>> Narrator: Live from New York, it's The Cube. Covering AWS Global Summit 2019. Brought to you by Amazon Web Services. >> Welcome back, I'm Stu Miniman and with my co-host Corey Quinn and we're here at AWS New York City Summit. Always happy when we have users on the program to tell their story, and joining us for the first time, Ahmad Haider who's the Lead Enterprise Data Science Architecter at AGCO, an agricultural company based down in Georgia. Ahmed thanks so much for joining us. >> Thank you for having me. >> All right so, agriculture obviously y'know we understand in general, y'know the joke I have for most people is well luckily, your industry isn't going through much change (laughter) and of course yeah, that's the response we get in most but y'know give us the thumbnail, AGCO, how long's the company been around? The focus and y'know right, some of those changes that you're seeing in the industry. >> Sure, so let me start just about AGCO, so AGCO is about a 9.4 million dollar agricultural equipment manufacturer, it's been around for 20 plus years and we are well known in the industry so some of our famous brands like Valtra, Fendt, Massey. Coming back to your other question, we are not going through a lot of change, I get that very often and you know what, it was an eyeopener when I joined AGCO. So the farming industry is actually going through a lot of change, you must have heard of Agrotech and so the farmers now, they want better efficient solutions that will help them manage their farms while they focus on the core work of farming and they are looking at companies which manufacture agricultural equipment to help provide that digital support, help provide solutions that help manage a farm better, help them to provide the maintenance better, help them optimize the equipment and so on and that's where we are trying to help them out. >> Yep, so it's always easy to look at any industry and they're like oh they have it easy and it's not changing that much. You've got data science in your title, talk a little bit about your role inside the company, y'know we know how important data is to most companies but of course with a data scientist, it's your job to help unlock that power. >> Yeah, definitely. Let me give you a little bit of background and that will help frame this much better so AGCO realized the part of data a while ago but very recently they started working on this so something called a digital experience, digital customer experience program. What that does is basically it creates you a set of connected solutions that manage the data of our customers, our dealers, our part and machine data in a fast, reliable and secure manner and all these digital solutions that we are creating, they are powered through analytics to leverage new market insights, to unlock new opportunities, to help understand our customers better. So given that particular space, I help design the AGCO's data science vision, that involves, first of all, setting up a data science platform that enables us to maximize the user data that we have. Secondly, working with our business to identify analytics use-cases which could be a part of the product roadmap and build them out and then execute this on the data science platform and thirdly, from the point of view of architecture, understanding what things go in the design, making sure everything's state of the art, help the design document and making sure that we are staying right at the top in terms of agriculture, in terms of data science and pushing at the boundaries in all their products. >> What are the, I guess, hidden secrets of data science across the board as the sheer amount of time and effort that has to be put into data normalization before you can start getting useful information out of it, was that a significant concern given what you do? Or given the fact that you more or less control the entire thing and you can reformulate the data as it's ingested? >> That was a very valid concern, I mean what most people don't talk about is the quality of data. They only talk about the data science, the fancy things, so we had the same challenges. Our data was distributed in different places, had different formats, had different levels of cleanliness so what I did was, during the building of the data science platform, I recognized this challenge proactively and made sure that we do cleanse the data, we normalize it to a format that's usable for our use-cases but we don't do it all at once, we go use-case by use-case, we identify our business priorities, we normalize the data, we cleanse it, we normalize it, bring it to a format that can be used going forward and we do it with every use-case. Over time, majority of it will be normalized but that will take an incremental, gradual of course. >> All right, Ahmad bring us into the role of cloud in your environment. >> Sure, so cloud is a very important component, so historically, we were more like an on premises organization and when we went on cloud data, it was a very important change, more so from the point of view, if you think about it, for a company to migrate or position itself, transform itself into a software organization in terms of data science, you need a lot of accelerators, you need data scientists, you need infrastructure, you need data engineers and you need people to manage all of this and all that hiring talent takes time but what cloud does is, there's the ability to procure services on demand and something which is fully managed, all services, that allows you to overcome a lot of those barriers quickly while you have time to actually build other solutions on top of the cloud. Over time when we understand our processes better, our demands better, then we can think about, okay where does it make sense to go hybrid but cloud is that great accelerator that allowed us to set up this data analytics platform which we did in roughly about fifteen weeks. Before that I was working in another organization where we did this on premises and I can tell you it took at least like three times if not more, so that I mean, I think that's the real value of cloud apart from all it's machine learning services and everything. It helped us to accelerate that process easily. How, I guess, in the workflow that you'd wind up going through how close is the data that you're generating to the cloud? Are you doing this at the edge, are you doing this in the field in some cases? I guess where is the data entering your pipeline? >> Yeah, so there are different forms of data that we have, we have a lot of data that is customer-related data that essentially is more or less slow-moving data that we have in the organization. That constitutes the major bulk of the data, apart from that, we have data that are coming from machines which are these smart machines operating in the field and data comes through the satellite and comes to our servers. We also have data that comes from the edge from some of these machinery that are operating in the factory and from there you will get data on the edge. Among all these different data sources that we have, I would say the predominant, or the initial focus, the pillar focus is to first start with the data that we have in abundance, so that's essentially the customer data, our dealer data to be able to understand that better, derive new market insights but our focus is to go forward, getting data from these machines combining that with the soil data with the farming data, with the agronomy data to deliver these very precise, things like precise planting schedules, things like predictive maintenance of machines as they operate out in the field and things like value driven care. So those are things that we are hoping to do with this as well. >> Right, you mentioned machine learning, y'know where are you along your journey kind of with the MLAI and the like? >> That's a really good question, so AGCO as a whole, I think we are at different stages at different parts of the organization so a lot of the organization is focused on generating value through descriptive analytics and explorative analytics whereby we are exploring the data and we are finding these insights and then making decisions on top of them. We are going into the area of predictive analytics fairly recently, about a year so and we essentially, that is our next step so we went into predictive analytics, we are creating machine learning models, we are creating combined stat models. We are using services like SageMaker on the cloud, we are using Spark libraries, we are using Cyclone, we are using Arc, all of that to create predictive analytics solutions. So in terms of the technology that we use right now, it's actually pretty much state of the art, we have created our own model management engines. We are using what Amazon provides and we supplement them with what we have. So we are pretty much at state of the art in terms of current what we are doing. We're hoping to take that state of the art and apply it to large parts of the organization. >> So as you look at, I guess some of the higher level differentiated services coming down in the world of machine learning, do you find that a lot of what you're doing today and in a few years is going to be something that's being handled automatically and then you're able to focus on the more interesting parts of the work? Or is there really no end in sight for I guess sort of some of the current block and tackle that a lot of data scientists are sort of struggling with today? >> I'm sorry I couldn't hear a part of your voice >> No, my apologies. Just a you see things continuing to evolve in this space, are you finding, are you predicting that there's going to be more I guess higher level services that solve some of this problem for you or is a lot of it I guess, block and tackle, not really having a relief point in sight? >> That's a very good question, I get that very often. So, I would like to say the answer, it depends but I'll describe that answer. So there are some parts of this machine learning AI that I think will be solved by newer services, by technology going forward. You can take an example, I'll give you a concrete example, SageMaker, which is fairly recent offering by Amazon about a year ago that we started using SageMaker, it didn't have a lot of competence that it currently has and we had to build a lot of the competence to get towards something called model management. Now, we built all of that but lo and behold after we went, they actually added a lot of these. So over technology, they will take care of a lot of these things which you currently do by smart automation. Now smart automation can take care of a lot of things, it helps you identify when you need to retrain a model, it helps you to deploy a model, it helps you to identify the trigger points but what analytics, I mean, where I think the challenge will come is how to actually apply it to the business because that needs a lot of context and for that you need to understand where are these perfect pinpoints, where do you actually apply it? Does it make sense to use it in a prioritization model? Does it make sense to use it as a explorative model? Does it make sense to use an attribution model? And to help define that use-case in the beginning to essentially say going from a business landscape to come to a specific problem that you want to solve, that is a part that I think will take some time and can't be readily addressed by these technologies but everything down the line, I fairly see that in a few years all of that will be available. >> All right, Ahmad are you speaking here at the conference? >> No, I actually spoke at the keynote in Atlanta. >> Okay >> And the summit >> Great, give us a little about y'know what you get out of coming to some of the regional summits here from Amazon. >> Yeah definitely, so I get a lot out of it. So, the biggest thing is I get to know what are the different things that are happening in the industry from the point of business, so not just about technologies right. Like lots of different technologies coming on but how are people using it? How does it make an impact in their business? Because for me the intersection of technology and business is the key point. So coming to a lot of these regional summits where they have these different business partners, they come in and they describe their work and connecting with them. That, for me, is the main draw, apart from that there's the other piece which is you get to know about the different things that are being done in this space. For example, if you go to AWS summit, you get to know everything that is coming to the cloud and you can try and experiment that and you can basically create like a nice ecosystem. If you go to an Azure summit, you get something similar. So that state of the art is also important but more important is the draw, that intersection. >> And I guess just one followup on that is y'know the data scientist community is y'know, what are some of your best sources of y'know learning and sharing today? >> That's a very good question, data science is one of those aspects because two parts to it. I don't know, I mean now there are machine learning engineers too, so but one part is the technical part of this, to be able to create these models with pinpoint accuracy and the second is applications. So in terms of the first part of learning about creating these models, the best sources in that case would be self-learning, I have, I went through, when I was doing this, I did my PhD, I learned a lot of stuff and then I go through a lot of articles when new things come out, you go through them, once you have the different sources, there are lots of them. The second part, right, applications, I have found the best source of learning there is actually interacting with people who use these technologies. Interacting with people, let's say who have no experience of data science, they have experience of business and then working with them to understand how can you take this insight that's created out of a model and impart into business, for that there's no other substitute than just talking to people, understanding the pinpoints and then solving those. >> All right, well Ahmad thank you so much for giving the update on AGCO and your role inside. >> Thank you >> All right, for Corey Quinn, I'm Stu Miniman, we'll be back with more coverage here from AWS' New York City Summit. Thanks as always for watching the cube. (upbeat electronic music)

>> Live, from Las Vegas, it's theCUBE, covering AWS re:Invent 2018, brought to you by Amazon Web Services, Intel, and their ecosystem partners. >> Welcome back to AWS re:Invent, along with Justin Warren, I'm John Walls, we are live here in Las Vegas. Day two of our three days of coverage of this event, seventh time we've been here and, as we've been saying all along, this show is getting bigger and better than ever. About 40,000 attendees this year. Joined now by Abbas Haider Ali, CTO of xMatters, and Chris Crocco, who is the lead solutions architect at Viasat. Gentlemen, thanks for being with us, good to see you. >> Thanks for having me. >> Thanks for having us on. >> All right, tell us a little bit about your respective endeavors and then why the two of you are here together, and Abbas I'll let you lead off. >> Sure, I'm CTO at xMatters, as you described, and our company is basically a digital service availability platform which, outside the marketing speak, and from a technical perspective, means, when bad things happen with technology, and all technology's great but, inevitably, things go wrong-- >> Bad things happen. >> Bad things happen and we're in the business to helping companies get those things fixed as quickly as possible, ideally before they become business-impacting. And basically, I asked Chris here to join me because you can have technology but you need someone to put it into practice and Chris has done a great job of bringing it in to real world at Viasat. >> Good transition, thanks Abbas. My role at Viasat, Viasat's a satellite-based technology and communications company, and my role is to help administer and deploy some of our automations for orchestration monitoring performance and incident management. A lot of that has to do, as it relates to xMatters, with notifying people when they eventually have to go hands-on-keyboard and minimizing the amount of administrative burden that they have so they can just focus on fixing a problem. >> You mentioned before that everyone who was traveling here on an airplane, if they were using the wifi, they're probably running over your service? >> Right, yeah, so one of our-- >> I am astounded that that even works at all, speaking of technology breaking all the time. Maybe explain to us a little bit about how xMatters helps you keep that thing actually functioning. >> Yeah, that's a great question. One of the things that we monitor very, very tightly is our customer experience, both on aircraft, and residential broadband, and so when we're starting to see things where those planes are passing through beams and maybe not handing off the internet connectivity well, if we're seeing people trying to get on the internet and they're either having a slow time or just not getting on at all, one of the things that we want to do is get that to the right people quickly. So, one of the things that we do is we have our customer care elements of commercial mobility in xMatters so that they can report that to the engineering level for that same area of business. When they do that it's opening up a sales force case, it's notifying a Hipchat room, it's getting hold of the on-call resource, and it's also administrating all of that stuff back to the originator of the problem, so that they can keep them informed of "this is what the engineer found, "this is how long it's going to take to get fixed, "this is what you need to tell the customers." So it's enabling a lot of communication while reducing some of the traditional operational elements that go along with incident management. >> Yeah, it's something that we've been hearing quite a bit this week here at AWS, is the importance of that operations side of things. It feels like the whole industry has moved from this being a new technology that we should start doing brand new things with, and it's matured a little bit, where we're actually relying on this stuff to run real multi-billion dollar businesses and operations starts to become really, really important so, as you said, when things break, we want to fix them as fast as possible, so that customers can keep using our services. >> Right, and kind of in the path, when you look at all the companies that are here, they're building fantastic new products, builders are a big part of this event, it's all about building their services and you hear a lot about automation and tool change and the CI/CD pipeline. Well, the CI/CD pipeline really ends at delivery. And that's kind of where our product picks up. So it's in the operations and support realm of it is, once it's out there, things inevitably will go wrong and a lot of the companies you see here are all about detecting that very, very quickly. You'll hear conversations about one-second resolution in detect issues, and those things have to be handled. And really, one of the things that we're seeing a big trend in is going through and saying, "How do we remove the manual process, "and administrative overhead, and the toil "in actually operating these services, "when, inevitably, something goes wrong." And it starts off small and can grow very quickly, so a lot of people use our product, to essentially tie those alerting systems directly into xMatters, it goes out, gathers a lot of the information that people would typically do by hand, the manual effort, delivers it to the right on-call person and arms them with the action and move them through. And really, that cycle of steps, if you think of it as every individual team and service has a series of flows that they go through when things go wrong. It's about taking those steps and putting them all together in the right order and swapping them out as you need to as your service matures and grows. And as your innovation is successful and as you grow in scope, those steps may change, but the flows across the teams remain remarkably-- >> Is there-- >> The same. >> You talk about flows, different avenues, different opportunities, or problems, is there one that tends to stand out amongst the crowd as "That's our biggest headache," whether, for Chris's business, or just, in general, for any of your clients, is there one that leaves you scratching your head? >> If we go around and just interview all the various enterprises, who are consumers and builders of a service and we ask them, saying, "Hey, what's the single biggest thing that's kind of a pain when things go wrong?" One of the biggest problems that we see is that a lot of these organizations have built kind of a distributed operation model. And one of the biggest problems we see is, if you think of it as, you've got a whole series of things, a series of, kind of spokes, and one thing goes wrong, other people are consumers of it, and other people are impacted. All get engaged, saying my thing is also sending me a signal saying "My work has gone sideways," but it's very difficult to figure out where the actual responsibility lies and how do you engage just the people who could actually fix the issue and then let everyone else who is impacted by it be informed, but told to stand down, so they don't waste their cycles on resolving that. And that's a very complicated problem that there is no magical solution for so if anyone's listening and looking for "Okay, "that's what I've got, give me an answer," I don't have a solution for you (laughing) but I can tell you that a lot of these sorts of operational tasks we're putting in place are designed to minimize the effort of figuring out what that is and really speeding up that information cycle so you waste as little time as possible. >> Does that sound familiar, Chris? >> Very familiar, yeah. Viasat's company motto is "Always a better way" and so one of the things we do with xMatters and other tools in our incident response chain is take what we learn when we do have an incident, when we do have a problem, and find a better way of approaching that. It allows us to refine our integrations into xMatters. It allows us to communicate more effectively to the right people. It allows us to really kind of harness our DevOps model and that company credo to our advantage and constantly perform better for our customers. >> We were talking before we went live here, this is dealing with issues at the scale of space, so these sort of problems, and it's a theme that we've been hearing over the last couple of days, that the amount of complexity on these kinds of systems, and something at the scale of a space-based platform. This is something which isn't really tractable for the human mind to deal with unaided, so we really do need tools like xMatters to actually cope with this. But what has putting in something like xMatters done for the business of Viasat? What does that actually change, that you're now able to do that you weren't able to do before? >> Again, xMatters enables a lot of opportunity for our DevOps teams to constantly improve. One of the things that I personally like about xMatters a lot is it's not a centralized tool. A lot of tools in this space are intended for you to be constantly looking at a dashboard or have an incident captain that's always, their life is that tool. >> A single glass of pane. >> Right, but all of these teams have their own single pane of glass that they consume, so we can plug in xMatters where it's appropriate and allow those tool chains and those automation flows to include xMatters but not have it be the end all, be all of their process, so it helps them improve on all of the other parts of incident management and monitoring and xMatters is just there to facilitate those transactions and those workflows. So, a lot of value there, a lot of learning opportunities and a lot of enablement for all of our DevOps teams. >> So you can improve the way that you're doing things without having to rip out everything else and replace it with one new tool. >> Exactly, one of the things that you don't want to do in any organization is throw the baby out with the bathwater, so to speak. There are tools that can be refined and we see a lot of this in the trend toward micro-services, right? Instead of having vendor lock-in, this huge one-stop shop for everything, you can pull and replace all of the smaller pieces in that chain without affecting your availability or your ability to respond to an event. >> And one really interesting thing about these distributed models is you still have places where information needs to wind up, so if I'm working on a particular part of my application and I've got a customer service team that uses Salesforce as their system of choice, I have to get information to Salesforce so they can consume it. It's not okay for me to hoard information, I actually want to make sure that I'm minimizing the friction and moving information along to where it needs to wind up, along that process. If I am a developer, my kind of world view of my tasks are Jira, I want to make sure the information winds up there. If I'm in a service management team and I use something like ServiceNow, kind of track information there, I have to make information wind up there. We collaborate in Slack, I have to make sure that it's available within that world as well. So the key thing that we're really focused about is every team picks their own flows, they pick their own tools, but the steps along the way are very similar. Something goes wrong, you pull in the information, you need help, you need a collaboration step, and you need a basic information delivery stage to put information back in the right places because after it's done, to Chris's point, if you just solved the problem very effectively and learned nothing, you've done a bad job. We have to be clear about that, right? Learning and improvement is a key part of a successful DevOps transition, and when you're running things at the scale we're talking about at re:Invent, you have to learn. And a key part is making sure information winds up in the right places so you're able to do that. >> Getting them halfway happy won't cut it, right? >> Right, I would fully expect that Chris and other customers in Viasat's position would be like, "Yeah, that's great, we did it great this time, "but when it happens again, we would have learned nothing." >> What do we do next? >> Right, exactly. >> Right. >> Gentlemen, thank you for the time. We appreciate you sharing your story and wish you success. >> Thanks very much for having us on. >> For the rest of this week, enjoy the show. >> Thank you very much. >> Off to a great start, that's for sure. >> Thank you. >> Back with more from AWS re:Invent, with Justin Warren, I'm John Walls, and you're watching theCUBE. (upbeat 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.