Okay, so let's get started. Just so that things are completely clear. I'm sorry for those who actually know this by heart. But let's imagine we are all new. This is a new model. Nobody has ever looked at it before. It is Friday afternoon. We have a great idea. And we want to do a simulation. Or now you don't want to do a simulation. We want to sample the probability distribution, which is the partition function of this new model. This new model has a z equals to sum over all spin configurations e to the minus beta e of sigma. So it's a new model. We don't know whether anybody has ever looked at it before. And we set up our first algorithm. This first algorithm will be Markov easing dot pi. So what we do is we pick, it's on the three by three letters. We take one spin. This spin is equal k, we take it randomly. Just so that we all, so we take a random spin. We take a random spin and the move we do is we try to flip it. Now we compute pi b and pi a. Now detail balance tells us that the probability pi a times the probability to go from a to b must be equal to pi b times the probability from b to a. So pi b is e to the minus beta energy of b. Pi a is this. And this makes that we have probability from a to b divided by probability from b to a must be equal to this if we satisfy detail balance, of course. And this is implemented through p from a to b equals to minimum of one e to the minus beta eb minus ea. So then, so this is just to answer to, again, it's your question, but it's probably all the question of other people. Then no other questions have to be asked. Then, as one question left, come on. Thank you. Exactly. So what is the correlation time of this algorithm? So we also have to check that it's a periodic and so on and so on, but this is just a detail. We just have to check, we just have to make, we have to find out on what time scale it converges from this initial choice. You see the initial choice is this. This is the initial choice, that this means that at time zero we have a random distribution. So this means pi, so we have the probability at time t equals to zero is random. And now it is the question on which time scale do we convert towards t infinity, a pi infinity which is the probability distribution, the Boltzmann distribution. Pi equals to pi infinity. So on what is the time scale? But besides this, we are completely clean. There's no question that has to be asked. We know that we will convert and there's not a single thing that we have to know. There's no mystery. We have to ask our thesis advisor, well, this is okay. We know it, right? Because we've proven it ourselves. All right? So then I had this discussion a little bit. So see here. Here we are at high temperature. We have little areas, right? Here we have like 15 spins that are up. Here we have 20 spins that are down. A few spins that are up. And now what we have to do is we'll take a random walk in some walk in configuration space and we have to sample configurations. Just like in this case of the Gaussian distribution that we had before. Sometimes we have to find a configuration that was up. We had a cloud. The distribution was something like this. Sometimes we have to find this here. We have to sample here. We have to sample here. And we have to sample here. So that's what I mean. We have to find samples, but not all the same. So what it means is sometimes we have to have a sample that is all minus here, but then there will be a sample that has the same energy, the same right to be here, where this will be plus. But flipping this 15 or three or four spins will be easy with this algorithm where we take one by one. It will be easy. So this algorithm will be fine at high temperature. The algorithm Markov-Easing, if we had more time, we should program it. Let me find a nice little... Okay, now I plug. So for configurations like... So let me look at this one. Anyway, so there are some configurations. So the configurations around T for T, around the critical temperature. We have these big blobs. So for large systems, this would be one million or 10 million more or less up spins. They are not all up spins, but 10 million spins that are more or less up. This is the... It's like this that this configuration look at the critical time. Then you have 150 million spins that are more down. So I'm just telling you. And now you have the same problem that we had before with this, with the Gaussian. You have to sample here and here and here and here. So you should go from these where everybody is up. 150 million particles are up. Understand what I'm telling you? The sampling means you have to get the representatives but different representatives. They should not all look exactly like this with just a few spins flipped. And that is where the Markov easing... Markov easing.pi that is a fantastic little algorithm but it has a problem there. So now we had discussed the first idea and now we go into seriously into our business here. Seriously. Now I want to show you that we can satisfy... Here we are in detailed balance. We can satisfy detailed balance. Okay. For any value of p. Now, let me put this away. I'll come over. Okay, now the way we go is now... But let's run the algorithm. Let's run the algorithm. I accept this with p. Then I accept this with p, with p, with p. This one I have rejected. Maybe. This one I have rejected. I think a system with two screens makes no sense. I mean, just think of it. I mean, this is just a parenthesis. A system with two screens with independent screens that would be useful. But a system with two screens, in my opinion, makes no sense. Maybe I will have to leave your answer on it.  I'm not Schrodinger's cat. So now... So now I'm like this, like this, like this. Okay, so this is... I have not yet accepted this move. It's just the move that I propose. Okay. Now, what I'm saying is I'm a little bit confused of what my problem is. So now you have some... So this is the cluster. Let's call this a cluster. And I want to flip it. But now I have to see that there's a principle of life. It means that I have some connections to negative... There are plus-minus here. So we have to count them. Could we count them? One, two, three, four. So it's a number. I think it's either 14 or 18. So the plus-minus, we'll go through this. We'll spend half an hour on this. So I think the plus-minus links are, I think it's 18. Maybe somebody can take it over here or over there. I think one, two, three, four, 18. Do you agree with it? So we have 18 links plus-minus. But we stopped there because we always... It was in our... We had the idea over beers yesterday. We decided only to have a cluster with plus-and-plus-and-plus because this is what we thought was more interesting. And we have the full right to build this cluster. But now we have also plus-plus-links. Plus-plus-links. So we stopped here because we have this plus-plus-links. And I think there are 14 of them. So now the cluster construction stopped here. That's what I tell you. This was when the cluster was stopped. So why did it stop here? Well, it stopped here because we had 14 chances of growing it. Because we would have accepted this one with probability P. Following me? Right? So we have... So we rejected this move. We accept each neighbor with probability P. But this one we did not accept. So there is somewhere at the end of our argument there will be a 1 minus P to the power of 14 in our argument. You agree with that?  Build a cluster. I take... You know, you can build a cluster. You take a neighbor, and this neighbor you take him or her with probability P. At some point the cluster construction is over. Over. So now why did you stop there? Well, because there are some links across the boundary of the cluster. And those you did not take. And each of them was independent. So you accepted each of everybody with probability P. You rejected each of these links with probability 1 minus P. So because 14 times you rejected it, there somewhere must be, at the end of the day, there will be 1 minus P to the 14. I'll show you in just a minute. So something has to happen here. So now I also have to see the... But let's do it later. We'll have to do the return move, and we'll do this later. We'll go through it twice, I think. So here we have it. Okay. Now, I don't know what I wrote on my slide. But now let me use the detailed balance condition. The detailed balance condition says Pi of A times the probability to move from A to B must be Pi of B, P from B to A. So that is a real rule. But now we say that this one here, according to Metropolis and Hastings, is the probability of Pi of A.  This is the Boltzmann distribution, not the Boltzmann weight. Pi of A times the A priori probability to go from A to B times the acceptance probability from A to B must be Pi of B times A B to A times probability acceptance from B to A. So everything in this equation is known except of... What is not known for us now? What do we have to compute? Is the Boltzmann weight unknown? No. This is the configuration A, excuse me. This is the Boltzmann... This is the configuration A. This is configuration A, and configuration B is the same configuration with the gray pluses down to minus. So is the Boltzmann distribution Pi of A is this known? Yes, right? It's the e to the minus beta energy. So is the... So the A priori probability to go from A to B is the probability to construct this cluster. So the probability to construct this cluster has a few... So there's a probability...  There must be a number of Pi's, but then it's really unfortunate that these same Pi's also appear in the configuration B. So this is configuration B. I should write it down here. This is configuration B and now I have to compute the probability to go from A to B and the probability from B to A. So some parts... So the cluster is plus and then there are some pluses here and some minus. This is configuration A and configuration B... And configuration B is this cluster here with little hole is minus and this plus, plus, plus and minus. This is configuration B. So now the cluster construction probability has some terms that are internal between the spin that is up and the spin that is up here. But you notice that this thing is the same as the probability if we have minus and minus. So what happens inside the cluster is not really interesting. It's not really important. But what is interesting is in the cluster construction probability is also the cluster... the end of the cluster construction. So why did we stop here at this configuration? So why did we stop here? Well, we stopped here with probability 1 minus P to the... what was it, 14 or 18? 14 I think. And here from B to A we stopped... we would have stopped because now we have not 14 links minus minus. We stopped this cluster construction because we have 1, 2, 3, backtrack and those will be 18. So we have this probability from A... the A power of B to A will be 1 minus P to the power of 18. All right. So this means... is this clear? Is this clear? Very, very easy. Very, very easy. You know, there's no... and then there's some chunk... let's say... there's some chunk that is internal and there's the same chunk that is internal. Okay, so we have inside... the probability to add a new link minus minus in the cluster that is minus and minus is exactly the same as the probability to add a new link plus plus in the cluster plus plus that unfortunately I have to take. So this thing here is the same as this here. So, you know, I can just... I can just take it out. Okay? All right, so we have finished. Time flies. No, time doesn't fly. So it's exactly contrary. So, but we'll tell other stories later. So we already know that P from A to B divided by P from B to A is equal to pi B divided by pi A times 1 minus P to the power of 18 divided by 1 minus P to the power of 14. So now, what remains is to compute pi B divided by pi A. Pi B is e to the minus beta energy of B and pi A is e to the minus beta energy of A. All right? So now... So now you see this is configuration A and we have to compute its energy. So we should compute what is the energy here. But, you know, it's kind of a little silly because now this is B, this configuration B. Next time I give this talk and put an enormous B here. It will be so great. Okay? So, but this one is the same as this one. So I don't have to take this into account. Then there's this energy. See this here? Two upspins. But this has the same energy as two downspins. So this does not play a role at... Okay? This does not play a role at all because I have to... I have to look at the audience. Oh, excuse me. All right? So this does not play a role. Okay? So the only thing that plays a role is the energy across the boundary. So what is the energy across the boundary? Can you help me again? So here we had class minus was 18, right? In configuration A and plus plus were 14. So the energy across the boundary about the boundary of the cluster is 18 times what is the energy of plus minus? It's minus one or plus one? Plus one. Thank you. And minus 14. And in configuration B how many plus minus links do we have? How many plus minus links do we have in configuration B? No, don't count. I'm just... 14. 14. Thank you. 14. And how many plus plus links do we have? Zero. Because we have no plus plus. How many minus minus links do we have? 18. So in A energy across the boundary is this and energy in B across the boundary is 14 minus 18. So now I have to look into my notes because one of the numbers... so energy is n1 minus n2 so this is... let's call this n1 and this call is n2 and then this is n2 and this is n1. All right. So now we are already finished. Already finished because now we have P A to B divided by P from B to A is equal to pi B is e to the minus beta the energy but only the energy across the boundary n2 minus n1 divided by 1 minus P to the power of 14 with n2 times 1 minus P to the n1 divided by e to the minus beta n1 minus n2. So how do we program this algorithm now? So we are finished. So I'm here. I'm finished. So how do we program this algorithm? If we have this equation this equation P A to B divided by P does anybody check the algebra? I mean just... algebra is a little big word for you know consistently putting the n1 instead of 18 and n2 instead of 14. So this is then metropolis algorithm means that P from A to B is what? Minimum, excuse me, thank you. This is where you see you have been successful and you're corrected. Minimum of what? 1 This whole story here, right? Let's do it later. All right? So now this is a number. So you see n1 is 18 n2 is 14 in this cluster construction. So beta is a number. n1 is a number. n2 is a number. As I finished my cluster construction I ended up I can look at how many n1s how many plus plus and how many plus minus I do have. And this number for the choice of beta is 156367. It's a number. It's not a function. It's a number. You following? It's a number. For any beta, beta is a number and this is a number. And then I have to accept this move is probably 0.1563678 and I have to reject it otherwise. And this number depends on P. See? So I told you that I would be able to find an algorithm that was valid for any value of P. And this is it. Except for P going to 1 I think this kind of... for P going to 1 I have a problem and that was my trivial algorithm that was soldering the spins together and this is just it. This is the acceptance. This is the acceptance. This is the acceptance. Yes. This is the... So this is the little P. This is the acceptance probability for the move that had a biased construction. So it has a biased construction to this A. So we are fully in the... we are fully in the... you know, in the bias. So the way we went from A to B is completely biased that we are taking the bias away. All right? So now... now let's do a little simplification. All right? You see, let's do all the N2's on one side and all the N1's on the other side. So here we have a e to the minus beta N2 and here we have an N to the plus beta N2. You see this beta N2. This makes e to the minus 2 beta N2 divided by 1 minus p to the N2 and then multiplied by 1 minus p to the N1 and this gives here e to the minus 2 beta N1. And this is nothing else, nothing different. This is equal to minimum of 1 e to the minus 2 beta divided by 1 minus p to the N2 1 minus p divided by e to the minus 2 beta to the N1. This is the same number 0.153367. So I didn't change anything. But now a miracle comes out. Miracle. Miraculoso. Completely miraculous is wunderbar. So completely wunderbar is that e to the minus 2 beta is equal to 1 minus p then this number is 1. So the magic value and this is what you should do in your thesis or postdoc work you know, be the first on a new subject and find the magic value if e to the minus 2 beta is 1 minus p or even better if p is equal to 1 minus e to the minus 2 beta then the acceptance probability again it exists. The algorithm of course functions for all p's but it is at its best value. So p is equal to 1 minus e to the minus 2 beta is the magic value. OK. I don't expect any questions on this derivation because it's so easy that everybody has understood it. Right? I mean is there any question one could be tempted to ask? OK. Who say, I don't know I don't know anything about critical temperatures. Yes, it is true. Of course. Yes. It will turn out that this is the percolation threshold at the critical point for the percolation problem that corresponds to this problem but this algorithm but the reason why I did not bring this up is because I got interested in this subject I was a few years younger and somebody was doing a thesis on this algorithm and he thought because it's common knowledge that this algorithm only works at any temperature and it's completely bullshit I mean I did not talk about this algorithm works at any temperature for any beta you choose 1 minus p p equals 1 minus e to the minus 2 beta you need really good good eyes to wow I really admire you I mean you should get a job with Lufthansa I mean if you can I know why your physicist if you are sitting so so far back and can still see things you should work with Lufthansa in addition they are always on strike so you don't have to work at all so anyway so this is p equals 1 minus 2 so I give a little bit short-handed answer but this algorithm works at all temperatures and now the question is what is the size of the clusters that the cluster sizes will be exactly at the percolation it will be percolating at the critical temperature so is there any other question just on the algorithm I don't expect any yes that is the only question that is really good I mean you got this I drew these pictures here see this guy here but you cannot you are not a Lufthansa pilot here so this is exactly for you I tried to get this one with p from this one with p from this one and with p from this one but once it's over it's over I ask once it's like not with dating but it's a little bit like this each one asks the other one once and if there is rejection from somebody else so it's a link it's on the edges anything else okay so we can all program this algorithm and sure enough okay so here again I thought I would need help but it's okay so it's the same but I just had so this is the algorithm the voice cluster algorithm alright this is the algorithm it's complete 14 lines I start oh yeah let me show you so now it would be really interesting to have a asynchronous system of presentation things here so anyway so I started here so now what I do okay let me go here excuse me so now what I'm doing is the following I'm using an idea that comes from a paper that I wrote with water and we call it the pocket algorithm and the thing is the following when we have we have a cluster so we are constructing the cluster there are some spins that have already been there for a long time and some spins that are newly inside the cluster you know what I mean I just added them I'm constructing this thing here so at each time there are some that just came in and they have not been checked on whether they wanted to have themselves new neighbors you get this idea and those that are kind of old folks they have been in the cluster for a while and I don't have to check again whether their neighbors want to be I already checked all the neighbors of the old folks okay you get this idea back there so now the new ones these new ones new spins in the cluster we call them the pocket it's like my right hand pocket I explain this in the algorithm here it is so now I take a random spin that is how I construct the cluster and initially I say the pocket is just that spin and the cluster is also just that spin alright following? because I just have one spin and that is the case so now I'm saying while the pocket is not empty I take one guy out of the pocket I check all its neighbors I check whether the neighbors have the same spin and they are not yet in the cluster and if they are the same spin and they're not yet in the cluster then I throw a random number between 0 and 1 check whether it's smaller than p and I add this new one into the pocket and add it to the cluster and then once I'm done with checking all its neighbors I take it out of the pocket because now it's an old fork it's an old guy alright and when the cluster is empty the construction is over I flip the cluster I flip the spins and that is the wealth cluster algorithm a loop in your eye effect where you touch the cluster again and there was one bone which was already not accepted and you are there again from the other side oh that is just no but that cannot happen because yes of course this is a counted two but I can tell you exactly how it is because it's the new spin see I take I put this in the pocket all the new spins I put them in the pocket I said they are not processed yet the new spins but each spin gets only taken once out of the pocket I take it out of the pocket I check all its neighbors so this link, this link and this link I take away the neighbors that are already in the cluster and then I have fresh links outside of the cluster and those I check but then this guy of which I'm checking the neighbors gets thrown out of the pocket so it will not come in again we can do it again but this is the 12 line wealth cluster algorithm and I think this is something that everybody should have thought about so there is no need to have this very complicated normally this is almost like poetry I find I mean I've written these programs also in 4277 they look a little different but I mean this is like it and this is the algorithm and I'm just saying here's the cluster here are the new guys here are the new guys these are the pocket they are inside the cluster but they call them the pocket side so now the algorithm is take this out take this pocket side check all its neighbors don't check those that are already in the cluster okay and then maybe add them don't add them but then take this out of the pocket and this becomes an old side okay and then this one will be in the pocket if I accept it so this again 15 line of code and it's very useful so now let me show you a movie excuse me no I don't have to thanks for the question I have another version of where I do it was an exam question last year but it's were you in Paris? no welcome anyway so that was the exam question I mean it's never a big question so the question is can we replace the random choice random choice of the pocket means I have a pocket full of sides that I have to check do I have to take a random choice or can I take just anyone so we proposed I replace this line by pop one out of the pocket and of course this algorithm is also acceptable it's the same it's a different algorithm but it's also it's too thankful question other inside this gets you have to think hard anyway so okay so that is the algorithm you know subliminal message you know there's no point in hiding these structures in 1500 thousand line codes I mean the idea is here so this again I said this is the algorithm of Uli Wolf from 1989 complete revolution one of the I would say together with the original works on molecular dynamics and on Monte Carlo this is like this is what kind of pulled off the whole revolution I can tell you there were lots of people around the question was not really for the easing model because it was already half so the question was how to use it for the XY model where this is a good idea to do and there were lots of people who almost got the good idea so I just encourage you to have a good idea almost half baked idea go through and find it find the answer and you won't be you'll be a man so now okay so now I have a movie I have a friend in Hollywood who runs them so this is the at the critical point one iteration after the other the clusters that I construct I'm colorblind so I cannot really see them very well but blue I think are the ups red are the downs and there is some kind of strange color that gives the cluster so sometimes this runs so at the critical point that was your question at the critical point sometimes you have small clusters here it was a very small cluster sometimes you have very large clusters they percolate and they have a finite proportion so in one time step you flip of the order of half of the system or one quarter of the system so this construction is extremely successful okay you see what I'm doing so I start the cluster it is actually that program or the graphics version of that program that is used and that is you can you can be sure that it is correct alright so let's marvel at this beautiful so this means that at each time step half of the system or of the order of N but sometimes very few but sometimes very many spins flip and of course this algorithm has a mixing time a correlation time which is almost independent of system size okay so this is at the critical point above the critical point the clusters are much smaller or get smaller below the critical point the clusters are the majority of the system and they only leave less than of the order of N for the best okay now I have so this finishes what I wanted to explain on the Wolff cluster algorithm again there is just metropolis hastings the only concept that you have to understand is metropolis hastings and the basic concept that any algorithm that you make P is the algorithm can be combined with the a priori probability to satisfy detailed or global balance in this case detailed balance so now in the last two hours I want to discuss another version of algorithms which are the heat bath algorithms so let's just before going into the heat bath algorithm let's just remind us what the metropolis algorithm meant the naive metropolis algorithm remember we had it for hot spheres and we had it for spin systems the naive metropolis algorithm meant that you have a probability pi of a I think everybody now understands that this is the Boltzmann distribution but Boltzmann wait for a times the a priori probability times the accepted probability is pi of b so this equation it's getting outdated because the global balance algorithms are coming up and you will see you know it would be just fantastic but the local algorithms was that the probability to move the spin from here to here was the same as the probability to move the spin excuse me the probability to move the disk from here to here to propose the move was the same as the probability to overdose the move from here to here in the local spin algorithm easing algorithm easing the probability to flip like this was the same the probability to flip like this to propose this move so in the metropolis algorithm do you understand what I mean So the proposal from here to here is the same as the proposal from here to here. The probability to move by one centimeter to the right is the same as the probability to move by one centimeter to the left. That is the DNA of the Metropolis algorithm. That is the DNA. So then the a priori probability is the same. And you can cut it off and you end up with pi of a to the formula that we all know.  So that is the DNA of the Metropolis algorithm. Now the DNA of the heat bath algorithm is the opposite. In the heat bath algorithm you have the same equation because that is the equation that we have to satisfy unless we work in Paris and go to nice restaurants and between restaurants we work on global balance algorithms. But anyway, so in the heat bath algorithm the a priori choice is not random. You want to go from a to b with the probability pi of b. You go to this new configuration with its equilibrium probability. You go from b to a with pi of a. And you see what this does in this equation. I mean if I don't have an answer I'll go on strike like the Lufthansa pilots. What happens if, I don't look at you. What happens if I choose a priori probability from a to b like pi of b and a priori probability. It's written here. The acceptance probabilities are equal to one or one half. You see this is different. So if I move into the new configuration with its equilibrium probability rate then I have no problem with rejection. I have no rejections. That is the DNA of the heat bath algorithm. But the idea of the heat bath algorithm is to apply this to a subsystem. Not to the whole system because if we could apply to the whole system we were back to direct sampling, right? We would be back to direct sampling. So we do direct sampling on a small system. Now let me apply this heat bath algorithm in the spin system. So I chose, so for example this guy. You marvel because it's such a beautiful picture or it's beautiful. I can sign it and then send it to you. So now this one, now, so I take this spin out and now I put it into plus with the probability pi plus and I put it into minus with probability pi minus and then I can accept it, okay? So take these spins away because they don't play. So now what is the, the field on this spin is now equals to two. I have three plus one minus makes two, spin it blue. So what is the probability of the spin up? It is e to the two h beta, I would say, right? Plus h beta. What is, so if it is up then the energy is, if it's up then the energy is minus one, minus one, minus two, minus three and minus two. Then the energy is minus two, let's say that. So if, just this is just a little reminder, if I am up then the energy is minus two. If it's down then the energy is plus two, okay? All right, so this means that I have to accept pi plus. I have to go to the plus configuration with probability e to, e to the beta h. Let me just write this down. So in this configuration the field is equal to two. And the energy of, if I choose a plus is minus two. The weight, if I choose a plus is e to the minus beta energy, okay? And e down is plus two and pi minus is e to the minus beta h. So now I would be well advised exceptionally to normalize the probabilities and to normalize them with this plus this. So I have this one. So now the heat bath algorithm is I take the spin away, I compute what is the probability of plus and minus and without taking into account what it was before, I take it to plus or take it to minus. Everybody knew that heat bath ising ising.pi would come up. This is the program heat bath ising.pi. All right, it actually implements this idea. You start with initial choice here. Then I start with k, random. I take a random number between zero and one. I compute h and then I have to check e to the beta h divided by e to the beta h plus e to the minus beta h. And I divide by e to the beta h. So this makes one divided by one plus e to the minus two beta h. You see, this is the same. So this is one. So this is programmed here. And if epsilon, if the random number is smaller than one divided by one plus expansion of minus two beta h, then I put the spin to one. And otherwise I put the spin to minus one. So this is the bonafide, completely exact equivalent algorithm to the Markov ising.pi, the Metropolis algorithm. And now comes the cherry on the cake I'll show you because I'll run it. So now you see I ran it from an initial choice that was plus and minus one for all sides. So I took an initial random. And it would be easy for all of us to change this line into saying s is equal to all plus. OK? We could change this. We would probably not, should not write on this blackboard, on this board here, but we could do it on the computer. We can say s equals two. You would see one multiplied by n can be done very easily. So then we can run it from an initial configuration that is all plus. So this is exactly what is the next Pixar movie. One of my students wanted to start with Pixar, but then he decided to work with Mathematica. Now he is the big developer of the big data. Anyway, so I started with plus. You see, at time equals to zero, I compute. I take out one spin and I replace it or don't. You understand what I'm doing here? I'm just showing the simulation from the all plus. And then I run it. Maxim Berman was the cameraman. Isn't that beautiful? So this is a local algorithm. So now we are iteration 500, 6,000, 7,000, 8,000, 9,000, 10,000, 11,000. And it gets lower, see? 11,729, 3132, 35. Chuck. So for some reason we chose to run it for 10,743 steps. And this was the final configuration. Anyway, so I used it already. So now I run the same program from the all minus configuration. There will be a little trick later. So pay attention. So it started all minus, but then the minus is getting away. The plus are taking over. There's a fight between almost, and I run exactly the same time. 10,742, this is the configuration. And now let's compare the two. So this is the final configuration from the ups. And this is the final configuration from the down. I can tell you if you ever want to read a great paper, read this paper by Prop and Wilson. Because Prop and Wilson, I think it was Prop. Wilson is one of my collaborators now. Very proud. Prop wanted to, he's a mathematician. He wanted to do Monte Carlo calculation. And he said, of course I'll do it this way. I'll show you. So now let me go to the program. Did you see this little line here? Anybody see that I had a random seed? 1, 2, 3, 4, 5, 6 here. So I used, you understand what this does? It seeds the random number generator. And all the random numbers that are generated are the same. So I had the two programs. I had the two programs. And at time step one, it was spin number 753 that was updated. And the random number was 0.75348. So I used the same random numbers for the one and for the other. And it so happens that using the same, so let's say t equals to 0, I started with an all up and I started with an all down. Excuse me. So the configuration, and then at each time step, you can look at the program yourself later. At each time step one, I updated this spin here, here and here. And I used the same random number, epsilon, to update. And now it's very easy to see this function, 1 divided by 1 plus e to the beta h. As a function of h, it goes like this. This function looks like this. So if what is clear, if I chose to put this spin here, and this spin has the h here of the minus configuration, is smaller than the h of the plus configuration. Here. And especially the sigma configuration, sigma, all the sigmas is smaller or equal than the sigma of the plus configuration. Smaller means that each spin is either the same or smaller. So here it's easy. Here we have a plus and minus, plus, minus, plus, minus, plus, minus, plus, minus. So it's clear that this configuration is smaller than this one. So what I can now prove is that because the spin here, the field, the h, if the spin is small, excuse me, the spin minus, I think I should write larger for the Hawks back in the pilots.  The spin configuration itself is smaller. This means that each spin is either smaller or the same. So I never have the situation that I have a plus here where I have a minus. So because it's like this, I can prove very easily you can do it yourself that the configuration at t equals one is also smaller than this one. So this configuration will always will evolve and this configuration will evolve, but it will always be smaller. But at some point, because both of them do a random walk, at some point they will couple. And at this point, they will continue to move together. So it was not just at 10,742 that I had the same configuration. For all later times, I also had the same configuration. So now I have the question, what happens? So now I prove that the all plus and the all minus merge. What happens to another initial configuration? For example, plus, minus, plus, plus, minus, plus, plus, plus, minus. So this configuration is also smaller than this configuration because it never has a plus spin, plus spin here where it has a minus spin, and it's also larger than this. So this green one will also be, will remain sandwiched in here and will probably merge with one of the other numbers there. So this is an example of what I was discussing yesterday, or the day before yesterday, of a coupling algorithm. And here, we had the coupling, it took place, coupling took place at T equals, I think it was 10,474. It depends on the choice of random numbers. But here, for this algorithm, for this choice of random numbers 1, 2, 3, 4, 5, 6, the coupling time for this, it was already in quite a large system that I showed you. The coupling was out of time. So now, what I wanted to show you, tell you is, this is really important, because in this Poppin Wilson paper, because they introduced the coupling time, or it was possible, it just goes back to a long time ago, but now we have a new time, which is the coupling time. And this coupling time is always larger than the correlation time, or in mathematical terms than the mixing time. So now, and this is the time at which all memory of the initial configuration is forgotten. At that time, doing Markov chain Monte Carlo, you are as good as doing direct sampling. So there's one detail I didn't show you. It is the coupling here has to be done from the past. We can discuss this later over beers, but so this is what I wanted to show is, you see here, I mean, do it yourself, get this program, run it once with this random seed, initial choice one, one, one, one, and once initial choice another one, and you see at some point they will couple, and they will happily evolve exactly in the same way ever after. And this means that the configuration back here down here, this is time, right, down here, will have forgotten all memory of the initial state. And this means that for this kind of problem, this means it must have this half order, it's called half order, but for the easing model, you have enormous power in Markov chain Monte Carlo methods because you can prove once you have converged. There is no burn in time. There is no saying, well, you know, you have little numerical errors and errors, they kind of, anyway, so you have a pure calculation and at the end of your simulation, you have a perfect sample. So we wrote the paper once, we wrote the paper, on these algorithms perfect was called perfect sampling, it's perfect sampling, you understand perfect sampling because it has no more influence of the initial configuration, understand that point? If you start from all plus or from all minus and get exactly the same result or from any other initial configuration get the same result, then you have really no influence, there's no influence of the initial configuration. So we wrote the paper on perfect sampling algorithms for spin glass and so on, and then we got back a referee report from physical revelators and they will say this paper has to be rejected because only God is perfect and you're not allowed to use the word perfect in the title of... So we changed the title and we called it exact sampling because this thing is called perfect sampling or exact sampling and then the paper got through. Is it the same for any given pair? No, no, this is the coupling time for everybody. All the two to the n configurations have coupled at that time. When all plus and all minus come together, they're like two shepherds. When they come together, then everybody has come together. Well, I have to run the all plus and the all minus and this gives the maximum. But then you understand that this time, how can this be compatible with the exponential decay of the correlation function? It can only be compatible if this coupling time is sometimes larger and sometimes shorter. Because if there was an upper limit for the coupling time for the easing model, then at that time the correlation function goes to zero. There's no correlation with the initial state left. So what happens is that this time, for this model it is the mixing time. In fact, what happens is the mixing time is of the same order of... The coupling time is log n larger than the mixing time. That means the correlation time. Let me put it like this, correlation. Sometimes it's larger and the way it goes, in fact, you have to run it, but this is a detail, you have to run it from the back. In fact, what you have to do is, you have to do a time t equals to zero, you have to have your perfect sample or your exact sample, and then you have to go from the back. This is an example of these new ideas on coupling where you can really control tau. You really know tau. Well, if you have this... Here you have a partial order. What's called a partial order. The way this is distributed is exponentially distributed. So it's the coupling time itself that has an exponential distribution and the mean value is the mean correlation time times the logarithm of n. You have an exponential distribution. You must have an exponential distribution, by the way. It must be exponential. This exponential distribution that we also showed, in fact, it's only... When we have this exponential distribution, it is the sum of the configurations, sum of the samples. Samples means choices of 1, 2, 3, 4, 5, 6. Exactly, exactly. Yes, yes, from the simulation. And you cannot do it in spring glasses, for example. You can do it for hard spheres only up to the density of 0.3. So there are big, big limitations because the coupling time is larger than the correlation time. And it is of the same order only if this half-order exists. For example, for spring glasses, you don't have this half-order anymore, and it can also be much larger. So you have to show that everybody is working very hard to get strict mathematical limits on what is the correlation time. So this means, for the easy model, you'll all be professors of physics or everywhere. So you don't teach metropolis algorithm anymore. You immediately teach these coupling algorithms because you want to show results in computation that are really trustworthy. So you don't discuss any burning time. It's nothing. You just do sampling and you stop once you have one sample. Then you start a new simulation. So I have 17 more slides. But then it will be over. Am I allowed to run this again? All right. So here it runs hundreds and hundreds and hundreds from the all-down configuration. And it will always be smaller. You'll never have a spin that is up while the other configuration is down. So this is the configuration up, down, coupling. So the conclusion was here for the easy model. We discussed the subject of enumeration. I didn't really discuss the connection between counting and listing. So what we did was the gray code. Gray code anybody should remember it. Gray code going through a list by changing one thing. So we did the listing. And enumeration means two things. It means either counting. Counting how many configurations are there of energy four. That is also enumeration. Or just enumerating all of them. And you can say, for example, the word solution of the easy model, the exact solution of the easy model, it's a counting algorithm, a counting enumeration of loops. Then we had the metropolis Markov chain something. Remember, what is the DNA of Markov chain because now we will soon leave each other. I have the last five minutes to teach you something. So what is the DNA of metropolis algorithm? The proposal probability. That is of the naive algorithm. So the DNA of the metropolis algorithm, the probability with which you propose this move is the same with which you propose the move back. This is overcome in the metropolis Hastings algorithm where you have an a priori probability to go from a to b and an a priori probability to go from b to a.  We did this. We had to move b and we had to compute all the algebra. What would be the move to accept the, what would be the probability to move, to accept the move from b to a? So then we had the cluster algorithms. And this, we used, this was in the framework of the metropolis Hastings algorithm. The cluster algorithm means that you can construct, you can do anything. You can have any algorithm, any algorithm and the metropolis Hastings, the a priori probability will always recover and will always recover detailed balance. Then we had the heat bath algorithm. Heat bath algorithm is, say it again, what is the, what is the characteristic of the heat bath algorithm?  And you always, you go to the new configuration with its equilibrium probability, with its probability, but you cannot do it for the whole system because then you would be doing, you would be doing direct sampling, you apply it to a subsystem. The subsystem, the spin system was enormous. We used it only for a subsystem, which was the spin and its four neighbors. But then, once we, but there were no, there was no ejection, of course. We, at the end of the day, we either put it up or put it down. So then, fantastic subject of all is the coupling. And coupling, it is clear. The coupling time is always larger than the correlation time. And when you have half order, then you have a logarithmic behavior between the two. But in spin glasses, below some temperature, for example, the coupling time can become infinite, or almost infinite, whereas the correlation time becomes finite. And then we had these nice algorithms, enumerating using the gray code, remember this? Thermoeasing, density of states, not necessary to do a calculation at any temperature if you can compute the density of states. Then we had this beautiful Markov easing with the metropolis algorithm, the cluster easing that was the wolf algorithm, and the heat bath easing, easing with the coupling. And the coupling came from the fact that I seeded the random number generator, right? So we used the same sequence of random numbers in the program that started from all minus and the program that started from all plus. And this is all I wanted to say to you, and I thank you for your attention and for your interest, and that is it. Oh, now it's a question time, question time, question time, excuse me. How many more decals in reference or do you mention a decal paper? Robin Wilson. Okay. Or not mine, yes, it's it. It didn't go that well, but you look in, I've written a book. It's on our MOOC. You just do coupling and you will find it. You can, it's, but it's easy. It's easy.  I mean, I always, I was brought up thinking that there's the world of direct sample, you know, where you have direct sample and Markov chain sampling can never, you know, there's some flaw in the Markov method because it can never be, it can never sample the equipment distribution. So I was brought up like this. Everybody was brought up like this. And all of a sudden these people did their first Markov chain calculation. They had not read a single paper and they thought, well, you know, I should not do, they were mathematicians. I should not do a calculation that doesn't know what, and they set it up like this. Beautiful. And so this, at that time, so it was 20 years ago, we in our community understood that finally the Markov chain methods are able to do perfect sampling and that is a real revolution. It can also apply, it's a whole industry. It's a whole industry. The problem is that sometimes, let's put it this way, it even applies for continuity, these coupling algorithms can be used to have strict limits on the convergence time, for example, of hard sphere algorithms they will be used, these are the best algorithms to give limits on the liquid failure. They have physical implications. But you have to work a little bit to, they are fantastic algorithms. I mean, go through the literature, it's really interesting. Tough, but fantastic algorithm. Okay, but so there's no separation between detail between Markov chain sampling and what was the other? Direct sampling, exactly, I forgot. Okay. You mentioned that there will be new codes that come from this global-bound idea to forget the details. Is there like anything like for spin, like for writing and so on? Yes, that is for example. For easy model, yes, so this is what I wanted to do but I have one paper from last week and one paper next week, one is on the XY model and the other one will be on the, but so we use this idea of global balance. So it's an archive, you can see it. It is not as fast as the Wolf-Glas diagram but it's an algorithm where you always, each spin always turns clockwise. So one spin turns clockwise and the other one turns and they are quite fast algorithms. They can be used in this. So you can come with me in the last term. No, no, it's just one spin that turns and then, but I didn't prepare it now but you can look it up, the paper is very nice. We didn't have many results so we wrote it more nicely. So anyway, so one spin turns and then at some point one of the neighbors will not be, the idea of this algorithm is, at some point one of the neighbors will object and then it's the one that objects instead of going back and retracting the move it's that spin that will start moving. Anyway, so we'll see whether, so these are new ideas, new algorithm, very simple to implement and we'll see whether they'll make an impact in spin glasses, for example, XY spin glasses or Heisenberg spin. We'll see, we'll have... But the idea is to speed up the actual... Of course, of course, of course. That's the idea, of course. Because they have what is tau. Any more questions, comments? Contradictions? Oppositions? All right. Thank you. Thank you.


I need the pain caused by the narcissist. When does the pain finally end? When does the emotional distress finally go away? Most of what causes you to be locked into experiencing the constant pain and emotional distress is your hope. You remain hopeful that things might get better. You remain hopeful that they might change. You have a feeling of expectation and desire for a particular thing to happen. Your emotions feed into this feeling of hope. It makes you want to stick around. Because you are hoping that maybe things will get better or maybe they will change. This can cause you to overlook what is happening in the present moment. Because your focus is on the potential outcome or results in the future. Take away your hope. Come to a place of acceptance. Believe and recognize that nothing is going to get better with a narcissist. And they are never going to change. Take away your hope and accept this. And you will find that these emotions begin to fade. When you make the final and soon decision that you are done with a narcissist, they can no longer affect your emotions. You are no longer connected or attached to them. It serves that emotional tie, but you have to be serious about it. You have to stop expecting anything to change or get better. You have to stop expecting anything from them or the situation. Once you take away that belief of something happening, it takes the focus off of them and puts it back on you rather than directing your emotions outwards towards a feeling of hope and expectation of the narcissist. Once you have made this decision to disconnect or detach from them and sever the emotional tie, you have to be serious about this decision. You can't just cut contact and still be holding on to the feeling of hope and expectation that maybe they will come back and want to resolve things. This needs to be the end of any engagement or interaction. Any situation or involvement with the narcissist. That doesn't mean the narcissist will just go away. They have to witness your decision to see that you're not just taking a break from them. You're not just trying to punish them. They have to witness your decision to see that you really mean it and that you're not going to allow anything that they do to affect you emotionally. At this point, you will no longer remain or exist in the narcissist's fake world or alternate reality. They might stalk and try to get back in with you. They might act as though they suddenly realise and understand everything that they've done wrong. They might try to make you believe that they have changed. But if you have taken away that feeling of hope and expectation of anything better from them or of them changing, you are not going to entertain that idea or belief. You are not going to fall for that idea or suggestion which has no real backing or support. It's just something that they think you might want to hear. But they have no plans to make any reality when the narcissist can no longer get a reaction out of you. They will become desperate. They have a great need or desire to get you to react to them and when they can't get a reaction out of you. They have a last ditch or a last resort. This is often their final course of action used only when all else has failed. It is often serious or dangerous and it is their last chance to really cause damage or put an end to you. This is where they will really put your emotions to the test and do some of the most sick twisted things you could ever imagine. All with the intention of getting a reaction out of you. They will go to some of the most unexpected extremes to re-secure you as a source of supply. They do not like the thought or the idea of losing. They will do whatever they have to do to prevent that from happening regardless of how it affects you or anyone else around them. In their minds they have to believe that you need them. It's their arrogance and audacity. Their exaggerated sense of their own abilities and importance. Deep down they feel inadequate as though they're not good enough for you. So they have to get you to believe that you need them and make you depend on them in some way so that you can reflect the belief that you do need them and it makes it more believable for them if they can get you to believe it and deep down they feel insecure.  But once you have made the final decision in your heart and mind that you want nothing to do with them, nothing they do is going to work. Nothing they do is going to make you want to be involved with them again. Once you have made the decision to separate yourself from them everything that they do will only push you away even more. It will only make you want to be as far away from them as possible.  Their dysfunctional behaviours will only push you away even more. The pain and emotional distress will not end until you have completely emotionally disconnected or detached from them and you must take away the feeling of hope and expectation of anything improving or of them changing even if you're wanting to get revenge. That is still connecting them to you.  It still makes them feel as though they are something significant or important to you. You want to get rid of them.  It's over and they know it's over. They know that they are not going to be able to manipulate you again. They might continue to do their little tactics. Narcissists are known for doing the same thing again and again and expecting a different result. It's the only thing they know how to do to deliberately cause you to believe something that is not true or to give you a mistaken impression for their own personal gain. They have no power of their own. They have to trick or manipulate you into giving your power to them and this is done by them causing you to believe something that is not true or giving you a mistaken impression. If they can lead you into doing that then you have just handed your power over to them but if they can no longer trick you into falling for their lies and illusions you will hold all of your power which will leave them completely powerless.  They will be forced to give up and move on especially if they have done certain damaging or reckless acts and they know that you will never see them the same way after them doing that. They will move on to easier targets who are more vulnerable or susceptible to their manipulation. They will focus their time and attention on them instead. They only stick around when they believe that you still have a feeling of hope that things will get better or that they might change. Once you take away the hope they know they can't come back after that. Once they see that you are resisting them or you have no interest in them they are not going to fight to get you back. They are not going to endure any struggles to overcome or prevent your resistance or disinterest towards them.   But once you take away the hope and they can no longer emotionally affect you it's a waste of their time and energy. They won't come back after that. They are not strong or built. They are not going to put up a fight or stand for anything. If it's something serious to have to go against they will just give up and find someone more vulnerable and susceptible to their manipulation. They are not going to involve themselves in something that they could potentially lose. If you want to end the pain caused by the narcissist take away the feeling of hope emotionally disconnect or detach from them. Sever the emotional ties and the narcissist will quickly fade away. Thank you for watching. I hope this video resonated with you. Please like, comment, share and subscribe. Click the bell icon to receive notifications for my future videos. If you would like to donate my PayPal link is in the video description. Coaching inquiries you can email me at narsforevercoaching at tumule.com. Check out the new merchandise in the Narsforever store where you can purchase your own Narsforever t-shirt, tank top or mug. The link is in the video description. Thank you for watching and I'll talk to you soon.


into now um yeah excuse me one more XP same same though same that sucks so Seth we do need more XP XP is the best we just need all of it all of it and more all of it and more need Valencia part two levels of XP we literally get a whole level every single quest what level is he? is he like level 58 he's like literally the same level as me that's crazy yeah okay and what is this okay that is fine do-do-do-do-do-do-do-do quick draw oh my companions have more power than me I find that sad yeah it sucks it's can you say sucks? no you can't it um it is in one okay so true Trevor speaks sucks yeah okay is that really you can't even really say that not really not really say that sucks good job ducks good job good job there buddy good job keep it up okay burst fire keep going let's do this super hurt no thank you no thank you please stop ouch that hurt yeah we'll just do that fine we will just do that fine let's make danger do it make danger relentless do-do-do-do-do do-do-do-do-do-do-do-do-do okay and first strike nice keep going pop off pop off do it and then finally attacking okay good job good job good job good job this is too good way too good and another one and another one oh don't unlucky block thank you now we get some repost action yeah go and now you're finally attacking I love swashbucklers so much swashbucklers and musketeers they just they just pop off it's great it's great Bucking it which doctors also pop off quite a bit as well with ready spell not quite as much as buccaneers and privateers so they're kind of like suck a bit just a bit just a bit just a tad okay noise how many more left do we have like one I think okay okay double tap double tap boop OP Chantel is OP very OP well GG boys we did it nearly first fire here we go we did it nice noise let's go next quest or next thing that was Tyler done okay nice we're getting so much stuff how much bag do we have okay we've got heaps which is good I love how you can just skip dialogue by holding space fire is so good so good so good it is actually my favorite thing to do in pirate I really wish they added that to was as well like just hold like instead of spamming space fire just hold it down and it skips the dialogue would be so good who are we going okay Marcus is over here somewhere up here probably yeah up here up here golem G I think we are ship fights so annoying don't like this zero out of 10 please stop we need to refuel apparently but we're not going to always got a cool ranch shit actually that's been a moosh you frigate noise don't board just smash don't board just smash don't board just smash easy clap we did not collect anything I don't think that's fun got a lot of not collecting welcome to keyboard spam as well so yeah I think this is the most I've ever seen people like fighting ships together it's crazy whoa Gigi nice one of six where to next boys there's another one here I mean just stay around here and we'll get plenty there's a good idea because they keep spawning and coming in because they see you being attacked yeah okay just alternate switching between them okay I'll get that I'll get that real quick cool beans okay we've got two of sex two of sex we need to heal need to really focus on my ship's health not doing too well at that at the moment not doing too well at all oh you can have ship battles and then broadside combat which is just the same except on the ship it's great and these we little like clouds and traps you see they from trap tokens which are put on the ship and broadside combat so you have to clear them in order to not have them so if you're having like lots of people you would generally have like one controlling the ship and the other were running around like clearing the trap tokens or two ships those are the two options there or three or four yeah over there you can use swords and guns you can use swords and guns here as well and bombs and traps and who do magic so yeah I love pirate it's a great game really well filled out it just um legs updates very much so legs updates okay are we done yeah we are bye two left three left two left three left I think three left shouldn't be too bad what is this the kitty's broken kitty was broken only when it's invisible though that's funny that's a bug that's a bug okay hopefully we should be fine I think this should be all good treasure bath nice gonna love treasure bath pirate extra damage noise well GG you're dead and do I have pirate I don't know if I have pirate I won't even get to see otherwise that's unfortunate this is not gonna kill I'm not gonna kill I did kill GG I actually killed wow I'm surprised myself I'm really surprised invisible but now we can go not gonna board the enemy ship because it's nearly dead three two one boom nice next ship boom let's get this boy down I'm at four X I love ship battles with lots of people I hate ship battles on my own it's so annoying because they just take forever but with other people it's so fun done into now did not realize it was right there but it is hello hello let's get you go what are we doing in here we are building dummies and something about war golems eradicate eradicate okay do-do-do-do-do-do-do-do-do-do-do-do well level two maxes noise I have max death with one of them have max death nice myth is fun is super fun when I watch YouTube streams I don't need to change quality because it doesn't stop yeah sometimes it's like that also twitch isn't quite as good with like like real time basically viewing because like I put the stream into like super duper like low latency like ultra low I think it's cool whereas YouTube does that a lot better yeah noise do-do-do-do-do-do-do-do-do-do okay well that was easy we've fed it a lot of them already okay okay but yeah YouTube is definitely a I think for me now it's more of a viable streaming platform then twitch at this stage until I get partner which I don't think I'll get on twitch but you never know never say never yeah okay okay then okay then played storm yeah these guys really don't have much health at all like these guys are bad also helps at like blood flames really OP really really OP explosive yeah destroy all of the others I love it I also love these because they destroy each other it's great so good sorry it's so funny when they destroy each other it's great I love it it's my favorite thing with war golems just making them explode each other so fun makes me so happy and I don't know why double tap one more hurt and it's dead yep Gigi I'm pretty sure that's Gigi right yeah easy clap easy clap boys war golems not difficult at all okay let's get on back to Marcus and then we have three quests left we're getting there we are really really getting there getting down the list of quests three left and then we're gonna end off the stream for today which is kind of sad because we might still have a lot of time left so we might start aqua today


Good afternoon, everyone's got that like getting ready for the evening energy. We have a fascinating panel talking about everyone's favorite subject, AI and early stage investing. I'm asking our panelists to go through and introduce themselves and then quickly talk about a recent, it doesn't have to be recent, but an AI investment they were involved in and maybe like a one sentence explanation of what the company does. So we start with you, Don. So I'm Don Stalter, Global Founders Capital based in San Francisco and we've invested in 250 plus businesses across the United States, a recent AI investment that we've made is in a business called Slope, which is a B2B payments business playing in the 125 trillion dollar B2B payments market, leveraging AI to do KYC, KYB and just to optimize all the payments processes. Very exciting company. Hi, I'm Corinne Riley, I'm an investor at Greylock focusing on B2B infrastructure and applications and yeah, the many AI investment related companies we've done. I work with a company called Base 10. Base 10 provides all the infrastructure you need to serve and deploy models in a scalable and more importantly, performant and cost effective way. Hey, everyone. I'm Natalie Vase. I'm a general partner at Spark Capital based in San Francisco. I just joined Spark Capital three months ago, so I'm going to talk about an investment I made at my prior firm, Amplify Partners. I was involved in an investment in a company called PostgreSQL, which brings hugging face transformers and all of your favorite ML models into the database, in this case PostgreSQL, which is usually the first database people get started with as app developers. So I'm very excited about that. And then just in terms of Spark Capital in general, two well known AI investments we did this year were adept and anthropic. So I was thinking, trying to think of like a really great metaphor for what you are dealing with right now, the three of you. So like, we're all like, we've lived in California or live in California. And so I was thinking about surfing and I'm a lousy surfer.  And then once you get it, it's like, if you get it, you ride it. It's amazing, right? And then sometimes you get a sequence of waves. And when I would go out, I just get hit bombarded by wave after wave and I couldn't even like get on my board.  Like, I can't imagine when you like introduce yourself at a party and then you're just like swamped by people. Natalie, can I'm just curious, can you like, how many pitches are you seeing on a weekly basis? How do you like filter out, that's also a question. It's like, how do you separate the sort of diamonds from the rough? I really appreciate your analogy. I'm a kite surfer. I'm a surfer myself. And it's not just about the waves, but also the conditions of the market or, I guess, the weather conditions that you're going out in. I think right now it's sort of a tsunami more than a set. And I think what we're sort of trying to figure out now is what happens when the dust settles. Every company, whether it's infrastructure, consumer, enterprise, has an AI angle. Whether or not their AI is like the fundamental piece of their business, I think that's what we're trying to figure out with every company that we talk to. What is the dust settling? I have no idea. Karen, do you have any idea? Is everyone sort of waiting for the next wave of companies to start raising their next investment? Is it like the next GBT model? Yeah, I think it depends on which layer you're looking at. So I think the infrastructure layer, when the dust settles, we'd be very different from the app layer. I mean, we're seeing huge outcomes in the app layer already these days. We have a portfolio company called Tome that helps you build presentations with AI. They see millions and millions of users in a very short period of time, versus at the infrastructure layer, I would say things are still shifting. And my opinion is they're going to continue to shift for quite a while longer. That doesn't mean we're not investing. Actually, the infrastructure layer is extremely busy right now. But when the dust settles, if it ever does, we'll really depend on what areas you're talking about. Can you help me, since I'm not as smart, and many people may not be as smart, define the infrastructure layer versus the application? What's a clear cut definition? Yeah, so we think of it in three layers. The model layer, where right now we have two investments at the model layer and the language models, inflection and adept, which in our opinion are two of the core private model companies right now. The infrastructure layer is any tooling that helps you serve, modify, deploy models within the company. And then at the application layer, it's anything that you can think of as from what people call your GPT wrappers to incumbents that are now adopting AI within the workflows they've already created. What do you, and maybe I'll turn to you, Dianne, what do you think, which one of those percent, I'm sure they all present different risks, but which one scares you the most right now of those three? I feel like this is a topic, a discussion that a lot of people are delving into and constantly discuss. I mean, there are quite a few concerns around how the application layer is going to be obviated by some of the infrastructure businesses out there. So maybe OpenAI will build a customer service app that kills all the other customer service apps that are built on it or whatever else. I think it's two early days to tell is my perspective. I'm an early stage investor. For me, it's all about investing in that really smart excited founder who has a vision, who isn't necessarily chasing kind of that shiny object, though, because there are a lot of those, and just trying to think about what the unit economics of that business will look like over time, and to really just help them build a real business. That's how we think about it. And what are the shiny objects? Like, I'm sure you're encountering companies I certainly have that just slapped on.ai to their name like six months ago. I mean, their businesses that were founded eight years ago who all of a sudden are AI founders. And I think there are ways to implement generative AI. There are sort of enablement strategies around it, which are fantastic. I think it's early days again. And it's OK for people to evolve in that direction. But again, I feel like 90% of founders when they start talking about AI don't really sort of delve into the use cases around what they're building necessarily. I think the first sort of big recommendation I'd have for founders is don't start describing that shiny object. Really talk about what you're building. What do you, one thing that comes up a lot in AI conversation is just the talent pool and how expensive the talented engineers. How do you think about that? And with your, I'll start to go back to you, Natalie. With your companies you're investing in, are you looking to see how many research papers there engineers have put out or their founders? Do you tell them to go out and spend as much money hiring the best? Or is it like save that money and have a really small team? Yeah, and that's a good question. I mean, I think there's an interesting point in time right now where talent for AI is particularly expensive. But you also have a lot of liquidity in the talent market because a lot of big companies have done layoffs. So it's actually a really good time as a startup to be hiring because there's a lot of people looking for jobs. You also have remote work, which is opening up the universe of places that you can hire from for your company. So in many ways, it's a great time to be a startup hiring. To your point about how we assess technology, what research we look at, I do a lot of investments at the infrastructure layer. And I think infrastructure in particular is led by research. And so even if you look at a lot of these foundational AI companies, you can trace back their work to research that was either at a company or at an organization like DeepMind or at a university. And so I like the title of this talk, Lab to Launch, because I think particularly in AI, research is leading industry. And I see that a lot in infrastructure. So I'm absolutely looking at the foundational research papers that people are writing. Who are the author of those papers? Where do those people go? Those are a great talent pool for these startups to be hiring from too. You mentioned DeepMind, which is in some ways the world's most well-funded research lab and in sort of has been for the past decade plus. Do you have that concern? Like, is it current? Do you have any, like, are there companies that you're like, OK, maybe this research you're doing is great, but maybe you need to start commercializing it? Or is everyone from the get-go now like have a commercial model? I would say, I mean, from the model, if you're investing at the model layer, right? First of all, we don't have a concern because we invested, we then backed Mustafa Suleiman, who was the previous founder of DeepMind and we've now backed him in his second venture, which is inflection.ai. We have a very large belief in the talent behind those networks. I would say the core question, right, when you're talking about AI talent is you have AI researchers, which some companies, like the model companies, aren't strong in need of, but not everyone needs a pool of AI researchers in their company in order to deploy AI. And actually, my belief is this is a big difference between the ML ops era, pre-transformer, and now, before you had to have this set of researchers that knew everything about ML in order to successfully deploy it within the company. And nowadays, the tools and the infrastructure that people are building are making it that any software engineer is essentially an AI engineer. And so I think the level of knowledge you need to have in order to use AI in your day-to-day engineering is going to be very quick to acquire for basically the existing cohort of engineers in anyone coming in the future. I'm not super worried about the talent from that perspective. Are you worried about valuations? About what? Valuations. I think valuations are in the control of the choices that us as investors make every day, right? I would say I'm more concerned about the companies that we are in. At Grillock, we make a very select number of nespans per year, helping them find value, find product market fit, and then scale up. I would say that's the core concern day today. Don, are you going to? I was going to say data talent is really important when it comes to AI in general. Being able to help build a data moat within a startup company and being able to leverage the time series data via machine learning to make great decisions as accurately as possible, I feel like it's the core of a lot of these businesses. And that's a skill set, that talent set that's been around for a very long time and that a lot of schools are promoting more heavily than before. At the University of Chicago, there's a new data science program that's very progressive, but that a lot of AI startups are hiring out of. So it's all about the data, I feel like. That's interesting. Your company was reminding me of the name of the company you mentioned. Slope. Slope, which is not necessarily like FinTech, right? It's a B2B payments business, so it operates kind of within a FinTech space. Now, the traditional way you think about it is like an AI company. Is that are you looking in the payments space or certain vertical applications? Is that where you think a lot more potential? So they're leveraging AI in order to better understand bank data, in order to process bank data more quickly, and also to do KYB and compliance. So it's KYB. It's like banking compliance effect. No, your bank. Exactly. KYB. And they're leveraging an LLM model. They call transformative to do it. And so they own that data. And they're building a massive team around it. You mentioned open AI before I did. But before, was it last Friday? When was it? It's only been like a week? Well, before that Thanksgiving Friday, before with the main question about open AI was it's relevant for you. So they had their dev day. Was it earlier this month or last? And there was all these jokes. And probably like, I think we even wrote an article about, well, there go all these eulogizing all these startups that were killed because open AI had just introduced this new product feature. And I think the same thing, that's not a new problem, right? For startups, it's like, how does Google, Microsoft, what if Google or Microsoft or Amazon or Meta does this thing? But it feels just because it feels like the pace of AI development is just moving so quickly. What do you do? I'm curious. Maybe you want answers. But are there any companies in your portfolio that kind of freaked out on that dev day? I think any company that's building in AI adjacencies was paying attention to that weekend. And I think it was just more representative of how quickly things are moving and how hard it is to predict the next day. So I think everyone was paying attention because everyone was asking questions about what this would mean for their company. And I think it sent ripples through the whole ecosystem. Oh, yeah. Well, that's it. I wasn't even talking about the SAM being fired and rehired thing. But just like when they announced their dev tool. Yeah, that too. Yeah, absolutely. All the startups that are building applications that now become a little bit easier to build with what they announced. But those startups can move just as quickly as Open AI can. We're really excited that Sam Altman actually led the most recent round in slope. Ostensibly, that builds sort of a defensive relationship kind of with Open AI. So he's supporting them. And I think maybe a lot of businesses are looking to get him involved from both a signal standpoint as well as a support standpoint. But fundamentally, it's really down to the teams, the operations, their ability to leverage data the right way. Was he candid with his communication in that investment? Sorry. He was very candid. But it was, for him, it was, I want to say, sort of a large angel investment more than anything else. So he's super operational. It's just a great signal. None of you would know exactly what happened down that weekend. You don't have any big reveals here. If anyone in the audience knows, feel free to find me afterwards. Feel like you're in this. But I mean, but it was, it's certainly, I mean, this joking aside, are any of your companies considered a nonprofit structure similar to Open AI, or? No. No. Would you advise them to do that now? I would say a precondition to being a venture capital invested company is that you're for profit. Typically, that's what we're looking for. Obviously, there is going to be exceptions in every case. But yeah, I mean, we've seen, over time, we've seen sort of nonprofit educational technology businesses come out of Y Combinator. And we've seen a variety of sort of nonprofits that shift to for profits. But you know, it's not something that we'll conventionally invest in. Yeah. I guess I'm curious, like, any thoughts about then? I mean, I clearly demonstrated that this, like, this world can change very rapidly. But I mean, you made a compelling point that, like, are you argue that your startups can all kind of out muscle, or they can move just as quickly as Open AI? Is there a point when the company gets, like, kind of, are you worried about it getting, like, big and bureaucratic and not moving quick enough, like, doing too many things? Is there, like, a mission drift problem with some of your companies, like, how do you feel, like, when you encounter that with some of the early-stage investments? My quick answer is that it's, I mean, at that point, right, once you're, we invest in Seed and Series A, primarily, right? So that's a core of our investments. And at that stage, the problem isn't, you know, do you have too many people in the building? If anything, it's a very lean team. You're trying to move quickly. The question that you're addressing, which is, you know, once you get to a larger state, right, how do you make sure that you're maintaining that speed of a startup, right? And not, and not quickly degrading? I mean, candidly, I think at that point, it's in the hands of the founder. And more importantly, where we have a hand is in making sure that the key hires that they're making at the executive level are the right people in those seats, right? And that's in particular a place where, actually, we spend a lot of our time with our portfolio companies is ensuring, hey, as you're hiring the head of sales, that's going to bring you from 10 million to 100 million ARR. Is it someone that can do that in a scalable way? Is that someone who can do that very quickly, right? Yeah, I mean, to add to that, you know, we love sort of co-investing with great funds on a lot of occasions, and building just really, really close relationships with founders, not necessarily taking board seats.  That's kind of our approach.  We want to just be real good supporters right up until, you know, they can raise that next round and be successful from an operational standpoint, but not, you know, sort of put in full-on guardrails. Are any of your companies stashing GPUs in their basement or something? Like, how real is that scarcity? Definitely, they absolutely are.  What, I mean, is it, are you, you're kind of like, just that's just a fact of life now that these companies have to spend, I don't know how much of their, like, early year investment on compute? Is it very, I guess it would vary by business model, but I assume across the board it's pretty hard.  It's actually the access, right?  If you're a very small company that has intermittent needs for these GPUs, you know, the large incumbents aren't going to give you that access. And that's why we have seen, I mean, there are a number of companies that are, you know, based on that premise, Together.ai, CoreWeave, RunPod, et cetera, that essentially allow you to use GPUs as you need them, and that's a great service to the startup ecosystem right now. I think most people, to my understanding, believe that the GPU crunch is going to end. In the next, the timeline is where everyone differs. Some people say as soon as within the year, some people say a year and a half or longer, but it will end eventually, at which point it'll be more accessible. And there's so many startups out raising money for kind of their new GPU platforms or GPU concepts. There are 50 million dollar seed rounds that we're seeing where, you know, the founder maybe has relationships in Taiwan with a big semiconductor company. So, you know, that gap is, you know, being quickly filled, it feels like, at the same time, you know, to your point on stashing GPUs and the basements and the addicts, like we do see it. We see people sort of love to geek out on those things and to try to vertically integrate or however you want to kind of describe their use case. I'm curious, I'm going to turn to you, Natalie, what, how early, is it, do any of your companies, like start thinking about regulation and regulatory risk? Honestly, not like at the pre-seed and seed, I would say. I think that's certainly going to be on people's minds as they are growing and doing go-to-market and trying to sell this, but I think in the really early product development, they're not necessarily thinking about it as much. And it may be because it sounds like you're not investing and say like, well, but like inflection, but it's definitely not early stage at this point, but like, they certainly have to wrestle with a lot of ethical issues around chatbots. I would imagine like that these companies are having conversations about ethical use of AI. Yeah, I think the core problem that most startups are just addressing is making sure that, you know, especially if you're building an app that is customer-facing or you're building infrastructure that people are relying on in order to interface with their customers, that you're doing it in a safe and secure way. And that is both a regulatory point, but it's also a security point in general. And I think candidly, I think we're just in the very early days of people figuring out what exactly that means, you know, what safeguards you need to have in place. There's a number of companies that are actually built upon this premise of making sure that as you, you know, are embedding, you know, the AI in there. Exactly. I was gonna say my fear with the regulatory stuff is how it affects startups. I think the big players are easier to adapt and to build in those, you know, processes. And I think it can be hard for startups to overcome that early. I was at Google in 2017 where every project was GDPR. And we had hundreds of people we could throw at it. And startups don't have that luxury. So I do worry about what the trickle down effect will be on early stage startups. But I think to Corinne's point and to Don's point, it's not always just about regulations, also about things that aren't regulated in law, but what is going to be your privacy policy, what's going to be your, you know, ethical, you know, guidelines for building the product. I think all startups at all stages think about those things. I write a lot about AI and so do many other people in the press. What, I'm sure there are things that really frustrate you. What do we get wrong about the technology and how it works? As in, yeah, what is like, what's the public perception of this sector that you think is like just dramatically wrong? I feel like people have gone in the direction of science fiction to a point where, you know, we're already talking about uploading consciousness, which, you know, is a really exciting theme. And, you know, it's great to let our imaginations run wild. But- You're not worried about Skynet quite yet. You know, for me, it's focusing on building a real business again.  We have this great company deal in our portfolio that does payroll and compliance, HR. And they're leveraging AI to do, you know, customer service and HR and they have this huge data set that they built around it. And that's a practical application of it. It's helping drive more productivity across the business, drive more revenue and everything else. I love that application. Have another business called Cedar.ai, which, you know, is software for the commercial rail space. And they have a computer vision technology that tracks the arrivals and the departures of the trains to make sure that they're on time. And that very simple use case is, you know, driven kind of meaningful value in the category. So I think, you know, those are the types of businesses that we get excited about right now. That's not to say that we shouldn't be excited about some of these massive visions. I mean, there are going to be some incredible businesses that kind of come out of those dreams. So there's like weird science fiction stuff kind of bothers you, okay. Anything else, do you guys have anything? I was just going to say, I think what people get wrong is that AI just happened overnight this year. The zeitgeist happened overnight, but the foundational things, the research that played into all the stuff we're seeing today has been in the works for, you know, a decade plus more. And I think what's happened is it's become consumerized, it's become accessible. And now, you know, it's in everyone's hands, everyone's household, but it's been an enterprise, it's been driving products we use for a long time, large language models, all of these things. So I would say it feels like it happened overnight, but it's been happening for a long time. Yeah, I guess the last thing I'll add is, the biggest thing people get wrong is that it's very much not done, right? So AI is very much under optimized in many ways in the way that it's actually being used in production today, and there's going to be significant changes coming out of these research labs, both in academia and these private labs, that are going to fundamentally change a lot of and improve, you know, these model architectures. And I think a lot of the infrastructure that's being built today is around today's architecture, and it's just always evolving, right? And so being ahead, being a couple of steps ahead of that is extremely helpful, both for founders who are using AI in their current products or who are thinking about building infrastructure, like staying ahead about what's to come from the research labs is extremely important, and I think people don't do enough. I imagine there are some founders, AI founders are aspiring ones out here.  I'm gonna start with you, Naly. I don't want to put you in a spot. I think the best pitches are when you teach the investor something they don't know. I think a lot of venture firms pride themselves on having themes or thesis areas that they explore, but I think in reality, the best theses come from founders. So if you have a vision for how the world should be, and you feel like you can impact that, what's the unique insight that you have that maybe the investor doesn't hold? So I think sometimes the best pitches are ones where they surprise you and teach you something that challenges maybe a point of view that you held deeply for a long time. Anything that irritates you? Well, you don't have to say. I mean, I think there's sort of an interesting balance at the very early stages around really, really smart founders who are maybe great engineers, great scientists, and then sort of the great sales people who have a ton of charisma and who are able to raise capital. So at the very early stages, that balance is so key to AI founders. And as an investor, we have to sort of trust their technical prowess, which is something that we can diligence, which we can talk to sort of experts around and we can read research papers around, but sort of their ability to build a team, their ability to bring in like-minded people who are sort of at that same level, as oftentimes very challenging unless they have the right sales acumen. Cool. Grant, anything that you like to hear? I don't like to hear. Yeah, I mean, I would say the conditions for an investment are still very similar to where they were pre-AI or in the past, right? Meaning that, at least in enterprise where I spend all of my time, you're looking for people who know how to solve customer problems, right? And the fact that you're using AI in that process is an extra, it's a primitive that you can now use to your favor, right? And that's great. I believe everyone should be using it, but that alone isn't enough. You have to have that precondition of I am solving a customer problem. So that narrative of, hey, I understand this space, I'm passionate about it, and more importantly, I understand what the customer wants is continues to be the main thing that we're looking for. All right, I'm gonna do a quick lightning round. Just yes or no. In the next five years, one of the next big AI companies might be created in the next five years, yes or no? Yes. Yes. Yes. In the next five years, one of these AI unicorns won't exist. Yes. Yes. Which one? All right, that's for next time at Slash. Thanks, everybody. Appreciate it. Thank you.


Hello from Atlanta Today's stop is actually right here. I Skipped the whole driving part and believe it or not today's Location is gonna be a tunnel well today's first location as you can see it is just ripe with street art or graffiti I'm not really sure which one Is the correct phrase, but people kind of use it interchangeably I would say the more detailed stuff is definitely street art You know and then this kind of stuff is more like graffiti Definitely a super cool spot over here in Atlanta. I'm on a lighted side across the way is Closed for business, so it's a little bit darker over there, but as you can see nearly everything here has some kind of spray paint on it or art or Graffiti or something like that, so Super chill spot really easy parking down here. I literally parked like 50 yards away from the entrance The roads driving down here not too great in a school bus, but Wasn't so bad but yeah, let's jump into some some GoPro shots in this place That you can come down here and do graffiti is because the properties owned by the CSX the rail company So if anybody's a muralist an artist, I don't know it got some extra nail polish or something Do your own don't just double-check, but it appears to be completely legal down here, so We have already hit the road. We're going to location number two Which is also going to be a very unique very fun place Just spotted a dude selling a boiled peanuts. All right, so it was the first time I'm gonna have boiled peanuts and I met my man Bert over here. It's super nice fellow from Miami and We're to try some peanuts first. I suppose which which one do you recommend? I like I do like spicy Alright, let's do it This is this is amazing. This is this is something out of my normal routine of a Southern California kid Yeah, look at that. No, I know it's probably a secret recipe. What kind of stuff he put in there? Oh garlic onion Bailey All right, it sounds good.  Mm-hmm some people Open them up, but it peanuts mean why so it don't matter not I think I'm gonna spit out the shawl right now They're good and peanuts are technically a legume, and they're a little on the spicy side Good though, I like it so far Here's a regular Mmm. Oh my gosh I mean the occasion is so good, but I can see why peanuts are a legume.  Oh man have the coolest conversation with Bert over there What a nice nice gentleman and I think I Might have got him hooked on the bus life All right today's next adventure.  So you're supposed to Find some of the art and I'm not really sure Or to be looking here because it's a bunch of trees, but someone said there's a sign for it once you get further along Also a big thank you to Anthony Gaston for signing up on patreon. I appreciate you man All right, here we go follow the red brick dust trail until further instructed and here we are the Direction markers in case you get lost It's right here. This looks like a Urban expressionist art right here. Just wanted to point out. There's a ton of these little fishing bobber things as well At a brick factory. There's probably tons of them But there's all kinds of things like I don't know some kind of water or a gas tank tons of garbage repurposed Reclaimed if you will into trash just want to show you guys Even on the trail itself. There's remnants of a bunch of bricks everywhere The thing here is also the so you just do a little loop around the area So I was just saying to some friendly people back there I find it I run people go to go and look at trash, right?  It becomes something more than just garbage and It can tell a story or provide entertainment or You know even a beauty. I found the beauty in it Because it's sort of like I don't know kind of like mocks us in a way because we're such consumers and we create so much garbage and waste that You know normally this stuff is meant to be hidden swept under the rug thrown in the trash hauled to the dump but here it's like on display and I think there should be more places like this because there's Plenty of trash out there. That's for sure. All right.  So whatever I recommend it Yeah, why not because here's the thing that's different about this hike as opposed to any other hike and you already saw it has art Installations made out of a garbage. So if you want an activity with Something different This is your spot. Hmm doll head trail So this is Dustin weaver. What's up y'all? Dustin was I think the biggest help when I first started getting interested in travel shows and stuff like that And I haven't seen him in how many years. It's probably six So no joke. He edited some of my first stuff, which by the way was really Terrible, but a for effort right from what we were working with. I thought it was pretty awesome I don't know. I thought like, you know, it could have been worse. Yeah. Yeah, that's true That is true. It wasn't terrible. Actually, let's roll that clip the international pillow fight is in downtown's Pershing Square and I assure you it is the only thing square today Thousands of pillar fighters invade this downtown block once a year to ruffle some feathers and let their inner child out as they fight to the death of their pillow Well, we're finally here. Let's go see who's feathers we can ruffle Even the Easter Bunny came out a day early to hop around the action that a Frito pie. It looks like badges The Canadian taco in a bag thing it is in gentlemen boys and girls that looks like a heart attack, but it is Tater tots and cheese That's actually where Santa Claus belly comes from is the tater dogs right there factual So anyways, I guess I'm gonna throw a clip in from the old stuff I don't know comment below how you liked it But Dustin was the first person to really help me like a real genuine friend and we got this Project I had no idea what I was doing, but somehow he poof turned it into something way better than the quality was So thank you man Look at him So check this out. I got this pretty looking lean brisket D. What'd you get over there? It looks like you got more food Look at how good this looks.  There's a great spot. I don't I don't Here is the first bite of the lean brisket Fantastic good spot man. I got fatty We're having our camera goodbyes right now So good to see you Jax If you can do me a favor and make it like this decade next time I see you That'd be great. I know I haven't seen you in maybe five years Probably It's such a great dude All right