says, Martin always has an entertaining and insightful story to tell. So I'm sure today will be no different. And the title of this talk is The Wisdom of Foolishness.
19:22
Thank you. You're welcome. So let's see. Let me go put the slide up. So there are two ideas. One is the wisdom of foolishness and the work that won me the end with the 2015 ACM Turing Award was in my case, derided by all my colleagues as foolish, crazy,
19:42
never go anywhere. And I have a talk that I gave to the Stanford Engineering School, which is available, which is more than three minutes on the wisdom of foolishness. And in it, I interviewed, actually, I have emails from five people, including Vince Surf, where you said that even after the success of the ARPANET,
20:04
which preceded the internet, people thought that the internet protocol would not be useful for voice or data because of latency. And they were wrong. And I've got many other people in that talk. And then just last year here at HLF, the Lindau lecture was given by Lou Iñado,
20:22
who won the Nobel Prize in, I think, 1998 in Physiology or Medicine. And his work was on nitric oxide, for which he won this award. And he fits with many Nobel laureates with whom I've talked. And I've asked them whether the work that won them their Nobel Prizes was initially encouraged
20:40
or discouraged as foolish, crazy, never go anywhere. And up there it says that Lou even had the dean come to him early on in his work and say, why are you doing this silly work, Lou? We hired you to do good things. And that won him the Nobel Prize. So don't be afraid of doing foolish things. And then this is not on the slide,
21:01
but I will mention it. The other thing, at the farewell dinner, maybe five years ago, one of the young researchers was asked what she learned at HLF. And she said, I learned that friends are better than enemies. And this was from a talk I gave. And I see in the audience Adi Shamir. And we were opponents, as you remember,
21:21
in the patent fight over RSA versus Stanford, MIT versus Stanford. And today we're good friends. It's a lot better having friends than adversaries. Thank you. Thank you, Martin. You can tell he did this last year, right?
21:42
Time to spare, no problem. Okay, our fifth speaker is Leslie Lamport. And Leslie will be talking about the Byzantine generals in three and a quarter minutes. So I'm already expecting this to overrun. And I actually had a really fantastic chat with Leslie
22:00
a few years ago now, where he told me his one remaining goal academically was to win an Ig Nobel Prize. Is that still the case? Still the case. That is still the case. All right, Leslie, over to you. Special dispensation for three and a half minutes. Once I get my slide deck up.
22:22
Okay, Byzantine generals in three and a quarter minutes. I'm going to present this paper, which you see here, in a little bit abbreviated in three and a quarter minutes. Okay, roll it.
22:40
They're supposed to be. I am the very model of a good Byzantine general for I would draw according to our strategies consensual
23:01
if they're impractical, insensible, or I'm skeptical. I'll cope and I don't mind it being possibly unethical. My fellow generals and I discuss our thoughts by word of mouth. Relate through trusty messengers who dart about from north to south. I will not fall for tricks or traps of comrades who are traitorous. Traitorous? Traitorous? Hate on us? No. Oh!
23:21
So I can choose a course which will avoid a tragic fate for us. So he can choose a course which will avoid a tragic fate for us. So he can choose a course which will avoid a tragic fate for us. So he can choose a course which will avoid a tragic fate for us. And I must tell an enemy from someone who's a friend to me as they might lie to wreck our plans and hide their true identity. In short, I'll act according to our strategies consensual.
23:41
I am the very model of a good Byzantine general. In short, I'll act according to their strategies consensual. He is the very model of a good Byzantine general. I start by asking everyone for what he thinks we ought to do, but also get them to reveal what did the elders plot to you. I then can cross check each of their responses for consistency
24:00
to see if there are traitors who said no to some but yesterday. For if the man were loyal he would say the same to all of us. So we could reach agreement and an action plan unanimous, but if he were a traitor he would lie to try and fray our force. Fray, play, day, say, bray? So we would lose as we attacked with men to few to stay our course.
24:20
So we would lose as we attacked with men to few to stay our course. So we would lose as we attacked with men to few to stay our course. So we would lose as we attacked with men to few to stay our course. And thus we loyalists must share an algorithm mutual, which we can each apply to our own knowledge individual. In short, we must arrive upon our strategies consensual, to be the very models of a good Byzantine general.
24:41
In short, we must arrive upon our strategies consensual, to be the very model of a good Byzantine general. Thus I would aggregate each vote by working out an average, no matter if it's mean mode, median, or else a mother cage. Because as long as fewer than a third of us are traitorous, the metric should reflect
25:02
a larger loyal honest measure us. Once that is done, we should have sets of votes which are identical, so that the algorithm shall produce the same plans epical, and anything that traitors do will be quite ineffectual. That's a hard one, isn't it? Oh!
25:20
As it gets rendered useless by our methods intellectual. As it gets rendered useless by their methods intellectual. As it gets rendered useless by their methods intellectual. As it gets rendered useless by their methods intellectual. Although this method helps design reliable machinery, I shrugged because Constantinople fell in 1453. But to the end I followed all our strategies consensual, I was the very model of a good
25:42
Byzantine general. But to the end he followed all our strategies consensual, he was the very model of a good Byzantine general.
26:06
Now that one is a hard act to follow. But note to future laureates who may want to speak if we do this again next year. You know, that is an excellent example of how to do a three-minute talk. Thank you, Leslie.
26:20
Okay, our sixth speaker is Efim Zelmanov, who will be talking about algebra. What's next? I'm very intrigued. I feel like this could go in many, many directions, Efim, so the stage is yours. Thank you. I have three minutes and one slide, so where is my slide?
26:41
Okay. I will just say a few words about general tendency in algebra that, in my opinion, will stay influential at least in this century. The first one is the great classification of finite simple groups, the biggest single
27:06
project in mathematics that started with Galois and the last publication appeared in 2011. This project has been finished. There are several big families of finite simple groups and 26 sporadic groups.
27:25
The text is more than 10,000 pages, and even to understand that you have to grow in one of these seminars. I remember I was at one of the conferences where major contributors to this classification
27:42
spoke, and I thought that I wish them all a long and happy life, but when this generation goes, this will become a great theorem that nobody knows where it came from. Knowledge can be obtained and knowledge can be lost.
28:02
What I'm trying to say is that we are in need of new ideas, new approaches, and nowadays students don't go there because who would hire somebody who works on a problem that has been solved? And this is the most important problem in algebra, maybe, and not only in algebra.
28:23
The second great tendency, well, is that representation theory becomes growing, increasingly noncommutative and increasingly infinite dimensional. That is the influence of physics, and it will continue.
28:41
Finally, the third problem that I want to mention is in linear algebra. Of course, it does not belong to algebra only. It is at the center of applied mathematics. If you have a huge system of linear equations, really huge, and to make things worse,
29:04
maybe you don't know all entries precisely, but only up to a certain probability, find something better than Gaussian n cubed. To make things easier, we assume that the matrix is sparse,
29:20
that most entries are equal to zero. This problem is important because it arises in so many applied contexts. And this is the influence of big data. Thank you.
29:45
Thank you, Evgeny. And perfectly on time. That's what we like. Okay, our seventh speaker, there's not many of you left. Vince Cerf will be talking about the status of the interplanetary internet because when you've helped to build the internet on one planet,
30:01
why stop there, Evan? Okay, no slides. I have a problem, and some of you will probably say that's simple. I hope to hell it's true because I haven't been able to sort this out. In the internet, when you have a router that's taking a packet in and it has to route it somewhere else, if it has no path to send it, it throws it away.
30:22
In the interplanetary network, that's dumb, especially if you're at the router at Mars, you were sending a bundle from Earth and it's on its way to Jupiter. And so instead of throwing it away, we hang on to it, so we store things in the network. So now just think a little bit about the connectivity of an interplanetary system.
30:41
It's episodic. The trajectories and orbits cause connectivity to come and go. So we have an episodically connected network. We have a finite amount of storage in each one of the nodes. We have a traffic matrix of some kind. My question for you is how do I calculate the capacity of that network
31:03
given that I know what the episodic connectivity is and the finite amount of memory I have in each of the nodes, how can I calculate what the capacity of the system is? That's the problem, and maybe over the break, some of you will come and say, oh, that's easy. I solved that 10 years ago.
31:21
I can hardly wait. Thank you. Thank you, Vint. Our penultimate speaker is going to be John Hopcroft, who will be talking about talent for the information age.
31:41
And ahead of this talk, John informed me that he enjoys hiking in his spare time, and when he sees a path in the woods, he is curious to see where it goes and feels the need to explore it further, which to me sounds an awful lot like doing research. So, John, thank you.
32:01
You get one life to live and find out what you really enjoy and focus your career on what you enjoy. You'll be much more successful if you focus your career on what you enjoy rather than on a high-paying job. To illustrate this, I'm going to talk about that I hire faculty
32:24
for a center I run at Shanghai Xiaotong University in China, and I tell the faculty not to focus on research, money, or number and quality of papers. I tell them to simply explore what excites them,
32:43
and there's an international organization that evaluates centers, and it ranks my center as number one in theoretical computer science in China. How could this occur since this international organization ranks centers
33:02
based on probably research, money, and number and quality of papers? And I tell my faculty, don't focus on those things. I think what happened is faculty at institutions that focus on number and quality of publications
33:20
find problems that they can improve and get a quick publication, and these publications are of very little value. The faculty at my center focuses on exploring what they're curious about, and if they discover something that they feel is important,
33:44
they realize that they should inform others of what they discovered and write a paper. Although they have very few publications, their publications are of high quality, and I think that's the reason our center is ranked number one
34:01
in theoretical computer science in China. So my message to you is if you focus on what you enjoy, you will be successful and have a good life. Thank you.
34:23
Thank you, John. Very, very wise words. Okay, so that just brings us to our final speaker. So our last speaker this morning will be Adi Shamir, who will be talking about how difficult is it to solve systems of equations over RELU-based neural networks. I don't know if this was your plan, but I felt like with that title,
34:41
you could have just said, very, and sat back down. But you do have quite a few more minutes, so Adi. Actually, it's easy, I'll surprise you. Okay, so if you look at the history of mathematics and computer science, you quickly realize that a central issue
35:01
had always been how difficult is it to solve equations in various domains. So for example, the question of whether you can solve with radicals fifth degree polynomial led to Galois theory and many, many other developments. The question of how to solve systems of polynomial equations led to Gobner basis
35:21
and to beautiful other sub-areas of mathematics. The question of how to solve systems of linear equations in computer science led to the question of how do you multiply efficiently two matrices, what is the complexity, bit complexity of this operation. If you look at the question of solving,
35:44
satisfying a Boolean expression, it's a kind of solving an equation with two on the other side. This led to SAT solvers and to the whole beautiful theory of NP completeness.
36:01
And if I go a little bit further out, given many plaintext and ciphertext of a particular cryptosystem, when you try to solve it, basically you are looking for the unknown cryptographic key which is created this transformation from plaintext to ciphertext. And what I realized is that recently
36:22
deep neural networks which are based on ReLU, so I immediately defined what the ReLU activation function is, are giving us a new kind of exciting kinds of equations that haven't been looked much and they will lead to all kinds of interesting developments.
36:41
So you can see the general structure of deep neural networks at the bottom left. You have a numeric input, a vector of numbers, and then you linearly mix them and then you go through a ReLU function, which for negative inputs it is giving zero as an output and for positive inputs
37:01
it is copying the input to the output. So then you mix it again and then you apply ReLU layer and so on and so on. And now the question is, can you solve equations over this new kind of expressions which mix together linear operations and this discontinuity
37:20
which will turn linear equations into piecewise linear equations. Okay, why are we interested in this question at all? Because if you are, you know that many companies are spending billions of dollars and many months training deep neural networks
37:44
and then they allow everyone to interact with those highly valuable assets through an API giving them inputs and getting the corresponding outputs. And the question is, is it foolish? Can someone look at the results
38:03
obtained by giving those deep neural networks all kinds of chosen inputs and by looking at the input-output relationships can you actually find out all the weights which are driving this deep neural network and essentially steal it?
38:20
So this is a question that had been looked at for the last 30 years but mostly in other contexts not in the case of ReLUs. The best previous available algorithm was exponential, exponential time and basically you have to guess whether each one of the ReLU is on its positive side or the negative side and if you guess it correctly
38:41
then the ReLUs disappear and you are left with a system of linear equations. But guessing on which side of each ReLU you are is an exponential time algorithm. Okay, so a very recent result which was presented in May this year at Eurocrit
39:00
used the fact that actually deep neural networks look very, very similar to block ciphers where you are alternately mixing all the bits together in a linear way, low but linear way and then you are applying some non-linearity to each piece separately so something which is called S-box.
39:22
And by using cryptanalytic techniques developed in order to break block ciphers I together with a team of other researchers actually were able to find a polynomial time algorithm for doing it in the general case and everything I told you so far
39:40
is actually an advertisement for a masterclass that I'm going to give tomorrow morning and you're all welcome to hear. Thank you. Okay, so that does bring us to the end of the session. Thank you once again to all of our laureates.
40:03
It is extremely challenging doing a talk in three minutes so I think I speak for everyone when I say we appreciate you taking on the challenge and hopefully it's a slightly different style of lecturing to sort of break up the days. So there is now a coffee break so please do go and speak to any of our laureates
40:24
who have given a talk, asked them any questions. Leslie I hear is very happy to hear auditions for his next talk if any of you would like to do that but otherwise thank you again to laureates, thank you to the audience and we'll see you all after the coffee break.