So, hey everyone, since I was going to model these characters for the Settlers project, I decided to just record the entire process. So throughout these videos I will go over my workflow and approach on creating them while giving some tips and tricks along the way. These videos are almost little tutorials but I'm not really spending much time on them to give any concrete structure or much of editing in general. You can see them a bit more like recorded live streams of sorts. You of course know the situation that's going on in the world right now which caused me and all of my coworkers to work from home for now. So my sound quality is not going to be the best and from time to time you will hear noises from outside my home or the inside since I am living with my colleague and roommate Hjalte and his little adorable cat Pixel which also has like a sixth sense for making noise in the right amount of time. So let's dive straight in with the first character called Lunte. Right now on the screen I'm just showing some of the original concept art from Vivian that she made. She gave a lot of different variations which is really interesting. A lot of these are, at first they were way more detailed than we originally wanted to go for like there is a certain level of complexity that we wanted to strike with this model with this character overall and some of these had like some really interesting elements that we wanted to pursue further like for example having a mostly flat face with like additional elements on top and these sort of like more stumpy triangle legs and general in general way more simplified shapes. So if you look at all of these there's a bunch of them that went way more complex than we wanted to go for like for example this one where like as soon as you add more intricate facial features that are all modeled into the face it becomes really difficult because then you really need to have a lot of topology to support these structures and also the various ways they can deform into. So that's definitely way more complex and some of these are looking really nice but they would only really work from a certain angle so that's also something we were constantly thinking about. So we wanted something that is in general relatively easy to model and to animate and would easily fit into mostly any scene that you would fit it into so you could just place it anywhere, pose it and it wouldn't just all fall apart immediately. So a very flexible little character. So the design that we kind of wanted to explore further is 11 over here which has had this really interesting idea of this like half, yeah this sort of like plate as a face like it's sort of a mask. We had various design ideas with like as an astronaut or a kid in like a pillow suit or anything sort of as an adventurer who's exploring new worlds. And this little guy is definitely really interesting with the design. So Vivian made some more concepts about the facial expressions, the different hairstyles and how this could exactly work in 3D. One of the interesting challenges that is important to mention for the modeling is definitely the flat face. So since we want to have this character work from different angles it's important that like if it would just be flat then you would really only want to show this character from the front because once you see this character from the side or the back it just doesn't really work anymore. So what we ended up deciding on is to make the mask over all more curved. So even if you see him from the profile or directly from the side you could still have some playroom to adjust the facial expression. So the idea is we wanted to make these facial expressions, these facial features as simple as possible. So this is just going to be separate shapes, modeled completely separately as like curves and anything that you can deform into various shapes. So you could just define the eyes to be perfectly spherical, more oval or more of a U shape or even square or whatever. You would have complete freedom over it and it would just snap onto the mask. So having this curved surface gives some playroom from more angles. So you would see it from the side and you could still kind of position the two eyes to be on one side of the mask on one half. So it can be really abstract and then over here with the facial expressions you can also see yeah you could really push it with the mouth. So we want to have this like kind of sausage rounded lip and then this is actually a pretty tricky question that we brought up with the design because the mask is going to be metal and it won't really deform with the mouth, it shouldn't at least.  So it will imply that it goes a bit inwards into the mask but it's going to be so abstract and stylized that it's just going to be an empty hole that doesn't go that deep. And then with the tongue that would just be tongue and teeth those would just be additional shapes that are going to be as flat as possible so that they don't intersect with the black plane with the inner mouth. So the mouth can be just basically still completely free to deform however you want and it can even just go outside of the mask and it can just handle it. Apart from that Vivian went into some more color variations but this is also an interesting point with the level of complexity of the mask and the eye shape. So over here like I really wanted to dissect all of these concepts to give us some to inform how the shapes should be modeled so that we can later on really more easily rig and animate this. This shouldn't have a lot of constraints on it as in it should be as easy as possible to pick up and to animate in any situation. So with these sorts of masks we really wanted to push this flat as possible face shape over here.  So this absurdity that's something that should be supported by the mask shape so the eyebrows over here shouldn't be hard modeled in a way that kind of frames where you can put these facial elements and this sort of little dividing line in the middle the sharp crease is also just going to cause problems if you want to place both eyes on one side for example. So we kind of went for H over here and we wanted to just subtly imply this little eyebrow line over here on the mask. So this is just going further with the concepts and Vivian already started exploring some more three-dimensional turnarounds so one of the things we came away with to support seeing those facial features from the side is to actually make like kind of bevel and round off the sides of the mask. So you could if you wanted to place the eyes on one side of the mask and the mouth really weirdly here on the side and it would just snap onto it. If it would be this beveled this essentially extruded face over here and that would just be this hard cut and you can't really easily place anything there. So another question that came with it is if it's in this like kind of half cylinder with the rounded edge on the bottom, how is this going to inform the shape from the top? So is there going to be this cut out in the like where the face essentially is or is it just going to be a solid shape? So we went for this cut out to kind of nudge the head and the hair further into the mask and really close off this entire shape because the body is really simple. It's essentially just a bunch of cylinders and it's really way simpler to model and later to animate. But with the mask, if you would see it like slightly from the back or the side, how is this all going to fit together with the face, with the actual face, the actual head of the character. So we try to merge all of this as much as possible. Almost like with if you ever watched Adventure Time, the main character is just this single shape like there is just no neck or like it's a seamless transition from head to neck to body. And this is something that really should happen over here. So we don't even imply that there is a head. It's just all hidden by the mask, the hair, and then the neck is really just an extension of the body. So we kind of ended up with this concept over here. This is the final painting or so far final painting from Vivian. And yeah, you can really see there's like this nice little modeled increase on the top of the mask. It's really implied that this is metal and there's like these bolts on the side and the eyes and the mouth are going to be these separate curved shapes that are just snapped onto the surface. And you can just freely move them around. They're not attached to anything really. Then the hair is probably going to be the most complex part in terms of modeling, but it's really important that like if I zoom in over here, this is just the turnaround that the hair is enclosing like this entire thing. So it's wrapping in so nicely with the mask that you never get to see any ears or any like a jaw or anything like that. And then the suit, the sort of rubbery suit is extending so far up that you only get the sort of turtleneck up here.  There's still, of course, what's so great. Like if you have a like normally sometimes you would start modeling a character just from a painting or a single drawing and you really need to interpret all of this yourself, but it can be really helpful to have this this extra turntable where you can just clearly see how the different shapes of the body relate to each other and how the proportions exactly work because this sort of angle, this is the the really complex part of even a simple character like this. How do you handle like how does the head actually relate to any of this? If I look at this, I might actually still increase the thickness of the mask because right now here's still some space where you could actually see a jaw or a head. And I really want to wrap this up with with the neck seamlessly going into the face. So you can see over here, this line over here, this is the turtleneck going up the body and it's kind of going all the way up here. And then it's just going to be this kind of thick sausage shape. That's how I imagine it. And this is just going to wrap around the this line over here. And that is then directly connecting to the hairline. So there's like all the hair over here, which is just directly touching the turtleneck and then over here, the straps of the of the metal mask that are just sinking directly into the hair. In terms of the rest of the body, it's it's really like with the hands, for example, it's just going to be basically just a bunch of extruded cylinders with enough geometry to to deform the character in various ways. Like it would be nice if this can be really animated in an elastic way. So that's something I want to aim for. And the thumb over here, you can see that it's kind of shrinking down towards the connection of the rest of the hand. So this could just be there could be just extra cartoony bones that just completely where you can scale and rotate and just completely deform these features however you want. So the geometry should just support this. So even though this is a very simplified shape, it should just still have enough geometry to skew and and just make it as flexible as possible. With the hair, it's just basically going to just be animated as like a single strand, like a single clump of hair. But I actually gathered some little inspirations. I wanted to look up some like style references online. Like, is there anything on like my huge Pinterest boards where I basically collect anything that looks remotely interesting or inspirational from the Internet? And I just wanted to look, is there anything that someone else has already done that could that I could draw some inspiration from? And I think this simplified model by Amad Mehab is really interesting where he also does this thing where the the head is essentially just a very simplified shape. It's just mostly just a slightly like on a slightly deformed sphere, like a cube sphere. And the eyes and the mouth are just extra elements that are either textured or just projected on top of it. So this is the sort of thing I want to go forward to, except for like we wouldn't have a nose or more complex elements like these seams, probably. I mean, we are going to have like smaller beveled creases in there. But it's mostly going to be pretty simplified and stylized. The only other like this is, of course, these are way more complex these models. But what I'm looking for specifically over here is the style of the hair. So what's interesting with this is the hair is definitely more complex than other parts of the body. There's more intricate little shapes and spikes that are coming out of it. And I'm I definitely want to go for something in that vein. We can still like texture or shade extra detail on top of it. But it should be a more hard modeled simplified shape. This is way more the hair shape, overall, is somewhat what I want to go for. But just with smaller spikes for our character. So this guy definitely has way smaller spikes going on over here. But overall, this would just be like just modeled straight into it. It's going to take quite a little bit more time with retopologizing it, but that's fine. And then with this one, it's also really interesting how these shapes kind of flow back into each other. And there can still be like some extra hair strands just with bump maps or any sort of texturing or shading just added on top. I'm just mostly thinking on like the basic shapes right now. And this is essentially it just for the for the overall background of like the design and what I want to go for. I will commentate more on top of it like once we actually get into the modeling. But yeah, let's just dive straight in.


Hello friends and how are you all today? My name is Priyanka and let us discuss this question. It says solve the following differential equation Now we are given d square y upon dx square is equal to e raised to the power x plus cos x given that dy by dx is equal to 1 is equal to y when x is equal to 0. So here let us rewrite the given differential equation on integrating this equation with respect to x we get integral d square y upon dx square dx is equal to integral e raised to the power x plus cos x dx or we can write it as dy by dx is equal to Integral e raised to the power x dx plus integral cos x we have dy by dx is equal to e raised to the power x plus equation. Now we know that when x is equal to 0 dy by dx is equal to 1 is equal to e raised to the power 0 plus c1 this implies that the value of c1 is equal to. So now on substituting this value of c1 equal to 0 in the first equation we get dy by dx is equal to e raised to the power x plus sin x plus 0 or we can write it as dy by dx is equal to e raised to the power x plus sin x. Again integrating with respect to x we get dy by dx into dx is equal to integral e x dx plus integral sin x that is y is equal to e raised to the power x minus cos x plus c2. Let this be the second equation. Now we know that when x is equal to 0 y is equal to 1 so on substituting these values we have 1 is equal to e raised to the power 0 minus cos 0 plus c2. That implies 1 is equal to 1 minus 1 plus c2 that implies the value of c2 is equal to 1. So on substituting the value of c2 in second equation we get y is equal to e raised to the power x minus cos x plus 1. Right? So this is the required answer to the given question. So hope you understood it well and enjoyed it too. Have a nice day.


Okay. For the sake of time, let's start the last session of today, which is going to be a second session on generative models. And I would argue a session on generative models for scientific computing. And the first talk will be given by Agil, who, unfortunately, is still in Berkeley. And take it away. All right. Thank you for having me. I'm sorry I couldn't make it there. I was really looking forward to it, but I had problems with my visa. And so the title of this talk is compress sensing using generative models. It'll be half-babe between theory and practice. And this is joint work with my collaborators from UT Austin. And yeah. So here's a brief outline of the talk. I will spend some time on background, then describe the posterior sampling algorithm we've been looking at recently. And finally, applications to compress sensing MRI. So what is the problem of compress sensing? Very simply put, if you want to recover some unknown signal, for example, an image from noisy linear measurements, then compress sensing can be used in these sorts of applications. So for example, if you want to get a brain scan from a patient, you would put them into an MRI machine. The machine would take some readings of their brain, and using those readings, you would like to reconstruct the brain scan. And similarly, in astronomy and oil exploration, you get some measurements of an unknown signal, and you would like to reconstruct that signal from those measurements. In the simplest form, we model this as a system of linear measurements where y denotes the measurements that you obtain. A denotes a matrix that takes you from the image to measurements. X star denotes the unknown image or signal. And you may have some additive noise. And for notational sake, M would be the number of measurements you obtain. And N would be the dimensionality of the signal that you're trying to reconstruct. And the fundamental questions in compress sensing are how many measurements do you need to recover the signal, and also what algorithm would you use for recovery. Now let's take an even simpler case where there's no noise in the measurements. Now we can write this as a system of linear equations where, again, you have the measurements over here, you have the measurement matrix, and you're trying to recover this unknown image using the measurements and the measurement matrix. And elementary linear algebra tells you that if you have fewer observations of the signal than there are dimensions in the signal, then this is an under-determined system of linear equations, and there are infinite solutions to the system. And hence, uniquely recovering X star is impossible if M is smaller than N. However, if you impose additional structure on this problem, it's indeed possible to recover X star exactly using very few measurements. So for example, the seminal result by Candice Roberg and Tao in 2006 showed that if X star is k-sparse, meaning that it's a large vector, but the number of non-zero entries are at most k, and the rest of the entries in the vector are zero. Then the number of measurements you would need scales as the number of non-zeros times the logarithm of the dimension of X star. And this also assumes that A, the measurement matrix, has some nice properties. So for example, if it's drawn Gaussian IID, then it will satisfy these nice properties. And the intuition is that since you're only considering vectors that are sparse, these form a low-dimensional subset of Rn. And since if you're choosing k entries where X star is non-zero, there are only n-choose case choices for the support. And the number of observations you need is roughly the log of those choices for the support, which is k log n over k. And the algorithm for recovery would be simply lasso, where you say that you optimize for your image X, such that once you multiply X with the measurement matrix A, it's as close as possible to Y in, say, L2 norm. And you also add a penalizer for the L1 norm of X to ensure that it is sparse. So if you run this with an appropriate choice of lambda, you will exactly recover X star using very few measurements. And now a natural question to ask is why do people care about sparsity? It's because if you look at images in some harmonic basis, like for example, in the wavelet basis, if you take this example, if you take this image of a castle and you perform a wavelet transform, you see that most of the wavelet coefficients are sparse. And now instead of recovering the image in the pixel domain, you can recover it in the wavelet domain. And since this is a bijective transform, you're OK if you just recover these sparse wavelet coefficients using compressed measurements of it. And this is a classical 90s, a 2000 signal processing approach to compression and compress nancy. And many algorithms like JPEG exploit sparsity in an appropriate harmonic basis to achieve tremendous compression rates. And in this talk, we will not use sparsity anymore. We will talk about how we can leverage machine learning. And I'm not trying to be adversarial to sparsity. I only mean to say that this is a more contemporary version of sparsity. And the intuition is that every year, millions of MRIs are taken. And this gives us some data driven model for modeling these images. And if you have these millions of images, you should be able to look at them and develop some better understanding or more complicated understanding of them than just simply saving them as sparse in a wavelet basis. And this structural understanding of the MRI or the structural understanding of what a brain MRI looks like should allow you to take fewer measurements in the future, which will imply lesser scan times and make MRIs more accessible and inexpensive. And if you want to model images in 2023, I think in my opinion, the best way are through deep convolutional neural networks or transformers. And in this talk in particular, I'm going to concentrate on generative models. So we had prior work in 2017, which said that if you consider low dimensional generative models such as GANs and VAEs, these are continuous differentiable functions from a low dimensional space RK to a high dimensional space RN, where K is much smaller than N. And the rough idea is that since your model is sufficiently smooth, and it's a low dimensional mapping from, it's a mapping from a low dimensional space to a high dimensional space, the range that of images captured by your generator model is low dimensional. And this is analogous to what Can you hear us, Ajil? Sorry, my zoom crashed. I'm not sure what went wrong there. Okay. Just give me a minute. Yes. Sorry about that. Okay. So I'm sorry about that. I don't know what happened. So the first thing we were able to prove back in 2017 is that if you have a generative model, which is ellipsis, then the number of measurements you need scales as the input dimension of your generative model times the logarithm of the ellipsis constant. And if you're now considering rallied neural networks with D layers, then the number of measurements scales as the input dimension times the depth of the neural network times the logarithm of the output dimension. And these results are really analogous to what we find in sparsity because in sparsity was just K log N. And now we have these substitutes, which are the ellipsis constant of the neural net of the neural net or the depth times the logarithm of the output dimension of the neural net. And really, there were lower bounds. It said that generative models are actually a strict generalization of sparsity. One can create generative models that output sparse vectors, but these would be handcrafted generative models. And instead of someone give you data, you will be able to learn generative models that capture richer structure in your data. And the algorithm is also a generalization of lasso. And it's provably poly time in certain settings. This is work that's not by us, right? So low dimensional generative models are good because they allow you to prove theorems that are very analogous to what we find in sparsity. But empirically, when we run them, we find this very interesting phenomenon where we trained a generative model that goes from a hundred dimensional space to like a 12,000 dimensional space. And the y-axis here shows you the reconstruction error between the estimated image and the true image. And the x-axis shows you how many measurements each algorithm was given. And what we see is that the red line is the algorithm we proposed in 2017. And the green and the blue lines are what lasso are the performance by lasso. And what we find is the red line drops off very quickly when you have few measurements. But once you hit 500 measurements, it plateaus. And the reason for this is that we only have a model that's going from R 100 to 12,000. And it has some number of layers. And once you hit 500 measurements, you've already found the best possible image that the generative model can produce. Because, for example, this, for example, was run on human faces.  And since the generative model is not perfect, it can't capture every human face. It faces some fundamental representation error or capacity or like limited capacity, which leads it to this plateauing phenomenon where after 500 measurements, you giving me more information doesn't help my generative model because it simply cannot do any better. In lasso, we can tune that lambda parameter, which allows for more or less capacity. But in generative models, this low dimensional space is fixed. And hence, there's no, there's nothing you can tune unless you train a new generative model from scratch. And another interesting phenomenon that was observed by Asim et al. is that if you train a GAN on human faces, it tries to impose a face on everything. So this shows that it has a huge data set bias. So for example, in this example of a barn that has like something that looks like eyes in a mouth, a generative model would try to reconstruct a face on this, whereas lasso gets grainy images, but it's at least able to tell that this thing is not a human face. And this really tells you that there's something really problematic here with using low dimensional generative models or GANs. And in and around this time is when diffusion models and score-based generative models started becoming more popular. In fact, score-based models were invented around 2018 or 2019 and diffusion models were invented around 2020. And for those of you not familiar with this, I'll briefly go through what a diffusion model is. I won't talk about how it's trained. And the rest of the rest of my talk is basically going to argue that we should all be using diffusion models and posterior sampling using diffusion models. So diffusion models try to do the following problem where if you have a probability distribution P and assume there's some variance beta square, let P tilde be the annealing of P where I'm taking P and convolving it with a Gaussian of variance beta square. So this makes P a little smoother. And of course, this P tilde would be the distribution of a random variable that is distributed according to P and it also has some Gaussian noise of variance beta square added to it. And there exists some algorithm where if you give it IED samples of X1 to Xm drawn from your distribution P, then a diffusion model can be trained to go from Rn cross R to Rn where the first parameter in Rn would be some image in the support in Rn and beta would be how much annealing is happening to the distribution. And this diffusion model is trained to approximate the gradient of the log of the annealed density at X. And the key point in diffusion models is that they are trained to map X over various beta. So you can pass in a range of betas and it will approximate the gradient of the log annealed distribution at that noise variance beta. And since these diffusion models are supported on the whole of Rn, they don't suffer the same capacity problems that GANs do. And what we observe is that they also don't exhibit the same data set biases observed in GANs. Before I go to the next part, are there any questions? Also feel free to interrupt me if there are questions. And now I'll talk about how we used diffusion models in procedure sampling in our experiments in theory. And procedure sampling is a very intuitive algorithm that one can run. So basically it says that assume your distribution had some probability distribution associated with it. And you're given linear measurements with Gaussian noise. Then a possible estimate for this unknown X star is to draw X hat, which is distributed according to the posterior distribution of images conditioned on the measurements. Now, if you ask a Bayesian this, they would tell you that this is the obvious thing to do. But I think until very recently, we just didn't have generative models that were rich enough to capture this procedure distribution and to also allow you to sample from it. And if you want to perform this procedure sampling, you can run, you can approximate it via Langevin Dynamics, which follows the following, which is the following iterative procedure, where you initialize your image to just be IED Gaussian noise. And then for T large enough, you run this process over and over again, where the image at time t plus one is the image at time t plus some positive step size along the gradient of the log posterior, plus some Gaussian noise whose variance is proportional to the step size that you just took. And now if you write this posterior out using Bayes rule, you get the gradient of the marginal density plus the likelihood density minus the log of the normalization factor. But since you're differentiating with respect to your current image, the gradient of this normalization factor with respect to your current image is zero and that goes away. And the diffusion model can provide some approximation for the gradient of the log marginal. And this log likelihood term is a Gaussian because the way these measurements were generated were through a linear transformation plus Gaussian noise. And so if you write that all out, the gradient of the log Gaussian density becomes this expression here, the gradient of the normalization factor is a constant with respect to x, so it's become zero. And now you have a closed form expression for what the Langevin updates should be. So this says that assuming you had access to the true posterior of the distribution of the image, if you're given linear measurements with Gaussian noise, then you can write out the update rules for Langevin dynamics to sample from the posterior distribution. And this gradient log p term comes from the diffusion model. And this is a little bit of a disclaimer because when I was running these experiments in 2020, the diffusion models are not very well understood and algorithms relating to diffusion models are also not well understood. So it wasn't clear how one should be sampling. And now there's been a lot of progress in it. But three years ago, I sort of hacked this procedure to actually get it to work in practice. And the reason things break is that it's not that the equations on the previous slide are incorrect, they are correct, but they don't consider the fact that diffusion models learn the annealed distribution. So while I said that a diffusion model would be able to approximate the gradient of the log marginal of your image, diffusion models don't actually do this. They learn some gradient log of p tilde, where p tilde would be an annealed or modified version of p. And since I don't consider that annealing, if you do actually try writing out the former equations using annealing, it breaks and it's no longer correct. And a more principled version of it appeared in Eichler 2023, which by these authors. So it actually took roughly two or three years to figure out what is a principle way of using diffusion models, such that you account for the posterior sampling and also the annealing that happens in while training diffusion models. But in my experiments, I simply introduced some hacks and hyperparameters that allow, that seemingly allowed me to get things to work in practice, at least empirically. It seemed to work empirically. Okay. And then we ran our experiments on the flicker faces data set. So recall, I said that GAN suffered this huge data set bias, data set bias, or some sort of bias, where the top row here shows high resolution images. The second row shows blurry, like downscaled versions of the upper row images. The third row shows reconstructions by pulse, which is an algorithm that uses GAN and does map estimation. And you can see that it's really propagating, destroying like ethnic and race features. Whereas if you use diffusion models and posterior sampling, we seem to preserve certain details much better. And the key point here is that the GAN and the diffusion model were trained on the same data set, which were flicker faces. So whatever racial biases existed in flicker faces is inherited by both of these generative models, but we're able to see that clearly one is better than the other. And also they have an algorithmic difference in that pulse performs a point estimate via map estimation, whereas posterior sampling is randomized and samples from the posterior. And recall that diffusion models are supported on the whole ambient space of RN. So it's not clear why we should be able to use them for compressed sensing. Most compressed sensing results, or almost all compressed sensing results, require some lower dimensional structure in the image that can be exploited to get fewer measurements. So now a question now would be if you were to take diffusion models, how do we characterize what this lower dimensional structure is? And in order to achieve this goal, we propose this new notion of approximate covering numbers, which is a measure of the complexity of a probability distribution. And it says that if you're given any distribution p and some parameters epsilon and delta, which are positive, then the approximate covering number at epsilon and delta of p is the smallest set of epsilon radius balls I need to cover one minus delta mass in p. So if you look at this heat map of a probability distribution, the blue areas are like low density areas, and the reds are the high density areas. If I take epsilon radius balls and keep them along the diagonal, then these cover most of the mass under p. There's some mass outside, but if you take the union of these balls, it covers a large fraction of p. And you look, and if you also count these balls, they seem to be only along the diagonal rather than in the whole plane. So this tells you that there is, if you're willing to throw out some probability mass in some probability mass captured by a diffusion model, then there may exist some lower dimensional structure. And you should be able to exploit that to get compress sensing results that are similar in spirit to what we are classically used to in compress sensing and sparsity. And we're arguing that this notion of approximate covering numbers exactly characterizes how many measurements you would need to do compress sensing recovery using this probability distribution. And we have the following theorems which which work for IID Gaussian matrices A. So in this setting A is scaled, the variance of A is scaled, that's that the norm of your measurements is roughly the same as the norm of your ground truth X star. And the additive noise eta is scaled such that it has norm roughly epsilon. And the upper bound we can show is that if you run posterior sampling for this measurement process where A is Gaussian and the noise is also Gaussian, then the number of measurements you need is scales logarithmically as the epsilon delta approximate covering number of the distribution of X star. And if you do posterior sampling, then the estimate X hat is epsilon close in alto norm to X star with probability one minus three delta. So this guarantee is, it's the sort of guarantee that you would get in like frequentist statistics in compress sensing, but it's an algorithm that's randomized. And there's also some failure probability that depends on how much mass in your probability distribution be that you're not considering. Because recall that this epsilon delta covering number number tries covering a one minus delta fraction of P using small radius balls. And this result tells you that if you did posterior sampling with measurements that scale logarithmically as this epsilon delta covering number, then the posterior sampling estimate is epsilon close in alto norm. And furthermore, we are able to show this robustness result which says that if there's a mismatch between the distribution of your ground truth image, so if it's drawn according to some distribution R, and you only have an approximate posterior meaning that you're sampling X hat from P of X condition on Y, then the upper bound still holds as long as the distribution of your image R and the distribution of your generator model P are epsilon square root delta close in Wasserstein distance. And the reason I say that posterior sampling is almost optimal is that we're able to show a very close lower bound which says that if your image is drawn according to P and assuming it's compact, meaning that the norm of X star is at most R, then any algorithm that gets epsilon close to X star that any reconstruction algorithm that gets epsilon close to X star with probability one minus delta requires measurements that scale as the logarithm of the epsilon delta covering number. Now the reason I say almost optimal is that there's an extra additive, there's an extra multiplicative log one plus R square factor in the denominator and these epsilon and delta constants that the constants that multiply epsilon and delta are different between the lower and the upper bound. In the upper bound I had log epsilon delta and the lower bound I have three epsilon and four delta. An interesting thing to note about this lower bound is that in traditional compress sensing lower bounds we would construct a minimax instance P which is hard to reconstruct and then we would show a lower bound for that. In contrast this lower bound works for any probability distribution. You give me a distribution P of your choice and this lower bound will still hold for it. This is not a minimax lower bound it's an instance lower bound and our approach to showing this lower bound is purely information theoretic. Recall that the upper bound said that if you want to get epsilon close with probability one minus three delta the number of measurements you need is log of the epsilon delta covering number and if you want to show the lower bound you should think of this whole process as being a Gaussian channel. The mutual information between X star which is the ground truth image and X hat which is the reconstructed image is at most the mutual information between X star and Y. This first inequality is via the data processing inequality and the second inequality follows from Shannon's AWG and theorem which says that the mutual information between X star and Y is at most M times the log SNR and the reason this holds is that Y is a linear transformation of X star and has added Gaussian noise to it so you can directly apply Shannon's AWG and theorem and now the only part that remains is to show that if you're able to successfully get epsilon close to X star then the mutual information between X star and X hat should be at least the log of the epsilon delta covering number and this is actually very close in spirit of Thanos inequality and the main difficulty here is that Thanos inequality is typically proven or is proven for a discrete distribution and a uniform distribution over discrete elements whereas here P is continuous and arbitrary and we need to show this lower bound and I'm not going to talk about how we show it but we are able to show some version of that and if you now take this capacity inequality between the which gives an upper bound of the mutual information between X star and X hat in terms of the number of measurements and you have this lower bound for the mutual information in terms of the log epsilon delta covering number you put these two things together and the lower bound directly transfers and it says that the number of measurements you need should be at least the epsilon delta covering number and now we'll talk about applications of posterior sampling that we've been doing for the last year or two so compress sensing MRI has become very popular and it's actually getting a lot of FDA approval to build devices that actually use deep learning based compress sensing techniques and the basic way to model compress sensing MRI or to model MRI as a compress sensing problem is is the following equation which says that you should think of X star as being your brain scan and once you put a person into an MRI machine the way the machine works is that it performs a Fourier transform of your brain with some discretization level so this F would be the discrete Fourier matrix and then it selects some subset of the Fourier coefficients based on some suggestion by the lab tech or the radiologist so the whole process is your brain gets Fourier transformed and then the machine selects some subset of those Fourier coefficients and there's also some additive Gaussian noise of variance epsilon square and this is very clearly a linear measurement process so everything I said directly transfers because you can just run Langevin dynamics for this for this compress sensing MRI problem and we compared our results to model and varnet which are state-of-the-art deep learning techniques which are trained to use one-third of the Fourier coefficients and reconstruct the brain so you you feed in a certain third of the Fourier coefficients and these deep learning models will spit out brain reconstructions and what we find is that if we run Langevin dynamics using a diffusion model trained on brain scans we are competitive so the the leftmost image shows the ground truth that a radiologist would like to see the next two columns show reconstructions by state-of-the-art deep learning baselines and the last the last column is our algorithm that uses Langevin dynamics and diffusion models and we are competitive with these models which is quite surprising because these things have been trained end to end so they they have been trained using examples of here's one-third Fourier coefficients and here's the brain scan I would like to see and you you train this sort of like a regression framework to say that you will take in Fourier coefficients and then spit out a brain scan and since it's been optimized for this setting we were expecting to be beaten a whole lot more by model and varnet but what we find is Langevin which has no prior information about what this measurement process would be or which Fourier coefficients are going to be selected is competitive with these algorithms and now if you change the measurement process a little bit and you say that okay instead of taking one-third of the Fourier coefficients I'm going to take one-twelfth of the Fourier coefficients then these deep learning baselines fail because they have been taught how to use one-third of the coefficients and get a good brain scan out whereas Langevin doesn't care at all it's been trained only on brain scams and now if you tell it that okay I'm going to give you these one-twelfth Fourier coefficients it just doesn't care you run the same algorithm again you just have to change the the matrix because now you've gone from one-third to one-twelfth but as long as you you're able to specify that matrix to Langevin dynamics it gets reconstructions that are much much better than these baselines so this is one reason to to use generative models in that they are much more modular than end-to-end deep learning techniques for performing compressive reconstructions so you can use the same generative model and recall that these models are very expensive to train so if you train one you can use them for any lap setting or scan setting in the clinic and another interesting thing we observed is that if you train all of these models on brain scans and you test them on a similar compress sensing problem but with knee scans these algorithms don't break completely and we find that Langevin tends to be a little bit more robust so in this case you get one-fourth of the Fourier coefficients of this knee scan and these again the the left column shows the ground truth that a radiologist would like to see it's the gold standard and the next two columns are the deep learning base the end-to-end deep learning baselines which seem to introduce much more artifacts than Langevin dynamics Langevin still has some you can see some artifacts over here as opposed to here but this was this was very surprising in that all of these models have never even seen a knee before they've been trained purely on brain scans and you feed them Fourier coefficients of this knee and supposedly these models can incorporate information about the so the Fourier coefficients contain information that this is a knee but since you've heavily sub-sampled and selected only a quarter of the required Fourier coefficients there will be some blurriness but if you use the these models they they know that a brain has some smoothness and structural information in there and it it it compiles that information along with information that you you just scan the knee via the Fourier coefficients to get pretty reasonable knee scans for models that have never even seen a knee or know what a knee is and quantitatively we find that Langevin is Langevin tends to be better than other algorithms so we tested it across different anatomies scanning techniques and acceleration factors where we we tune how many Fourier coefficients are shown to the models and this blue line is Langevin and you can see that it tends to be higher than the rest in the majority of cases another interesting application we've had is motion correction so during an MRI scan if a patient moves their head like they can either rotate it or translate it then this movement manifests as a blur so for example this L1 wave width reconstruction shows what happens if a patient moves you're not able to tell what state it was in but assuming that the rotation is rigid you can actually modify the Langevin updates to estimate both the brain scan and what angle opposition the brain was in so if you do that we're able to see that the our reconstruction over here which which is using corrupted motion corrupted measurements that have motion in them you're able to see that the reconstruction quality is close to what L1 wave width would obtain if there was no motion so the the third column is for L1 wave width if there was no motion at all whereas the fourth column is our Langevin technique even with motion corruption in the measurements and then the bottom row shows comparisons of like a zoomed in section of the ground truth image so the ground truth image is here this is L1 with motion corruption L1 without motion corruption and this is ours with motion corruption so you can see that it's much better and then these are the errors in each of the algorithms magnified by a factor of 10 yeah okay that concludes my talk here's the this is the code for our MRI project we've also released our models publicly so if you would like to use them if you feel go ahead and these are the references from my talk thank you do we have questions for Ajil hi very nice talk um i was wondering if you could tell us something about the comparison between the computational complexity of the Langevin approach you proposed versus the one based on deep learning right um so when I was running these things it took okay so we don't have uh just to be clear we don't have any theory guarantees for how long Langevin would take on this problem I'm speaking purely in like uh processing time on the computer uh it took me roughly five to six minutes per image whereas the end-to-end baselines are much quicker they just take five to ten seconds but I think that's a problem that was only true in 2020 or 2021 now you can do uh posterior sampling or like I don't know if it's actually doing posterior sampling but there are some uh sampling techniques MCMC sampling techniques which can be done in like 10 to 20 seconds so speed is no longer a problem hi um I would like to know so if you are able to sample the posterior instead of just taking one simple why wouldn't you average over it shouldn't be better oh yeah um uh the the pragmatic reason is that it was very slow so averaging would be would make it even slower uh but we saw that um and also if I was doing it more than once I could also I could I could pick and choose a cherry pick which reconstruction will be will be is best but that would violate the statistical validity of my results so then we just chose to take the first sample but we also ran experiments where we sample multiple times and then created uncertainty estimates and yeah that we see we we saw some diversity uh over multiple rounds of lunch with yeah so it's totally valid to do this multiple times and take averages or median or yeah some word some statistic based on that okay thank you I have a question so I guess I will go ahead uh thank you very much for the nice talk so I would argue that one of the of the risk of those algorithms that are based on generative priors is that the generative model has actually a lot of information and in some sense is able to hallucinate a solution even if you don't have enough measurements to actually uh do a reconstruction so you could have something that is very good looking and be very um confident that this is the right one but then maybe not so I don't know if you have any comment on how your methods uh deal with this this issue uh yeah we don't have a comparison right now and actually uh it's not just generative models uh all deep learning models have some artifact or the other so even model and varnet which you think would be more robust if you train on MRI scans that were done using say GE scanners and you use it on like semen scanners um it it starts hallucinating artifacts it it may not look like a tumor but there will be like some shading uh some artifacts that happen so yeah both of these both uh end to end deep learning baselines and generative model techniques do hallucinate um and I guess like the the threshold should be that radiologists are human and they do make mistakes then as long as the generative model or the deep learning model makes mistakes that are rarer than a radiologist mistakes I think they're okay but yeah obviously this needs a lot more study and um I know that my collaborator John Tamir is actually working with people or radiologists at UT's medical center to try and see like how these things compare okay thank you very much maybe one last quick question okay and if not I guess for the sake of time we will leave it there thank you very much Agile


Not my day of walk on Man, you tell me, man, it's going down, man Another day, man, and we ain't even been up here, man You know, we been chillin' I gotta put in some overtime, man You're puttin' in overtime and editing Yeah, I know what I do with it I'm doin' what I gotta do, check it, man We got a special guest in here today, man And he don't really need no introduction, man He been workin', man If you just, hey, if you Google him You know what I'm sayin', pull him up, man Whatever you gotta do, man My boy, YSM, flippers in the building What's goin' on, man? Man, what's poppin'? Man, it's good to see you, man All right, shit Good to see you, man Good to be here, good to be here, friend Yeah, yeah, yeah, man And I didn't know, I thought you was gonna cancel on me Like I said, I kinda felt that way with, you know With what just happened with Wadi, man Yeah, but, yeah But we had already scheduled this, you know A lot of people, a lot of time People don't realize how this thing would be goin' And then not only that We had already had one I was supposed to pull up with Wadi Yeah, I know, that's what I was sayin' That was the whole reason Yeah, so, you know We had been rescheduled this couple weeks ago, I think Yeah, we did I ain't wanna do y'all like I did last time Yeah, I kinda felt like, oh, that's how he rolled The nigga roll like that, you know But I heard you was sleep Yeah, I was, I think I was asleep, but Kinda tired night before or somethin' I don't even remember, I don't even remember That was like, I don't even remember That was a month or so ago That was a month ago Yeah, man, and you know And we had talked about you that day It was a gang up here, it was like We can't even get a hold of them Cause Trey was linkin' up with you some kinda way And they wasn't, they would link up with you Yeah, I think I was DMing him back, but Uh, when I don't know, I was probably asleep, too I don't remember I don't even remember what I was doin' Yeah, so, man So tell us how you guys decided How did you get into the music? Like, are you just, how did you Start growing up Tell us a little bit about yourself Where are you from? Where did you grow up? You know what I'm sayin' I always stayed in Dallas my whole life Damn, you know what I'm sayin' About 8th grade, 9th grade That's when I met Woody and Mario I wasn't rapping But by like, I'd probably say 11th grade, or 10th grade It was probably 10th or 11th grade Mario had already been rapping And Woody was rapping, too So they motivated you to start rapping?   You tryin' to figure out what's gonna work I'm tryin' to see everything I'm tryin' to see what's how it's gonna work But now, they got me start rapping Which one, was it Woody that got you started? It was really, uh, Dullo Dullo? Dullo, cause he been rapping since we was like Younger than that, like middle school You know what I'm sayin'? Before I even came over there Wow But What did he say to you to get you to start rapping? I think I used to like, rap at lunch Like, you know what I'm sayin'?   Or this is just something you're just doing I don't know I kinda, I kinda Like doing it, but It's cool I mean, do you get a lot of views on YouTube? You get a lot of impact on Instagram? Those are the things that other, other, I guess Striving artists? Yeah, that's all of the artists is trying to do A lot of them would love to do what you're doing But I had to put in, that wasn't just me not trying though Like, I had to really like, I wanted to rap like, like how, like I don't know, like every day, I just did it every day I just wanted to perfect the craft like And whose studio was you using back when you first started? I know you started at the house somewhere I think my first song was at somebody house, yeah But then after that, I started going to, I started going to Vaughan's favorite fated studio Okay He was where I was making like, we made like, probably like a hundred, two hundred songs Wow Then we started going to This one studio, the music box With Beazie and Wasty Okay They had their own room, so they used to, they used to like I used to, when I wanted to, when I wanted to rap I used to just stay there all night, like spending night there Yeah I used to be there for days Just rapping I learned how to record myself, so I bought all the equipment That's what's up That's more than a hobby, cause when you, you seem like you making it your life I mean, it just, it's like, I don't know It's just something to do You find a love for it I get, like he said, I get views and stuff and just people just Use and impact People just be DM me all the time, like drop, drop, drop, so And now you got a fan base, right? Even with, yeah, but even with my like the trailers and the little, little Just the little snippets I be dropping It just be, it just be on it, so Where do you get your inspiration for your songs? I don't know, probably, probably me and the people I be around Yeah Just, you know, we be just talking about stuff like Stuff we do or where we on or I don't know, I don't really be listening to nobody Don't listen to nobody's music, but you, but of course the camp Yeah That's about it I mean, I don't know, I don't really get no inspiration from nobody Cause I don't, I don't want to rap now that I don't, like nobody, I don't want to sound like nobody So who do you, who would you say that you, I know you don't sound like nobody there But I know that growing up you probably listen to like a bigger artist growing up and got inspired by one of them Let me see Who was it? Probably soldier boy Really? Soldier? Yeah, cause he used to like That boy on the wall up there?  Do what? Switches, switches, switches flow up I mean, yeah, I'll try to Yeah, yeah Well, let me ask you something about the music, what about, and look like you and Barrio, y'all together a lot Yeah, that's like my brother All of us We really, we all be with each other a lot, but Barrio, it just, I don't know, I don't know Y'all be making, y'all, you seem like y'all tip-a-tap on the music Even outside the music, even with just life, just me and Barrio be at it We probably talk to each other every day Okay, and that's building the relationship That's saying we vibing and we'll rock out at that studio So if y'all talk every day, that studio is on your mind Studio, it's like we have our own studio Y'all just livin' that thing No, we don't, it's just like, it's just like you want to pull up, pull up And if we so happen to be there at the same time, then we'll record a song Because he be movin' and I be movin' I don't say we all be doin' our things But if we pop up at the studio at the same time, we'll hit each other like, meet me up there It ain't nothin' to do a song, cause we've been doin' it Like, he used to spend the night with me at the studio when I used to like We've been doin' it so bad, so much, so we know how to like feed off each other Well, tell me a little bit about Swipe Talk What, how did that song come about? What was you guys doing? Just kinda run me through it No, no, we'll probably just, I think we'll probably, I think we recorded it at his house Okay And so, you know what I'm sayin'? He, I go first or he'll go first, whoever went first on that song I think it was me, and he'll record me, I'll record him He'll record me, I'll record him, he's just like that Yeah So, and then what about Kenny B? He's pretty close with the camp too or what? Yeah, can it be, can it be that he, yeah, he, he, he, he, he with us Okay He, he gang, but he like, you know, he from Fort Worth Yeah, of course, he is from Fort Worth, y'all are from Delaware, bro Yeah, so, well, that's what he from That's what he from, you from Dallas Yeah, so, so, Kenny, he, you know, he from Fort Worth So, it came with him, he like, we just been in the studio one day And he just clicked with us That's how that, that's how that happened? Nah, I mean, we been had songs before that one, but That one's just the one, like, that one's just one of the ones we liked so much So, we just, you know, we tried to be there on anything Man But Kenny B with us too, just like everybody else Everybody So, do you, okay, and do you, do, what, tell me about Try? Uh, it's the last video I dropped Yeah I don't know, like, every video, it's probably one of my favorites right now Of course, it's the last one Cause Moe be going, nah, cause my favorite is really, uh, what's my favorite video? I don't know It's probably Law & Order Law & Order? Yeah, I like that concept, but, but Try there was nice too Yeah I got some Moe hard stuff in the drop Oh, yeah? Some videos, yeah Who do you like working with as far as your videographer? Moe always my go-to Oh, yeah? It's like he, he gang, he be there with me too, like out of town You know what I'm saying? He like working with you Yeah, he shoot everywhere with me It's good when you can find somebody who you, when you explain something to They totally get it, they understand exactly what you need and what you want Yeah, we just be chillin' Moe, he gang Yeah, yeah, and that's dope, man, so Go ahead My fault No, no, no But I often to say, uh, with the other camera man though, I like, I like visuals by D You know what I'm saying? I've been messing with Ali's since like when they first start Yeah You know what I'm saying? How important is it to have visuals though? I don't know, to me, I really don't mean like Moe will call me and be like, nah, we gotta shoot You gotta meet me here, here, here, like, that's how Moe be, so That's how I be so active with Moe, cause he'll tell me, yeah, get up, do this, do that And meet me here You know what I'm saying? I think the visuals He's a motivator I think visuals are super important when it comes down to music I mean I don't reason because that's what everybody can see and they gravitate to it to me You know, the lyrics, okay, I don't know because when you're in the car You just putting on some music, you're gonna bang out, right? Yeah But I don't know, I like the visuals, man I like that picture, man, cause every time I see you turning up, it's like yo The visuals, the visuals be cool too Because everybody always have their phones, so they're always looking at videos On YouTube, you know, checking stuff out, they want to see the person That's it, that's totally it, and it's so convenient now, right? Yeah That's why they be on your IG and, you know, Facebook and whatever, cause they want to see you They want to see those skits, they want to see all of that It's, what's going on in that DM? You got a lot of people What's the craziest thing ever come across your DM? Craziest thing? I don't know People say, I'll tell you what's up, sometimes people will be like Sometimes they'll be mad at me for something They just make up something Then they'll be like, well can you send me some money? No People always ask for money Really? People ask for money Cause they know he getting it, they feel like he getting it And then he's showing it I got it, nigga, I got it I'll be showing it I see it on your IG, you be showing it I'll be showing it So do you, what can I say, you know, do you have a favorite rapper outside of Soulja Boy That really like made you feel like, damn, I got to come on with it Like if you listen to a song and be like, damn, man, I got to make mine better than that What pushes you? I probably say people out there be around and push me They push you more than anything Yeah, cause I really don't even be trying to record I pull up to the studio just to shoot dice If there's a lot of people up there, I pull up, shoot dice You know what I'm saying, but I record They'll probably tell me, like, yo, this beat right here, hold on If I like it, I go in there and record Wow That's how we become across some of our songs Like, all of us at the studio with me, Kenny, and Gwadi, and Trill You know what I'm saying, we just all let the studio that day, shootin' dice Yeah, yeah, that poor boy, I seen that one Yeah And like, I was recording in a room back there, they shootin' I ain't, you know what I'm saying I tell somebody else, go hop on it I hopped in the dice game, then he'll come back and tell you You hopped on it, then he hopped back in the dice game They're like, we all at the studio, they go hop on there Yeah, it was having fun Like, we didn't even have to hear what he said Like, nobody had to hear what I said, like, you know what I'm saying They in a whole another room, just come in there Yeah, that's how easy it be Man, you know, I have to talk about the elephant in the room, man Wadi, you just mentioned it, man How do you move past when you lose somebody like that? When I got the call yesterday To be honest, I just said his name, and he still feels unreal Yeah, like he's still here Because last thing when me and him was talking, he was like, I gotta get my music on my YouTube You remember what I'm saying?  To get it where it's you pretty much are the one that, you know what I mean? Controlling it in the narrative Because you got fans, of course, and that's what me and him was talking about Like, when you got these people following you You putting it out on all these other people's platforms They benefiting from it, you know what I mean? Yeah But how, I mean, how does that... I mean, because the way I heard it, I know nothing about it But the guy that was here with him last time They evidently got into a fight or argument or something at the club Were you there that night?  But all of y'all, he was a part of the whole clique too, right? I mean, he wasn't really... You know what I'm saying? He wasn't really like... How does he end up here with him? Because I know what it told me to interview him He was out... I don't even know how to explain it, bro It's just... He doesn't switch out You know what I'm saying? He was cool with us But he wasn't immediate So did he go to school with you guys? Nah, he just... I can't really explain it I can't even answer your question right now I was just trying to understand how he ended up in the store standing in the video Like he's a part of everything But then that happened I can't... You don't even know how I'm thinking about it You're trying to figure out what the hell happened I can't comprehend So I can't tell you And I get it, man And I really don't say that because It just... Because I talked to them yesterday The family, the mother The godmother, per se And my thing is, man Because I just got to meet them And got Blake and all of us so linked in My thing is You know, first thing I tell my wife is Could I have said something else to him? Or, you know, you start trying to figure out What you could have done different With the time that I had with him, you know? I don't know, I talked to them that day You know what I'm saying? We was on live I didn't even know they were going out so You didn't even know? I didn't even know they were going nowhere But... I can't even tell you what happened because I don't know, I wasn't there I was there, it wouldn't have happened It would have been nothing because Whatever they had going would have just been squashed But I don't know what they had going So I can't tell you Yeah, it's sad, man Because at the end of the day Man The guy was a good dude He came here respectfully He blessed our platform We didn't have to come over here and do that But he knew my son Like you talking back and forth with Blake Blake is my son's cousin And People call me after that They're like, man, I ain't know you tapped into the streets Like that, I'm like, what? I'm like tapping to the streets Man, man, man What it be, he be out there They really, they about that life I'm like, dude, these are my people Like I really know that they family You know what I'm saying? So I didn't look at it the same way like that Plus, you know, I come from a lot So you know what I'm saying? But the thing is, man, I really loved Talking with him that day I thank God that I got to be able to speak to him that day Didn't think that would be our last time talking But the thing I hate about situations like this And things like this happen on a regular basis You see it on the news all the time Is the fact that it's simple Things like that That ended up in something so detrimental You know what I mean? Something that could easily be Discussed and squashed and you know Ended in a With the right people around Like you just see With the right people around It could have been a narrative that changed But if the wrong people around They don't know how to either engage Or they intimidate about a situation on a whole So, you know, I just, you know I just know that God is real You know We got to make sure we Protect the people that are still here In a way to where we keep them From endangering themselves Or doing something bad to somebody else Because Especially people like you, you got kids You know what I'm saying? When I was, when my son And I don't even like to tell this But when my son was young I ended up going through some stuff And had to go away for a minute You know what I'm saying? And my daughter was here To have to Deal with something like that You don't think about until you're in a situation Trying to deal with it Because if you didn't die You're basically in that situation And you can't get to them You know what I'm saying? So those are things that you have to think about Before you make crazy decisions But a lot of people do things in the heat of the moment And not think about their children Or their mom or their family Their loved ones, you know what I mean? Fast forward, so Back to the music So do you feel like, what's the next big hit now? Are you going to do something in dedication to Wattie? Uh Me and Wattie got, we got hella songs Y'all still got a lot of music? Yeah, we're gonna put it out Oh no I'ma see I talked to Mr. Lee man, Mr. Lee was on He said it's hard to do that We had a video That hadn't came out yet? I got other music still I just dropped a little tape People kept asking for a lot of music So I just gave them a lot of shit That they kept asking for Did water have kids? He didn't have any kids And I asked that because I asked that every time I was just thinking the same thing before you actually asked Because I'd be thinking about The music or anything that goes out If it accumulates money that it would go towards The children, that's what I was thinking Yeah, but I say man Keep pushing that music You know already what he would want for you, right? Yeah, for sure He'll be like, let's get it, right? And what his mindset was at Like, let's get to it So you gotta keep that whole mindset going What's the next big song? What can I expect? The people wanna know What's the next one you gonna let go? I don't know I got hella stuff in my phones But I probably still got stuff that's on the laptop Still at the studio Studio? I don't know You don't know yet? Are you only doing singles or are you gonna actually do a project Where you're gonna have like an album come out? I don't know, I just dropped the little mix tape About like four or five days ago Got like nine or ten songs I don't even remember Which one you like doing the most? The projects Or just dropping some with a visual? Uh I'd say the single The single fun, ain't it? It's the last work It's the last work How much more work you have to do When you drop a whole album compared to a single? It's like You gotta have a lot of songs In more than one song That's work right there Then Then after that You know what I'm saying Like you'll have to probably like See which one people like and so you can shoot that video Or people probably like multiple ones So you'll probably get multiple videos Or even just Putting it all together Like sometimes somebody Try to put a whole bunch of old songs With songs they probably just need And don't even saying the same or something So most of the time I just Do all fresh songs Or if I do some old songs I do all old songs Because what I see a lot of people do Or what they'll say They'll do some singles, put it out See the feedback on it If people love certain ones They'll put a couple of those on the album Because they know they'll want to buy the album Or get the album because Because their favorites are on there I do that sometimes I just put that on that mixtape That was the first song since everybody liked it But Other than that they was out of new songs Yeah, yeah Do you plan to work anymore Can it be? Can it be always working We got a lot of songs too That's coming We don't need to be talking about when we're going to drop It's just like We'll probably be like He'll just hit me up and say We need to drop this We need to shoot this so we can drop it Yeah How do y'all pick whose song it is? It don't matter It don't matter I didn't think so, I thought about that They don't care I guess we ever go first We ever go first That's a good relationship It's your song man So do you have enough music to do a whole project Like for Woody Like with you and him Like a 9 out of 10 song project Probably some That may be something You know what I mean That would be dope You gotta find some kind of way to put it out To where people can see what he was Where he was at with it But it'd probably be hard for you You know what I'm saying He just got a video We're gonna drop that one for him We're just gonna see what else See what else we got See what else we got for him Any time you around You know you can come over here Talk about it We're gonna be doing pressing it this way Pushing it that way My platform is open for that Be honest with you You show a lot of love to this platform We were new on the block You know what I'm saying He done that just like you here And we love you man Let me ask you the name across your forehead Is that your baby's name That's my mama's name Mama mean a lot right No games about mama Already man Top three artists of all time Top three Number one Any genre I can have to say something boy That nigga love social Have you ever met him? Like you say though He's just smart That nigga smart I like Kodak too Kodak number two T-Herbo I've not heard of him Where he from Chicago I got him You say you love social boy Cause he's an all round artist And he's a hustler He does everything Are you striving to do everything In your craft Or do you just want to just rap I'll probably see what I can do Like Inga songs like me and Kenny did Those new stuff to me And you liked it I mean it was cool So you open to venture but Because even with learning certain things You have to go and research You have to go and figure it out You have to go and ask a lot of questions And then I think on that video I think we don't even have that many views Then we got deleted so we had to repost it But that's one of your favorites Yeah that's one of my favorites So do you If you could go back and talk to your younger self Although he's so young already I'm talking about 15 15? 16? What would you say? What would you say to your younger self? Stay away from rap What? I'm just playing I don't know Cause really I'm good I'm chilling I don't really have no regrets You know what I'm saying? So you would tell him just keep on rolling You for the hit You for to be rapping and everything I don't know I don't know what I tell my younger self For real? He would say juke juke What is that? Juke juke Is that his slogan or is that something you all say? I mean that's something we all say He used to use it more What does it mean? Get to it I figured that That's what He said something on here that was so dope He was like if I ain't living it I ain't for to be at no studio If I ain't doing good I'm not going to be at the studio He's like I'm going to be out there getting to it But then we got different We would probably be like we're not getting to it But We getting to it But we probably just want to be better than what we doing So It's not that we don't Want to be around each other It's probably like I'm doing something right now Yeah One thing man I can tell you why it's him flip man Man You got things that you got to take care of So you're a little bit more responsible Man All I can say is that when you talk to the guys around you I know right now it's a place Where they don't even want to listen to nothing But you got to be the one to keep things going Like damn But it's the truth man I'm like You got to keep things Life is You don't even want a responsibility But it got to be Somebody got to step up What it was a leader man Tell me how you feel You feel like y'all just leave me out of this Is that how you feel I just Not talk about it And I get it Because it's so early But I just For me That's the only thing I say is I wish I could have said something about what did I not say But I know God is the one that got the ultimate plan So I don't I know he had, like me and you talking here now I know already I pray for you guys here I know already I say Man give me something to say to this young brother Because I've been through so much And I made it through You know what I'm saying And for me to be here I'm kind of like I'm in a winning position because I made it this far You know what I'm saying From where I am you got to come What you've lived already And it's the old man talk And live longer than what you've lived already You see what I'm saying So I feel like I won because I've already lived this long You know what I mean But at the same time I know already there's something special in you And it's going to be You got way more chance than me now Because I'm telling what you can do Accomplish in the time you got Does that make sense? I'm going to be watching you man I'm going to be watching to see How you take it to the next level Because at the end of the day You the future bro Like I said man Where do you see yourself in the next two years In music I don't know Probably taking it more serious It's like I don't know I be focused on a lot of other stuff Because do you have a goal? I mean In music I just I learn to just chill I learn to just let things be when I'm doing this music stuff Just do what I do Let's go with the flow And I get results from them Since I've been doing this Don't stress over it I know what you got to do So if a younger person Then I got other responsibilities outside of rap With the kids and stuff Just everything Just a lot of stuff just me handling I take care of a lot of people And you so young Just me taking care of everybody Does it feel like a weight on your shoulder To take care of a lot of people? I mean not really That's good It's only people that you know So That's good Because Being a man that It shows that you take on that response But you take it on proudly Are you the only child? No I'm the second oldest I got a big sister You're the first boy So it falls on your shoulder With a lot of stuff Just do what I do That's good One thing I can say Because With what happened The one thing I can say is The friction The fight and I talk Y'all boys Boys gonna be boys They gonna argue Get into it whatever man Like I said if I can't say nothing else I can say You gotta be a leader And you like whatever but I'm telling you Because at the end of the day A lot of people count on you You know what I'm saying? You just said that He's like I'm the one Say man we love you bro We love you and we definitely appreciate you For coming on our show How can people get a hold to you man? People like who? Know if they want to do some music Or feature or something like that Like that man Instagram Yeah they can just hit me up on Instagram What's your handle on Instagram? Y's and Flips If you want to do some music You can just hit me up on Instagram It takes you my budget I don't wanna hear your budget It takes you my budget And then you gonna get at them But if A young artist come to you Or somebody who wants to Because I know that a lot of people are probably in your DM You be like bro how did you get here You know I wanna be You know like you don't want to connect And stuff like that How would you advise him like how many times a week Does he need to be in studio How many songs he needs to be writing a day If he I never wrote so if he You punch him But if you're writing then that's cool You just gotta write a lot You know what I'm saying You can think of it Just think faster But I don't know But if you just start You need to be recording at least At least two Three songs a day So you need to be in studio every day If you want to make a name For yourself or if you want people to listen to you You need to perfect the craft Not even nobody need to hear our your songs You know what I'm saying It's just you can find out how to use You can find out how to say different stuff Find out how to put it in a different way A different meaning Just perfect what you got to say Wow And what's the one thing that someone has Told you Over the past that has stuck with you Over the years you know concerning Music that you're like you know what That's a gem like I'm gonna take that and really use that I'm gonna I'm gonna really tell me to probably be more Consistent Be consistent When I really When I want to take it serious I'll be I'll probably be in studio more I'll record myself I got it at home too so And I hear you say a lot that you record yourself Because I know a lot of people that go To studio and get like an engineer or somebody To record them I like my engineer recording me too though His name 24 I like him He make beats It's way easier Mhmm Man we thank you for coming on the show We love you brother I appreciate you Say man It's going down man It's a unique hustle And it's been another great segment Of boss talk 101


Live from the Julia Morgan ballroom in San Francisco, extracting the signal from the noise, it's theCUBE, covering Structure 2015. Now your host, George Gilbert. And we're back. This is George Gilbert. We're at Structure 2015. And we have a very special guest, Stacey Higginbossen, who along with a very select few colleagues powered the rise of GigaOM and also the Structure series of conferences. And she's here to tell us what she's seen today and how it's changed over time. Well, welcome, Stacey. Thank you, George. Yes, I had the privilege of being at the inaugural, I guess this is the second inaugural Structure conference, but at the initial Structure conference all the way back in 2008, it was. And that was a much smaller event. And I remember being there on a panel with Vijay Gill who has moved around so much, but we were talking about, my God, what is a Paz? And at the time I had no idea. So it was a perfect panel for me to moderate. And back then we were like, oh my gosh, what is this cloud thing? Amazon had launched AWS two years ago. We were still like, we couldn't even sell this event. And now we're, it's huge. And we didn't know, you know, were we gonna move to the public cloud? And the consensus was no one's gonna put any workloads in the cloud if they're a real legit business. From today where we've got Disney putting things in the cloud, we've got the federal government having things in the cloud. But there's actually kind of been this pushback where people are like, okay, we accept that there's the cloud, but now we're like gonna build our own kind of thing and we're gonna take some of the lessons of the cloud with DevOps and the agility that kind of the cloud offers and we're gonna bring it back home. So there's a lot more kind of talk about what we've learned and taking it on-prem. So yeah, let's dive into that a little bit because for the longest time we were told virtualization, carving up these underutilized servers was gonna sort of give everyone the benefits of the public cloud and, you know, the lower CAPX but the operational processes that made the public cloud so efficient didn't quite migrate to the private cloud. When did we first start seeing that and when did we become aware that that was a challenge? I think some companies are actually still dealing with that. Even today we had someone from GE and he was talking about the cloud really isn't about OPEX for us, it's about agility. And I was kind of shocked to see that because that felt like something that we had been talking about four or five years ago. So four or five years ago. So I was like, oh, meanwhile we still have like, you know, Facebook and Google and these hyperskill guys and they feel like they're moving, you know, they're talking about microservices and utilization rates that are far above and away like what any of these private cloud guys could even be achieving right now. And they're like, I never want anyone to think about a VM anymore, you know, I just want to let people push services live no matter what. Well, this is an interesting comment. Do you think that, you know, there's been a law of sort of legacy systems that's held for like six decades which is they run, you don't touch them. Could we see that sort of all new green field apps get built on this new hardware infrastructure with this new, with these new software processes and we sort of ring fence the legacy systems? Is that a? I think so. So one of the things I talked with Diane Bryant yesterday morning and one of the things I thought was great about her talk was she, she spoke about all of these new IOT kind of options out there. So like John Deere building these new connected tractors and agricultural, I'm going to say tractors as a service kind of, just like farms as a service. And all of that's being built on their own on-premise cloud things. And so all of these new services. On Deers. On Deers on-premise clouds. Yes, like on-premise agricultural field, clouds, words. So all of that's being built on their own cloud and a lot of other companies like GE are building their own IOT services on their own clouds. And so all of these are new greenfields opportunities and they're being built on-prem, on clouds that they're hosting. And so there's going to be these legacy systems that no one's going to deal with. I mean, IBM's still selling their mainframes, right? Then there's going to be these like fun testing and QA and weird workloads that you're like, send them to Amazon, send them, I don't know, maybe to Google. Since, you know, maybe Google's going to get into the enterprise a little more seriously or Microsoft.  And maybe those won't even be on a cloud. So it's interesting that you mentioned the Internet of Things apps as greenfield apps because we don't have anything that they're replacing but to think of them as that their first or natural home might be on the vendor's premises, on the enterprise's premises. Have you gotten any insight as to why that might be? Because of their data, some of that is just so precious to the company that has it or maybe it's like a hospital or medical data or like, sorry, from a medical device. So like, if you're Johnson and Johnson and you're selling some sort of connected medical device, you want to keep that data secure as possible because my God, if something goes awry and you're like insulin pumps start shooting out sugar into somebody's like, I don't know what you shoot insulin into.  Yes, that's terrible. That's bad. You really want to lock that down. So that's one example. And the other is because, you know, this is precious. One day you might be able to sell it to somebody else and you don't want that in Amazon if you can help it. So what about the concept of data gravity or someone told us the other day, data mass? Like data isn't drawing the planet. Have you been talking to Dave McCrory? Yeah. Yes, we give him credit. But the notion that, you know, if you've got information coming in from all sorts of devices everywhere, it might more easily come into data centers that are publicly managed because they're more strategically placed and that they have the cabling, the optical cabling for low latency, you know, replication or messaging if need be. And so it almost, that infrastructure might lend itself to Internet of Things apps. I have no idea how to respond to that because I still am a big fan of like the problems of bandwidth and we haven't gotten around that. But a lot of the data that we're talking about with the Internet of Things is smaller. It's time series, it's, you send it someplace, you do the processing there, you handle it and you've got a, I don't know what this is called, this thing that's happening with my fist. But you've got a decision that's made and then you send it out. Right. So with that, the concept of data gravity doesn't really necessarily have to apply as much. And I just don't think, like in an ideal world, that would be the case. But in a, the way the business models are evolving, it is appearing to be very much like I keep my data, I'll let you have access to some of it and through some sort of kind of data exchange. The challenge is we still don't have those business models yet. So I think we're kind of at a place where we're like, maybe we have a magical data lake, but everyone I'm talking to in like the IoT world is like the problem with data lakes is nobody can grab anything out of it when they want it in time. It's not curated, yeah. So they hate that. And that's what I think of when we think of kind of data gravity. And the problem with data exchanges is nobody has a business model yet that makes it really work. So it's really kind of this data mess. And so I don't, I don't really know the answer. Okay, so that's interesting. The takeaway is that we're kind of in between generations, between sort of distributed applications and the new era of internet of things applications.  Yes, but they are characterized by capturing and processing much more data towards the origin of that data. Right, at the edge. At the edge. So what are some of the things that surprised you about what you saw here or maybe perhaps disappointed you that you didn't see more of? I would have loved to talk more about this, but. We have a conference. I was like, we have a conference hopefully in June that we're going to do a little bit of this at because this is something I'm really excited about and kind of figuring out architectures for this exact problem because it's data synchronization, like how do you do with that? It's got bandwidth problems. It's figuring out like, how do you move software and processing like around at the edge? Because sometimes you're going to want it at the edge. Sometimes you're going to want it at the core and it may differ. So would the sweet spot of the applications that we're dealing with now and the infrastructure be the software defined data center? The sort of terminology that we were driving towards eight years ago. I don't think so. So the software defined data? Not for IoT, but for structure. So for structure, I don't know. I mean, so the software defined data center, I feel like maybe the data center is everywhere. I feel like that's probably a better way to start thinking about it. That's interesting. The infrastructure is everywhere and how do you build for that?  Now, what we've got is sort of something virtualized and the distance between the elements is what we don't have to worry about. It's spreading, so. Okay, that's interesting. But I'm just kind of a crazy person out here, so who knows? Well, that's why we want to talk to you. Not the crazy part, but the vision part. The out there part. Maybe the two go together. All right. So if you look back a couple years and then take that as a connect the dots and look out a couple years, what do you think at Structure we'll be talking about a couple years in the future? Oh man, this is the kind of question I ask people and I'm always waiting for their answer and I never want to think about it on my own. I think security, we've got to figure out. I think machine learning is going to be a big topic. I'm really interested to think about what kind of hardware, how we kind of build data centers around that. I've been waiting for years for ARM to be invading the data center. I'm still waiting, so I don't know how we're gonna, what we're gonna see on that front, so. And I'd kind of like someone to take Intel down a peg just in terms of the monolithic processor. They've got 96% of the market in servers. That's a lot. I heard a statistic that was kind of interesting that if you, once we get to the 10 nanometer geometry for transistor size, all the transistors that we will need for all the data centers in the world will be produced in one fab, or the capacity of one fab. And the rest is memory. Any thoughts on what that might mean for what the data centers and Intel look like? That's a crazy stat. Is that just for servers? Basically, yes. Okay, because, I mean, we'll still need chips for everything else, so. But less and less Intel chips. Right, well that's why Intel's gotten into the fabrication business, like fabbing other people's chips. So I would imagine we'll see more aggression from them in making other people's chips because that does make sense. So that would be my thoughts on that is, ooh, they better start signing up some more customers. Have you thought about systems management and as we disassociate the physical boundaries of a data center from sort of the capabilities of a data center, what does it mean to manage that infrastructure? Oh. That wasn't meant to stump you. No, no, I'm like, oh, George. I don't think a lot about systems management outside of IoT, so I do think about it in terms of managing sensors. Yeah, so, okay. So I think about like, God, ILM on sensors and deploying any sort of. ILM being the information lifecycle management. But not really information lifecycle management, but not technically that. But when you do updates on sensors, how can you roll that back? Because right now there is no management for if you have a massive array of sensors in a factory, for example. If you update all of them and it breaks something, you really can't control that right now. And so getting some sort of orchestration layer on top of that is really important. So I think about those kind of things, but I don't think about it really for the data center right now. Okay. All right, Stacey, as always, fun to talk to you and have you on, very insightful. We'll have to leave it there. This is George Gilbert, and we are at the Julia Morgan Ballroom in downtown San Francisco at the Structure 15 conference, and we'll be back in a moment.


So we've already made use of the fundamental equations for the four different types of energy to derive some thermodynamic relationships, the ones I've called the fundamental thermodynamic relationships. But they are going to continue to provide us more gifts. They're going to allow us to derive a few additional thermodynamic relationships as well. So let me explain that with going back to this basic example of a two-dimensional function. If we think of these energies as functions of their natural variables, S and V, or T and P, or whichever, any function of two variables, we've used multiple times the idea that we can write down the differential as df dx times dx plus df dy times dy. That's what let's us say, for example. And I'll go ahead and write down this statement dg dt. Is negative S. And from here, dg dt is equal to V. Two derivatives we've seen before. We can read those derivatives off the coefficients. Coefficient in front of dx is the derivative with respect to x. The coefficient in front of dy is the derivative with respect to y. But now let's think about second derivatives. If I ask you what is the second derivative of f with respect to x and y. So the mixed second partial derivative, df dx dy. d squared f dx dy. We can think of that in two different ways. We can think of that as the x derivative of the y derivative. So first take the y derivative, then take the x derivative. Or we could think of it the other way around, the y derivative of the x derivative. First take the x derivative and then take the y derivative. And it doesn't matter what order I take those derivatives in. I'll get the same answer in either way. The second mixed partial derivative is the same regardless of which order I take it in. What that means is, looking at this diagram, if I take the first derivative with respect to x and then take dy, I'll get the second mixed derivative. Or if I take this coefficient, df dy, and take dx of it, the x derivative of it, I'm going to get the same result. So I can start with either one of these coefficients, take a derivative, and get to the same answer. What that means for these fundamental equations is, if I'm thinking about the second derivative of g with respect to t and p, I can either take the first derivative with respect to t and then take the derivative with respect to p. So take the pressure derivative of this thing. So take the pressure derivative of s with a negative sign. Gives me minus ds dp. Or if I prefer, I can do it the other way around. I can use this first pressure derivative and then take the temperature derivative, temperature derivative of v. Either one of these should be this mixed second partial derivative. Notice that they don't look anything like one another. Negative ds dp at constant t must be equal to dv dt at constant p because it doesn't matter what order I take these mixed partial second derivatives in. So that's a thermodynamic relationship that's very useful. We might not have known anything about how the entropy changes as I change the pressure isothermally. But I know it's related to, it's the negative of how quickly the volume changes as I change the temperature at constant pressure. So what that means is we've, this fundamental equation has given us a new thermodynamic relationship minus ds dp at constant t is equal to dv dt at constant pressure. So and I can read that directly off the fundamental equation now that I know where it comes from. Derivative of this with respect to this at constant this is equal to derivative of this coefficient with respect to the other variable while holding this one constant. So I can do the same with a little less work now for the rest of these fundamental equations. Just taking the derivative of each coefficient with respect to the opposite variable while holding its own variable constant, I learned that dt dv at constant s is equal to negative dp ds at constant v from the fundamental equation for the internal energy. Enthalpy tells me that dt dp at constant s is equal to dv ds at constant p. And the Helmholtz free energy tells me negative derivative of s with respect to v at constant t is equal to negative derivative of p with respect to t at constant v. So that's a collection of thermodynamic relationships, relationships between one thermodynamic derivative and a completely different looking thermodynamic derivative that are true and followed directly from these fundamental equations. So again, it's very useful to have in mind either the fundamental equations or memorize one and be able to write down the rest of them easily. And then when you need one of these relationships, you can obtain it very easily from the fundamental equations that you know how to write down. Each of these four relationships is useful. We'll have occasion to use them again. The name of these relationships is called Maxwell relations. So each one of these four is called a Maxwell relation. And again, the idea behind these Maxwell relations is each one of them is equal to the second derivative of an energy with respect to two different variables. And either way I have of writing down that second derivative is bound to give me the same answer. So that's what gives me this relationship between the two halves of the Maxwell relation.