So, good afternoon, and thank you for the introduction and for the invitation. It's a very interesting workshop for me. Let me say that my talk is going to be slightly orthogonal to the previous Giuseppe, who talked about very interesting topics, but this is going to be more numerics. I hope you won't be too scared by the numerics, but I'm going to do my best in order to present it in also more theoretical way if you want. So, today I would like to discuss some recent applications we have been doing and also other people I've been doing in this field. And the idea is to use machine learning techniques, and in particular neural networks based techniques, to study quantum systems. So, what I would like today is, first of all, to give you a short introduction or rather a short introduction to the basic idea that we have and we are using in machine learning. So, basically, I will give you a crash course in machine learning so that we can understand a little bit what are the techniques and the simple mathematical tools that we are using, actually. And then I'm going to discuss how we can use these ideas in the context of quantum mechanics. So, even though maybe most of you don't know that, but we can say that one of the involuntary fathers of machine learning is David Hilbert, right? So, David Hilbert is one of the guys who has done a lot of things, great mathematician, and at some point he had a collection of problems of unsolved problems at this time, at this time, some of those are still unsolved. And one of those was to solve to somehow basically is the following.  Actually, the precise form is not very important, and you want to find the roots of this polynomial, right? So, we know that if the degree of the polynomial is larger than 4, it's very hard to write down in a polynomial. I mean, you cannot write down in algebraic form the roots of this polynomial, but he was asking whether we can find still some compact form to write the roots of the polynomial as a function of if you want of A and B of the coefficients that you have in this thing. So, and this question was answered actually in a much more general way by Kolmogorov and Arnold, so other two pretty clever guys, and they realized that in general, if you have a genetic function of many variables, so in particular, you can even think that the roots of this polynomial are a function of A and B, so in this case, just two variables. But in general, if you have a function of several variables, so let's say f of x1 up to xn, then they showed that this result has been refined in the last years. I mean, it has been refined in the form that I'm going to write by Spragner in the 60s or 70s. Well, basically they showed, and this is the refined result, that this complicated or in general complicated, any complicated but bounded function of n variables can be written as a linear combination, as a finite linear combination, so notice that this n is the same n that you have here, of just two one-dimensional functions. So the first one that I'm going to call phi, capital phi, and this function takes, if you want, as an argument, also another linear combination, again over a small number of variables, lambda p of another one-dimensional function, small phi, of my variables. So here q is the same integer that I have here, and eta is just a number. And here the important thing is that what can mogorov and Arnold match to show is that in order to write an arbitrary but again bounded function of n variables, it's enough to have two one-dimensional functions. So two functions, univariate functions, if you want, phi, capital phi, and small phi. These are one-dimensional functions, and they are also continuous, and you can also take, for example, this phi to be monotonously increasing. So this is rather a surprising result, if you want, because it means that somehow all the complexity of the i-dimensional function is hidden in those two one-dimensional things. So this is an exact statement? Yes. It's called mogorov. Of course, I mean, this is a beautiful mathematical result, but in practice it's not necessarily useful in the sense that those functions can have a very complicated fractal structure, and all the complexity in computing, if you want, this f is hidden in computing, these one-dimensional functions. So in practice, from a complexity point of view, you are dealing still with the same complexity, but still this gives you an idea of the fact that's what I want to... P goes from what? P from one to n, again, and it's again the dimension of the number of variables there. Do you know about the lambdas? The lambdas, they are between zero and one, just coefficients, but the important thing that I wanted to show here, that I wanted to stress with these results and actually why this is somehow related to machine learning, is that we immediately see from these that taking, if you want, functions of functions, so like combinations of functions, is an extremely powerful object that allows us to represent in a much more compact way than just taking linear combinations, if you want, of basis function and arbitrarily i-dimensional function. And this thing has been discovered, if you want, independently also by nature, in a sense, since basically neural networks, which are, if you want, like a very simplified way of describing the brain, work in a way which is similar to forming function of functions of functions. Right, so this is what, where the connection between these two words of pure mathematics and machine learning counts, because what is going to be important in the following is the notion of artificial neural network. Sorry, what about the thing you started with, this polynomial? Ah, right, yes, so at the end, I mean, these guys managed to show that it's true that you cannot write the root as a simple algebraic form, but you can write it as a composite function, so it's still a relatively compact. But is that something special about this example it shows? No, this was the original motivation that then Arnold, then Komogorov, and then Arnold later. Is it important you had a seventh order polynomial or is it just an example? It's important, it's larger than four, if you want. In this case, they were able to find exactly the function. Yes, so in this case, I think that they were able to find exactly those two phi and capital small, but this result was more general and it can be extended to an arbitrary high-dimensional function, so that was the main statement. Now, the point is, so what I'm going to use in the following is an artificial neural network. So an artificial neural network can be seen basically as a high-dimensional function. So basically, I will deal again with NF of x1, x2, up to xn, and I will represent basically those input variables as like, basically dots. So you can think of those as, for example, real values. And what this network does basically is that it takes this input and it transforms it through a nonlinear circuit which is basically a function of a function of a function. So how does this work? Well, basically, the idea is that each neuron, so I assume that each of these input is a neuron in this artificial neural network, takes the input and transforms it into a linear combinator. So basically, it takes a linear combinator, so there will be a lot of variables that we go through, for example, the next layer of neurons. So those are the input variables. So basically, they are just inputs for this network. And then each of those neurons, each of those input is fed into the second layer of neurons. So basically, what this means is that, for example, this variable here that I can call, for example, y1, y2, and y3, y4, et cetera, is basically a function. So more formally, I can say that yj is equal to some function, so some nonlinear function of the linear combination that it's coming inside those variables, okay? So, for example, this will be a linear combination of all the way, with some weights of the input variables plus a bias term. But it's the same phi for all of them. Yes, so in typical applications, we take the same phi, okay? So you see that this somehow resembles this object that I was using before. And then the idea is that you can compose those variables at the next level. And in particular, you can define, for example, another layer of neurons that we can call z1, z2, up to zk, which is, again, if you want, again, a function of a linear combination, now, of those yj, right? With some other weights, generally. So j and k of my yj, with some other bias term, which is k, okay? So you see the idea, the idea is that, at the end, so you take your initial input, so this i-dimensional vector, and you transform it through a sequence of functions of functions, taking a teach step linear combinations of those variables. Okay? Not necessarily, this is the simplest case where we take the same phi, but you don't need to. So the main point now is that from nature, we know that basically those kinds of functions, so those phi of x, are typically, first of all, continuous functions because they come from the biology if you want of the brain and in particular of the neuron. But what we know is that those objects, which are called activation functions, are typically functions which, that are called activation functions because they are, for example, as a function of x, they are typically zero force, if the signal is smaller than some threshold value, which can be changed in tune, changing this bias term b. And then they activate this spike if you want, if you are dealing with a neuron. If this threshold, if the value of the input is larger than some threshold. So, but it's very important that this object is nonlinear. Otherwise, if you deal with linear phi, so you are somehow back into the case of just linear combination of basis functions, which is not as powerful as taking functions of functions. But to go back to your motivating example, you mentioned that Arnold and, they found that the fees could be fractal or could have been non-continuous. So, in the general case, this phi is continuous. But if f of x1 through xn is continuous or smooth, does that guarantee that the fee, no, okay. So, that's the tricky part. So, if f is continuous, I mean, if it's, I don't know, lip sheets or something, it doesn't mean that you can find the phi which is lip sheets. Actually, at the end, but the point is that in practical applications, we have to fix the form of this phi to something we can work with. For example, an apropolic tangent or something. And then in that case, of course, this fear and breaks in the sense that this sum does not go to n, but to a larger number, which is not necessarily over the n that can be. In general, exponentially large in n, actually. But still, this is the motivating idea why we want to use functions of functions. So, in this way, you avoid loops and feedback loops? Yes, you can also insert feedback loops if you want and this actually increases the computational power of these networks. So, you can show that if you introduce loops, you have a much more powerful machine in terms of computational complexity. But in this case, it's not. But isn't the feedback included in the non-linearity? Exactly. It depends what you mean by feedback. So, the non-linearity of phi or function, general function kind of takes care of the looping. By loop, I meant that the output can be fed back into the input. But so, that's what I mean and it's not included in this architecture, this specific one. But yeah, we can discover it. So, this is the notion of artificial neural network that will be needed by us in the following. So, let's see a little bit now what we can do with those artificial neural networks and what kind of applications people have been done, let's say, in real life. So, the easiest thing you can do is the so-called supervised learning, which is basically the simplest form of machine learning that you can do. So, the basic idea is that you can imagine that you have a task, so, a generic task. So, you want to automate a task, you want to solve a problem. And the solution to this problem is given by some F bar, if you want, of some input variables. So, let me give you an example. Imagine that my input, so, as a vector x is equal to a string. So, the string is just we. So, in French, right? And you want that, for example, that given this string, F bar of x is equal to im, right? So, like the English translation of this string. So, this is a very specific example, but this is like, if you want a basic version of Google translate. So, Google translate works, more or less, in this way. It takes a string in some language and translates it into another language. So, this case is French from English, but it can be whatever. So, the goal, if you want, in this case, so, the translator, in this case, the goal of the machine would be to find a good approximation of this F bar, of this unknown F bar, right? Which is a very complicated high dimensional function. So, how can we do that? Well, the basic idea, the paradigm of machine learning is that we work with a large amount of data. So, we have, for example, at the end, a lot of pre-translated text. So, if you want, in this context. But formally, from a mathematical point of view, this means that I have a collection of labeled examples, X, L, and of pre-translated sentences. And I have a lot of them. So, L is an integer which goes between, I don't know, between one and Ns, where Ns is much larger than one. So, this means that I have a collection of pre-translated sentences. And to each of those, I know what, for each of those, I know what the translation is, right? So, if you want, I only have a partial knowledge of this function on those points. And I want to reconstruct, I want to infer the value of the generic value of this function for some other strings that have not been pre-translated before. So, this is how Google translates works. I mean, like in a very, at zero level, at zero order, that's how it works. Now, how do we do that? Well, this is basically, as I was mentioning, an inference problem. And the idea is that we define a loss function. So, in general, I will have, what I want to do is that I want to approximate this unknown high-dimensional function. So, F bar of X with my artificial neural network. So, F, A, and N, if you want artificial neural network, which in general will depend on some parameters P, some parameters P, which can be, for example, those weights that I have inside my functions or whatever you want. So, also the architecture of the network itself. Now, what I do is that, I mean, to solve this equation numerically, as you can guess, is that I define a loss function, which depends on the, if you want, on the parameters in the network, which is basically just the sum of my labeled examples of basically the square loss or another generic loss, basically of what I expect by, as I mean, the output of the neural network at the current values of the parameters, minus the pre-translated thing. So, the y, so the output that I was expecting for those samples that I already have classified, okay? So, now I have this function, which depends on the parameters, I basically just minimize it and find the optimal value for those parameters. So, this is the learning part, if you want, of the algorithm. So, there are two parts. So, in the machine learning, there are two things. So, the machine, which is, in this case, the artificial neural network, so this i-dimensional function, which depends on parameters P, on a set of parameters P, and the learning part, which is basically an optimization problem. So, it's a i-dimensional optimization problem, where we want to minimize some quantity, in particular, in this case, this loss function, okay? So, one of the interesting aspects is that this optimization is done in a stochastic way. So, I will just briefly sketch this because it's somehow interesting. And, in particular... When you have something non-linear, I mean, pretty messy, I have to say, you might have many minima, right? Yeah, that's precisely where I want to go. Very good point. So, the idea is that that's exactly the problem. But it's solved in a very elegant way. And I would say that people in the machine learning community were not aware of this from a physical perspective until very recently. But somehow, if you are a physicist, you can realize why the optimization algorithm they have works so well and avoids local minima. And the idea is the following. Basically, what they did, what people used to optimize this i-dimensional function, is just a wrong version of the gradient descent, right? So, in general, the gradient descent tells you that... The gradient descent tells you that if you are at iteration k and you want to find the parameters at iteration k plus 1, basically you take the old set of parameters and you subtract, basically, eta is a small parameter, which they call the learning rate. You basically subtract the gradient of this function that we want to minimize, right? So, let me call it g of p. So, g is a vector itself. So, this is the standard gradient descent approach. You know that this thing will converge to a local minima of the function. Now, it turns out that what the people in the machine learning community do, now it's going to be problematic. Okay. Well, never mind. So, the g of p. So, I mean, what these people were doing, I mean, what is done in the community of the machine learning is that instead of taking the full gradient, so the full gradient would be the sum over all the examples that you have in your library of pre-translated strings, if you want. So, let me call it g of x, l and p, right? So, probably small g. Okay. So, you see that basically, if you take the gradient of those individual terms in the sum, it's just a small gradient here. So, what it's commonly done is that instead of taking the full sum, we approximate this full sum with a partial sum over batch, so over a number of samples, which is much smaller than the total number of samples. So, l over n batch batch. So, where nB is much smaller than nS, okay? So, typically, it can be 100 or 50 even of this thing. Now, this means, in practice, that instead of taking the full gradient, we are taking a stochastic approximation of the gradient. So, this means that instead of taking the full gradient, we now have what's called a stochastic gradient descent if you want gradient, which is equal to the exact gradient g of p plus a sigma. So, plus, if you want a normal distribution, we've basically, we've variant sigma, where this variant sigma. So, let's assume now that all the components of the gradient are uncorrelated just to be on this side, where this sigma basically skates like one over the number of samples that have taken here in this small batch, okay? But it turns out that if you do this thing with a noisy gradient and you put it back here in the standard gradient descent, you end up with a Langevan equation. So, a stochastic differential equation, the time discretized version of the Langevan equation, where at the step k plus one, you take your old parameter p of k, basically minus eta, the true gradient g of p, minus eta, this normal variable. And this can be easily identified with the standard, with the Langevan equation, since if we make now the simple substitution that eta, so this learning rate, is a time step in time, so delta tau, and that this sigma, so basically the variance in my gradient, is equal to, actually sigma square is equal to twice the temperature over delta tau, the time step. So, this is the first order Langevan equation. And the important point is that, in the asymptotic regime, what is sampled by this first order Langevan equation, is basically the probability of finding a certain set of parameters p, is proportional to the exponential of minus this loss equation L of p over t. Depends much on the barrier. Yes, yes, no, but what I would say, no, but this statement is true. If the components of the gradient are all uncorrelated, it's always true that the probability distribution sampled by this stochastic differential equation, is the Boltzmann equation, where the effective energy is the loss function. So here, the benefit of adding a noise, if you want, is that instead of doing a simple standard optimization gradient descent, we are doing basically, we are exploring the full, if you want, classical energy spanned by those parameters p, and in particular what we can do and what people do to optimize those parameters, is that we can change the effective temperature in the system. So for example, if we anneal the value of beta, so if we slowly turn it down, it's completely equivalent to changing the temperature. So if we change the temperature, we can then go into the global minimum of this function. So it's much easier to optimize this neural network that we are dealing with. So we have a double benefit, because this is also intrinsically much faster to compute numerically, but we are also approaching the actual minimum of the function we want to optimize. Okay. So this was, let's say, the physical interpretation of the stochastic Newtonian descent, which I find particularly nice. Yes. So physical interpretation might be useful especially for us, but when I look at that cost function, do I want to think that this has to do, anything to do with the Lagrangian? No, the name L is loss, not. Sure, sure. But what I'm saying is that there is no notion of locality there, probably. No, no. Precisely because these connections in networks can be highly non-local, typically, yes. Our physical intuition is probably, for most of us, built on local objects, on local light engines or Hamiltonians. It should be, should we... No, the only interpretation, the physical interpretation you can take from here is that you are dealing with a classical Lagrangian, I mean, classical energy, which is highly non-local, but I mean, the interpretation you can take here is that the annealing, the procedure you are using is like a simulated annealing for Hamiltonian, which is unphysical, yeah, I agree. But the fact that it's non-local may even be helpful because it helps formalize faster as opposed to... No, it helps describing more complex functions. For example, in the case of quantum systems... What I want to know is if I can take my intuitions about thermalization in physics, right, to here, whether the fact that this is not local, this cross-function is not local, it's gonna be an abstraction to that or actually it's gonna make thermalization... I think that locality is not necessarily something that is related to how many local minima you have in this i-dimensional thing. At least that's not how I see it. But in practice it's true that the best networks that people have studied and are using have this notion of locality, somehow built in. So this convolutional neural networks, for example, have local filters and those are also easier to optimize. So in a sense, it might be that the two things go together, that somehow locality helps optimizing, yeah. But I guess that's if your function has some natural locality, like for image processing maybe, but not for a... Yes, yes. Yeah, so, yeah, I mean, yeah, exactly. So if you have, let's say, a low, slightly entangled input, if we anticipate already the following discussion, then it's clear that a local function with some local structure is better. The other cases that behave like spin glasses, where there's like a trouble finding the cross-function. Yes, certainly yes. There are cases where it's very hard to optimize those functions, it takes days, years. So, and the people have studied this from the perspective of spin glass system, there are, there's a lot of leaders on this, actually. I can give you the references. Okay, now... That is clear. Thank you. I'm fishing. Would it be possible to turn the lights off, please? Just to show you a little bit some slides. Thank you. Yeah. Yeah, okay, so what I wanted to say, it's okay. So, basically this idea that you have a function which allows you to solve a complex problem can be generalized to many other problems, not only to language translation. For example, optical character recognition. In this case, the input is the image and the output would be the digitalized version of the input, if you want. Or speech recognition, so the input is a wave sound and then the output is the string of text and all other things, sort of things that you can think. So, this approach is very general. It's really something that can be applied to a lot of applications. Now, that's why, for example, machine learning, since this approach is very general, that's why also people have started using this approach in many domains of science. For example, in the case of particle physics, we can use this machine learning approach to help spot events in a sea of events that happens in an accelerator and try to identify those and see whether they are associated or not with some, for example, Higgs boson or to design molecules, all sort of things. But, I mean, just to, and people, I mean, have started wondering whether, at the end, like having a machine that is able to solve the problem for us would somehow transform the scientific method itself. Right? Because if we have a machine which decides for us whether, you know, like a problem has been solved or not, or whether this molecule is going to be this or this other thing, at some point we're going to have also probably a shift in the scientific method. But, of course, we are not there yet. So, I just wanted to discuss with you, for example, one of the first applications that have been done in the context of matter, which is very recent. So, the idea here is that we can use this kind of approach, so this kind of supervised learning, so where we basically minimize this loss function to identify phases of matter. So, you can think that in this case my input are, for example, images or something of different objects and you want this argument to identify whether those input images are in a certain phase of the matter. For example, solid, liquid, solid, liquid, et cetera. So, we have a set of pre-classified images if you want in this case, so where x1 is already associated with solid, x2 to a liquid, and so on. And so we can do this procedure of basically minimizing this loss function over this finite set of pre-classified images and then we can ask, we can give a new image and say, what do you think this is? Is it a solid or a liquid? In this case, we can use in this context the machine learning technique to classify phases on a more refined level. That's what Juan Carraschi and Roger Melko have been doing last year, basically published in this paper. And as a toy example, as a more concrete physical example than those images I was showing you before, they took the icing model. zelo, Instead of as input configurations, as samples taken from the classical partition function of the Ising Model, as these x1, x2, x3, x4 and those images are taken at different temperatures in the phase diagram of the Ising Model. And basically for each of those images, one can pre-classify them and say, for example, that those were obtained when the temperature was lower than the critical temperature, so they were in the ordered phase, so the label was Y1, Y2, which is ordered, and then those other phases instead were in the disordered phase. So we have, again, this large chunk of data that we've taken, and we have pre-classified and then we use a machine to see whether, for example, it is able to identify this phase transition on another model, for example. So in this case, they trained the model on a square lattice, so really the machine was able to identify the phase transition in the as-in model on the square lattice, and then they took the very same machine and they applied it to the as-in model on the triangular lattice, where it was able to predict the phase transition, so the critical temperature with very good accuracy. So basically, the output that the machine was giving was compatible with the exact known results from other Monte Carlo simulations. So the basic idea here is that the machine was able to learn the order parameter in the magnetization, if you want, in the system, and use it to learn a phase transition in another system where it was not previously trained on. So that's the idea. The learning here is on the visual part or just including, I don't know, magnetization, see if it's... No, it's just on the bare spin configurations. Just visual. So you treat if you want those things as images and you classify them with either zero, one if they're ordered or unordered. It's not simple just to go to the magnetization. But because you are a physicist and you know that the order parameter is the magnetization, but the idea is that we want the machine to find out that the order parameter is the magnetization. So that's the idea. How big was their training database? I honestly don't remember in this case. We should have a look at the paper. It's in the thousands, I guess. How do you reformat the triangle of lattice so that a configuration on the triangle of lattice looks like... I mean, it's... Ah, right, yeah. Yeah, that's a good point. Yeah, I don't know. Actually, I should ask... Yeah, that's true. In order for the machine to make a prediction, it has to take as input something that can be compared to Hollywood's triangle. So probably take the dots, you pick... I don't know if you have that appointment. Well, yeah, but you can probably just do a simple... I think it's the same, it speaks for a diagonal. Yeah. It does take the same pattern. For the uniform magnetization, it probably does not matter how much it... Right, right. No, but I mean, what you were saying is, how do you map a square on a triangle as the input image? Yeah, and whether that can affect the result of it. Like, you mean... Yeah, I think they were taking something like that. Like... That's what they are doing. Yeah. Well, I guess. But I don't know, I have to check what one did. No, but then we have a problem here. No, like this, yeah, I think. Is that the... Like this, yeah. Is that the diagonal one? Yes, yes. So I think that you can do this kind of... Yeah. So this was one of the first applications of those ideas to classifying phases of matter. It has been also used for other things. But now what I would like to do is to show what we did in the context of quantum mechanics, like to really find, if you want the ground state of some Hamiltonian, possibly a correlated Hamiltonian, and to see how we can use machine learning to solve this problem. So... OK, so... So what's the goal? So what's the thing that we would like to solve? Well, we have a Hamiltonian, so we have a many body Hamiltonian. Say we have the upper model or the Assembler model. And one of the main tasks that we would like to solve that we would like the machine to give us some help for is to find the ground state of this Hamiltonian. Right, so we would like to find, if you want, this psi which solves the Schrodinger equation. The ground state of this object. So in order to use a machine learning approach, the first thing that we have to do is to somehow change or this Schrodinger equation into an optimization problem. So something which is suitable for the learning approaches that I was discussing before. But this is something which is relatively easy to do. We know indeed that the ground state of the Hamiltonian is nothing but the minimum over all the possible, if you want, many body physical ground states of the energy functional E of psi, right? So we're basically... We're basically E of psi is nothing but the expectation value of the Hamiltonian over some normalizable physical state psi. Right? So in principle, we already know from the variational principle that if we manage to... We can immediately transform if you want the Schrodinger equation into an optimization problem. So if you want the learning part of transforming the quantum mechanics into a learning problem, it comes from free, thanks to the variational principle. Now, the other part that we need is the machine, right? Because there are several possibilities that... There are several ways we can use, for example, machine learning or in general neural networks to solve this problem. So one possibility would be that, for example, we solve for the Schrodinger equation for some Hamiltonian and then we try to find the solution for some other Hamiltonians in the spirit of what I've described before. So we solve for all the Isenberg models and then we say, ah, but what's the ground state for the Isenberg model? But of course, you can understand that the machine will get confused because the two fingers are not necessarily well connected also from a physical point of view. So what we do instead is that was our idea, is that we represent the many-body state as an artificial neural network. So what we do basically is that, first of all, we introduce some many-body basis for my problem. So, for example, let's assume that I have a spin one-half problem and that my many-body basis is just a collection of n spin numbers along the z-direction, okay, so sigma one up to sigma z. And then what I do is that I represent the many-body state. So basically, those amplitudes psi of x as an artificial neural network. So in particular, I will call those amplitudes, which are in general complex values because I want to describe the most general wave function. So this is a function, if you want, in this case of all my magnetizations, so along the z-direction for all the sites that I have in my system. So basically, what I do is that I want to approximate the exact ground state, so in general, a state of my, which is associated to my Hamiltonian, with some artificial neural network, right? So for a reason that will be apparent in a moment, what I will do is actually that I will associate the log, if you want, of the wave function with an artificial neural network. So what I will do is that I will say that my artificial neural network describes the log of the wave function. And this log of the wave function will depend again on some parameters p. So this parameter p can be, for example, the connectivity metrics that I have in my network can be whatever you have as a parameter in your artificial neural network. And, I mean, from a physical perspective, those parameters now become variational parameters for my variational wave function, which is now in the form of an artificial neural network. So what I can do now is that I can find the ground state of this Hamiltonian, for example, solving a learning problem, an optimization problem, which is in a very similar form of the optimization problem that we've seen before. It's more complicated, but the idea is more or less the same. And in particular, the main ingredient that you need to know is that if you want to compute, for example, the expectation value of the energy for a given set of parameters. OK, so if I call E of p, again, the expectation value of the Hamiltonian for a given set of parameters divided by the normalization, then this object can be written in stochastic way, so as a Monte Carlo average, if you want, over configurations, so over many bodies, spin configurations, which are sampled according to psi of x. So x now, again, is my many body variable, which indicates all the magnetization of p square, so modulo square of these, times an estimator, which is called the local energy in Geringon. So in practice, you can show that the local energy, I mean, just to show you what it is, in practice is defined very easily as the sum over the basically all the non-zero elements for which those matrix elements of the Hamiltonian are non-zero, of psi over x prime and p in general over psi of x and p. So this is the definition of the local energy. So basically, what this expression is telling you, and you can easily derive it, is that the quantum expectation value of the Hamiltonian can be written as a statistical expectation value over this probability distribution psi square of some object, which is not a classical energy. It's somehow an effective classical energy that people call the local energy. So in a sense, you can recast the full quantum mechanical problem into a fully classical problem, where the classical energy that corresponds to the quantum one is this local energy. And in particular, what you can do, so this is the heart of the variational Monte Carlo approach, and at the end what you can do is that you can also compute the gradients of the expectation value of the energy and you can minimize it in the same way we were doing for the other quantities. So this is how this approach works. Basically, do you train the machine? Yes, so I train the machine. So at each step, so this approach works as well. So the first one is that we sum, so we fix the parameters in my network, the p's. And I sample from, so I generate a lot of samples psi of x, which are generated according to the current wave function of the squared. OK, so those are generated, for example, via Markov chain Monte Carlo. So I generate a lot of sample, which are generated according to psi squared. Then using those samples, I use basically the gradient computed as an expectation value, statistical expectation values, to feedback the parameters. So basically I will say that p at k plus 1, so the next step will be equal to p of k, minus some estimation of the gradient, stochastic estimation of the gradient that I have at step k. So this stochastic estimation of the gradient is obtained using the samples that I have generated in one. And then I go back to one, because I've changed my parameters, I resample and then until I converge to the minimum. So it's more complicated than what I've shown you before in the sense that here, this is a self-consistent procedure where I don't have pre-labeled examples of the solution that I want to find. I have to generate them myself. So it's more similar to have a machine, which learns how to play a game. For example, if you have the game of Go, which is the one that Google excelled last year, basically it happens that there you have an energy, so you have some function that you want to minimize, which is the final score that you get in that game. But in that sense, you don't have a winning trajectory, you don't have a winning strategy beforehand. You have to find it yourself in a self-consistent way. For example, playing against yourself. And it is the same idea here. So we are playing against Schirlinger until we beat it and we find the best energy. So let me show you just some numerical results. Before the numerical results. So you said this is variational Monte Carlo using an artificial neural network as a variational answer. Is that it? And so the question is, whether this is a good answer, is that true? Yes. And do you have, so now we look at the numerical? Yes. So there are some, in principle, reasons why this is a good answer, and there are some numerical evidence. So I think the answer is yes. It's a complementary answer if you want to NPS or then some networks. No, but if somebody knows variational Monte Carlo, all they have to do is to choose this as their variational waste function. And the selling point would be the numerics or there is some... No, the selling point is that you can increase systematically if you want the precision of this object, increasing the capacity of the network. So you can put more and more neurons and systematically converge to the ground state. So in a sense, like the sites of the network is the dual of the bond dimension in the NPS language. The number of sites, yeah, the number of neurons that you have in the network in the deep part. So I'm going to discuss this in a second. We have a quick follow-up question. For NPS, we actually know that they capture like the properties of local Hamiltonians and that's why this is the right answer that's maybe to represent ground states of local Hamiltonians. But this ansatz doesn't have locality, but this is still like a reasoning why this would be the right or efficient ansatz for ground states of local Hamiltonians. Or would it be the same, like if it is for example... I was expecting this question. No, I mean, no, the problem is that the fact that this thing is no local is also beneficial because you can describe more easily highly entangled states. So here you don't have a limitation in the sense that if you have a volume-low state, you can efficiently describe it with a polynomial number of parameters because if you take long-range connections, it's trivial that you satisfy a volume-low, right? So in this sense, not having localities can be an advantage to describe, for example, chiral states and those kind of things where you can have a strong volume-low. But there is a way of recovering locality.  But whether it's local or local, it depends on the architecture. Yes, so at the end it might even be that the architecture which is found by the network is effectively local. So we are giving the freedom to be no local, but at the end the network is free to choose to be local. Of course, if you constraint to be local, it might be easier to optimize. So that's the thing we were discussing. So is it the right time to ask whether you will have any computational problem if we are trying to evaluate this network? Yeah, okay, so. Numerics first? Yeah, so first I wanted to discuss, okay. So the, no, just a second. So the actual answers that we use is of this restricted Boston machine, RBM form. So in this case, basically what we do is that we take this phi to be, the log of, I mean, if you can derive it like that, basically it's just the log of the hyperbolic cosine of X. So this is the activation function that we use and this activation function comes from some effective Boltzmann distribution of an object which is done like that. So where you have your input nodes, sigma one, sigma two up to sigma n. So those are my physical degrees of freedom which are connected through some weights, so those W's, okay, and to some hidden nodes h1 up to hn, hm, so where m is a free parameter. So the more of those I put, the more the bigger network. And basically I say that the output of my, basically the wave function of my system, so psi of X, psi of sigma in this case is nothing but the Boltzmann weight associated with this object. So it's basically the sum over these hidden variables of the exponential of sum over j, w, i, j, sigma, sigma i, hj. So basically this is a classical partition function where I have interactions between my physical variables and some hidden degrees of freedom which are the neurons in the network if you want, okay. So the more of those I put, the larger the brain, if you want this artificial network is and the smarter I can make it. So there are actual representation fields and that guarantee that if m is large enough I can represent any n dimensional function. Okay, so now I have this parameter m and in particular I have what I call alpha which is the ratio between m and the physical number of values. So m over n that I can play with. So I can increase alpha and increase the accuracy of my calculation. So if you can, no, sorry. The complex numbers are coming from somewhere here? Yes, so the w's are complex valued. So of course the interpretation as a classical partition function breaks down at this point. And this is something which makes this thing very different from traditional applications that people have done in the classical context. So what we need more if you want is to put this object complex. So okay, so here you can see for example the energy as a function of this iteration number when we optimize the energy for the one dimensionalization model. So this is a model where you can do numerics with the MRG or you can even find the exact ground state with basically better answers. So you can see that when we increase alpha we can systematically improve the accuracy. So from this plot you cannot see it very well but you see basically you see it here. So this is a zoom of the final part of my iterations of my optimization. You can see for example that going from alpha equals two to alpha equals four, the energy goes down. And you can also see from the scale that we are very close to, we have a very high accuracy on the ground state energy. So you see for example that the scale is... So what is alpha? So alpha, sorry, it's introduced here, I introduce it here very briefly. So it's the ratio of the number of hidden units over the number of visible units. So if you wanted so many neurons you have after the input layer. So the larger it is, the better you find the ground state. So this is, I think this is 80 sites, but you can do 80, yes, 80. So, but you can see it also for other models. So this is the relative error you do on the energy on the ground state energy as a function of alpha. For example, for one dimensional model we typically find more or less a power flow behavior as a function of alpha. So this is a log-log plot. And you see, for example, for the 1D transverse fieldizing model for different values of the transverse field that you can systematically converge, typically also to very large accuracies. And you see that alpha equal four, it's not necessarily a very large number, but you can already achieve very typically very high accuracies. And a very interesting thing, which I believe is somehow also worth being explored more, is that this is a rather compact representation of the wave function. For example, if you compare the equivalent NPS, which has the same accuracy, for example, for HE equal one on the critical point of, say, 10 to the minus four, and you say how many parameters I have in this NPS, and you compare the number of parameters that we have in the RPM, you see that they can be easily a factor of 100 or sometimes even more. So, in a sense, the fact that we have a nonlinear decomposition of the wave function can be more expressive than a multilinear decomposition like the NPS. Of course, it means also that it's harder to optimize on this, I think, we agree. Now, the thing is that, of course, in 2D it's more problematic in the sense that converging is more delicate, as you can see here. We still managed to do a bit better than some perhaps results, but it's harder than 1D. So, this is something also that it's not entirely understood at the moment why the optimization is harder in 2D. Most likely it's not a limitation of the answers itself, but it's an optimization issue due to this high-dimensional space where we are optimizing our parameters. Okay, so this, I don't want to go too much into the details, but basically what I wanted to show you is that in some cases you can see that the ways that come out are local. For example, in the two-dimensionalizing model, you can see that those weights have a local structure, which is somehow reminiscent of the local anti-ferromagnetic correlation that you have in the system. Sorry, how do we read that plot? Yeah, I didn't want to go too much into the detail, but so basically here we also use translation symmetry in the system. So this W now depends only on one index. So basically, yeah, you have to mention this as a convolution on your network, I don't know if you were worried about it, but basically you have a filter that you translate at each time. But okay, this is a bit technical, I didn't want to discover this. But W14 is a weight, is it a number? It's a weight, yeah, so this is the weight here basically. And why does it, what does it mean? That's a complex number? So this means, yeah, no, sorry. So this is the, in the case of the isomer model, you can take it purely real because you know that if you do the rotation, you can put it purely real for the ground state. So what does it mean that a given coefficient has a representation in two dimensions? Ah, because this is a two-dimensional isomer model. So what I'm doing is that here, basically, I'm fixing, if you want J, so I'm fixing the hidden unit and I'm varing I. So this I now is a two-dimensional index. So I'm fixing the index of the hidden unit. So I'm fixing, for example, this hidden unit and I'm showing the value of this weight over all the other spins, which is a two-dimensional object. Should we think of it as just some sort of indication that the wave function has some degree of locality? Yes, yes, yes. In this case yet, but it's not always the case. For example, if you look at this, for the isomer 1D, the weight is highly non-local. And we've seen clearly that it depends strongly on how you optimize the wave function. So if you force it to be local, it stays local. So this is something also interesting. Is that with periodic boundary condition? This is, those are all with periodic boundary. Because then it still shows to be local, no? In this case, well, okay, okay, it's true that this filter, for example, is relatively centered into this point. But less than, let's say, this one, is it? Anyway, what I wanted to say, okay, if you want, you can also have a look at some codes that are online that I wrote to somehow show how to apply this scheme, numerical scheme for the isome model and other cases. And more general code will be hopefully uploaded before next spring. So where you can really play with it and also extend it if you want. Okay, no, now I think that my time is almost, is basically finished. I wanted to say that we can do also unit dynamics. I don't have time to discuss this, but we can also do solve the time-dependent shedding equation using the time-dependent rational Monte Carlo. It's a method that we developed some time ago. And then, yeah, okay, in our paper, we compared also unit dynamics to the exact results and found that also in this case, it's more delicate, but you can also find very good results for the dynamics. This is a quantum quench. You can use also it in two dimensions and that's something which is coming out. Okay, and then I don't have time to discuss this, but we have also applications to basically tomography, which is the problem of reconstructing the state of a quantum system from given experimental measurements. Okay, so for, I guess, some of you are interested in the properties of those states. We can discuss them later, and I apologize, but I ran out of time. In particular, we can describe, we can discuss some applications that people have done to carry out spin liquids, where this answer has been shown to be superior to existing approaches. Okay, so let me, yeah, so I can just last think. Is that basically there is this strong representability theorem by Gao and Duane, which shows that you can represent any physical state, so basically any output of any finite depth quantum circuit. We have a neural network with only two layers. So if you have the second layer here in the Boltzmann machine, you can show that you can write exactly and with only a polynomial number of neurons, the output of this circuit, which is a pretty strong result. And in this case, you can show that the weights that you have in this network are purely local, so they correspond if you want to the gates that you apply at each step. And at this point, we also have a construction to generate those weights for simple, so this is for coming work, where we have a procedure to generate if you want the weights in this network for some models like the Ising model or the Ising model. So we have, if you want, this is an alternative to the standard patindega representation, which can be done in the space of artificial neural networks, of two-layer artificial neural networks. The important point is that only two layers are enough to describe all quantum mechanics, basically, which is tontiga. Okay, so I finish here, and if you have more questions, I will be happy to answer to them later. Thank you. So if you have, if two layers is good enough, is there any advantage to going deeper? Okay, so the tricky part is that two layers is in, it's a Boltzmann factor for two layers. So it's not a function of a function like I wrote before, unfortunately. So the tricky thing, if you want, I mean the thing that at the end matters is that you cannot compute exactly this amplitude, because it would involve tracing out the second layer, which you cannot do analytically anymore. So only if you have one layer you can do that analytically. If you have a second layer, you cannot do that anymore analytically, and you have to do some approximations, or to find ways to compress this second layer back to the shallow layer. So that's the important part. In dynamical system literature, when you iterate a function, iterate a function, so on, at the end emerges some kind of universal, right? So it doesn't matter the precise form of the function, simply because you apply many, many times. It's the same also here. I mean, it matters a lot if you choose one function there. No, in practice numerically we've seen that, okay, you can use this log of cosh, which is a function like that, but you can also use other functions, basically people typically use function, which is zero, and then it goes like that, and they don't give the same results, basically, at the end. They give the same results. So the important thing is that you have some nonlinearity. So that's the only thing is that you have some nonlinearity, and that's the only really thing that matters. Then the specific form of the function is not so important, but I have to say that if you want to use complex value, the variables become stricier, because you have to make sure that you are dealing with some, typically with some analytical activation function, at least for the way we optimize the parameters. So typically this choice is what we use. I mean, just an addendum, but this is, how to say, experimental result, or there are some theory behind it, which ensures you that something's going on. No, there is no theorem about the specific activation function and why they should give you the result. Apart from the genetic thing that tells you that if m is large enough, and you have a genetic activation function, which is just a bounded function. So, okay, so the theorem is the following. If you have a genetic activation function, which is bounded between zero and one, but monotonously increasing, then if m is large enough, you can describe an arbitrary function. So this is the theorem. But in the quantum context, I don't know, this can be probably refined, but I don't know. Okay, it seems like in some 2D cases, your method gives better results than other existing wave functions that people construct that isn't other techniques. Yeah, so it gives comparable or slightly better than depends on your taste or on your... But what I want to tell is that, for other methods... In this case, it's sensibly better. For other methods, I know that even computing expectation values of certain operators in 2D case becomes problematic, because it's hard to contract objects indices. For your method, for your wave variation, wave functions to compute this energy estimator, to how large volumes can you go? So let's say, in the PEPS case you were mentioning, it's problematic to contract the state to find the amplitude, right? In our case, what's MPR or MP complete is optimizing the parameters. So this optimization that we have to do is a computationally hard part, which... And we can easily, not easily, but if we are not careful, we can get stuck in some local minimum and we don't find the ground state. But for us, computing the amplitude of the wave function or the variational state is very easy. So it's polynomial. But can you recycle information to go to client parallel lattices?  And if you do this, you recover a formal locality also in the weights, typically, not always. I mean, if you have a gap system, you know.


Coach, good morning, Sean here from Making Money, Coaching Sports, and I am ready to talk to you about selling, selling, selling, but what are you selling? You should be selling team. Now, do I coach a team sport? It does not matter. Okay. We're talking about aquatics here and how to make money coaching aquatics. That's the goal of the channel. We're trying to make money coaching sports. If you want to find out more information about that, we have our Accelerator program with groups right now that are just killing it, making $20,000, $30,000 extra, extra, all right, with promotions and programs that we have in our group and you can feed off each other's motivation to get better and better. Contact me in the description below for more info. Now, selling team, all right, so I'm going to just, you know, I'm not going to use the team sports like artistic swimming and water polo as my example here because that just kind of feeds itself. Let's talk about diving, swimming, right? What does it mean to be part of a team? Okay. Being part of a team is an aspect where you can trust your coach is the leader of the team and then you have teammates that are helping you get better, right? So if I'm not fostering it as a coach, I'm not providing my team with leaders that are going to help lead other people, promoting leaders so they can become in a leadership role and help others and promote hopefully a team aspect. There should also be, you know, a team and then there's community and we'll talk about community and other video, community slash family that we can institute and we can sell that as well because we are a tribe of people as a human race. So being part of a team, you need to be together as a group. You cannot be by yourself. Things need to be done together. Solo work is on the side, right? If you're trying to do team stuff. Even if you're a private coach, there should be moments where your private clients come together as a team. That's a huge selling point because individuality is tough and dealing with the individual and just being part of one thing is very hard to sell, okay? You can give that unique big, huge ticket offer to the one person, but you want to be able to bring people together and then the more people you can have as a team in one setting with only you provides you with more money, right? So if you're coaching 20 kids at one time, each paying you $100 to $200, it's a lot more money than one kid, right, at one time. So then you said, what are we selling? We're selling how to be better at working with a group and team. If you have a job right now, I imagine you do as a coach outside of coaching or you wouldn't be watching our content, right, is you are already part of a team in your job and how you get along with that team dictates how well you guys do as a group and whatever you're doing helps you guys promote, sell, teach, whatever you do on the spare time, okay? To sell that you are part and you create team so that the kids know how to work with the team later in life, okay? It also allows you to do team building activities that allows you to add extra value to your program when you add value by not having costs, right? It doesn't cost you anything to do a team building activity, fun stuff they can do where they have to work together even though maybe individual sport like swimming or diving where they're working on themselves but there's a team aspect in terms of points, okay? And then the other big thing is they will always perform better in practice and events if they know they're doing it for a greater good, right? Like maybe they didn't perform great but they're going to hustle and work for their teammates so that the overall group does better, okay? That's a huge mentality. That's just something that humans we want to do good for the group. And if you instill that as a coach, it makes your life a lot easier. If you want to work on these habits, instill these habits, contact me in the description below. You can text me at the number. You can email me at the email. Again, we have tons of coaches in the accelerator program right now that are excelling at using our tactics and making lots of good money, okay? Don't want you to be left behind. You want to make money coaching sports, all right, see you later.


Walleye regulations at Upper Red Lake are remaining the same this summer as they were last winter and last summer. Anglers fishing Upper Red Lake this spring will again be able to keep four walleye of which only one may be longer than 17 inches. DNR officials say the harvest under the four fish bag limit, one over 17 regulation, resulted in about 152,000 pounds for the winter season. That was a record high for winter harvest since reopening walleye fishing in 2006. But the DNR says there remains room within the target harvest range to allow the regulation to continue into the open water season. If you enjoyed this segment of Lakeland News, please consider making a tax-deductible contribution to Lakeland PBS.


What is going on guys, welcome back to the channel and I appreciate you being here today I bring you coverage of something a real interesting so let's get into it. So Ryan Kay at Bungie tweeted out this image. He is the visual design lead so it does make this image a little more interesting. So what exactly do we see here?  We see a crest of some kind and a shield too. There is no text nor anything else into what this is. Now if this was tweeted out by someone else I would say this is nothing more than fan art of some kind but the fact Bungie's visual design lead tweeted this out I think is definitely something of interest. Now I've seen a few people suggest what this could be. Some people saying it's a DLCT's while others with more of a clue suggest what I actually believe this is and this will make many folks happy. What I think this is is a grimoire card or grimoire card art of some kind. It looks so familiar in that sense. Check it out beside a grimoire card from D1. So what does this mean? Finally 5 months after release we're getting something which should have been in the game from day 1. Honestly folks to further forward we go with Destiny and the more they announce these better changes come into the game I can't help but think the base game of Destiny 2 was nowhere near finished. If it was finished and the base game was planned to be this bad I don't know what is going down within the Bungie studios but it definitely needs to be fixed up. We know the game was rebooted around 15 months until it was planned to be released. Maybe they were pushed by Activision to get the game out within that timeframe. Bungie must have known only 15 months to go that they could not achieve what they wanted for their game. With that in mind it makes sense as to why all these changes are being incorporated now and why the base game was well lacklustre content wise. I'm happy these changes are being made. If these are grimoire cards although they ain't at the top of my list of things Destiny 2 needs to survive it's still an addition the first game had which was taken away for the sequel. This and around 1000 other things. But hey at least now where most have boycotted their game they are listening and trying to salvage what's left by giving us what we originally should have got. They could just give up you know. I know this would look real bad on Bungie for sure but they could. Game developers have done this in the past but I feel they are obliged to go on. Yes it's costing them big time both affecting their banks and their community but in my opinion it's the only thing Bungie can do now to even start trying to revive their game. Many are saying it's too late while others are really excited. I personally am in the middle. I'm super excited for Destiny 2 to become the game it should have been but at the same time I don't think a perfect Destiny 2 will have the same effect it would have or should have. I feel many people have moved on and found other games which swallow their lives even more. Coming back would be a hard stretch and this is no thought of anyone but Bungie. Now people I ain't bashing here I'm just stating the truth I see so many comments on my video saying why do you always bash on Bungie while still playing their game. People it's called tough love.  I bash on what they do because it's affecting the game we all paid money for and we should have received better it's as simple as that.  So these Grimoire cards for sure will be a great addition and many many folks will fall out their knees if this is confirmed to be them but we will see. So we're going to move on from that let me know down below in the comment section what you think that is do you think it's Grimoire let me know. So faction rallies people is here later which faction will you be choosing I'm definitely going with dead orbit for sure I need those ornaments people I actually thought I had their future walkout ornaments on my Hunter 2 but I was wrong luckily I'm a hunter scrub and I have two hunters so I can pick both dead orbit and future walkout happy days a few changes coming to you faction rallies though which should be good last sector chests do not lock you out so you can continuously farm them you just have to defeat that last sector boss before you can open up that chest which is fine they've also added in a few new weapons into the faction engram root pools which you'll see on screen now and also the winners weapons as you can see on screen now look half decent we will see which faction wins I'm going to guess it's going to be dead orbit but we know future walkout hasn't won yet is this their time we will see and that not guys I am out I will be streaming faction rallies later so make sure you have that bow tick next to that subscribe button so you don't miss out on it and yes people I will be playing with you is so guys hopefully I will see you there if you enjoyed the video leaving a like really does help me out and I will catch you on that next one


Hey guys, welcome back to Come Again, TV the only place on YouTube where all geek culture collides. I'm Shannon and today on the show we're taking a look at the Transformers siege war for Cybertron. This is Megatron. So first things first, let's go ahead and move them over to the side. We'll take a look at the box. The box isn't anything special. Just like usual, same side here, same front except it's got Megatron there. Megatron right there. He is a Voyager class. Got the Septicon logo on the top. On the back it shows the different things you can do. You get battle master, you can add the little blast things to him, make it look like he's getting hit or like he's firing himself. It also comes with the directions. I don't transform this guy too often because the first couple of times transforming him, the directions are pretty confusing. So I mainly just set him on my shelf like this. Now I did go over his transformation right before I started the video or right before I started filming. Excuse me a second while I adjust my tripod.  Now I really, I do really like this figure right off the bat. I want to apologize to you guys if you hear a little humming or buzzing in the background. That's my window AC unit. We're going through a little bit of a heat wave here in central Illinois. I'm not going to turn my window AC unit down. I don't have central air. I wish I did but right before we moved in here the central air unit shut down. Sorry about that. So anyway I'm going to try and correct the buzzing, humming, whatever it is in the background in post-production with some compression and maybe some pitch adjustment. See if that helps at all. But otherwise I'm sorry guys you're just going to have to deal with it because even right now my AC units can barely keep up even with them going. They're set at like 75 and or no they're set at about 65 and it's getting so hot outside that they get up to around 80 in here with them going. So you're just going to have to be patient guys. I'm sorry about that. So anyway let's start. As you can see here he does come with a sword which I really like and it does can transform into a gun. You can take the blades off. Now I do have a little bit of difficulty getting these blades on and off but if you turn them just right. If you turn them where you can see right there you should be able to just pop them out just like that.  Fold it back up. Alright so let's go ahead and start with Megatron. Once again I have to say I really like this figure. The transformation sequence not so much. The more you do it the more the easier it comes. But he is definitely a lot better than the old G1 version of Megatron where he shrank and became a gun. That was just ridiculous. I really like his In the Go 90 series. The Prime Trilogy. I really like how they portrayed him. He's really gotten early Vegeta style vibe to him. Vegeta being from Dragon Ball Z and Dragon Ball Super. Really more of an anti hero. I've always liked those portrayals. That's what kind of drew me to Vegeta in the first place and what has drawn me to Megatron. He's just he's not a villain anymore but he's not a hero. He is kind of out for himself in a way but at the same time he's not wanting to rule. He's more or less just fighting for survival now. So anyway let's take a look at him. He's got some battle damage on him. Some scratches and whatnot and he does come like that. So we're going to go ahead. First things first take according to the directions take these clips on his shoulders and fold them up. I forgot to fold them back down after I transformed him back and then take his hands fold them up just like that. Take his gun again according to the instructions. Fold it up like that. Once that's done you raise his backpack. All right his arms unclip at the sides and fold back and there's a peg right here on the gun that pegs into this hole here. Peg it together. Then you bring the backpack up just like this. You fold hold tight just a second guys. I'm going to bring this up a little bit.   And then you kind of push it down so that because if you don't Megatron's head is going to kind of be sticking out. So you push it down just like that. All right once you do that take the waist and rotate it all the way around. All right now let's go ahead and bring this back down. Well we'll just kind of angle it down like that so you guys can see. All right so then take the legs here pull those out. Okay bring them up to the side just like that and then fold them down. So see that spot right there you fold them down just like that. One second guys. All right so then once you do that you raise up the leg and as you're doing that you turn this spot here. Now you're going to have to hold on to this part with your other thumb and just rotate it around just like that. Flip that in and there is right there that goes into that slot there. If I can get it sit tight then you do the same thing with this side.  Clip it in connect it and then once you do that you just take the feet fold them up and you got Megatron in tank mode. Now you can do this two ways you can have it like that which is how the instructions say which has the barrel of the Canon pretty flush with the backpack. I don't like that. You can also rotate it around and now I like that a lot better that looks more like a tank to me and you can take a sword. A sword cannon whatever you want to call it and there's no spot on the Canon itself to attach the other one but you can attach it to the side just like that which you know looks kind of awkward. You almost need two of them to really make it look cool and you know the gun can the Canon can rotate around which is really nice. You can also attach it to the back right there just like that or if you know you want to have have them look like he's cutting through some enemies put it out to the side like that. It's kind of cool but again you almost need two to make it look good make it not look so lopsided but yeah or can you put it in the barrel yeah you can add it to the barrel and make it look extended out maybe even bring it up and have this kind of a tripod which doesn't look too bad looks okay I don't know but there's a number of things you can do with this really it's not bad I like it I like it a lot. So yeah there you guys have it the Transformer Siege War for Cybertron Megatron and like I said I do really like what they've done with him in the Go 90 Prime Trilogy animated series really like it like how they kind of turned him into an anti-hero fits him. Starscream really should be the main villain because he's just so so power hungry whereas Megatron it fits his personality to just not give a crap about anyone but himself and just be out for his survival and if that means aligning himself with the Autobots to guarantee his survival then he's got to do that you know especially when it came to going up against Megatronus you know he kind of tried to ally himself with Megatronus he played it off like two options really self-survival and trying to trick him now I can also do something like that that looks okay but he does roll around has wheels on the bottom so in the way that you have it guys Transformer Siege War for Cybertron Megatron I'm going to try to do a few a lot more of these Transformer videos I know a lot of you really like the history and origins videos especially my Islander series I have not given up on that I will continue to do those but as I've said multiple times Comic-getting TV is a place where all geek culture collides and so there's a lot of Transformer Geeks out there I'm one of them now I don't really keep up on the history I'm trying to read up more on the history and learn more about them I just more or less like them because they're transforming robots always wanted more Transformers as a kid but they were just so expensive the G1 style you know they they were they were still pretty expensive even though they're kind of generic they were still pretty expensive and I really loved Battle Beasts as a kid they were cheap they're set in the same universe as Transformers I think I had the whole collection every time we went to Kmart or whatever as a kid I always picked up a set I think they came in a two pack at the time so my mom let me get a couple of them they were really cheap like a dollar or two this was back in the 80s and I loved the hologram on them on their chests used to play with them for hours on end I kind of wish they'd bring Battle Beasts back in that same style that they had before I tried looking them up online on eBay and stuff they're pretty expensive now which makes me wish I would have never lost all my Battle Beasts so anyway there you have it guys I'm Shannon for Comic Getting TV the only place on YouTube we're all geek culture collides take care geeks if you enjoyed that video make sure you hit the subscribe button right there so you can stay up to date on all things geek culture also make sure you check out one of these two playlists on the side for more videos just like the one you just watched I'm Shannon for Comic Getting TV the only place on YouTube we're all geek culture collides take care geeks


He's one of the greatest actors of our time, but when the truth about his personal life came to light, his House of Cards came tumbling down. How did this happen? Ladies and gentlemen, this is Matt Rogers.  Not long before then, we had releases such as Rebel in the Rye, Baby Driver, Nine Lives, which we won't talk about, and of course All the Money in the World. The movie that had the Academy ready to give him his third Oscar. However, director Ridley Scott wanted nothing to do with him after the allegations and cut him out of the movie altogether. Netflix then cancelled an original title, Gore, which had Spacey in the lead role. However, this year, director James Cox decided to keep Kevin Spacey on for what may very well be his final movie. The Billionaire Boys Club. Filmed in 2015, Billionaire Boys Club is based on the true story of a bunch of teenagers that hit the big time back in the 80s, which eventually turns deadly. Spacey playing Ron Levin, a high-roller that takes an interest in Ansel Elgort's character, Joe Hunt. The two actors having worked together previously in Baby Driver.  But as usual, he does play it effortlessly. Issue is, though, his character spends his scenes admiring these young boys, which hits a little too close to home knowing what we know now. The movie itself? Not so great. It's sort of like a worse version of the social network, or jobs. The pacing's all off, the story's cheesy, and in its opening weekend, the movie brought in a dismal $126 US. In all fairness, due to the media shitstorm surrounding it, the promos and trailers went unseen, and it was an extremely limited release in cinemas, so it didn't really stand a chance. But the producers decided that they didn't want the misconduct of one man to stop the world from seeing the hard work put into the film. They scrubbed Spacey from the posters and sent off the finished product as is. I remember Spacey's movies like The Usual Suspects and my all-time favorite movie American Beauty were so iconic, and it's a shame that this movie is the full stop on his filmography. Barty obviously has to face the consequences of his alleged actions, and as much as I hate to believe it, it's hard to argue with 20 odd accusations. But have you seen Billionaire Boys Club and do you think it will be his final movie? I'll be interested to hear what you guys have to say. Make sure you subscribe as I'm bringing you all new videos every single week. But until next time, thanks so much for hanging out. If you had a good time, then spank that like button. And if you subscribe during this video, then walk them aboard. This is Matt Rogers, and that is all.


I have stood up for many causes, but in many ways the bunch of you who are here, we would like to record your presence here and make sure people know that you wrote for a cause that is not a choice but a must. So this Kaveri Kugu, Kaveri calling, did it actually struck you back then or how was it? At that time if she didn't need our care, we were just enjoying her care. Today, unfortunately she needs our care, very sad. A life that's much larger than us, a life which runs for millions of years and we are puny creatures who come and go, but we've put her down on the knees right now. So many projects are there, we need to find out more about it, why we don't have the opportunity to do it. When we look at our children, we can see that they are growing up in this country. This is the land, this is the place where we are going to find out more about it, we will ask them what they are going to do to find out more about it. We are not going to leave the forest, we are going to leave our land, we are going to leave the forest, we are going to leave the forest, we are going to leave the forest, we're going to leave the forest, we're going to leave the forest, we're


My name is Mike Schassburger. I'm an engineering manager that leads a team of engineers that helps our partners with integration of our application. We want to be able to provide our customers with a consistent, great user experience across all of their devices. So when they think of Netflix, they think of Netflix anywhere. We started off as a very small team. We've grown the number of devices in the tens from when I started into the thousands now. So it's not just internal cross-functional effort. It's external cross-functional effort. And being able to switch between those things on the fly day to day keeps the job very fresh. I'm Shamsen Doga Padoveshan, my partner engineer at Netflix. Our role requires us to collaborate with a lot of partners, both internally and externally. And together, we learn and grow. We solve a lot of interesting problems in multimedia systems and embedded system platform. We do a lot of prototyping. It helps us understand and define what the performance curve will look like for a partner. And it's not already in the true sense, but it's more about research and rapid development. We are less about failing and more about figuring out how we eventually succeed, right? So I'm Sue Abelera. I'm an engineering manager here at Netflix, part of our partner engineering team. We help our partners port Netflix to a variety of devices. So we're focusing primarily on TVs, set top boxes, Blu-ray players, streaming media sticks, things like that. And each one of those devices has a lot of variety. So they're all different kinds of devices. They have different proprietary hardware and software. So there's a lot of challenges in porting Netflix to those variations. It's really a global role in a lot of ways to understand how these technologies differ from country to country, from space to space. Some of the technological challenges and the functionality, sometimes it's in software, sometimes it's in hardware. Most of the software we work on, it's the software that's touching the hardware. So those engineers that really like that fuzzy line between hardware and software, they love this role. They really like to be part of something bigger. They want to be part of the global reach. I love to be able to basically have a job. That's simple enough that I can even explain to my grandmother what I do. Because I can go into Best Buy and I can show her, look at the TVs. See how Netflix is running in the TVs? I did that. That's what I love. Every year we get a new technology that's coming in. When I started it was on Flash, then we went to Qt WebKit and now we're using a JavaScript-based engine. I'm looking for engineers that can go out, meet partners, be a leader, represent the company, and drive the external and internal initiatives necessary to deliver a successful product. Since we're a global company, we take our integration very seriously. We want our device experience to be consistent and ubiquitous across any device that you choose.


Nostalgia! It's Pinocchio. I'm a real boy.  This is essentially a recreation of the animated one because that's what Disney's doing. I don't know how many times they're gonna use this creepy-ass real CG, but it's not working. They can't do the wild expressions that are needed to convey messages.  That's in this too, but they get a sugar rush. They're just drinking root beer and going down a candy mountain and, you know, just really hanging out at Neverland Ranch until eventually they do in fact turn into CGI abominations. So we have lifeless animation. We have actors that don't seem to give two shits about the project. I don't know what else there is to say. Disney's been killing it. As in our childhood, constantly the last decade or so. I can't wait to see what they do next.


Going on everyone Sam here with late and sports cards rip in 23 peninu origins football hobby eight box break number 22 pick your team style Yeah, I guess so guess it worked for a couple of people We've got Andy F with the Niners Ben L Packers Brett W Ravens Charles a with the Seahawks Charles a n with the Seahawks Charles at with the Chargers Chris V Colts Dennis K with the Vikings Felix N Bangles Saints and Bucks George M. Jags Greg E with the Patriots Jason M. Giants Joseph M with the Cowboys Justin C chiefs Matthew S. Texans Eagles Matthew R with the Raiders Cardinals and Lions Matthias N with the Commanders Nate S with the Broncos Omar Y with the Bears Sean P Falcon Steven W Rams William Q with the Steelers and Willis T selling us out with the Bills Panthers Browns Jets Titans and dolphins, so thank you all everybody. Let's get started on this one Kind of a stud That's pretty cool fire Nashi Harris the 149 And Daven Coke to 75 matter samples a big brown CMC and Aiden O'Connell rookie where you drop that in the trash Marvin Mims the 199 do it again for the Broncos nice one there Denver got Zay flowers rookie Jersey Auto Congrats on that Ravens Zay tovin and Then we've got Aiden O'Connell. That is rookie jumbo a patch autograph orange. Go to the Raiders. Congrats Raiders Raiders Literally him and hard and this might be a shot shucker now Also, no no who great A lot of shots to be taken Franchise I know Let's hit the brakes Joel to 25 is Nick Chubb the franchise call in someone else the franchise in 2125 Desmond Ritter Sound great, dude To Will Anderson We've got Luke Shoenmaker 299 from Hamden, Connecticut Nice one. Let's go CT baby Big ups with Connecticut there will Anderson jr. 299 Rookie Auto for the Texans every knows the handings. Oh, yeah And Roshan Johnson rookie Jersey Auto for the Bears Crath Bears We've got Aaron Jones to 75 and to 149 Darius Davis Hages like Parsons will have us rookie Doose Vaughan to 199 for the Cowboys This one here is gonna be for the Vikings Jordan Addison to 49. That's on that there Minnesota Knock off God and rookie jumbo Jersey Auto at Rams Stetson Bennett this one there ramps I'll pull it off real quick. What is it the last post on Instagram? Or he says it's so difficult to not comment on that last post booklet Got the booklet in here everybody Aiden O'Connell to at 75 and orange to 125 Don Tabion Wicks To a country Miller rookie on LH aerial gunner. Oh geez Nick. Yeah, that's rough To at 49 is Stetson Bennett. I got you Get him out of here, man. I just went in here Devon achan to 75 color match your ink orange with the Dolphins booklet sir Tyler Scott rookie Auto for the 49 Michael Meyer going to the Raiders nice one there Yeah, it was a great touchdown two-color RPA booklet on cards Yeah, breeze we had it we both had a prize picks scored take it right back All right, we got Zach Charbonnet to 125 and Khalil Herbert to 99 we got QJ Johnson and origin story Jackson Smith and jigba on the case hit Grats on that. What nice JSN birds. I'm not originally from here to be fair Nick But we all kind of like different teams. Yeah, it's a 199 is Dorian Thompson Robinson. Nice one there True Keishan bouti to 99 Grats on that one there patrons and Redemption is Bijan Robinson going to the Falcons rookie jumbo Jersey Auto Falcons Bijan Grats on that falcons in O'Connell to 125 for the Raiders and 299 John Matchy for the Texans John Matchy again Tanner McKee rookie No, say flowers to 99 nice one there for the Ravens Grats Baltimore Zato Quentin Johnson rookie auto nice QJ congrats on that one there Los Angeles Pj and jaren hall rookie Jersey Auto for the Vikings. There you go again, Minnesota. Minnesota doing well There you go, Dennis Yeah, he did Jalen Geithan is back after like missing two years with like a knee injury and these scores that touched on what the heck What are we doing to 149 Devonte Smith and a 50 AJ Terrell for the Falcons nice one there and Devonte base of Miles Garrett in Israel Abinaconda Tank Bigsby 299. I ain't touch it What that that whole thing just move Shmere Gibbs, I don't like that rookie auto nice one their lines And jay caner rookie patch auto 299 read for the Saints Got Dalton Kincaid to 149 and to 125 George Pickens Deandre Swift and Jordan Addison rookie and as a jumbo Jersey 299 will Leviss for the Titans Kendra Miller rookie auto on card for the Saints the Tyler Scott rookie Jumbo Jersey Auto going to the Bears nice one there. That's Chicago. Alright, do a quick recap here everybody start with the jerseys We had a will Leviss That is think Bigsby say flowers Dorian Thompson Robinson Stetson Bennett juice Vaughan Luke Schoonmaker Marvin Mims Michael Meyer jumbo RPA booklet We had a B. John Stetson Bennett my Aiden O'Connell tank our will Anderson K. Sean Boutie Kendra Miller Jameer Gibbs Quentin Johnston Debonne Achan Tyler Scott Jordan Addison Zay flowers Roshan Johnson Jaren Hall Jake Hainer Tyler Scott Jackson Smith and jigba. I'll do it for the break everybody Thanks again for the fail coming up next is the random for the Joe Burrow


I'm on this quest to rebuild civilization by building myself up technologically from the very beginning. Breaking into the world of electricity and electrical components, I ran into one minor hurdle. Wire. Turning metal into long, thin pieces of wire has turned out to be a little bit more difficult than I expected. But let's dive into this and see exactly what it'll take to make some wire. I've actually done a few videos trying to make wire before. Several years ago I did some gold dry panning in the desert with William Osmond and attempted to turn the gold we collected into a long piece of wire. The actual process ended up being frustratingly difficult, with it continuously breaking and losing really expensive pieces of gold piece by piece. Actually drying it into a long piece of wire never ended up really working out. Later I explored similar topics covered in the anime series Dr. Stone where they addressed the challenge with a creative, although dubious, centrifuge device to theoretically produce thin gold wire using basically a cotton candy machine. My attempts to recreate this were quite unsuccessful as well though. Historically this process has been done for centuries, basically using the same method as what I tried the first time with the gold wire. However there were clearly some tricks I was missing. When it comes to historical methods of drying your own wire, I basically found only one source online, Ironskin. So I set up a call to talk and get some tips from them. I'm Sebastian from Ironskin. We are a small business of four people and we help people with chainmail. So we do tailored chainmail, we help provide tools and instructions. So I did this whole video on trying to make wire before without much luck. I think my biggest issue is that I ended up starting with gold, it's kind of expensive material to mess around with. What's your general advice when somebody is first learning how to pull wire? Before you start pulling, blacksmiths and shape it to somewhat smooth shape. So materials, some of them become very brittle after a short time of cold working and that's what you're doing when you pull wire. Soften the wire by heating it up, that's called a kneeling and you do that every couple of steps. Another mistake is you need to have proper drawing plates and they need holes to be spaced in a correct ratio. You can't just go from a very large hole to a very small, they need to be say 10% or less decreasing in size. What's the largest project you've made with riveted mail? Most of the time I make shirts for large and for small people, can weigh up to 15 kilograms. Add that up, a shirt contains about 30,000 rings. That takes me about two minutes per ring, 1000 for two minutes a ring. How long did that take you to do? Yeah, almost half a year. What we found most useful from his videos was the use of a windlass to apply extra power to the pulling. He also demonstrated a basic rig that holds the pliers tight while the rope is under pressure that greatly helped in this endeavor. Thanks again to Sebastian, be sure to check out their website ironskin.com for lots of useful information on historical wire drawing and chainmail making. But first thing you need to do to sponsor BetterHelp, a new from a personal experience that there are often times when you need some outside help to help you get through some difficult situations. Trying to handle your struggles on your own is a heavy burden and getting professional help can be all the difference in the world. Whether through BetterHelp or other avenues, it's incredible how seeking professional help can make a real difference. The very first step of just finding your therapist can be kind of the largest burden to overcome. But today's sponsor BetterHelp can make those first steps super easy by connecting you with a licensed therapist best suited for your needs. You can take the first steps by heading to their site betterhelp.com slash htme. BetterHelp matches you with an experienced professional tailored to your needs. The best part you can engage with your therapist from the comfort of your own space through messaging, phone calls, or video chat. BetterHelp usually matches you within 48 hours, ensuring a swift start to your mental health journey. What better help be your guide to a better and happier you? Visit betterhelp.com slash htme or choose htme during your sign up for an exclusive discount on your first month. Remember, mental health matters and taking that first step is a sign of strength. While tackling this topic and achieving a better success added has been the top of my list. My new assistant Elliot had his own special interest in this topic and spent several days troubleshooting and figuring out how to finally achieve success in the process. I took some schooling and electrical engineering. Also I'm just an enthusiast and hobbyist of electronics. I've been messing with them since I could turn a screwdriver. Wire in particular I think just has a lot of uses. A lot of people like the obvious one is chainmail. Small wire in particular means you can make magnet wire. So very high gauge, tiny, tiny filaments of wire, meaning you could make generators, motors, electromagnets of pretty much any kinds. There's just a lot you can do with magnet wire. The process is kind of insane. It's very laborious and it was a huge learning curve for me. First of all, understanding the annealing process. Honestly, I'm surprised it worked at all. What we're going to start out with today is just a scrap piece of round rod. I'd say it's probably some motors between quarter and half inch round rod. The idea is we're going to draw that out to the most narrow diameter we can. We're going to start out drawing it out square. Get that as long as we can. And then we're going to knock out the corners, make it into an octagon, and then round that off to finish it off. But the idea is the smaller we can get it here, the less work we have to do when we pull it through the draw plates. So that's the idea. We'll see how it goes. Okay, so we've got our basic rod forged out. It measures in at just under four millimeters. So I think that's a pretty good starting point considering that was all done by hand. Then we have our basic rig set up here. The holes in this die basically increment, I believe, in tenths of millimeters. And then what we have set up here is a basic kind of like tension system. So as this pulls, it'll tighten down on the pliers and hold them attached to the rod. Down here, we just have a basic kind of crank system set up. So I guess we can give it a try, see how we do. It takes quite a bit of force, especially when we're at this size of rod. And it kind of bounces around like that in the first few holes just because we've got some inconsistencies in the size of the rod. And there we are. We just do that about 40 more times. This is pretty much our end product at this point. We figured we started at about maybe five inches of raw material and we've ended up with basically 50 inches of wire. So a 500% increase in length, not too bad. Final diameter, I think, came in at 2.2 millimeters. I'm pretty pleased with the result, considering what we started out with. Also, during the like hand forge stage, getting out as many of the imperfections as possible before getting to the drawing stage is ideal. Finally, the rig, I think, has room for many improvements. It's incredible how much force it takes, really, to pull this. At one point, I was lifting up the entire workbench just to crank it. I wouldn't underestimate how much cranking power you need. So we just have another, what, half-mile to go? After the point of making actual wire, our project is going to kind of split in two directions now, historically. Wires used in pre-modern time was primarily for jewelry or for making armor with chainmail. The two closely cut rings are riveted together, deforming nearly impenetrable piece of armor. It's an incredibly slow process, so actually finishing the armor will be part of a later video. For now, our focus is going to be on a more modern use of wire, electronics. So for that, we're going to want to use the more conductive metal of copper to draw some wire. Overall, the process is pretty similar to drawing iron wire, but potentially easier. Starting with a two-inch chunk of ingot, we hammered it down to about two feet. By slowly drawing it down through narrower and narrower draw holes, the wire was stretched longer and longer. To let the end, we reached over 40 feet long. It was, at this point, the wire started to break, so called it good enough, reaching the diameter of about a 16-gauge wire. To demonstrate the new potential that this wire allows for us, we attempted to construct a crude electromagnet by wrapping the wire around a piece of iron and keeping everything insulated from each other through the use of beeswax and cloth. When a current is applied, it can create a temporary magnet that can be turned on and off by applying a current or disconnecting it. To power it, we brought back the original first battery we made last year, the Voltaic Pile. With our size of battery, though, it didn't contain a lot of power, so the effect was pretty minimal, but it's enough to prove the concept. So we are getting decent voltage. That's like a nine-volt battery right there, but we're operating in the order of milliamps. So improving the battery, not using fair wire would be nice, because the more tightly wrapped the coil is, the more power we're gonna get out of the magnet, and then just many, many more turns of the wire. I think it works. So the concept of wire is probably not the most interesting or fascinating. This little device really opens the door, especially when you use it to make things like the electromagnet. This is a fairly crude one that was mostly just for demonstration purposes, but a little bit of refining, mostly by getting some actual insulation on our wire so we can wind it a lot more and tighter, and probably most important, getting a stronger battery, we can actually build some pretty powerful electromagnets. It is a pretty crucial invention for doing things like motors, generators, the telegraph, and we're actually gonna try and make our own telegraph system pretty soon here, and basically invent our own very first telecommunication network. So this invention and process of making actual wire has been with us for centuries, and it's only with real modern knowledge can do a little bit more advanced things with electricity. You know what I'm just gonna allow us to make some major jumps ahead in kind of the time scale we're in. That being said, we're still working on the chainmail, and it's gonna be one component of the suit of armor that we'll be building, and we're basically building that just to destroy it and to see just how durable some armor is. Kind of a different ends of the spectrum on the uses of wire from both durable production to eventually being used to help spread information at the speed of light. Thank you again to all of my supporters on Patreon. Thanks for watching. If you enjoyed this video, be sure to subscribe and check out other content we have covering a wide variety of topics. Also, if you've enjoyed these series, consider supporting us on Patreon. We are largely a fan-funded channel and depend on the support of our viewers in order to keep our series going. Thanks for watching.