>>The cube presents HPE discover 2022 brought to you by HPE. >>Welcome back to the cube. Lisa Martin and Dave ante here covering day one of HPE discover 22 live from Las Vegas. We've been having some great conversations today. So far. We've got three full days coming at you. This is close to the end of day one. We're gonna have an interesting conversation next with a may the executive vice president and chief people officer at HPE. Alan. Welcome to the cube. >>Thanks Lisa. Great to be here. Thanks Dave. >>It's great to be back in person. The keynote this morning, standing room, only people are ready. People are ready to be back to hear what HPE has been doing the last couple of years since the last conference, but I've heard you and Antonio talk about the human side of change. It's challenging humans. Humans are uncomfortable with change, right? Unfortunately we are, but it is a big challenge. How, what are some of the things that you're seeing as organizations are really looking and have to transform digitally? They gotta bring the humans along >>Well. You know, our folks as anybody is just bombarded with data these days bombarded with issues and, and it's really down to share of mind when it comes down to it. If, if you're asking someone to change first, you gotta break through the clutter. There's so many things going on in their world and in their life as individuals. But to me, the foundation is you really have to define what is the mission and purpose of the organization, and then make sure that individual feels safe and comfortable participating at work. I know those sound like soft things, but at the end of the day, you're not gonna have the gumption or the desire to change unless you care about something bigger than yourself and that you feel safe bringing your authentic self to work. >>So you have to be kind of, yeah. Have to be good at sales, I guess, because you have to sell the mission. Well, what do you do if somebody's not comfortable? If they, how do you get them to align? I mean, you, you, it's always a challenge. And that's like, I think what makes the people side of the equation so hard? What's your sort of secret sauce there? >>Well, I wouldn't say it's secret sauce, but you know, we define our mission is improving the way people work and live. Now that sounds so general. But the good thing about that is I think about every one of our 60,000 associates around the world can write theirselves into that mission. Sign >>Up >>For that. Yeah. It's not so specific that you think am I opting in, I am opting out. The other piece is you've gotta give employee voice. You have to give your team members an opportunity, not just to, you know, follow blindly, whatever you're saying, you don't want that. You actually want them to challenge it. You want 'em to say, Hey, what does that really mean, Alan? What does that mean, Antonio? When you say we're improving the way, you know, people work and live, what does it mean when we say commit and go or force for good, these are not just pithy phrases. They're ways to engage dialogue. That's how you get people to think and to create and innovate and to change >>And creating that employee experience and changing that and, and transforming that as obviously the world change, especially the last couple of years, but the employee experience and what they think. And are they, are we part of the vision? Are we, part of the mission is directly relates to the customer experience. Those two things to me are inextricably linked well >>In, in our company, it's all about innovation, but not innovation just for the sake of designing things, but to meet customer needs. So you've actually gotta inculcate in your workforce. A couple of things. One obviously is that freedom to be creative, but the other piece is actually actively listening to our customers and recognizing and understanding what they need and how we can satisfy those needs. When you can bring both of those things together, I tell you, you can do all kinds of things with your workforce. >>So, I mean, I'm hearing you obviously look for common ground, but sometimes there's, there's the dissonance, right? The, you know, creating that great human condition might not necessarily be advantageous for short-term profits. You're a public company. So, so how what's that discussion like, and, and, and I presume there's gotta be a long-term vision, but still how, how do you handle those types of >>Things? Well, that, that's what I call dynamic tension. Good, great organizations, encourage dynamic tension. They don't simply ask people to blindly adhere to whatever they're saying. They actually ask their employees to think and to create and to debate and to argue respectfully, of course, that's how you really get to that virtuous circle of innovation and people moving forward. Now, look, I, I'm not naive. We don't have 60,000 team members totally aligned on every point every day. But I think we've got the vast majority knowing ultimately where we're going. And frankly, some of the fun is figuring out how to get there. And that means that you've gotta have those open discussions to get there. >>Well, you talk about dynamic tension and at the first sort of thought of it, it sounds like it can be a challenging thing, but it also sounds like it can really be an accelerant to the culture and the ability for the company to move forward and obviously meet those customer demands. >>Well, if you're defining what's new in the world, that's the only way you get there because nobody has, you know, basically a lock on innovation or what's the best next thing. When you have the power of bringing a diverse set of individuals together and really create forms for them to explore debate, argue, as I mentioned, that's where you really move forward. >>How do you think about how, how, how has your thinking changed? The company's thinking changed post pandemic with regard to hybrid work, you have something Elon Musk, you gotta come to work at least 40 hours, or you're gone. We, we, we heard someone on wall street have similar things, say similar things and others have said, Hey, we have no headquarters anymore. You know, we're moving to, you know, someplace remote what's H HP's point of view on >>That. Well, thanks for that question in particular. And Dave, what you outlined is we seem to have a world of two extremes out there. Yeah. Where either companies say it's back to the old days pre COVID and you're not working unless I see the sweat on your brow and you're there at eight o'clock on Monday morning, then we have other companies say, Hey, it doesn't matter. Mail it in wherever you are around the world. You know, we're in between that, we think it's important that people do get together face to face. And in fact, we've asked our team members to come back a couple of three days a week in the office, but to do it in a purposeful, thoughtful way, it doesn't mean just coming in, swiping your bad shame that you were there. It means coming in to collaborate, to meet with customers, to celebrate, to innovate, to work with groups. >>So what we're trying to do now is orchestrate those moments that matter for our team members, for a reason, for them to be together. Now, there's no reason for them to come in the office. If they're on zoom or team meetings all day, we know that. But the fact is we believe that our culture thrives when people get together at least a bit during the week. So we're looking for that happy medium. I can't say we've got it all figured out, but I can tell you right now, we're not on those two extremes. We're absolutely center the plate. >>So you encouraged that. That was a great description. If somebody says, Hey, but I, I really want to go move to Bozeman, you know, and hang out there and I'll work remote and I'll, I'll be productive. You, you enable that as well. Or would you discourage that? Yeah. We've >>Hired people all over the world and we actually have people based upon their job classified. If they're so-called hybrid employees, the, the, the situation I mentioned, which is you're not required to come to the office, but we encourage it. In some cases we do have telecomm commuters. If they have the kind of job where they can work from Bozeman or from Bangalore or from any place else, we're open to that as well. Cuz we don't wanna rule out that talent. But the vast majority of our folks, we'd like to be pretty close to one of our centers of excellence to one of our offices, to one of our locations because that fuels our customers, our, our culture, and really it creates community. Now I can't predict the future, but frankly, a lot of the issues that we've seen through a, the, the pandemic around mental health, around isolation, around increased stress, those are not all gonna go away because people are getting back together. But I do think that the pandemic accelerated and exacerbated, some of those conditions, people do want to be together and we're gonna make that happen. >>I, I can't predict the future, but I often try and I, I predict, I think the hybrid model, it will be the dominant model going forward. And I think that that, that smart organizations will put incentives in place to get people together. Not, oh, you won't get promoted. No, but you're gonna, you're gonna actually enjoy getting together periodically with, with your teammates and we're gonna support you, you know, wherever you want to live. >>Yeah. >>What are some of the key skill sets these days that HPE is looking for to attract these folks in an increasingly digital world? What are some of those things you say ABC gotta have it. >>Well, interesting. You ask that. Get asked that question a lot. And people expect me to say, they gotta know C plus plus they've gotta, you know, know all the latest on AI. They gotta be a mathematical wizard to do all kinds of things that we do in algorithms. You know, it's not, it's not those factors. It's the behavioral factors. We're looking for people. First of all, that have intellectual curiosity. They thrive to learn. They thrive to innovate. They don't want to just do a job. They want to come in and they want to create something big. So I think that's first and foremost, the second one is we look for people that have some resiliency have they had in their experience broadly in life ever had to deal with stress with resistance, with, you know, uncomfortable situations. Not because that's our work environment, but because that's the world, the world is an actively changing one. >>And we need people who have got that resilience and that intellectual curiosity to kind of move forward. And then last but not least. And this goes back to our founder DNA. I, I talk about this a lot. Our founders, bill and Dave talked a lot about basic things, respect for one another collaboration, teamwork. That's our culture. Now that's not the culture that a lot of other firms have out there. And in some companies they have maybe a harder edge, but those are the things that really propel our organization. Those are the things our customers appreciate the most. >>What's your point of view on the, the so-called great resignation? Is it a sort of a media created dynamic? Is it something that is maybe a, a somewhat of a knee jerk reaction in the post isolation economy? How do you think about that? >>You know, I, it's real obviously, and, and we've seen some uptick in our, our turnover, although I'm happy to say our turnovers a half to a third of what our competitors are. So we, we seem to have been able to retain our folks pretty well. But I do think that coming out of the pandemic was a, an inflection point. For many people. It was such a searing experience in so many ways. It caused people to really reflect and say, do I want to do something different now? That's great. But I'd like to have them do something different in HPE, if they're one of our employees. So what we're focusing on is gigs. What's your next opportunity to learn something new, do something new, move to a different area. You know, we used to call it career development. Those days are gone of just job ladders and wait for the next job and wait for the next promotion. It's all about how can you give someone a new opportunity and challenge them. And when you're able to do that, I think you can create a real positive dynamic that results in greater retention. But I do think the great resurrection it's real, it's gonna persist one other data point. Well, before COVID supply and demand, I'm an economist, not a psychologist. And at the end of the day, we have fewer and fewer people available to do the kinds of work that we're trying to hire. So those two factors together do create some, some turnover. >>You know, what's interesting is certainly pre pandemic. The prediction was that machines were gonna replace humans, which has always happened, but for the first time ever, it's in cognitive functions. And there's a lot of concern in the press about, you know, the impact on, on jobs and employment seems like the reverses happened, which is often the way, but, but, but longer term, what's your point of view on, on, on that, that piece of, of the equation, people are talking about digital transformation, AI, we see robotic process automation. Initially, a lot of employees are really concerned. Whoa, they're gonna replace my job. We've certainly seen that. And you know, if you were, you see kiosks at the airport, people used to actually put up, you know, billboards and with, with the glue and paper and you know, those jobs are gone, but now other jobs are, are, are at risk. How do you think about that? What, what should companies like HPE and society do to help people get to the point where they can thrive in that environment? >>Yeah. Look, I, it, it's an observation that, that I could say based upon my career, I've seen for many, many years, I can remember back manufacturing when at least from a us perspective, many of those manufacturing firms were shedding jobs because of automation. And there are short term disruptions and those are real. Those are human. And we do have to help people through those. Now I think one obligation an employer has, is let's start with our own folks. Let's make sure we retrain them. Let's make sure we expose them to the latest skills. Let's give them an opportunity to grow and develop. So I think if we do those things, we can help people through those transitions over the long haul. I'm actually very optimistic. I believe that over time, people self-select, these things don't happen overnight. I'll give you one tiny little anecdote before the pandemic. All of this world about autonomous vehicles can eliminate truck drivers. Well, you know, back in the day I actually drove a truck and it's not just driving. You've gotta interact with somebody in a dock door. You've gotta do all kinds of other tasks that can't be automated. And so things will happen over time, but I don't think we're gonna see this massive social disruption people were worried about. There is an incumbent responsibility on firms to train their own people and to keep them up to speed. And that's something we're deeply committed to at HPE >>Is information technology, employment, a parallel. I mean, everybody thought the cloud was gonna destroy the it, you know, worker that didn't happen. They just sort of changed their skillset. They became, you know, cloud experts or cloud architects. Is there a parallel there? >>Yeah, I think there's absolutely a parallel. And while probably the, the rate of change is quicker in, in some tech industries than perhaps others. All we're doing is creating new markets and new opportunities. And ultimately the lack of, of skill that we have, the lack of talent in the external marketplace is gonna mean that it's still very much an opportunity for people to learn, grow, develop, and be employed. >>Do you think that's, it's a matter of, of, of awareness on people not really understanding that whether it's still fear? >>Well, I, I think there may be some of that, but again, I, I, I do think from a, a broader social perspective, there's probably some things that in the public policy we can do to improve education and training, particularly for new entrants and make sure they're learning the skills for tomorrow's jobs and not just today's, but can I'm optimistic. And I actually think most responsible companies get this. And if you talk to their CEOs, the top tier or three issues that they have include access to talent. So why don't we recycle repurpose and reuse to use the sustainability phrase instead of throwing people outta work that have all kinds of intellectual property and capability to be very productive. And that's what we do at HPE. >>And that curiosity, that's something that you can't teach, right? Exactly. Have it, or >>You don't. Exactly. >>So last question, in terms of, of looking at culture corporate culture, as a, as an accelerant, as a catalyst of digital transformation, how do you advise leadership teams? >>Well, I, we've done a fair amount of work in the last five years, defining the culture in very small frankly soundbites. And the way you make that come to life is back what I mentioned before. You have to engage people and ask them to debate it. What does it mean to say, commit and go? What does it mean to say force for good, those kind of conversations, help your culture evolve, help your culture become real and not just a bunch of words on some piece of paper or, or posters someplace. I will say from my experience, and, and particularly with a new entrance to the workforce, if you can't define your culture quickly for this next generation coming in, you're, you're, there's no way you're gonna attract that talent. And so put me on the spot. HPE is here to help people live and grow and work better, and we try to be a force for good. We focus on that and we create work that fits your life. Not the other way around. That's my elevator speech. It sounds pithy, but it's an invitation to have a deeper discussion. >>I love it. And I think this is only day one for us here, but I think that we're, we're seeing, and we're feeling that culture there's 8,000 or so HP folks, executives, partners, customers, ready to come back and innovate with each other. I think that culture is palpable, that you've created. >>Great. It's exciting. And thank you so much for being part of it. >>Thanks, Alan. Pleasure. Thanks, Alan. We appreciate your insights. Okay. For our guests. I'm Dave ante. I Lisa Martin stick around. You're watching the cube, the leader in live tech coverage, and we're gonna be back after your short break.

>>Hi, everybody. Welcome back to Caesars in Las Vegas. My name is Dave ante. We're here with the chairman and CEO of snowflake, Frank Luman. Good to see you again, Frank. Thanks for coming on. Yeah, >>You, you as well, Dave. Good to be with you. >>No, it's, it's awesome to be, obviously everybody's excited to be back. You mentioned that in your, in your keynote, the most amazing thing to me is the progression of what we're seeing here in the ecosystem and of your data cloud. Um, you wrote a book, the rise of the data cloud, and it was very cogent. You talked about network effects, but now you've executed on that. I call it the super cloud. You have AWS, you know, I use that term, AWS. You're building on top of that. And now you have customers building on top of your cloud. So there's these layers of value that's unique in the industry. Was this by design >>Or, well, you know, when you, uh, are a data clouding, you have data, people wanna do things, you know, with that data, they don't want to just, you know, run data operations, populate dashboards, you know, run reports pretty soon. They want to build applications and after they build applications, they wanna build businesses on it. So it goes on and on and on. So it, it drives your development to enable more and more functionality on that data cloud. Didn't start out that way. You know, we were very, very much focused on data operations, then it becomes application development and then it becomes, Hey, we're developing whole businesses on this platform. So similar to what happened to Facebook in many, in many ways, you know, >>There was some confusion I think, and there still is in the community of, particularly on wall street, about your quarter, your con the consumption model I loved on the earnings call. One of the analysts asked Mike, you know, do you ever consider going to a subscription model? And Mike got cut him off, then let finish. No, that would really defeat the purpose. Um, and so there's also a narrative around, well, maybe snowflake, consumption's easier to dial down. Maybe it's more discretionary, but I, I, I would say this, that if you're building apps on top of snowflake and you're actually monetizing, which is a big theme here, now, your revenue is aligned, you know, with those cloud costs. And so unless you're selling it for more, you know, than it costs more than, than you're selling it for, you're gonna dial that up. And that is the future of, I see this ecosystem in your company. Is that, is that fair? You buy that. >>Yeah, it, it is fair. Obviously the public cloud runs on a consumption model. So, you know, you start looking all the layers of the stack, um, you know, snowflake, you know, we have to be a consumption model because we run on top of other people's, uh, consumption models. Otherwise you don't have alignment. I mean, we have conversations, uh, with people that build on snowflake, um, you know, they have trouble, you know, with their financial model because they're not running a consumption model. So it's like square pack around hole. So we all have to align ourselves. So that's when they pay a dollar, you know, a portion goes to, let's say, AWS portion goes to the snowflake of that dollar. And the portion goes to whatever the uplift is, application value, data value, whatever it is to that goes on top of that. So the whole dollar, you know, gets allocated depending on whose value at it. Um, we're talking about. >>Yeah, but you sell value. Um, so you're not a SaaS company. Uh, at least I don't look at you that that way I I've always felt like the SAS pricing model is flawed because it's not aligned with customers. Right. If you, if you get stuck with orphaned licenses too bad, you know, pay us. >>Yeah. We're, we're, we're obviously a SaaS model in the sense that it is software as a service, but it's not a SaaS model in the sense that we don't sell use rights. Right. And that's the big difference. I mean, when you buy, you know, so many users from, you know, Salesforce and ServiceNow or whoever you have just purchased the right, you know, for so many users to use that software for this period of time, and the revenue gets recognized, you know, radically, you know, one month at a time, the same amount. Now we're not that different because we still do a contract the exact same way as SA vendor does it, but we don't recognize the revenue radically. We recognize the revenue based on the consumption, but over the term of the contract, we recognize the entire amount. It just is not neatly organized in these monthly buckets. >>You know? So what happens if they underspend one quarter, they have to catch up by the end of the, the term, is that how it works or is that a negotiation or it's >>The, the, the spending is a totally, totally separate from the consumption itself, you know, because you know how they pay for the contract. Let's say they do a three year contract. Um, you know, they, they will probably pay for that, you know, on an annual basis, you know, that three year contract. Um, but it's how they recognize their expenses for snowflake and how we recognize the revenue is based on what they actually consume. But it's not like you're on demand where you can just decide to not use it. And then I don't have any cost, but over the three year period, you know, all of that, you know, uh, needs to get consumed or they expire. And that's the same way with Amazon. If I don't consume what I buy from Amazon, I still gotta pay for it. You know, so, >>Well, you're right. Well, I guess you could buy by the drink, but it's way, way more expensive and nobody really correct. Does that, so, yep. Okay. Phase one, better simpler, you know, cloud enterprise data warehouse, phase two, you introduced the, the data cloud and, and now we're seeing the rise of the data cloud. What, what does phase three look like >>Now? Phase, phase three is all about applications. Um, and we've just learned, uh, you know, from the beginning that people were trying to do this, but we weren't instrumental at all to do it. So people would ODBC, you know, JDBC drivers just uses as database, right? So the entire application would happen outside, you know, snowflake, we're just a database. You connect to the database, you know, you read or right data, you know, you do data, data manipulations. And then the application, uh, processing all happens outside of snowflake. Now there's issues with that because we start to exfil trade data, meaning that we started to take data out of snowflake and, and put it, uh, in other places. Now there's risk for that. There's operational risk, there's governance, exposure, security issues, you know, all this kind of stuff. And the other problem is, you know, data gets Reed. >>It proliferates. And then, you know, data science tests are like, well, I, I need that data to stay in one place. That's the whole idea behind the data cloud. You know, we have very big infrastructure clouds. We have very big application clouds and then data, you know, sort of became the victim there and became more proliferated and more segment. And it's ever been. So all we do is just send data to the work all day. And we said, no, we're gonna enable the work to get to the data. And the data that stays in more in place, we don't have latency issue. We don't have data quality issues. We don't have lineage issues. So, you know, people have responded very, very well to the data cloud idea, like, yeah, you know, as an enterprise or an institution, you know, I'm the epicenter of my own data cloud because it's not just my own data. >>It's also my ecosystem. It's the people that I have data networking relationships with, you know, for example, you know, take, you know, uh, an investment bank, you know, in, in, in, in New York city, they send data to fidelity. They send data to BlackRock. They send data to, you know, bank of New York, all the regulatory clearing houses, all on and on and on, you know, every night they're running thousands, tens of thousands, you know, of jobs pushing that data, you know, out there. It just, and they they're all on snowflake already. So it doesn't have to be this way. Right. So, >>Yes. So I, I asked the guys before, you know, last week, Hey, what, what would you ask Frank? Now? You might remember you came on, uh, our program during COVID and I was asking you how you're dealing with it, turn off the news. And it was, that was cool. And I asked you at the time, you know, were you ever, you go on Preem and you said, look, I'll never say never, but it defeats the purpose. And you said, we're not gonna do a halfway house. Actually, you were more declarative. We're not doing a halfway house, one foot in one foot out. And then the guy said, well, what about that Dell deal? And that pure deal that you just did. And I, I think I know the answer, but I want to hear from you did a customer come to you and say, get you in the headlock and say, you gotta do this. >>Or it did happen that way. Uh, it, uh, it started with a conversation, um, you know, via with, uh, with Michael Dell. Um, it was supposed to be just a friendly chat, you know, Hey, how's it going? And I mean, obviously Dell is the owner of data, the main, or our first company, you know? Um, but it's, it, wasn't easy for, for Dell and snowflake to have a conversation because they're the epitome of the on-premise company and we're the epitome of a cloud company. And it's like, how, what do we have in common here? Right. What can we talk about? But, you know, Michael's a very smart, uh, engaging guy, you know, always looking for, for opportunity. And of course they decided we're gonna hook up our CTOs, our product teams and, you know, explore, you know, somebody's, uh, ideas and, you know, yeah. We had some, you know, starts and restarts and all of that because it's just naturally, you know, uh, not an easy thing to conceive of, but, you know, in the end it was like, you know what? >>It makes a lot of sense. You know, we can virtualize, you know, Dell object storage, you know, as if it's, you know, an S three storage, you know, from Amazon and then, you know, snowflake in its analytical processing. We'll just reference that data because to us, it just looks like a file that's sitting on, on S3. And we have, we have such a thing it's called an external table, right. That's, that's how we basically, it projects, you know, a snowflake, uh, semantic and structural model, you know, on an external object. And we process against it exactly the same way as if it was an internal, uh, table. So we just extended that, um, you know, with, um, with our storage partners, like Dell and pure storage, um, for it to happen, you know, across a network to an on-prem place. So it's very elegant and it, it, um, it becomes an, an enterprise architecture rather than just a cloud architecture. And I'm, I just don't know what will come of it. And, but I've already talked to customers who have to have data on premises just can't go anywhere because they process against it, you know, where it originates, but there are analytical processes that wanna reference attributes of that data. Well, this is what we'll do that. >>Yeah. I'm, it is interesting. I'm gonna ask Dell if I were them, I'd be talking to you about, Hey, I'm gonna try to separate compute from storage on prem and maybe do some of the, the work there. I don't even know if it's technically feasible. It's, I'll ask OI. But, um, but, but, but to me, that's an example of your extending your ecosystem. Um, so you're talking now about applications and that's an example of increasing your Tam. I don't know if you ever get to the edge, you know, we'll see, we're not quite quite there yet, but, um, but as you've said before, there's no lack of market for you. >>Yeah. I mean, obviously snowflake it it's, it's Genesis was reinventing database management in, in a cloud computing environment, which is so different from a, a machine environment or a cluster environment. So that's why, you know, we're, we're, we're not a, a fit for a machine centric, uh, environment sort of defeats the purpose of, you know, how we were built. We, we are truly a native solution. Most products, uh, in the clouds are actually not cloud native. You know, they, they originated the machine environments and you still see that, you know, almost everything you see in the cloud by the way is not cloud native, our generation of applications. They only run the cloud. They can only run the cloud. They are cloud native. They don't know anything else, >>You know? Yeah, you're right. A lot of companies would just wrap something in wrap their stack in Kubernetes and throw it into the cloud and say, we're in the cloud too. And you basically get, you just shifted. It >>Didn't make sense. Oh. They throw it in the container and run it. Right. Yeah. >>So, okay. That's cool. But what does that get you that doesn't change your operational model? Um, so coming back to software development and what you're doing in, in that regard, it seems one of the things we said about Supercloud is in order to have a Supercloud, you gotta have an ecosystem, you gotta have optionality. Hence you're doing things like Apache iceberg, you know, you said today, well, we're not sure where it's gonna go, but we offering options. Uh, but, but my, my question is, um, as it pertains to software developments specifically, how do you, so one of the things we said, sorry, I've lost my train there. One of the things we said is you have to have a super PAs in order to have a super cloud ecosystem, PAs layer. That's essentially what you've introduced here. Is it not a platform for our application development? >>Yeah. I mean, what happens today? I mean, how do you enable a developer, you know, on snowflake, without the developer, you know, reading the, the files out of snowflake, you know, processing, you know, against that data, wherever they are, and then putting the results set, God knows where, right. And that's what happens today. It's the wild west it's completely UN uncovered, right? And that's the reason why lots of enterprises will not allow Python anything anywhere near, you know, their enterprise data. We just know that, uh, we also know it from streamlet, um, or the acquisition, um, large acquisition that we made this year because they said, look, you know, we're, we have a lot of demand, you know, uh, in the Python community, but that's the wild west. That's not the enterprise grade high trust, uh, you know, corporate environment. They are strictly segregated, uh, today. >>Now do some, do these, do these things sometimes dribble up in the enterprise? Yes, they do. And it's actually intolerable the risk that enterprises, you know, take, you know, with things being UN uncovered. I mean the whole snowflake strategy and promises that you're in snowflake, it is a, an absolute enterprise grade environment experience. And it's really hard to do. It takes enormous investment. Uh, but that is what you buy from us. Just having Python is not particularly hard. You know, we can do that in a week. This has taken us years to get it to this level, you know, of, of, you know, governance, security and, and, you know, having all the risks around exfiltration and so on, really understood and dealt with. That's also why these things run in private previews and public previews for so long because we have to squeeze out, you know, everything that may not have been, you know, understood or foreseen, you know, >>So there are trade offs of, of going into this snowflake cloud, you get all this great functionality. Some people might think it's a walled garden. How, how would you respond to that? >>Yeah. And it's true when you have a, you know, a snowflake object, like a snowflake, uh, table only snowflake, you know, runs that table. And, um, you know, that, that is, you know, it's very high function. It's very sort of analogous to what apple did, you know, they have very high functioning, but you do have to accept the fact that it's, that it's not, uh, you know, other, other things in apple cannot, you know, get that these objects. So this is the reason why we introduce an open file format, you know, like, like iceberg, uh, because what iceberg effectively does is it allows any tool, uh, you know, to access that particular object. We do it in such a way that a lot of the functionality of snowflake, you know, will address the iceberg format, which is great because it's, you're gonna get much more function out of our, you know, iceberg implementation than you would get from iceberg on its own. So we do it in a very high value addeds, uh, you know, manner, but other tools can still access the same object in a read to write, uh, manner. So it, it really sort of delivers the original, uh, promise of the data lake, which is just like, Hey, I have all these objects tools come and go. I can use what I want. Um, so you get, you get the best of both worlds for the most part. >>Have you reminds me a little bit of VMware? I mean, VMware's a software mainframe, it's just better than >>Doing >>It on your own. Yep. Um, one of the other hallmarks of a cloud company, and you guys clearly are a cloud company is startups and innovation. Um, now of course you see that in, in the, in the ecosystem, uh, and maybe that's the answer to my question, but you guys are kind of whale hunters, <laugh> your customers are, tend to be bigger. Uh, is the, is the innovation now the extension of that, the ecosystem is that by design. >>Oh, um, you know, we have a enormous, uh, ISV following and, um, we're gonna have a whole separate conference like this, by the way, just for, yeah. >>For developers. I hope you guys will up there too. Yeah. Um, you know, the, the reason that, that the ISV strategy is very important for, you know, for, for, for, for many reasons, but, you know, ISVs are the people that are really going to unlock a lot of the value and a lot of the promise of data, right? Because you, you can never do that on your own. And the problem has been that for ISVs, it is so expensive and so difficult to build a product that can be used because the entire enterprise platform infrastructure needs to be built by somebody, you know, I mean, are you really gonna run infrastructure, database, operations, security, compliance, scalability, economics. How do you do that as a software company where really you only have your, your domain expertise that you want to deliver on a platform. You don't wanna do all these things. >>First of all, you don't know how to do it, how to do it well. Um, so it is much easier, much faster when there is already platform to actually build done in the world of clout that just doesn't, you know, exist. And then beyond that, you know, okay, fine building. It is sort of step one. Now I gotta sell it. I gotta market it. So how do I do that? Well, in the snowflake community, you have already market <laugh>, there's thousands and thousands of customers that are also on self lake. Okay. So their, their ability to consume that service that you just built, you know, they can search it, they can try it, they can test it and decide whether they want to consume it. And then, you know, we can monetize it. So all they have to do is cash the check. So the net effecti of it is we drastically lowered the barriers to entry into the world, you know, of software, you know, two men or two women in a dog, and a handful of files can build something that then can be sold, sort of to, for software developers. >>I wrote a piece 2012 after the first reinvent. And I, you know, and I, and I put a big gorilla on the front page and I said, how do you compete with Amazon gorilla? And then one of my answers was you build data ecosystems and you verticalize, and that's, that's what you're doing >>Here. Yeah. There certain verticals that are farther along than others, uh, obviously, but for example, in financial, uh, which is our largest vertical, I mean, the, the data ecosystem is really developing hardcore now. And that's, that's because they so rely on those relationships between all the big financial institutions and entities, regulatory, you know, clearing houses, investment bankers, uh, retail banks, all this kind of stuff. Um, so they're like, it becomes a no brainer. The network affects kick in so strongly because they're like, well, this is really the only way to do it. I mean, if you and I work in different companies and we do, and we want to create a secure, compliant data network and connection between us, I mean, it would take forever to get our lawyers to agree that yeah, it's okay. <laugh> right now, it's like a matter of minutes to set it up. If we're both on snowflake, >>It's like procurement, do they, do you have an MSA yeah. Check? And it just sail right through versus back and forth and endless negotiations >>Today. Data networking is becoming core ecosystem in the world of computing. You know, >>I mean, you talked about the network effects in rise of the data cloud and correct. Again, you know, you, weren't the first to come up with that notion, but you are applying it here. Um, I wanna switch topics a little bit. I, when I read your press releases, I laugh every time. Cause this says no HQ, Bozeman. And so where, where do you, I think I know where you land on, on hybrid work and remote work, but what are your thoughts on that? You, you see Elon the other day said you can't work for us unless you come to the office. Where, where do you stand? >>Yeah. Well, the, well, the, the first aspect is, uh, we really wanted to, uh, separate from the idea of a headquarters location, because I feel it's very antiquated. You know, we have many different hubs. There's not one place in the world where all the important people are and where we make all the important positions, that whole way of thinking, uh, you know, it is obsolete. I mean, I am where I need to be. And it it's many different places. It's not like I, I sit in this incredible place, you know, and that's, you know, that's where I sit and everybody comes to me. No, we are constantly moving around and we have engineering hubs. You know, we have your regional, uh, you know, headquarters for, for sales. Obviously we have in Malaysia, we have in Europe, you know? And, um, so I wanted to get rid of this headquarters designation. >>And, you know, the, the, the other issue obviously is that, you know, we were obviously in California, but you know, California is, is no longer, uh, the dominant place of where we are resident. I mean, 40% of our engineering people are now in be Washington. You know, we have hundreds of people in Poland where people, you know, we are gonna have very stressed location in Toronto. Um, yeah. Obviously our customers are, are everywhere, right? So this idea that, you know, everything is happening in, in one state is just, um, you know, not, not correct. So we wanted to go to no headquarters. Of course the SCC doesn't let you do that. Um, because they want, they want you to have a street address where the government can send you a mail and then it becomes, the question is, well, what's an acceptable location. Well, it has to be a place where the CEO and the CFO have residency by hooker, by crook. >>That happened to be in Bozeman Montana because Mike and I are both, it was not by design. We just did that because we were, uh, required to, you know, you know, comply with government, uh, requirements, which of course we do, but that's why it, it says what it says now on, on the topic of, you know, where did we work? Um, we are super situational about it. It's not like, Hey, um, you know, everybody in the office or, or everybody is remote, we're not categorical about it. Depends on the function, depends on the location. Um, but everybody is tethered to an office. Okay. In words, everybody has a relationship with an office. There's, there's almost nobody, there are a few exceptions of people that are completely remote. Uh, but you know, if you get hired on with snowflake, you will always have an office affiliation and you can be called into the office by your manager. But for purpose, you know, a meeting, a training, an event, you don't get called in just to hang out. And like, the office is no longer your home away from home. Right. And we're now into hotel, right? So you don't have a fixed place, you know? So >>You talked in your keynote a lot about last question. I let you go customer alignment, obviously a big deal. I have been watching, you know, we go to a lot of events, you'll see a technology company tell a story, you know, about their widget or whatever it was their box. And then you'll see an outcome and you look at it and you shake your head and say, well, that the difference between this and that is the square root of zero, right. When you talk about customer alignment today, we're talking about monetizing data. Um, so that's a whole different conversation. Um, and I, I wonder if you could sort of close on how that's different. Um, I mean, at ServiceNow, you transformed it. You know, I get that, you know, data, the domain was okay, tape, blow it out, but this is a, feels like a whole new vector or wave of growth. >>Yeah. You know, monetizing, uh, data becomes sort of a, you know, a byproduct of having a data cloud you all of a sudden, you know, become aware of the fact that, Hey, Hey, I have data and be that data might actually be quite valuable to parties. And then C you know, it's really easy to then, you know, uh, sell that and, and monetize that. Cause if it was hard, forget it, you know, I don't have time for it. Right. But if it's relatively, if it's compliant, it's relatively effortless, it's pure profit. Um, I just want to reference one attribute, two attributes of what you have, by the way, you know, uh, hedge funds have been into this sort of thing, you know, for a long time, because they procure data from hundreds and hundreds of sources, right. Because they're, they are the original data scientists. >>Um, but the, the bigger thing with data is that a lot of, you know, digital transformation is, is, is finally becoming real. You know, for years it was arm waving and conceptual and abstract, but it's becoming real. I mean, how do we, how do we run a supply chain? You know, how do we run, you know, healthcare, um, all these things are become are, and how do we run cyber security? They're being redefined as data problems and data challenges. And they have data solutions. So that's right. Data strategies are insanely important because, you know, if, if the solution is through data, then you need to have, you know, a data strategy, you know, and in our world, that means you have a data cloud and you have all the enablement that allows you to do that. But, you know, hospitals, you know, are, are saying, you know, data science is gonna have a bigger impact on healthcare than life science, you know, in the coming, whatever, you know, 10, 20 years, how do you enable that? >>Right. I, I have conversations with, with, with hospital executives are like, I got generations of data, you know, clinical diagnostic, demographic, genomic. And then I, I am envisioning these predictive outcomes over here. I wanna be able to predict, you know, once somebody's gonna get what disease and you know, what I have to do about it, um, how do I do that? <laugh> right. The day you go from, uh, you know, I have a lot of data too. I have these outcomes and then do me a miracle in the middle, in the middle of somewhere. Well, that's where we come in. We're gonna organize ourselves and then unpack thats, you know, and then we, we work, we through training models, you know, we can start delivering some of these insights, but the, the promise is extraordinary. We can change whole industries like pharma and, and, and healthcare. Um, you know, 30 effects of data, the economics will change. And you know, the societal outcomes, you know, um, quality of life disease, longevity of life is quite extraordinary. Supply chain management. That's all around us right >>Now. Well, there's a lot of, you know, high growth companies that were kind of COVID companies, valuations shot up. And now they're trying to figure out what to do. You've been pretty clear because of what you just talked about, the opportunities enormous. You're not slowing down, you're amping it up, you know, pun intended. So Frank Luman, thanks so much for coming on the cube. Really appreciate your time. >>My pleasure. >>All right. And thank you for watching. Keep it right there for more coverage from the snowflake summit, 2022, you're watching the cube.

>> From the Cube studios in Palo Alto in Boston, bringing you data-driven insights from the Cube in ETR. This is breaking analysis with Dave Valante. >> Throughout the pre-vaccine COVID era, IT buyers indicated that budget constraints would constrict 2020 spending by roughly 5 percent relative to 2019 levels. But the forced march to digital, combined with increased cyber threats, created a modernization mandate that powered Q4 spending last year and this momentum has carried through to 2021. However, COVID variants have delayed return to work and business travel plans and as such our current forecast for global IT spending remains strong at 6 to 7 percent but slightly down from previous estimates. Notably, CIOs and IT buyers expect a 7 to 8 percent increase in 2022 spending, reflecting investments in hybrid strategies in a continued belief that technology remains the underpinning of competitive advantage in the coming decade. Hello and welcome to this week's Wikibon Cube Insights, powered by ETR. In this breaking analysis we'll share the latest results of ETR's macro spending survey and update you in industry and sector spending patterns. First, let's summarize the key take-aways from ETR's latest demand-side survey. Based on ETR's latest survey. Currently with 869 responses as shown here at the bottom, we expect a slight pull-back in spending expectations from CIOs and IT buyers to roughly 6 to 7 percent, down from 7 to 8 percent earlier this year. This reflects caution over return to office strategies but buyers continue to expect robust spending as we said into next year as they support hybrid models, modernize their HQ infrastructure and continue to move forward on digital transformation initiatives. Cyber security and cloud remain the top 2 priorities with data initiatives overtaking collaboration and productivity on the priority list. Although all of these remain strong. Organizations now expect around 44 percent of employees to be working in a hybrid model over the long-term with 37 percent currently working in a hybrid fashion. Now here's the data behind the revised projections it compares the spending growth expectations from the March, June, and September 21 surveys. This by no means is a radical change as you can see from the downward trajectory of the yellow bar. It reflects the reality of the continued injection of uncertainty caused by the pandemic. Organizations are dealing with the reality and remaining flexible with regard to strategies and spending outlook, but the 2022 bar on the far-right at 7 and a half percent stands out in its telling as buyers expect spending levels in 22 to outpace historical norms by quite a large margin. Now as shown here, the spending compression is an across the board trend. Only Latin America, industrial materials manufacturing, and retail consumer show an uptick from previous surveys. With non-profits, education, energy, and APAC showing the steepest declines. But the longer term spending outlook remains robust across the boards. This chart shows that generally the outlook for 2022 spending is strong with retail consumer and government leading the charge. Only the historically cautious education sector stands out as softer, but even so its spending outlook is comparable to historical norms. Now be careful putting too much emphasis, by the way, on Latin America as the ends are small as ETR noted here. Now let's take a look at the sector analysis. This picture has been amazingly consistent. ETR asks respondents to rate their spending priorities and the chart shows the ratings from highest to lowest priority for the top technology sectors. Now this data only shows the top 7 sectors, so even though for instance RPA appears down the list, it remains one of the highest in the survey. In fact, although we are not showing this data, we went in and looked at this. Machine learning, containers, cloud, and RPA remain the top 4 areas from a net score or spending momentum standpoint. Well above the 40 percent mark we talk about all the time. Back to the priorities we asked the CIOs. Cyber security is noticeably above the rest with cloud migration remaining very strong. The data sector i.e. analytics and data warehousing have overtaken collaboration and productivity as priorities. However, collaboration remains strong as do networking, AI, and RPA. Now when we dig into some of these sectors to see which vendors are showing spending momentum, let's take a look. In addition to the large cloud players, especially AWS and Microsoft, we saw that snowflake continued to hover at around 80 percent net score level. Some others that we haven't cited as much recently are popping up either with spending momentum, or showing a larger presence in the market or both within these sectors. Toughtsbot has popped up now this AI specialist has shown up every now and then in the survey but they seem to be getting traction in the data set and they have an elevated net score. Datadog also stood out as did Cockroach Labs and Databricks is starting to show some strength even though they have shown strength in past surveys, they're starting to show larger presence in the survey. Now Networking Arista who has always had strong momentum shows continued strong momentum. And Maraki which has a large presence in the data set, is also notable. Not as high, but as a much larger share. Monday.com is also hitting the radar in collaboration and Twilio is popping up as well. Let's take a look at the return to office trends and the actions organizations have taken as a result of COVID and see how that's changed over time. This data shows the time series going back to the June 2020 survey. Let's start with the percent of organizations with employees working from home and you'll note that has ticked up since June and is now back up to 75 percent. And you can see the noticeable drop in the percentage of companies that have employees fully returning to the office. Also, more organizations are canceling business trips. So these are some of the factors that contribute to the slightly more cautious spending outlook that we're reporting here. Now continuing on the chart even though layoffs are trending downward, it's no surprise given the skill shortage you see a slight uptick in hiring freezes and a downtick in new hiring. New IT deployment freezes they remain low but there is a slight down tick in accelerating new IT deployments. So look, these are not radical changes, but they do reflect the on-going day-by-day, month-by-month, quarter-by-quarter adjustments that we've seen companies make throughout the COVID era. And it underscores the need for organizations to be more agile, flexible, resilient, and responsive to change. What does that mean? It means modernizing infrastructure and apps, better leveraging data, applying AI, and taking care of governance, compliance, and security. And CIOs expect these spending priorities to continue for the foreseeable future, at least for the next 15 months. Now as we've declared in previous episodes, every CEO, CXO, corner office, boards of directors, they're trying to get hybrid right. Interestingly, we see some companies mandating a return to work. We've seen this with some of the Wall Street firms, for example, but tech is a leading example of advocating for remote or hybrid work. To it, Michael Dell's public posture that he's wide-open for remote and, or hybrid work and Frank Slootman has moved Snowflakes' executive offices to Bozeman, Montana reflecting his sentiment that the days of big corporate towers are over. And why not? Productivity is through the roof, and the cost savings from working remotely can be enormous. This chart shows data back to the December 2020 survey. And we've seen a steady decline in remote work, but it's still the dominant model of 53 percent of the work force. In other words, people are starting to come back to office but still very, very high remote. Now jump to the third set of bars. And organizations expect a 39 percent of employees to be working remotely in 6 months. Now jump back to the second set of bars, 37 percent of employees are currently working in a hybrid model and that's up from 33 percent in June. Now jump to the fourth set of bars and the expectation is around 44 percent will be working in a hybrid model within the next 6 months. Organizations expect remote workers to settle in and level around 30 percent. Now that's down from previous highs of 35 percent last December but it's up significantly from the historical average of 15 to 16 percent. And the expectation as you can see in the last set of bars is that more than 40 percent of employees will be working in a hybrid model, on a permanent basis. So look, the world is going hybrid. It's the future and that requires technology investments to support new ways to work. And that's one main reason why we see the spending momentum continuing into 2022. So let's drill a little bit into what this means. In order words, how are organizations thinking about their hybrid models. This chart shows the responses from the June and September surveys when ETR began asking organizations to describe their hybrid approaches in more detail. The dominant model, around 50 percent of organizations say time will be split between remote and required on-site days. This is where leaders will ask employees to come to the office at designated times for whiteboard sessions, or planning meetings, et cetera. So hybrid is the dominant model. Then we see a big drop to primarily on-site with exceptions as needed and a low single digit number of organizations with no hybrid option. So the message is clear: Hybrid is the way forward and IT infrastructure will evolve to support these models and this bodes well for tech spending in our view. It speaks to continued cyber investments, leverage the cloud for flexible capacity shoring up on-prem infrastructure as we now see more vendors offering flexible capacity on-prem. Modernizing applications, building layers with micro-services and kubernetes that can actually connect to the cloud or assist in moving workloads, evolving the network architecture, flattening that out we hear a lot of talk about the edge, driving automation, and new ways to work and putting data at the core of digital business strategies. These are the technology approaches that organizations are tapping to deal with the changing dynamics of the pandemic, and adapting to new business models. Across the board, technology has become one of the most important enablers for competitiveness ain the coming decade and we expect that momentum to continue until some exogenous factors derail the spending trend. At the moment, that risk doesn't appear to be a slow-down in an economic recovery, although we continue to watch uncertainties around interest rates, inflation, tax policy, and global economic tensions, especially with China. And as always, we'll be here to update you as the data changes. Okay we're going to leave it there for now, remember these episodes are all available as podcasts you just got to search "breaking analysis podcasts" and we publish each week on wikibon.com and silliconeggle.com. You can connect with me on twitter @Devalante or email me at david.valante@silliconeggle.com. Appreciate the comments on LinkedIn and don't forget to check out ETR.plus for all the survey data. This is Dave Valante for the Cube insights powered by ETR, be well, and we'll see you next time. (music)

>>don't talk mhm, >>Okay, thing is my presentation on coherent nonlinear dynamics and combinatorial optimization. This is going to be a talk to introduce an approach we're taking to the analysis of the performance of coherent using machines. So let me start with a brief introduction to easing optimization. The easing model represents a set of interacting magnetic moments or spins the total energy given by the expression shown at the bottom left of this slide. Here, the signal variables are meditate binary values. The Matrix element J. I. J. Represents the interaction, strength and signed between any pair of spins. I. J and A Chive represents a possible local magnetic field acting on each thing. The easing ground state problem is to find an assignment of binary spin values that achieves the lowest possible value of total energy. And an instance of the easing problem is specified by giving numerical values for the Matrix J in Vector H. Although the easy model originates in physics, we understand the ground state problem to correspond to what would be called quadratic binary optimization in the field of operations research and in fact, in terms of computational complexity theory, it could be established that the easing ground state problem is np complete. Qualitatively speaking, this makes the easing problem a representative sort of hard optimization problem, for which it is expected that the runtime required by any computational algorithm to find exact solutions should, as anatomically scale exponentially with the number of spends and for worst case instances at each end. Of course, there's no reason to believe that the problem instances that actually arrives in practical optimization scenarios are going to be worst case instances. And it's also not generally the case in practical optimization scenarios that we demand absolute optimum solutions. Usually we're more interested in just getting the best solution we can within an affordable cost, where costs may be measured in terms of time, service fees and or energy required for a computation. This focuses great interest on so called heuristic algorithms for the easing problem in other NP complete problems which generally get very good but not guaranteed optimum solutions and run much faster than algorithms that are designed to find absolute Optima. To get some feeling for present day numbers, we can consider the famous traveling salesman problem for which extensive compilations of benchmarking data may be found online. A recent study found that the best known TSP solver required median run times across the Library of Problem instances That scaled is a very steep route exponential for end up to approximately 4500. This gives some indication of the change in runtime scaling for generic as opposed the worst case problem instances. Some of the instances considered in this study were taken from a public library of T SPS derived from real world Veil aside design data. This feels I TSP Library includes instances within ranging from 131 to 744,710 instances from this library with end between 6880 13,584 were first solved just a few years ago in 2017 requiring days of run time and a 48 core to King hurts cluster, while instances with and greater than or equal to 14,233 remain unsolved exactly by any means. Approximate solutions, however, have been found by heuristic methods for all instances in the VLS i TSP library with, for example, a solution within 0.14% of a no lower bound, having been discovered, for instance, with an equal 19,289 requiring approximately two days of run time on a single core of 2.4 gigahertz. Now, if we simple mindedly extrapolate the root exponential scaling from the study up to an equal 4500, we might expect that an exact solver would require something more like a year of run time on the 48 core cluster used for the N equals 13,580 for instance, which shows how much a very small concession on the quality of the solution makes it possible to tackle much larger instances with much lower cost. At the extreme end, the largest TSP ever solved exactly has an equal 85,900. This is an instance derived from 19 eighties VLSI design, and it's required 136 CPU. Years of computation normalized to a single cord, 2.4 gigahertz. But the 24 larger so called world TSP benchmark instance within equals 1,904,711 has been solved approximately within ophthalmology. Gap bounded below 0.474%. Coming back to the general. Practical concerns have applied optimization. We may note that a recent meta study analyzed the performance of no fewer than 37 heuristic algorithms for Max cut and quadratic pioneer optimization problems and found the performance sort and found that different heuristics work best for different problem instances selected from a large scale heterogeneous test bed with some evidence but cryptic structure in terms of what types of problem instances were best solved by any given heuristic. Indeed, their their reasons to believe that these results from Mexico and quadratic binary optimization reflected general principle of performance complementarity among heuristic optimization algorithms in the practice of solving heart optimization problems there. The cerise is a critical pre processing issue of trying to guess which of a number of available good heuristic algorithms should be chosen to tackle a given problem. Instance, assuming that any one of them would incur high costs to run on a large problem, instances incidence, making an astute choice of heuristic is a crucial part of maximizing overall performance. Unfortunately, we still have very little conceptual insight about what makes a specific problem instance, good or bad for any given heuristic optimization algorithm. This has certainly been pinpointed by researchers in the field is a circumstance that must be addressed. So adding this all up, we see that a critical frontier for cutting edge academic research involves both the development of novel heuristic algorithms that deliver better performance, with lower cost on classes of problem instances that are underserved by existing approaches, as well as fundamental research to provide deep conceptual insight into what makes a given problem in, since easy or hard for such algorithms. In fact, these days, as we talk about the end of Moore's law and speculate about a so called second quantum revolution, it's natural to talk not only about novel algorithms for conventional CPUs but also about highly customized special purpose hardware architectures on which we may run entirely unconventional algorithms for combinatorial optimization such as easing problem. So against that backdrop, I'd like to use my remaining time to introduce our work on analysis of coherent using machine architectures and associate ID optimization algorithms. These machines, in general, are a novel class of information processing architectures for solving combinatorial optimization problems by embedding them in the dynamics of analog, physical or cyber physical systems, in contrast to both MAWR traditional engineering approaches that build using machines using conventional electron ICS and more radical proposals that would require large scale quantum entanglement. The emerging paradigm of coherent easing machines leverages coherent nonlinear dynamics in photonic or Opto electronic platforms to enable near term construction of large scale prototypes that leverage post Simoes information dynamics, the general structure of of current CM systems has shown in the figure on the right. The role of the easing spins is played by a train of optical pulses circulating around a fiber optical storage ring. A beam splitter inserted in the ring is used to periodically sample the amplitude of every optical pulse, and the measurement results are continually read into a refugee A, which uses them to compute perturbations to be applied to each pulse by a synchronized optical injections. These perturbations, air engineered to implement the spin, spin coupling and local magnetic field terms of the easing Hamiltonian, corresponding to a linear part of the CME Dynamics, a synchronously pumped parametric amplifier denoted here as PPL and Wave Guide adds a crucial nonlinear component to the CIA and Dynamics as well. In the basic CM algorithm, the pump power starts very low and has gradually increased at low pump powers. The amplitude of the easing spin pulses behaviors continuous, complex variables. Who Israel parts which can be positive or negative, play the role of play the role of soft or perhaps mean field spins once the pump, our crosses the threshold for parametric self oscillation. In the optical fiber ring, however, the attitudes of the easing spin pulses become effectively Qantas ized into binary values while the pump power is being ramped up. The F P J subsystem continuously applies its measurement based feedback. Implementation of the using Hamiltonian terms, the interplay of the linear rised using dynamics implemented by the F P G A and the threshold conversation dynamics provided by the sink pumped Parametric amplifier result in the final state of the optical optical pulse amplitude at the end of the pump ramp that could be read as a binary strain, giving a proposed solution of the easing ground state problem. This method of solving easing problem seems quite different from a conventional algorithm that runs entirely on a digital computer as a crucial aspect of the computation is performed physically by the analog, continuous, coherent, nonlinear dynamics of the optical degrees of freedom. In our efforts to analyze CIA and performance, we have therefore turned to the tools of dynamical systems theory, namely, a study of modifications, the evolution of critical points and apologies of hetero clinic orbits and basins of attraction. We conjecture that such analysis can provide fundamental insight into what makes certain optimization instances hard or easy for coherent using machines and hope that our approach can lead to both improvements of the course, the AM algorithm and a pre processing rubric for rapidly assessing the CME suitability of new instances. Okay, to provide a bit of intuition about how this all works, it may help to consider the threshold dynamics of just one or two optical parametric oscillators in the CME architecture just described. We can think of each of the pulse time slots circulating around the fiber ring, as are presenting an independent Opio. We can think of a single Opio degree of freedom as a single, resonant optical node that experiences linear dissipation, do toe out coupling loss and gain in a pump. Nonlinear crystal has shown in the diagram on the upper left of this slide as the pump power is increased from zero. As in the CME algorithm, the non linear game is initially to low toe overcome linear dissipation, and the Opio field remains in a near vacuum state at a critical threshold. Value gain. Equal participation in the Popeo undergoes a sort of lazing transition, and the study states of the OPIO above this threshold are essentially coherent states. There are actually two possible values of the Opio career in amplitude and any given above threshold pump power which are equal in magnitude but opposite in phase when the OPI across the special diet basically chooses one of the two possible phases randomly, resulting in the generation of a single bit of information. If we consider to uncoupled, Opio has shown in the upper right diagram pumped it exactly the same power at all times. Then, as the pump power has increased through threshold, each Opio will independently choose the phase and thus to random bits are generated for any number of uncoupled. Oppose the threshold power per opio is unchanged from the single Opio case. Now, however, consider a scenario in which the two appeals air, coupled to each other by a mutual injection of their out coupled fields has shown in the diagram on the lower right. One can imagine that depending on the sign of the coupling parameter Alfa, when one Opio is lazing, it will inject a perturbation into the other that may interfere either constructively or destructively, with the feel that it is trying to generate by its own lazing process. As a result, when came easily showed that for Alfa positive, there's an effective ferro magnetic coupling between the two Opio fields and their collective oscillation threshold is lowered from that of the independent Opio case. But on Lee for the two collective oscillation modes in which the two Opio phases are the same for Alfa Negative, the collective oscillation threshold is lowered on Lee for the configurations in which the Opio phases air opposite. So then, looking at how Alfa is related to the J. I. J matrix of the easing spin coupling Hamiltonian, it follows that we could use this simplistic to a p o. C. I am to solve the ground state problem of a fair magnetic or anti ferro magnetic ankles to easing model simply by increasing the pump power from zero and observing what phase relation occurs as the two appeals first start delays. Clearly, we can imagine generalizing this story toe larger, and however the story doesn't stay is clean and simple for all larger problem instances. And to find a more complicated example, we only need to go to n equals four for some choices of J J for n equals, for the story remains simple. Like the n equals two case. The figure on the upper left of this slide shows the energy of various critical points for a non frustrated and equals, for instance, in which the first bifurcated critical point that is the one that I forget to the lowest pump value a. Uh, this first bifurcated critical point flows as symptomatically into the lowest energy easing solution and the figure on the upper right. However, the first bifurcated critical point flows to a very good but sub optimal minimum at large pump power. The global minimum is actually given by a distinct critical critical point that first appears at a higher pump power and is not automatically connected to the origin. The basic C am algorithm is thus not able to find this global minimum. Such non ideal behaviors needs to become more confident. Larger end for the n equals 20 instance, showing the lower plots where the lower right plot is just a zoom into a region of the lower left lot. It can be seen that the global minimum corresponds to a critical point that first appears out of pump parameter, a around 0.16 at some distance from the idiomatic trajectory of the origin. That's curious to note that in both of these small and examples, however, the critical point corresponding to the global minimum appears relatively close to the idiomatic projector of the origin as compared to the most of the other local minima that appear. We're currently working to characterize the face portrait topology between the global minimum in the antibiotic trajectory of the origin, taking clues as to how the basic C am algorithm could be generalized to search for non idiomatic trajectories that jump to the global minimum during the pump ramp. Of course, n equals 20 is still too small to be of interest for practical optimization applications. But the advantage of beginning with the study of small instances is that we're able reliably to determine their global minima and to see how they relate to the 80 about trajectory of the origin in the basic C am algorithm. In the smaller and limit, we can also analyze fully quantum mechanical models of Syrian dynamics. But that's a topic for future talks. Um, existing large scale prototypes are pushing into the range of in equals 10 to the 4 10 to 5 to six. So our ultimate objective in theoretical analysis really has to be to try to say something about CIA and dynamics and regime of much larger in our initial approach to characterizing CIA and behavior in the large in regime relies on the use of random matrix theory, and this connects to prior research on spin classes, SK models and the tap equations etcetera. At present, we're focusing on statistical characterization of the CIA ingredient descent landscape, including the evolution of critical points in their Eigen value spectra. As the pump power is gradually increased. We're investigating, for example, whether there could be some way to exploit differences in the relative stability of the global minimum versus other local minima. We're also working to understand the deleterious or potentially beneficial effects of non ideologies, such as a symmetry in the implemented these and couplings. Looking one step ahead, we plan to move next in the direction of considering more realistic classes of problem instances such as quadratic, binary optimization with constraints. Eso In closing, I should acknowledge people who did the hard work on these things that I've shown eso. My group, including graduate students Ed winning, Daniel Wennberg, Tatsuya Nagamoto and Atsushi Yamamura, have been working in close collaboration with Syria Ganguly, Marty Fair and Amir Safarini Nini, all of us within the Department of Applied Physics at Stanford University. On also in collaboration with the Oshima Moto over at NTT 55 research labs, Onda should acknowledge funding support from the NSF by the Coherent Easing Machines Expedition in computing, also from NTT five research labs, Army Research Office and Exxon Mobil. Uh, that's it. Thanks very much. >>Mhm e >>t research and the Oshie for putting together this program and also the opportunity to speak here. My name is Al Gore ism or Andy and I'm from Caltech, and today I'm going to tell you about the work that we have been doing on networks off optical parametric oscillators and how we have been using them for icing machines and how we're pushing them toward Cornum photonics to acknowledge my team at Caltech, which is now eight graduate students and five researcher and postdocs as well as collaborators from all over the world, including entity research and also the funding from different places, including entity. So this talk is primarily about networks of resonate er's, and these networks are everywhere from nature. For instance, the brain, which is a network of oscillators all the way to optics and photonics and some of the biggest examples or metal materials, which is an array of small resonate er's. And we're recently the field of technological photonics, which is trying thio implement a lot of the technological behaviors of models in the condensed matter, physics in photonics and if you want to extend it even further, some of the implementations off quantum computing are technically networks of quantum oscillators. So we started thinking about these things in the context of icing machines, which is based on the icing problem, which is based on the icing model, which is the simple summation over the spins and spins can be their upward down and the couplings is given by the JJ. And the icing problem is, if you know J I J. What is the spin configuration that gives you the ground state? And this problem is shown to be an MP high problem. So it's computational e important because it's a representative of the MP problems on NPR. Problems are important because first, their heart and standard computers if you use a brute force algorithm and they're everywhere on the application side. That's why there is this demand for making a machine that can target these problems, and hopefully it can provide some meaningful computational benefit compared to the standard digital computers. So I've been building these icing machines based on this building block, which is a degenerate optical parametric. Oscillator on what it is is resonator with non linearity in it, and we pump these resonate er's and we generate the signal at half the frequency of the pump. One vote on a pump splits into two identical photons of signal, and they have some very interesting phase of frequency locking behaviors. And if you look at the phase locking behavior, you realize that you can actually have two possible phase states as the escalation result of these Opio which are off by pie, and that's one of the important characteristics of them. So I want to emphasize a little more on that and I have this mechanical analogy which are basically two simple pendulum. But there are parametric oscillators because I'm going to modulate the parameter of them in this video, which is the length of the string on by that modulation, which is that will make a pump. I'm gonna make a muscular. That'll make a signal which is half the frequency of the pump. And I have two of them to show you that they can acquire these face states so they're still facing frequency lock to the pump. But it can also lead in either the zero pie face states on. The idea is to use this binary phase to represent the binary icing spin. So each opio is going to represent spin, which can be either is your pie or up or down. And to implement the network of these resonate er's, we use the time off blood scheme, and the idea is that we put impulses in the cavity. These pulses air separated by the repetition period that you put in or t r. And you can think about these pulses in one resonator, xaz and temporarily separated synthetic resonate Er's if you want a couple of these resonator is to each other, and now you can introduce these delays, each of which is a multiple of TR. If you look at the shortest delay it couples resonator wanted to 2 to 3 and so on. If you look at the second delay, which is two times a rotation period, the couple's 123 and so on. And if you have and minus one delay lines, then you can have any potential couplings among these synthetic resonate er's. And if I can introduce these modulators in those delay lines so that I can strength, I can control the strength and the phase of these couplings at the right time. Then I can have a program will all toe all connected network in this time off like scheme, and the whole physical size of the system scales linearly with the number of pulses. So the idea of opium based icing machine is didn't having these o pos, each of them can be either zero pie and I can arbitrarily connect them to each other. And then I start with programming this machine to a given icing problem by just setting the couplings and setting the controllers in each of those delight lines. So now I have a network which represents an icing problem. Then the icing problem maps to finding the face state that satisfy maximum number of coupling constraints. And the way it happens is that the icing Hamiltonian maps to the linear loss of the network. And if I start adding gain by just putting pump into the network, then the OPI ohs are expected to oscillate in the lowest, lowest lost state. And, uh and we have been doing these in the past, uh, six or seven years and I'm just going to quickly show you the transition, especially what happened in the first implementation, which was using a free space optical system and then the guided wave implementation in 2016 and the measurement feedback idea which led to increasing the size and doing actual computation with these machines. So I just want to make this distinction here that, um, the first implementation was an all optical interaction. We also had an unequal 16 implementation. And then we transition to this measurement feedback idea, which I'll tell you quickly what it iss on. There's still a lot of ongoing work, especially on the entity side, to make larger machines using the measurement feedback. But I'm gonna mostly focused on the all optical networks and how we're using all optical networks to go beyond simulation of icing Hamiltonian both in the linear and non linear side and also how we're working on miniaturization of these Opio networks. So the first experiment, which was the four opium machine, it was a free space implementation and this is the actual picture off the machine and we implemented a small and it calls for Mexico problem on the machine. So one problem for one experiment and we ran the machine 1000 times, we looked at the state and we always saw it oscillate in one of these, um, ground states of the icing laboratoria. So then the measurement feedback idea was to replace those couplings and the controller with the simulator. So we basically simulated all those coherent interactions on on FB g. A. And we replicated the coherent pulse with respect to all those measurements. And then we injected it back into the cavity and on the near to you still remain. So it still is a non. They're dynamical system, but the linear side is all simulated. So there are lots of questions about if this system is preserving important information or not, or if it's gonna behave better. Computational wars. And that's still ah, lot of ongoing studies. But nevertheless, the reason that this implementation was very interesting is that you don't need the end minus one delight lines so you can just use one. Then you can implement a large machine, and then you can run several thousands of problems in the machine, and then you can compare the performance from the computational perspective Looks so I'm gonna split this idea of opium based icing machine into two parts. One is the linear part, which is if you take out the non linearity out of the resonator and just think about the connections. You can think about this as a simple matrix multiplication scheme. And that's basically what gives you the icing Hambletonian modeling. So the optical laws of this network corresponds to the icing Hamiltonian. And if I just want to show you the example of the n equals for experiment on all those face states and the history Graham that we saw, you can actually calculate the laws of each of those states because all those interferences in the beam splitters and the delay lines are going to give you a different losses. And then you will see that the ground states corresponds to the lowest laws of the actual optical network. If you add the non linearity, the simple way of thinking about what the non linearity does is that it provides to gain, and then you start bringing up the gain so that it hits the loss. Then you go through the game saturation or the threshold which is going to give you this phase bifurcation. So you go either to zero the pie face state. And the expectation is that Theis, the network oscillates in the lowest possible state, the lowest possible loss state. There are some challenges associated with this intensity Durban face transition, which I'm going to briefly talk about. I'm also going to tell you about other types of non aerodynamics that we're looking at on the non air side of these networks. So if you just think about the linear network, we're actually interested in looking at some technological behaviors in these networks. And the difference between looking at the technological behaviors and the icing uh, machine is that now, First of all, we're looking at the type of Hamilton Ian's that are a little different than the icing Hamilton. And one of the biggest difference is is that most of these technological Hamilton Ian's that require breaking the time reversal symmetry, meaning that you go from one spin to in the one side to another side and you get one phase. And if you go back where you get a different phase, and the other thing is that we're not just interested in finding the ground state, we're actually now interesting and looking at all sorts of states and looking at the dynamics and the behaviors of all these states in the network. So we started with the simplest implementation, of course, which is a one d chain of thes resonate, er's, which corresponds to a so called ssh model. In the technological work, we get the similar energy to los mapping and now we can actually look at the band structure on. This is an actual measurement that we get with this associate model and you see how it reasonably how How? Well, it actually follows the prediction and the theory. One of the interesting things about the time multiplexing implementation is that now you have the flexibility of changing the network as you are running the machine. And that's something unique about this time multiplex implementation so that we can actually look at the dynamics. And one example that we have looked at is we can actually go through the transition off going from top A logical to the to the standard nontrivial. I'm sorry to the trivial behavior of the network. You can then look at the edge states and you can also see the trivial and states and the technological at states actually showing up in this network. We have just recently implement on a two D, uh, network with Harper Hofstadter model and when you don't have the results here. But we're one of the other important characteristic of time multiplexing is that you can go to higher and higher dimensions and keeping that flexibility and dynamics, and we can also think about adding non linearity both in a classical and quantum regimes, which is going to give us a lot of exotic, no classical and quantum, non innate behaviors in these networks. Yeah, So I told you about the linear side. Mostly let me just switch gears and talk about the nonlinear side of the network. And the biggest thing that I talked about so far in the icing machine is this face transition that threshold. So the low threshold we have squeezed state in these. Oh, pios, if you increase the pump, we go through this intensity driven phase transition and then we got the face stays above threshold. And this is basically the mechanism off the computation in these O pos, which is through this phase transition below to above threshold. So one of the characteristics of this phase transition is that below threshold, you expect to see quantum states above threshold. You expect to see more classical states or coherent states, and that's basically corresponding to the intensity off the driving pump. So it's really hard to imagine that it can go above threshold. Or you can have this friends transition happen in the all in the quantum regime. And there are also some challenges associated with the intensity homogeneity off the network, which, for example, is if one opioid starts oscillating and then its intensity goes really high. Then it's going to ruin this collective decision making off the network because of the intensity driven face transition nature. So So the question is, can we look at other phase transitions? Can we utilize them for both computing? And also can we bring them to the quantum regime on? I'm going to specifically talk about the face transition in the spectral domain, which is the transition from the so called degenerate regime, which is what I mostly talked about to the non degenerate regime, which happens by just tuning the phase of the cavity. And what is interesting is that this phase transition corresponds to a distinct phase noise behavior. So in the degenerate regime, which we call it the order state, you're gonna have the phase being locked to the phase of the pump. As I talked about non degenerate regime. However, the phase is the phase is mostly dominated by the quantum diffusion. Off the off the phase, which is limited by the so called shallow towns limit, and you can see that transition from the general to non degenerate, which also has distinct symmetry differences. And this transition corresponds to a symmetry breaking in the non degenerate case. The signal can acquire any of those phases on the circle, so it has a you one symmetry. Okay, and if you go to the degenerate case, then that symmetry is broken and you only have zero pie face days I will look at. So now the question is can utilize this phase transition, which is a face driven phase transition, and can we use it for similar computational scheme? So that's one of the questions that were also thinking about. And it's not just this face transition is not just important for computing. It's also interesting from the sensing potentials and this face transition, you can easily bring it below threshold and just operated in the quantum regime. Either Gaussian or non Gaussian. If you make a network of Opio is now, we can see all sorts off more complicated and more interesting phase transitions in the spectral domain. One of them is the first order phase transition, which you get by just coupling to Opio, and that's a very abrupt face transition and compared to the to the single Opio phase transition. And if you do the couplings right, you can actually get a lot of non her mission dynamics and exceptional points, which are actually very interesting to explore both in the classical and quantum regime. And I should also mention that you can think about the cup links to be also nonlinear couplings. And that's another behavior that you can see, especially in the nonlinear in the non degenerate regime. So with that, I basically told you about these Opio networks, how we can think about the linear scheme and the linear behaviors and how we can think about the rich, nonlinear dynamics and non linear behaviors both in the classical and quantum regime. I want to switch gear and tell you a little bit about the miniaturization of these Opio networks. And of course, the motivation is if you look at the electron ICS and what we had 60 or 70 years ago with vacuum tube and how we transition from relatively small scale computers in the order of thousands of nonlinear elements to billions of non elements where we are now with the optics is probably very similar to 70 years ago, which is a table talk implementation. And the question is, how can we utilize nano photonics? I'm gonna just briefly show you the two directions on that which we're working on. One is based on lithium Diabate, and the other is based on even a smaller resonate er's could you? So the work on Nana Photonic lithium naive. It was started in collaboration with Harvard Marko Loncar, and also might affair at Stanford. And, uh, we could show that you can do the periodic polling in the phenomenon of it and get all sorts of very highly nonlinear processes happening in this net. Photonic periodically polls if, um Diabate. And now we're working on building. Opio was based on that kind of photonic the film Diabate. And these air some some examples of the devices that we have been building in the past few months, which I'm not gonna tell you more about. But the O. P. O. S. And the Opio Networks are in the works. And that's not the only way of making large networks. Um, but also I want to point out that The reason that these Nana photonic goblins are actually exciting is not just because you can make a large networks and it can make him compact in a in a small footprint. They also provide some opportunities in terms of the operation regime. On one of them is about making cat states and Opio, which is, can we have the quantum superposition of the zero pie states that I talked about and the Net a photonic within? I've It provides some opportunities to actually get closer to that regime because of the spatial temporal confinement that you can get in these wave guides. So we're doing some theory on that. We're confident that the type of non linearity two losses that it can get with these platforms are actually much higher than what you can get with other platform their existing platforms and to go even smaller. We have been asking the question off. What is the smallest possible Opio that you can make? Then you can think about really wavelength scale type, resonate er's and adding the chi to non linearity and see how and when you can get the Opio to operate. And recently, in collaboration with us see, we have been actually USC and Creole. We have demonstrated that you can use nano lasers and get some spin Hamilton and implementations on those networks. So if you can build the a P. O s, we know that there is a path for implementing Opio Networks on on such a nano scale. So we have looked at these calculations and we try to estimate the threshold of a pos. Let's say for me resonator and it turns out that it can actually be even lower than the type of bulk Pip Llano Pos that we have been building in the past 50 years or so. So we're working on the experiments and we're hoping that we can actually make even larger and larger scale Opio networks. So let me summarize the talk I told you about the opium networks and our work that has been going on on icing machines and the measurement feedback. And I told you about the ongoing work on the all optical implementations both on the linear side and also on the nonlinear behaviors. And I also told you a little bit about the efforts on miniaturization and going to the to the Nano scale. So with that, I would like Thio >>three from the University of Tokyo. Before I thought that would like to thank you showing all the stuff of entity for the invitation and the organization of this online meeting and also would like to say that it has been very exciting to see the growth of this new film lab. And I'm happy to share with you today of some of the recent works that have been done either by me or by character of Hong Kong. Honest Group indicates the title of my talk is a neuro more fic in silica simulator for the communities in machine. And here is the outline I would like to make the case that the simulation in digital Tektronix of the CME can be useful for the better understanding or improving its function principles by new job introducing some ideas from neural networks. This is what I will discuss in the first part and then it will show some proof of concept of the game and performance that can be obtained using dissimulation in the second part and the protection of the performance that can be achieved using a very large chaos simulator in the third part and finally talk about future plans. So first, let me start by comparing recently proposed izing machines using this table there is elected from recent natural tronics paper from the village Park hard people, and this comparison shows that there's always a trade off between energy efficiency, speed and scalability that depends on the physical implementation. So in red, here are the limitation of each of the servers hardware on, interestingly, the F p G, a based systems such as a producer, digital, another uh Toshiba beautification machine or a recently proposed restricted Bozeman machine, FPD A by a group in Berkeley. They offer a good compromise between speed and scalability. And this is why, despite the unique advantage that some of these older hardware have trust as the currency proposition in Fox, CBS or the energy efficiency off memory Sisters uh P. J. O are still an attractive platform for building large organizing machines in the near future. The reason for the good performance of Refugee A is not so much that they operate at the high frequency. No, there are particular in use, efficient, but rather that the physical wiring off its elements can be reconfigured in a way that limits the funding human bottleneck, larger, funny and phenols and the long propagation video information within the system. In this respect, the LPGA is They are interesting from the perspective off the physics off complex systems, but then the physics of the actions on the photos. So to put the performance of these various hardware and perspective, we can look at the competition of bringing the brain the brain complete, using billions of neurons using only 20 watts of power and operates. It's a very theoretically slow, if we can see and so this impressive characteristic, they motivate us to try to investigate. What kind of new inspired principles be useful for designing better izing machines? The idea of this research project in the future collaboration it's to temporary alleviates the limitations that are intrinsic to the realization of an optical cortex in machine shown in the top panel here. By designing a large care simulator in silicone in the bottom here that can be used for digesting the better organization principles of the CIA and this talk, I will talk about three neuro inspired principles that are the symmetry of connections, neural dynamics orphan chaotic because of symmetry, is interconnectivity the infrastructure? No. Next talks are not composed of the reputation of always the same types of non environments of the neurons, but there is a local structure that is repeated. So here's the schematic of the micro column in the cortex. And lastly, the Iraqi co organization of connectivity connectivity is organizing a tree structure in the brain. So here you see a representation of the Iraqi and organization of the monkey cerebral cortex. So how can these principles we used to improve the performance of the icing machines? And it's in sequence stimulation. So, first about the two of principles of the estimate Trian Rico structure. We know that the classical approximation of the car testing machine, which is the ground toe, the rate based on your networks. So in the case of the icing machines, uh, the okay, Scott approximation can be obtained using the trump active in your position, for example, so the times of both of the system they are, they can be described by the following ordinary differential equations on in which, in case of see, I am the X, I represent the in phase component of one GOP Oh, Theo f represents the monitor optical parts, the district optical Parametric amplification and some of the good I JoJo extra represent the coupling, which is done in the case of the measure of feedback coupling cm using oh, more than detection and refugee A and then injection off the cooking time and eso this dynamics in both cases of CNN in your networks, they can be written as the grand set of a potential function V, and this written here, and this potential functionally includes the rising Maccagnan. So this is why it's natural to use this type of, uh, dynamics to solve the icing problem in which the Omega I J or the eyes in coping and the H is the extension of the icing and attorney in India and expect so. Not that this potential function can only be defined if the Omega I j. R. A. Symmetric. So the well known problem of this approach is that this potential function V that we obtain is very non convicts at low temperature, and also one strategy is to gradually deformed this landscape, using so many in process. But there is no theorem. Unfortunately, that granted conventions to the global minimum of There's even Tony and using this approach. And so this is why we propose, uh, to introduce a macro structures of the system where one analog spin or one D O. P. O is replaced by a pair off one another spin and one error, according viable. And the addition of this chemical structure introduces a symmetry in the system, which in terms induces chaotic dynamics, a chaotic search rather than a learning process for searching for the ground state of the icing. Every 20 within this massacre structure the role of the er variable eyes to control the amplitude off the analog spins toe force. The amplitude of the expense toe become equal to certain target amplitude a uh and, uh, and this is done by modulating the strength off the icing complaints or see the the error variable E I multiply the icing complaint here in the dynamics off air d o p. O. On then the dynamics. The whole dynamics described by this coupled equations because the e I do not necessarily take away the same value for the different. I thesis introduces a symmetry in the system, which in turn creates security dynamics, which I'm sure here for solving certain current size off, um, escape problem, Uh, in which the X I are shown here and the i r from here and the value of the icing energy showing the bottom plots. You see this Celtics search that visit various local minima of the as Newtonian and eventually finds the global minimum? Um, it can be shown that this modulation off the target opportunity can be used to destabilize all the local minima off the icing evertonians so that we're gonna do not get stuck in any of them. On more over the other types of attractors I can eventually appear, such as limits I contractors, Okot contractors. They can also be destabilized using the motivation of the target and Batuta. And so we have proposed in the past two different moderation of the target amateur. The first one is a modulation that ensure the uh 100 reproduction rate of the system to become positive on this forbids the creation off any nontrivial tractors. And but in this work, I will talk about another moderation or arrested moderation which is given here. That works, uh, as well as this first uh, moderation, but is easy to be implemented on refugee. So this couple of the question that represent becoming the stimulation of the cortex in machine with some error correction they can be implemented especially efficiently on an F B. G. And here I show the time that it takes to simulate three system and also in red. You see, at the time that it takes to simulate the X I term the EI term, the dot product and the rising Hamiltonian for a system with 500 spins and Iraq Spain's equivalent to 500 g. O. P. S. So >>in >>f b d a. The nonlinear dynamics which, according to the digital optical Parametric amplification that the Opa off the CME can be computed in only 13 clock cycles at 300 yards. So which corresponds to about 0.1 microseconds. And this is Toby, uh, compared to what can be achieved in the measurements back O C. M. In which, if we want to get 500 timer chip Xia Pios with the one she got repetition rate through the obstacle nine narrative. Uh, then way would require 0.5 microseconds toe do this so the submission in F B J can be at least as fast as ah one g repression. Uh, replicate pulsed laser CIA Um, then the DOT product that appears in this differential equation can be completed in 43 clock cycles. That's to say, one microseconds at 15 years. So I pieced for pouring sizes that are larger than 500 speeds. The dot product becomes clearly the bottleneck, and this can be seen by looking at the the skating off the time the numbers of clock cycles a text to compute either the non in your optical parts or the dog products, respect to the problem size. And And if we had infinite amount of resources and PGA to simulate the dynamics, then the non illogical post can could be done in the old one. On the mattress Vector product could be done in the low carrot off, located off scales as a look at it off and and while the guide off end. Because computing the dot product involves assuming all the terms in the product, which is done by a nephew, GE by another tree, which heights scarce logarithmic any with the size of the system. But This is in the case if we had an infinite amount of resources on the LPGA food, but for dealing for larger problems off more than 100 spins. Usually we need to decompose the metrics into ah, smaller blocks with the block side that are not you here. And then the scaling becomes funny, non inner parts linear in the end, over you and for the products in the end of EU square eso typically for low NF pdf cheap PGA you the block size off this matrix is typically about 100. So clearly way want to make you as large as possible in order to maintain this scanning in a log event for the numbers of clock cycles needed to compute the product rather than this and square that occurs if we decompose the metrics into smaller blocks. But the difficulty in, uh, having this larger blocks eyes that having another tree very large Haider tree introduces a large finding and finance and long distance start a path within the refugee. So the solution to get higher performance for a simulator of the contest in machine eyes to get rid of this bottleneck for the dot product by increasing the size of this at the tree. And this can be done by organizing your critique the electrical components within the LPGA in order which is shown here in this, uh, right panel here in order to minimize the finding finance of the system and to minimize the long distance that a path in the in the fpt So I'm not going to the details of how this is implemented LPGA. But just to give you a idea off why the Iraqi Yahiko organization off the system becomes the extremely important toe get good performance for similar organizing machine. So instead of instead of getting into the details of the mpg implementation, I would like to give some few benchmark results off this simulator, uh, off the that that was used as a proof of concept for this idea which is can be found in this archive paper here and here. I should results for solving escape problems. Free connected person, randomly person minus one spring last problems and we sure, as we use as a metric the numbers of the mattress Victor products since it's the bottleneck of the computation, uh, to get the optimal solution of this escape problem with the Nina successful BT against the problem size here and and in red here, this propose FDJ implementation and in ah blue is the numbers of retrospective product that are necessary for the C. I am without error correction to solve this escape programs and in green here for noisy means in an evening which is, uh, behavior with similar to the Cartesian mission. Uh, and so clearly you see that the scaring off the numbers of matrix vector product necessary to solve this problem scales with a better exponents than this other approaches. So So So that's interesting feature of the system and next we can see what is the real time to solution to solve this SK instances eso in the last six years, the time institution in seconds to find a grand state of risk. Instances remain answers probability for different state of the art hardware. So in red is the F B g. A presentation proposing this paper and then the other curve represent Ah, brick a local search in in orange and silver lining in purple, for example. And so you see that the scaring off this purpose simulator is is rather good, and that for larger plant sizes we can get orders of magnitude faster than the state of the art approaches. Moreover, the relatively good scanning off the time to search in respect to problem size uh, they indicate that the FPD implementation would be faster than risk. Other recently proposed izing machine, such as the hope you know, natural complimented on memories distance that is very fast for small problem size in blue here, which is very fast for small problem size. But which scanning is not good on the same thing for the restricted Bosman machine. Implementing a PGA proposed by some group in Broken Recently Again, which is very fast for small parliament sizes but which canning is bad so that a dis worse than the proposed approach so that we can expect that for programs size is larger than 1000 spins. The proposed, of course, would be the faster one. Let me jump toe this other slide and another confirmation that the scheme scales well that you can find the maximum cut values off benchmark sets. The G sets better candidates that have been previously found by any other algorithms, so they are the best known could values to best of our knowledge. And, um or so which is shown in this paper table here in particular, the instances, uh, 14 and 15 of this G set can be We can find better converse than previously known, and we can find this can vary is 100 times faster than the state of the art algorithm and CP to do this which is a very common Kasich. It s not that getting this a good result on the G sets, they do not require ah, particular hard tuning of the parameters. So the tuning issuing here is very simple. It it just depends on the degree off connectivity within each graph. And so this good results on the set indicate that the proposed approach would be a good not only at solving escape problems in this problems, but all the types off graph sizing problems on Mexican province in communities. So given that the performance off the design depends on the height of this other tree, we can try to maximize the height of this other tree on a large F p g a onda and carefully routing the components within the P G A and and we can draw some projections of what type of performance we can achieve in the near future based on the, uh, implementation that we are currently working. So here you see projection for the time to solution way, then next property for solving this escape programs respect to the prime assize. And here, compared to different with such publicizing machines, particularly the digital. And, you know, 42 is shown in the green here, the green line without that's and, uh and we should two different, uh, hypothesis for this productions either that the time to solution scales as exponential off n or that the time of social skills as expression of square root off. So it seems, according to the data, that time solution scares more as an expression of square root of and also we can be sure on this and this production show that we probably can solve prime escape problem of science 2000 spins, uh, to find the rial ground state of this problem with 99 success ability in about 10 seconds, which is much faster than all the other proposed approaches. So one of the future plans for this current is in machine simulator. So the first thing is that we would like to make dissimulation closer to the rial, uh, GOP oh, optical system in particular for a first step to get closer to the system of a measurement back. See, I am. And to do this what is, uh, simulate Herbal on the p a is this quantum, uh, condoms Goshen model that is proposed described in this paper and proposed by people in the in the Entity group. And so the idea of this model is that instead of having the very simple or these and have shown previously, it includes paired all these that take into account on me the mean off the awesome leverage off the, uh, European face component, but also their violence s so that we can take into account more quantum effects off the g o p. O, such as the squeezing. And then we plan toe, make the simulator open access for the members to run their instances on the system. There will be a first version in September that will be just based on the simple common line access for the simulator and in which will have just a classic or approximation of the system. We don't know Sturm, binary weights and museum in term, but then will propose a second version that would extend the current arising machine to Iraq off F p g. A, in which we will add the more refined models truncated, ignoring the bottom Goshen model they just talked about on the support in which he valued waits for the rising problems and support the cement. So we will announce later when this is available and and far right is working >>hard comes from Universal down today in physics department, and I'd like to thank the organizers for their kind invitation to participate in this very interesting and promising workshop. Also like to say that I look forward to collaborations with with a file lab and Yoshi and collaborators on the topics of this world. So today I'll briefly talk about our attempt to understand the fundamental limits off another continues time computing, at least from the point off you off bullion satisfy ability, problem solving, using ordinary differential equations. But I think the issues that we raise, um, during this occasion actually apply to other other approaches on a log approaches as well and into other problems as well. I think everyone here knows what Dorien satisfy ability. Problems are, um, you have boolean variables. You have em clauses. Each of disjunction of collaterals literally is a variable, or it's, uh, negation. And the goal is to find an assignment to the variable, such that order clauses are true. This is a decision type problem from the MP class, which means you can checking polynomial time for satisfy ability off any assignment. And the three set is empty, complete with K three a larger, which means an efficient trees. That's over, uh, implies an efficient source for all the problems in the empty class, because all the problems in the empty class can be reduced in Polian on real time to reset. As a matter of fact, you can reduce the NP complete problems into each other. You can go from three set to set backing or two maximum dependent set, which is a set packing in graph theoretic notions or terms toe the icing graphs. A problem decision version. This is useful, and you're comparing different approaches, working on different kinds of problems when not all the closest can be satisfied. You're looking at the accusation version offset, uh called Max Set. And the goal here is to find assignment that satisfies the maximum number of clauses. And this is from the NPR class. In terms of applications. If we had inefficient sets over or np complete problems over, it was literally, positively influenced. Thousands off problems and applications in industry and and science. I'm not going to read this, but this this, of course, gives a strong motivation toe work on this kind of problems. Now our approach to set solving involves embedding the problem in a continuous space, and you use all the east to do that. So instead of working zeros and ones, we work with minus one across once, and we allow the corresponding variables toe change continuously between the two bounds. We formulate the problem with the help of a close metrics. If if a if a close, uh, does not contain a variable or its negation. The corresponding matrix element is zero. If it contains the variable in positive, for which one contains the variable in a gated for Mitt's negative one, and then we use this to formulate this products caused quote, close violation functions one for every clause, Uh, which really, continuously between zero and one. And they're zero if and only if the clause itself is true. Uh, then we form the define in order to define a dynamic such dynamics in this and dimensional hyper cube where the search happens and if they exist, solutions. They're sitting in some of the corners of this hyper cube. So we define this, uh, energy potential or landscape function shown here in a way that this is zero if and only if all the clauses all the kmc zero or the clauses off satisfied keeping these auxiliary variables a EMS always positive. And therefore, what you do here is a dynamics that is a essentially ingredient descend on this potential energy landscape. If you were to keep all the M's constant that it would get stuck in some local minimum. However, what we do here is we couple it with the dynamics we cooperated the clothes violation functions as shown here. And if he didn't have this am here just just the chaos. For example, you have essentially what case you have positive feedback. You have increasing variable. Uh, but in that case, you still get stuck would still behave will still find. So she is better than the constant version but still would get stuck only when you put here this a m which makes the dynamics in in this variable exponential like uh, only then it keeps searching until he finds a solution on deer is a reason for that. I'm not going toe talk about here, but essentially boils down toe performing a Grady and descend on a globally time barren landscape. And this is what works. Now I'm gonna talk about good or bad and maybe the ugly. Uh, this is, uh, this is What's good is that it's a hyperbolic dynamical system, which means that if you take any domain in the search space that doesn't have a solution in it or any socially than the number of trajectories in it decays exponentially quickly. And the decay rate is a characteristic in variant characteristic off the dynamics itself. Dynamical systems called the escape right the inverse off that is the time scale in which you find solutions by this by this dynamical system, and you can see here some song trajectories that are Kelty because it's it's no linear, but it's transient, chaotic. Give their sources, of course, because eventually knowledge to the solution. Now, in terms of performance here, what you show for a bunch off, um, constraint densities defined by M overran the ratio between closes toe variables for random, said Problems is random. Chris had problems, and they as its function off n And we look at money toward the wartime, the wall clock time and it behaves quite value behaves Azat party nominally until you actually he to reach the set on set transition where the hardest problems are found. But what's more interesting is if you monitor the continuous time t the performance in terms off the A narrow, continuous Time t because that seems to be a polynomial. And the way we show that is, we consider, uh, random case that random three set for a fixed constraint density Onda. We hear what you show here. Is that the right of the trash hold that it's really hard and, uh, the money through the fraction of problems that we have not been able to solve it. We select thousands of problems at that constraint ratio and resolve them without algorithm, and we monitor the fractional problems that have not yet been solved by continuous 90. And this, as you see these decays exponentially different. Educate rates for different system sizes, and in this spot shows that is dedicated behaves polynomial, or actually as a power law. So if you combine these two, you find that the time needed to solve all problems except maybe appear traction off them scales foreign or merely with the problem size. So you have paranormal, continuous time complexity. And this is also true for other types of very hard constraints and sexual problems such as exact cover, because you can always transform them into three set as we discussed before, Ramsey coloring and and on these problems, even algorithms like survey propagation will will fail. But this doesn't mean that P equals NP because what you have first of all, if you were toe implement these equations in a device whose behavior is described by these, uh, the keys. Then, of course, T the continue style variable becomes a physical work off. Time on that will be polynomial is scaling, but you have another other variables. Oxidative variables, which structured in an exponential manner. So if they represent currents or voltages in your realization and it would be an exponential cost Al Qaeda. But this is some kind of trade between time and energy, while I know how toe generate energy or I don't know how to generate time. But I know how to generate energy so it could use for it. But there's other issues as well, especially if you're trying toe do this son and digital machine but also happens. Problems happen appear. Other problems appear on in physical devices as well as we discuss later. So if you implement this in GPU, you can. Then you can get in order off to magnitude. Speed up. And you can also modify this to solve Max sad problems. Uh, quite efficiently. You are competitive with the best heuristic solvers. This is a weather problems. In 2016 Max set competition eso so this this is this is definitely this seems like a good approach, but there's off course interesting limitations, I would say interesting, because it kind of makes you think about what it means and how you can exploit this thes observations in understanding better on a low continues time complexity. If you monitored the discrete number the number of discrete steps. Don't buy the room, Dakota integrator. When you solve this on a digital machine, you're using some kind of integrator. Um and you're using the same approach. But now you measure the number off problems you haven't sold by given number of this kid, uh, steps taken by the integrator. You find out you have exponential, discrete time, complexity and, of course, thistles. A problem. And if you look closely, what happens even though the analog mathematical trajectory, that's the record here. If you monitor what happens in discrete time, uh, the integrator frustrates very little. So this is like, you know, third or for the disposition, but fluctuates like crazy. So it really is like the intervention frees us out. And this is because of the phenomenon of stiffness that are I'll talk a little bit a more about little bit layer eso. >>You know, it might look >>like an integration issue on digital machines that you could improve and could definitely improve. But actually issues bigger than that. It's It's deeper than that, because on a digital machine there is no time energy conversion. So the outside variables are efficiently representing a digital machine. So there's no exponential fluctuating current of wattage in your computer when you do this. Eso If it is not equal NP then the exponential time, complexity or exponential costs complexity has to hit you somewhere. And this is how um, but, you know, one would be tempted to think maybe this wouldn't be an issue in a analog device, and to some extent is true on our devices can be ordered to maintain faster, but they also suffer from their own problems because he not gonna be affect. That classes soldiers as well. So, indeed, if you look at other systems like Mirandizing machine measurement feedback, probably talk on the grass or selected networks. They're all hinge on some kind off our ability to control your variables in arbitrary, high precision and a certain networks you want toe read out across frequencies in case off CM's. You required identical and program because which is hard to keep, and they kind of fluctuate away from one another, shift away from one another. And if you control that, of course that you can control the performance. So actually one can ask if whether or not this is a universal bottleneck and it seems so aside, I will argue next. Um, we can recall a fundamental result by by showing harder in reaction Target from 1978. Who says that it's a purely computer science proof that if you are able toe, compute the addition multiplication division off riel variables with infinite precision, then you could solve any complete problems in polynomial time. It doesn't actually proposals all where he just chose mathematically that this would be the case. Now, of course, in Real warned, you have also precision. So the next question is, how does that affect the competition about problems? This is what you're after. Lots of precision means information also, or entropy production. Eso what you're really looking at the relationship between hardness and cost of computing off a problem. Uh, and according to Sean Hagar, there's this left branch which in principle could be polynomial time. But the question whether or not this is achievable that is not achievable, but something more cheerful. That's on the right hand side. There's always going to be some information loss, so mental degeneration that could keep you away from possibly from point normal time. So this is what we like to understand, and this information laws the source off. This is not just always I will argue, uh, in any physical system, but it's also off algorithm nature, so that is a questionable area or approach. But China gets results. Security theoretical. No, actual solar is proposed. So we can ask, you know, just theoretically get out off. Curiosity would in principle be such soldiers because it is not proposing a soldier with such properties. In principle, if if you want to look mathematically precisely what the solar does would have the right properties on, I argue. Yes, I don't have a mathematical proof, but I have some arguments that that would be the case. And this is the case for actually our city there solver that if you could calculate its trajectory in a loss this way, then it would be, uh, would solve epic complete problems in polynomial continuous time. Now, as a matter of fact, this a bit more difficult question, because time in all these can be re scared however you want. So what? Burns says that you actually have to measure the length of the trajectory, which is a new variant off the dynamical system or property dynamical system, not off its parameters ization. And we did that. So Suba Corral, my student did that first, improving on the stiffness off the problem off the integrations, using implicit solvers and some smart tricks such that you actually are closer to the actual trajectory and using the same approach. You know what fraction off problems you can solve? We did not give the length of the trajectory. You find that it is putting on nearly scaling the problem sites we have putting on your skin complexity. That means that our solar is both Polly length and, as it is, defined it also poorly time analog solver. But if you look at as a discreet algorithm, if you measure the discrete steps on a digital machine, it is an exponential solver. And the reason is because off all these stiffness, every integrator has tow truck it digitizing truncate the equations, and what it has to do is to keep the integration between the so called stability region for for that scheme, and you have to keep this product within a grimace of Jacoby in and the step size read in this region. If you use explicit methods. You want to stay within this region? Uh, but what happens that some off the Eigen values grow fast for Steve problems, and then you're you're forced to reduce that t so the product stays in this bonded domain, which means that now you have to you're forced to take smaller and smaller times, So you're you're freezing out the integration and what I will show you. That's the case. Now you can move to increase its soldiers, which is which is a tree. In this case, you have to make domain is actually on the outside. But what happens in this case is some of the Eigen values of the Jacobean, also, for six systems, start to move to zero. As they're moving to zero, they're going to enter this instability region, so your soul is going to try to keep it out, so it's going to increase the data T. But if you increase that to increase the truncation hours, so you get randomized, uh, in the large search space, so it's it's really not, uh, not going to work out. Now, one can sort off introduce a theory or language to discuss computational and are computational complexity, using the language from dynamical systems theory. But basically I I don't have time to go into this, but you have for heart problems. Security object the chaotic satellite Ouch! In the middle of the search space somewhere, and that dictates how the dynamics happens and variant properties off the dynamics. Of course, off that saddle is what the targets performance and many things, so a new, important measure that we find that it's also helpful in describing thesis. Another complexity is the so called called Makarov, or metric entropy and basically what this does in an intuitive A eyes, uh, to describe the rate at which the uncertainty containing the insignificant digits off a trajectory in the back, the flow towards the significant ones as you lose information because off arrows being, uh grown or are developed in tow. Larger errors in an exponential at an exponential rate because you have positively up north spawning. But this is an in variant property. It's the property of the set of all. This is not how you compute them, and it's really the interesting create off accuracy philosopher dynamical system. A zay said that you have in such a high dimensional that I'm consistent were positive and negatively upon of exponents. Aziz Many The total is the dimension of space and user dimension, the number off unstable manifold dimensions and as Saddam was stable, manifold direction. And there's an interesting and I think, important passion, equality, equality called the passion, equality that connect the information theoretic aspect the rate off information loss with the geometric rate of which trajectory separate minus kappa, which is the escape rate that I already talked about. Now one can actually prove a simple theorems like back off the envelope calculation. The idea here is that you know the rate at which the largest rated, which closely started trajectory separate from one another. So now you can say that, uh, that is fine, as long as my trajectory finds the solution before the projective separate too quickly. In that case, I can have the hope that if I start from some region off the face base, several close early started trajectories, they kind of go into the same solution orphaned and and that's that's That's this upper bound of this limit, and it is really showing that it has to be. It's an exponentially small number. What? It depends on the end dependence off the exponents right here, which combines information loss rate and the social time performance. So these, if this exponents here or that has a large independence or river linear independence, then you then you really have to start, uh, trajectories exponentially closer to one another in orderto end up in the same order. So this is sort off like the direction that you're going in tow, and this formulation is applicable toe all dynamical systems, uh, deterministic dynamical systems. And I think we can We can expand this further because, uh, there is, ah, way off getting the expression for the escaped rate in terms off n the number of variables from cycle expansions that I don't have time to talk about. What? It's kind of like a program that you can try toe pursuit, and this is it. So the conclusions I think of self explanatory I think there is a lot of future in in, uh, in an allo. Continue start computing. Um, they can be efficient by orders of magnitude and digital ones in solving empty heart problems because, first of all, many of the systems you like the phone line and bottleneck. There's parallelism involved, and and you can also have a large spectrum or continues time, time dynamical algorithms than discrete ones. And you know. But we also have to be mindful off. What are the possibility of what are the limits? And 11 open question is very important. Open question is, you know, what are these limits? Is there some kind off no go theory? And that tells you that you can never perform better than this limit or that limit? And I think that's that's the exciting part toe to derive thes thes this levian 10.

>>Hi everyone, This system A fellow from the University of Tokyo before I thought that would like to thank you she and all the stuff of entity for the invitation and the organization of this online meeting and also would like to say that it has been very exciting to see the growth of this new film lab. And I'm happy to share with you today or some of the recent works that have been done either by me or by character of Hong Kong Noise Group indicating the title of my talk is a neuro more fic in silica simulator for the commenters in machine. And here is the outline I would like to make the case that the simulation in digital Tektronix of the CME can be useful for the better understanding or improving its function principles by new job introducing some ideas from neural networks. This is what I will discuss in the first part and then I will show some proof of concept of the game in performance that can be obtained using dissimulation in the second part and the production of the performance that can be achieved using a very large chaos simulator in the third part and finally talk about future plans. So first, let me start by comparing recently proposed izing machines using this table there is adapted from a recent natural tronics paper from the Village Back hard People. And this comparison shows that there's always a trade off between energy efficiency, speed and scalability that depends on the physical implementation. So in red, here are the limitation of each of the servers hardware on, Interestingly, the F p G, a based systems such as a producer, digital, another uh Toshiba purification machine, or a recently proposed restricted Bozeman machine, FPD eight, by a group in Berkeley. They offer a good compromise between speed and scalability. And this is why, despite the unique advantage that some of these older hardware have trust as the currency proposition influx you beat or the energy efficiency off memory sisters uh P. J. O are still an attractive platform for building large theorizing machines in the near future. The reason for the good performance of Refugee A is not so much that they operate at the high frequency. No, there are particle in use, efficient, but rather that the physical wiring off its elements can be reconfigured in a way that limits the funding human bottleneck, larger, funny and phenols and the long propagation video information within the system in this respect, the f. D. A s. They are interesting from the perspective, off the physics off complex systems, but then the physics of the actions on the photos. So to put the performance of these various hardware and perspective, we can look at the competition of bringing the brain the brain complete, using billions of neurons using only 20 watts of power and operates. It's a very theoretically slow, if we can see. And so this impressive characteristic, they motivate us to try to investigate. What kind of new inspired principles be useful for designing better izing machines? The idea of this research project in the future collaboration it's to temporary alleviates the limitations that are intrinsic to the realization of an optical cortex in machine shown in the top panel here. By designing a large care simulator in silicone in the bottom here that can be used for suggesting the better organization principles of the CIA and this talk, I will talk about three neuro inspired principles that are the symmetry of connections, neural dynamics. Orphan, chaotic because of symmetry, is interconnectivity. The infrastructure. No neck talks are not composed of the reputation of always the same types of non environments of the neurons, but there is a local structure that is repeated. So here's a schematic of the micro column in the cortex. And lastly, the Iraqi co organization of connectivity connectivity is organizing a tree structure in the brain. So here you see a representation of the Iraqi and organization of the monkey cerebral cortex. So how can these principles we used to improve the performance of the icing machines? And it's in sequence stimulation. So, first about the two of principles of the estimate Trian Rico structure. We know that the classical approximation of the Cortes in machine, which is a growing toe the rate based on your networks. So in the case of the icing machines, uh, the okay, Scott approximation can be obtained using the trump active in your position, for example, so the times of both of the system they are, they can be described by the following ordinary differential equations on in which, in case of see, I am the X, I represent the in phase component of one GOP Oh, Theo F represents the monitor optical parts, the district optical parametric amplification and some of the good I JoJo extra represent the coupling, which is done in the case of the measure of feedback cooking cm using oh, more than detection and refugee A then injection off the cooking time and eso this dynamics in both cases of CME in your networks, they can be written as the grand set of a potential function V, and this written here, and this potential functionally includes the rising Maccagnan. So this is why it's natural to use this type of, uh, dynamics to solve the icing problem in which the Omega I J or the Eyes in coping and the H is the extension of the rising and attorney in India and expect so. >>Not that this potential function can only be defined if the Omega I j. R. A. Symmetric. So the well known problem of >>this approach is that this potential function V that we obtain is very non convicts at low temperature, and also one strategy is to gradually deformed this landscape, using so many in process. But there is no theorem. Unfortunately, that granted convergence to the global minimum of there's even 20 and using this approach. And so this is >>why we propose toe introduce a macro structure the system or where one analog spin or one D o. P. O is replaced by a pair off one and knock spin and one error on cutting. Viable. And the addition of this chemical structure introduces a symmetry in the system, which in terms induces chaotic dynamics, a chaotic search rather than a >>learning process for searching for the ground state of the icing. Every 20 >>within this massacre structure the role of the ER variable eyes to control the amplitude off the analog spins to force the amplitude of the expense toe, become equal to certain target amplitude. A Andi. This is known by moderating the strength off the icing complaints or see the the error variable e I multiply the icing complain here in the dynamics off UH, D o p o on Then the dynamics. The whole dynamics described by this coupled equations because the e I do not necessarily take away the same value for the different, I think introduces a >>symmetry in the system, which in turn creates chaotic dynamics, which I'm showing here for solving certain current size off, um, escape problem, Uh, in which the exiled from here in the i r. From here and the value of the icing energy is shown in the bottom plots. And you see this Celtics search that visit various local minima of the as Newtonian and eventually finds the local minima Um, >>it can be shown that this modulation off the target opportunity can be used to destabilize all the local minima off the icing hamiltonian so that we're gonna do not get stuck in any of them. On more over the other types of attractors, I can eventually appear, such as the limits of contractors or quality contractors. They can also be destabilized using a moderation of the target amplitude. And so we have proposed in the past two different motivation of the target constitute the first one is a moderation that ensure the 100 >>reproduction rate of the system to become positive on this forbids the creation of any non tree retractors. And but in this work I will talk about another modulation or Uresti moderation, which is given here that works, uh, as well as this first, uh, moderation, but is easy to be implemented on refugee. >>So this couple of the question that represent the current the stimulation of the cortex in machine with some error correction, they can be implemented especially efficiently on an F B G. And here I show the time that it takes to simulate three system and eso in red. You see, at the time that it takes to simulate the X, I term the EI term, the dot product and the rising everything. Yet for a system with 500 spins analog Spain's equivalent to 500 g. O. P. S. So in f b d a. The nonlinear dynamics which, according to the digital optical Parametric amplification that the Opa off the CME can be computed in only 13 clock cycles at 300 yards. So which corresponds to about 0.1 microseconds. And this is Toby, uh, compared to what can be achieved in the measurements tobacco cm in which, if we want to get 500 timer chip Xia Pios with the one she got repetition rate through the obstacle nine narrative. Uh, then way would require 0.5 microseconds toe do this so the submission in F B J can be at least as fast as, ah one gear repression to replicate the post phaser CIA. Um, then the DOT product that appears in this differential equation can be completed in 43 clock cycles. That's to say, one microseconds at 15 years. So I pieced for pouring sizes that are larger than 500 speeds. The dot product becomes clearly the bottleneck, and this can be seen by looking at the the skating off the time the numbers of clock cycles a text to compute either the non in your optical parts, all the dog products, respect to the problem size. And and if we had a new infinite amount of resources and PGA to simulate the dynamics, then the non in optical post can could be done in the old one. On the mattress Vector product could be done in the low carrot off, located off scales as a low carrot off end and while the kite off end. Because computing the dot product involves the summing, all the terms in the products, which is done by a nephew, Jay by another tree, which heights scares a logarithmic any with the size of the system. But this is in the case if we had an infinite amount of resources on the LPGA food but for dealing for larger problems off more than 100 spins, usually we need to decompose the metrics into ah smaller blocks with the block side that are not you here. And then the scaling becomes funny non inner parts linear in the and over you and for the products in the end of you square eso typically for low NF pdf cheap P a. You know you the block size off this matrix is typically about 100. So clearly way want to make you as large as possible in order to maintain this scanning in a log event for the numbers of clock cycles needed to compute the product rather than this and square that occurs if we decompose the metrics into smaller blocks. But the difficulty in, uh, having this larger blocks eyes that having another tree very large Haider tree introduces a large finding and finance and long distance started path within the refugee. So the solution to get higher performance for a simulator of the contest in machine eyes to get rid of this bottleneck for the dot product. By increasing the size of this at the tree and this can be done by organizing Yeah, click the extra co components within the F p G A in order which is shown here in this right panel here in order to minimize the finding finance of the system and to minimize the long distance that the path in the in the fpt So I'm not going to the details of how this is implemented the PGA. But just to give you a new idea off why the Iraqi Yahiko organization off the system becomes extremely important toe get good performance for simulator organizing mission. So instead of instead of getting into the details of the mpg implementation, I would like to give some few benchmark results off this simulator, uh, off the that that was used as a proof of concept for this idea which is can be found in this archive paper here and here. I should result for solving escape problems, free connected person, randomly person minus one, spin last problems and we sure, as we use as a metric the numbers >>of the mattress Victor products since it's the bottleneck of the computation, uh, to get the optimal solution of this escape problem with Nina successful BT against the problem size here and and in red here there's propose F B J implementation and in ah blue is the numbers of retrospective product that are necessary for the C. I am without error correction to solve this escape programs and in green here for noisy means in an evening which is, uh, behavior. It's similar to the car testing machine >>and security. You see that the scaling off the numbers of metrics victor product necessary to solve this problem scales with a better exponents than this other approaches. So so So that's interesting feature of the system and next we can see what is the real time to solution. To solve this, SK instances eso in the last six years, the time institution in seconds >>to find a grand state of risk. Instances remain answers is possibility for different state of the art hardware. So in red is the F B G. A presentation proposing this paper and then the other curve represent ah, brick, a local search in in orange and center dining in purple, for example, and So you see that the scaring off this purpose simulator is is rather good and that for larger politicizes, we can get orders of magnitude faster than the state of the other approaches. >>Moreover, the relatively good scanning off the time to search in respect to problem size uh, they indicate that the FBT implementation would be faster than risk Other recently proposed izing machine, such as the Hope you know network implemented on Memory Sisters. That is very fast for small problem size in blue here, which is very fast for small problem size. But which scanning is not good on the same thing for the >>restricted Bosman machine implemented a PGA proposed by some group in Brooklyn recently again, which is very fast for small promise sizes. But which canning is bad So that, uh, this worse than the purpose approach so that we can expect that for promise sizes larger than, let's say, 1000 spins. The purpose, of course, would be the faster one. >>Let me jump toe this other slide and another confirmation that the scheme scales well that you can find the maximum cut values off benchmark sets. The G sets better cut values that have been previously found by any other >>algorithms. So they are the best known could values to best of our knowledge. And, um, or so which is shown in this paper table here in particular, the instances, Uh, 14 and 15 of this G set can be We can find better converse than previously >>known, and we can find this can vary is 100 times >>faster than the state of the art algorithm and cp to do this which is a recount. Kasich, it s not that getting this a good result on the G sets, they do not require ah, particular hard tuning of the parameters. So the tuning issuing here is very simple. It it just depends on the degree off connectivity within each graph. And so this good results on the set indicate that the proposed approach would be a good not only at solving escape problems in this problems, but all the types off graph sizing problems on Mexican province in communities. >>So given that the performance off the design depends on the height of this other tree, we can try to maximize the height of this other tree on a large F p g A onda and carefully routing the trickle components within the P G A. And and we can draw some projections of what type of performance we can achieve in >>the near future based on the, uh, implementation that we are currently working. So here you see projection for the time to solution way, then next property for solving this escape problems respect to the prime assize. And here, compared to different with such publicizing machines, particularly the digital and, you know, free to is shown in the green here, the green >>line without that's and, uh and we should two different, uh, prosthesis for this productions either that the time to solution scales as exponential off n or that >>the time of social skills as expression of square root off. So it seems according to the data, that time solution scares more as an expression of square root of and also we can be sure >>on this and this production showed that we probably can solve Prime Escape Program of Science 2000 spins to find the rial ground state of this problem with 99 success ability in about 10 seconds, which is much faster than all the other proposed approaches. So one of the future plans for this current is in machine simulator. So the first thing is that we would like to make dissimulation closer to the rial, uh, GOP or optical system in particular for a first step to get closer to the system of a measurement back. See, I am. And to do this, what is, uh, simulate Herbal on the p a is this quantum, uh, condoms Goshen model that is proposed described in this paper and proposed by people in the in the Entity group. And so the idea of this model is that instead of having the very simple or these and have shown previously, it includes paired all these that take into account out on me the mean off the awesome leverage off the, uh, European face component, but also their violence s so that we can take into account more quantum effects off the g o p. O, such as the squeezing. And then we plan toe, make the simulator open access for the members to run their instances on the system. There will be a first version in September that will >>be just based on the simple common line access for the simulator and in which will have just a classical approximation of the system. We don't know Sturm, binary weights and Museum in >>term, but then will propose a second version that would extend the current arising machine to Iraq off eight f p g. A. In which we will add the more refined models truncated bigger in the bottom question model that just talked about on the supports in which he valued waits for the rising problems and support the cement. So we will announce >>later when this is available, and Farah is working hard to get the first version available sometime in September. Thank you all, and we'll be happy to answer any questions that you have.