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It depends on how you structure these five networks so each one of these five networks typically has one hidden layer and then one in two layers" +02. Learning in the Machine. Pierre Baldi_clip_152_1363.09_1376.47.wav, that you see also in when you do the work of Lily Krupp is that the random weights start here so they play a role in learning for the layer before the the layer after the layer. +02. Learning in the Machine. Pierre Baldi_clip_248_2259.59_2273.39.wav," it gets there. I mean, why I ask is because basically in reinforcement learning with the temporal differencing you also work with noisy gradients at one point. And empirically it shows that noisy gradients cost you something." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_132_1187.53_1197.94.wav," increasingly refined representation, let's say. And then a final discrimination path where you train the entire architecture." +02. Learning in the Machine. Pierre Baldi_clip_182_1635.04_1648.81.wav," function of T minus O, a linear, a random matrix of T minus O will work, a random sparse matrix will work. You can reduce the precision on T minus O quite a bit." +02. Learning in the Machine. Pierre Baldi_clip_69_617.18_629.2099999999999.wav," one by one. So we did that for polynomial learning rule of low degree, for linear neurons. In some cases, you can do also nonlinear neurons. And you can study all these rules and their properties." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_133_1195.51_1206.58.wav," you train the entire architecture. And in 2006, this was shown to work very well on certain problems. And so it was very intriguing and restarted the interest that we have in this." +TheQuarksOfAttention475000-500000.wav," layers and things like that, right? But it's not about existential questions of what functions can be approximated with or without attention. Okay. Now it turns out, of course, that attention has actually been a very popular topic in deep learning over the past 10 years, especially kind of..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_305_2792.13_2802.089.wav," for the backbone, the C-alpha, C-beta of the protein, or you can do an all-atom calculation if you want the side chains. There is quaternary structure." +TheQuarksOfAttention1175000-1200000.wav," And then of course this multiplied output or IOJ travels along the axon of neuron I towards say a target and neuron K here, which is going to receive as input this term here, which now of course is quadratic, right? So this is new in the standard model. You start seeing these new quadratic terms appearing inside the neural network. Synaptic gating is" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_135_1216.83_1227.869.wav," thing you have to do is to understand autoencoders better. So let me say a few things about autoencoders, what we know about autoencoders today and what they're doing, and then I'll show you some other algorithms complementary." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_175_1582.539_1596.25.wav, I get vectors you're training this data now and you are projecting on to further smaller subspace so if you go from 100 to 50 to 10 At the end of the day is like if you had +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_178_1612.97_1625.51.wav, that when you should stop and etc that's a different set of questions but if you were to do it that's what it would do but of course in machine learning and other areas +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_45_414.5_424.94.wav," very mysterious and that's the fundamental problem of learning and it's a deep learning problem because you have these many layers. If a synapse is on the periphery, either on the visual..." +TheQuarksOfAttention500000-525000.wav," coming from the field of natural language processing of NLP where people have been developing all kinds of so-called attention mechanisms in a sort of a ad hoc fashion, but in ways that have been very powerful for the applications. And the idea, the basic idea in natural language processing and applications of attentions in NLP." +02. Learning in the Machine. Pierre Baldi_clip_48_433.22_445.79.wav," Because really if you look at the literature, these are pretty much the only two algorithms that are available for training networks. So why are there so few algorithms? So if we put ourselves" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_141_1268.159_1277.82.wav," So if you do that, you'll see there is many types of autoencoders. There is linear autoencoders, nonlinear autoencoders. If you take linear autoencoders, you can do them over the complex numbers." +02. Learning in the Machine. Pierre Baldi_clip_78_701.78_712.67.wav," visl, etc. But in his favor he said, well, we have adjustable weights between the layers and we're going to learn using Hebb's rule, some local learning rule." +02. Learning in the Machine. Pierre Baldi_clip_95_847.55_858.41.wav," There is also information about all the weights above layer H, and we'll come back to that. Because it would seem from this equation that you need to know." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_358_3273.45_3284.5499999999997.wav," If you're trying to predict contact map, the first thing you have to realize is that you are in a situation where you are trying to predict outputs that have different size. If a protein has 100 amino acid, it's gonna be." +02. Learning in the Machine. Pierre Baldi_clip_51_460.85_471.08.wav," to you. So I'm going to rescale things by a factor of a million. Synapse is about 10 to the minus 7, so you rescale it by a million, it's 10 to the minus 1 meters." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_79_717.87_729.66.wav," and his paper on the theory of the learnable. By the way, this took up the Nobel Prize in Computer Science over the last three years, the Turing Award. So that shows that machine learning has come." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_126_1135.21_1148.47.wav," from Google, for instance, and you train a first autoencoder that learns how to compress the data without knowing anything about elephants in this representation." +02. Learning in the Machine. Pierre Baldi_clip_160_1433.86_1444.57.wav," if you want, so to speak, training set, test set. You can see they all converge to good performance, et cetera, et cetera. These are experiment done with sparse random." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_107_970.55_981.6.wav," And if the layer is smaller, like in this case, it's a sort of a bottleneck, you're forced to compress data. And we know that compressing the data means understanding the data." +02. Learning in the Machine. Pierre Baldi_clip_125_1120.15_1130.77.wav, most plausible one is that you have a completely distinct channel that has different architecture and different numbers of neurons etc but of course which talks to the the forward pathway +02. Learning in the Machine. Pierre Baldi_clip_193_1738.51_1755.94.wav, trajectory that ends up here. And here is the same thing except for this little piece of this hyperbola where actually the points are unstable and the trajectories tend to diverge from those. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_1_0.03_13.59.wav," Okay, let's go ahead and start. I'm pleased to be able to introduce Pierre Baldy. So he is Chancellor's Professor of Computer Science at UC Irvine." +02. Learning in the Machine. Pierre Baldi_clip_13_117.65_128.09.wav," and many other great Jewish scientists and pacifists and so on. But anyway, if you had met Einstein a few hundred meters from here..." +02. Learning in the Machine. Pierre Baldi_clip_214_1929.36_1940.61.wav," to complex ideas in algebraic geometry like a Kozoo complex. I won't go into that. And in some cases, you can solve the nonlinear case. For instance, if you have a." +02. Learning in the Machine. Pierre Baldi_clip_164_1472.05_1485.97.wav," it's like this, etc. So as K grows, you have more and more black dots in this picture, right? The picture becomes more and more complicated. It has to do with Betti numbers. And basically the task of your network is you give" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_205_1877.559_1888.6299999999999.wav, Hamming distance and all the ones that are closest to this output for the Hamming distance etc. So you get a partitioning of the hypercube created by the images of these vectors and now if you +02. Learning in the Machine. Pierre Baldi_clip_157_1407.76_1418.4699999999998.wav," If you remove the derivatives, these guys are not learning. This is the training set. This is the test set. This is another set of experiments where we are..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_183_1660.159_1671.26.wav," distance and between these two layers you can put any Boolean function you want. And same thing here. So you are completely free, you are unlimited power in terms of the Boolean function you want." +02. Learning in the Machine. Pierre Baldi_clip_154_1382.23_1392.6100000000001.wav," gradient descent from the top layer, then all these algorithms start to break down. I can show you some example of simulation on NIST or CIFAR." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_23_206.84_218.66.wav," So around 1950, a lot of the concepts we have today were already in place. People knew that brains had specialized area, Broca, Wernicke, Foucault," +02. Learning in the Machine. Pierre Baldi_clip_17_159.17_170.80999999999997.wav," you look like. So that's what we're going to do. And I'm going to first give you a few simple examples of this style of thinking for neurons. But the place where we're going to get, I think, some." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_337_3065.43_3078.0.wav," There are many, many students and postdocs that I should thank and I could thank, but rather than do that, I want to leave you with this picture, which is really the topic of my... of this..." +02. Learning in the Machine. Pierre Baldi_clip_64_572.0_583.1899999999999.wav, the targets could also be considered as local variables in the output layer of a feedforward network. So that's the definition of a local learning rule. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_349_3173.06_3183.8900000000003.wav," mice that has not been running the maze or a mice that, or in other parts of the brain, we know by now that there is all kinds of proteins that are very specific to learning that are activated." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_283_2592.62_2603.57.wav," which can be produced by this Bernoulli selector variable, for instance, but it could be another distribution P. And this is the geometric average, the product of all the outputs weighted by the distribution." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_124_1116.88_1127.8300000000002.wav," using neural networks because it's exactly the same thing. And this is the idea. So you want to build a deep architecture for some problem, let's say image recognition, you want to detect." +02. Learning in the Machine. Pierre Baldi_clip_171_1540.99_1551.49.wav," tell you about what needs to be communicated in this channel. And basically, you can see that you can reduce the amount of information that is needed." +02. Learning in the Machine. Pierre Baldi_clip_270_2514.56_2533.67.wav," a formal connection between variational inference and what you're trying to do here? Possibly. I haven't really thought about it, but... In a way, so..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_263_2417.85_2429.7000000000003.wav," and the claim is that it works very well. People have tried this on data and it does work quite well. It's not a universal solution, but it has some very interesting properties." +02. Learning in the Machine. Pierre Baldi_clip_237_2141.829_2153.599.wav, synapses and their environment leads to the notion of local learning. The rules for adjusting a synaptic weight should depend only on local variables. This leads to the notion of local learning. +02. Learning in the Machine. Pierre Baldi_clip_235_2122.15_2135.95.wav," converge to a correct solution. OK, I'm out of time. So let me summarize. Learning the machine looks at learning in physical neural system, not in the digital fantasy." +02. Learning in the Machine. Pierre Baldi_clip_76_684.2_695.9.wav," And the question is, what can you do with this system? What can you learn? This is actually an old idea that goes back at least to 1980 with Fukushima, who can" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_130_1171.75_1182.34.wav, unit that decides what's the probability that there is an elephant in the image or not and now you train this whole thing by back propagation and the claim is that so you have a complete +02. Learning in the Machine. Pierre Baldi_clip_181_1627.59_1639.27.wav," So basically what seems to work, the minimal amount of things that you need to send is some function of T minus O, a linear, a random function of T minus O." +02. Learning in the Machine. Pierre Baldi_clip_204_1835.74_1847.44.wav," you get for back propagation. So can we solve such systems? Well, in general, no. These are actually very complicated systems. These are polynomial systems." +TheQuarksOfAttention1250000-1275000.wav," In this case, you could assume that OIOJ is broadcasted everywhere to all the neurons, which are downstream of neuron I, whereas here it's a more precise mechanism that affects only this connection between neuron I and neuron K. You don't have a broadcasting on all other connections. But both mechanisms are quite interesting, can be added to the standard." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_59_541.18_551.949.wav," separable, the algorithm works very well. So that was Rosenblatt contribution. And we drew off, made it a little bit more general by using, instead of having" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_293_2683.95_2694.18.wav," to show that yes, indeed, these networks, when you take, when you divide the weights by two, if p equals 0.5, are computing something very close to this, which is." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_256_2356.85_2367.02.wav," to train these deep architectures in all kinds of tasks, combining unsupervised learning with supervised learning and in different ways." +TheQuarksOfAttention1475000-1500000.wav," dot product of two vectors, let's say a vector X and a vector Y, and let's say that X and Y are the output of some neurons, you have to compute the sum of the X sub I, Y sub I. So you have to multiply X sub I by Y sub I, you have to multiply the output of two neurons together to compute one component of the dot product and do it again n times and then." +02. Learning in the Machine. Pierre Baldi_clip_238_2150.66_2163.109.wav, on local variables. This leads to the notion of deep learning channel. If you depend only on local variable and you have a feed-forward network you will never be able to learn anything interesting. +TheQuarksOfAttention1950000-1975000.wav," because of these fundamental level, there is symmetry between matter and nine time matter. It's not true at the level of the entire universe as we know it, but at the elementary level, there is this fundamental symmetry. So on one branch of the tree, you're getting matter, particle of particles of matter. On the other branch, you have to get the same particle, but the opposite charge corresponding to antimatter. And then you can." +02. Learning in the Machine. Pierre Baldi_clip_245_2232.92_2245.34.wav," you get if you go away from the classical back propagation. Well you see here in these simulations, you know typically the top curve is back propagation so..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_214_1963.24_1974.6899999999998.wav," 2D lattice and you want to cluster into k clusters, for the Manhattan distance, the L1 distance on the lattice, that problem is NP-complete as soon as the number of clusters is" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_115_1037.039_1047.1200000000001.wav," claim they were good models of the brain, right? And that, of course, we know that a single artificial neuron is very far from being close to biological neurons. So there was a..." +02. Learning in the Machine. Pierre Baldi_clip_112_1003.58_1018.28.wav," on a scale of 10 to 100 milliseconds. For instance, a visual system, we often talk about feedback where you have a bottom-up sensory stream that meets." +02. Learning in the Machine. Pierre Baldi_clip_75_672.53_686.3.wav, layer etc all the way to the top layer. In the top layer you can have targets because the targets are available here but not of course in the deeper layers of this feed-forward network. And the question is what can you do with the data? +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_165_1484.22_1497.18.wav," transposition. And you also understand what happens when you do stacking, because if you do stacking like this, if I train, I'm going to extract the first P1 principal components of the data" +TheQuarksOfAttention2700000-2725000.wav," neurons to produce the final output, right? Now it's a little bit different if you're using zero one neurons or one minus or one minus one neurons, because if you're taking zero one neurons, taking the product, right, as you see here, is the same thing as doing an end. If you have one one, you get a one, in all the other cases you get a zero." +02. Learning in the Machine. Pierre Baldi_clip_47_423.98_434.33000000000004.wav," a question that may seem somewhat strange but important. And why are there so few learning algorithms? Because really, if you look at the." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_182_1652.539_1662.6789999999999.wav," any Boolean function between, so your input is binary, your vectors are zero and ones, your error function is the Hamming distance, and between these two lines, you have a function that is called a Boolean function." +02. Learning in the Machine. Pierre Baldi_clip_141_1265.659_1276.429.wav," But why not adopt also the weights in the backward channel? Maybe if they are made of the same hardware, you should use HAB or back propagation in both channels, in the forward channel and the..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_235_2162.619_2175.01.wav," is a sample in that way. This is an example of a training experiment where we use threshold gates, which by the way if you have threshold gates they are not differentiable so you cannot do gradient descent." +TheQuarksOfAttention2125000-2150000.wav," But you get the basic idea permutation are very important. You can permute the inputs, the vectors in any possible way. And so transformers are a very, very suitable architecture for these kinds of problems. These are just some of the results we're getting where we can show that we're much better than the existing methods and especially much faster." +02. Learning in the Machine. Pierre Baldi_clip_4_37.43_49.879000000000005.wav," is not a real native neural metric, right? You don't have synaptic weights, you don't have neurons, you have a fantasy of such objects implemented in a digital computer. And this makes a big difference." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_20_178.13_192.59.wav," with millions of layers, something like 10, 20 small numbers. That's the kind of things I have in mind when I mention deep architectures and deep learning." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_380_3510.76_3522.34.wav," know, results that show that certain function requires, you know, the scaling of the number of layers to be at least that many, etc. So there are a few isolated results in circuit complexity, but they are not..." +02. Learning in the Machine. Pierre Baldi_clip_33_300.169_311.62899999999996.wav," type of thinking. Now, note something interesting. When you do dropout at production time, your neurons are working perfectly. You just multiply the weights by the probabilities of dropping." +02. Learning in the Machine. Pierre Baldi_clip_29_266.69_276.349.wav, in the machine is drop out because you could have again looked at the world from the point of view of a neuron maybe you come up with the idea that neurons are quite +TheQuarksOfAttention600000-625000.wav," notwithstanding that the sequence would have different length as in this case, right? But you see this idea of attention, the ability to switch the importance that you give to the various streams of information that are coming through the deep learning system, right? So that's the idea that people have been implementing in natural language processing. There has been over the last decade." +TheQuarksOfAttention2775000-2800000.wav," of course, just the beginning, you can do it with layers. You can imagine the output of this neuron multiplying the synapse of another neuron to do, you know, synaptic gating, but you can see how you can start creating all kinds of circuits where you want to compute their capacity. And I'm just going to give you the punchline. In this case, this neuron has capacity N squared, this neuron has capacity N squared." +02. Learning in the Machine. Pierre Baldi_clip_225_2030.83_2042.2.wav," etc. So basically you can take the equation of A1, you can write A1, there is the product P of all the AI, you replace each AI as its function of A1." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_300_2747.28_2760.4500000000003.wav," to a deep neural network by replacing the conditional probability distribution between the nodes by a neural network. And if your graph has some kind of regular structure, you can do weight sharing." +TheQuarksOfAttention2750000-2775000.wav," neuron, you have two to the n square possibilities. The capacity is n square, the same thing for the red neuron, but then what happens when you multiply them together? So that's the new mathematical problem that you can try to solve to try to understand how many functions are created, how many Boolean functions are created in the circuit by allowing the multiplication of these two outputs. And that's." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_163_1467.0_1478.91.wav," by C, C minus one here, changing coordinates in the hidden layer. So the real case is, I would say, completely understood, and if you look at the complex case" +02. Learning in the Machine. Pierre Baldi_clip_128_1144.59_1155.97.wav," with learning, with rates, etc. in these different scenarios. Now one important result that was obtained..." +TheQuarksOfAttention1425000-1450000.wav," All right. And then you apply a softmax to the rows of this, of this matrix where you have put all these top products and you use the softmax to change the value of the weights in the top layer. So the top layer is just combine all, combining all the value vectors, right? Using some weights, some synaptic weights." +TheQuarksOfAttention1900000-1925000.wav," the collision point and these particles they decay, they are detected by the detector. And physicists of course think about these things in terms of fine-mind diagrams. So you see here partial fine-mind diagram of a possible decay process. And without going." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_340_3091.98_3104.25.wav," use learning over billions of years to understand how to take advantage of carbon-based computing and to build genomes that are capable through development, interaction with the world." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_324_2954.52_2965.53.wav," the sequence, the protein folds. If they end up at less than 8 angstrom away in the folded structure, you put a 1 in the matrix, otherwise you put a 0. There are subtleties you can" +02. Learning in the Machine. Pierre Baldi_clip_173_1558.24_1568.9799999999998.wav," all the weights below and all the derivatives above. Backpropagation alone already tells you that you only need in fact to send t minus o, you don't need to do anything else." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_184_1669.49_1679.539.wav," in terms of the Boolean function you are using. You're not limited to threshold gates or, you know, AND gates, anything like that. You can use any Boolean function but you still have to adjust the threshold." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_246_2268.8_2280.5.wav," layer and then I do it again and I do it again. That's another approach where you do discriminative training at each level. And of course, there is many variants, but I'm going to go directly to the last one." +TheQuarksOfAttention1200000-1225000.wav," is similar, but now the attending neuron produces an output OJ, which multiplies the synaptic weights. So this is goes with the idea of a fast synaptic weights in neural networks, having weights with different timescales. But in this case, you have weights that can be modified on a rapid timescale compared to learning by the activity." +02. Learning in the Machine. Pierre Baldi_clip_153_1372.87_1384.3600000000001.wav," in learning for the layer before the last one, but the last layer is doing gradient descent. And that's absolutely necessary. If you remove the gradient descent from the top layer." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_74_676.29_686.5790000000001.wav, and a half-filled up caltech off and actually got his phd here says the corner but the hopfield developed a model where you took a person from connected +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_162_1458.69_1469.9099999999999.wav," of subtle points and one global optimum up to these symmetries that you have in the space that is multiplication of by c, c minus one here, changing coordinates." +02. Learning in the Machine. Pierre Baldi_clip_67_598.49_610.64.wav," the functional form the function f should have. For instance, we can work on polynomial learning rules, polynomials of low degree, maybe up to six. That could be an interesting set of function. But in." +02. Learning in the Machine. Pierre Baldi_clip_227_2047.72_2061.22.wav," end up with an equation that looks like this. dA1 dt equals a big polynomial of A1. And if you look carefully, the polynomial is of degree 2L minus 1." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_13_119.51_132.62.wav," that are given to you. And that's a deep learning problem. How do you adjust the parameters of all the functions that are between the layers, especially layers that are deep in the architectures?" +02. Learning in the Machine. Pierre Baldi_clip_199_1796.289_1808.11.wav, from the forward pathway which is this object here there is input transpose here and then there is the the feedback matrix Ci times the what is at the top +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_245_2259.38_2270.9599999999996.wav," do a different type of training where you train this layer directly to discriminate elephants. So I'm training this to discriminate elephants. It doesn't do very well, but I add a new layer and then I do it again." +02. Learning in the Machine. Pierre Baldi_clip_108_969.71_981.86.wav, you is that there has to be a channel that goes all the way from the motor output or from wherever error functions are computed all the way back to each one of these synapses. +TheQuarksOfAttention50000-75000.wav," Then I will try to organize all possible attention mechanisms in a systematic way and provide some kind of taxonomy. I will then explain how attention works in transformers, which are an important architecture in deep learning these days. I will demonstrate some application." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_289_2647.109_2660.19.wav," that's exactly an equality. Furthermore, if you take a Taylor expansion, you can show that this is an approximation to the expected value of the output of all." +02. Learning in the Machine. Pierre Baldi_clip_96_856.97_870.7700000000001.wav," from this equation that you need to know everything about all the weights above in order to find a solution and that's an important point that is actually not true. Okay, so Hebbian learning or" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_88_801.48_813.27.wav, not Hebbian and is problematic. Because you compute your error at the output layer and then you propagate it backwards every time you have to multiply the error terms by the transpose of the output layer. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_24_214.4_227.36.wav," specialized area, Broca, Wernicke for instance areas in speech if you have lesions here you get all kinds of speech deficit. Of course people knew from Darwin that the brain has been built" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_189_1715.659_1727.659.wav," what it means to determine A, and it can be any Boolean function. So we need to find the target of this vector. To do that, I look at the predecessors. I look at the binary vectors in the input." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_190_1725.35_1744.6290000000001.wav," at the binary vectors in the input that are mapped onto this vector from the function B. Yes? For those of us that don't know, is there a simple description of the classical Boolean functions? Any function from binary to binary is a Boolean function. Nothing else." +02. Learning in the Machine. Pierre Baldi_clip_106_948.11_963.65.wav," channel, etc. All classical Shannon theory of communication can be applied to this object. So if you think about the brain, if you think that, you know," +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_320_2919.6_2931.5400000000004.wav, of the protein is invariant to rotation and translations. And so how do you deal with that when you have neural network and networks? And one idea is to use a representation that doesn't depend on... +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_216_1981.45_1993.36.wav," that clustering on the hypercube is NP-complete? And the answer is yes, by this following mapping. You take your problem, so you have a clustering problem in the 2D lattice, and you map the 2D lattice." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_7_64.86_75.99000000000001.wav, from the 1950s up to today and then most of the time I'll spend on the algorithms and a little bit of theory about this deep architectures and deep learning. +02. Learning in the Machine. Pierre Baldi_clip_81_726.14_737.48.wav," network, you have data and you use HAP rule or any local rule here, here and here and here etc. you'll never be able to learn interesting functions." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_369_3376.26_3388.2.wav," up with five neural networks, one that computes the output, and four neural networks for the lateral propagations. So your question is, how many parameters the model has, right? It depends on how..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_196_1788.99_1799.669.wav," the majority vector. So the majority vector, the majority of all the vectors in the input space that are mapped onto a single vector in the hidden space, that is the majority vector." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_47_431.57_443.03.wav," a signal for what to do, but if the synapse is deep in the brain, 10 layers away from the periphery, how does it decide what to do? So the first person that..." +02. Learning in the Machine. Pierre Baldi_clip_167_1502.29_1513.75.wav," well the patterns, this is the data, this is what backpropagation produces, and these are some of the other algorithms, for instance random backpropagation, and you see that at low complexity it matches." +02. Learning in the Machine. Pierre Baldi_clip_21_194.18_207.38.wav," ones are together. With wrap around or not that's a detail. Okay so that's the task and I ask you you know is this simple, is it easy, is it linearly separable etc. How does it compare to pen?" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_226_2077.53_2089.1690000000003.wav," If you give me targets, you have all kinds of algorithms, shallow learning algorithms, to fix the weights between two layers. For instance, gradient descent, right? Or SVM type of..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_129_1162.51_1173.94.wav," You use the hidden layer of the first to train the second, etc. You stack these autoencoders on top of each other. And then you finally put your discrimination unit that decides what's the probability." +02. Learning in the Machine. Pierre Baldi_clip_65_580.49_593.42.wav," So that's the definition of a local learning rules. And I think this is nice, because now you can separate the variables that are in the learning rule, which need to be a local." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_193_1761.96_1772.669.wav, So you have to produce a single vector here that is the closest to these three in Hamming distance. So you can think of it as the Hamming center of gravity of these three vector. It turns out it's. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_365_3337.83_3349.89.wav," is going to be a window around i, a window around j, with all kinds of information. You know, the type of amino acid, their size, hydrophobicity, whatever. These are four hidden vectors in the four." +02. Learning in the Machine. Pierre Baldi_clip_200_1804.149_1816.21.wav, matrix Ci times the what is at the top T minus O when it combines with the input you get this this quantity here so this is the covariance matrix of the target +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_169_1521.26_1535.42.wav," optimal eigenvectors. If you are a mathematician, you may care about finite fields. It's not important for machine learning. So finite field, for instance, GF2 is the field where everything is like" +02. Learning in the Machine. Pierre Baldi_clip_230_2074.75_2086.27.wav," If you start anywhere, suppose you start here, it says the derivative is negative. So you're going to move like this, and you're going to end up to this fixed point here. If you start here, the same thing." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_101_916.94_928.6700000000001.wav," is going to play an important role is the idea of an autoencoder. So an autoencoder is a very simple circuit where you have an input layer of size M, you have a hidden layer of size P." +02. Learning in the Machine. Pierre Baldi_clip_120_1076.54_1086.94.wav," in both directions along axons, right? You can have systems where you have separate connections, but they are sort of identical. You use the transport." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_325_2962.86_2973.96.wav," There are subtleties, you can do contact maps at different thresholds, etc. But I won't go into the details, but that's the contact map. And so the idea is how you can predict a contact map." +02. Learning in the Machine. Pierre Baldi_clip_265_2463.07_2473.8999999999996.wav," out on the way back, which is a little bit like averaging an ensemble, we don't see, you know, any, any, but it doesn't hurt you, but it doesn't buy you anything obvious, at least in the simulation." +02. Learning in the Machine. Pierre Baldi_clip_24_220.519_233.84.wav," odd number of such beats, whereas here you just look at the pattern and you see immediately whether the ones are clumped together or not. That's your thinking when you use your visual system. But if now you..." +02. Learning in the Machine. Pierre Baldi_clip_5_46.28_58.76.wav, digital computer. And this makes a big difference. And I think there is a lot to be learned by looking at deep learning in a nature of learning. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_52_480.249_491.139.wav," There are many other forms. And by the way, nowhere in the book would you find any mathematical equation or anything like that. But it's the first time that at least some idea about this very..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_191_1744.71_1755.629.wav," So I look at all the predecessors, all the vectors in the input space that are mapped onto H, and now you have to think what should be the output." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_355_3230.78_3248.809.wav, for that storage that are happening at the level of all of the DNA. So thank you for your attention and I'll try to answer any questions. This will be a time for a few questions. +TheQuarksOfAttention1625000-1650000.wav," are invariant to permutations of their inputs. This seems a little bit strange because they come from NLP. In NLP, the order of the words in a sentence is very important. But surprisingly, transformers don't care about the order. They throw it away. And you see it here because if I switch around the inputs, if I permute." +02. Learning in the Machine. Pierre Baldi_clip_99_883.76_895.88.wav," and local deep learning. So what do I mean by that? Well, we have seen that a deep weight has to depend on the targets, for instance, right? So there has to be." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_121_1090.57_1102.93.wav," or computers and I think it's a little bit the same thing for neural networks so around 2006 this paper from Hinton, his group and other papers came out which restarted" +02. Learning in the Machine. Pierre Baldi_clip_240_2169.349_2179.7.wav, information about the targets all the way to the deep weights. The deep learning channel appears to be in simulation very robust to all kinds of perturbation and variations. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_91_827.85_838.8.wav," bit of the sum learning, you are in the flat part of the logistic functions. Your derivatives are close to zero. Every time you traverse a layer, you multiply by zero, essentially. Very rapidly, you..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_86_783.03_794.5500000000001.wav," and you want to change this weight, you get a learning term that is the product of two terms, a presynaptic term, which is the output of this neuron," +02. Learning in the Machine. Pierre Baldi_clip_206_1854.85_1865.95.wav, of x that we understand qualitatively quite well. I will show you an example at the very end but basically you cannot have oscillations you either have convergent to fixed points or divergent. +02. Learning in the Machine. Pierre Baldi_clip_179_1609.09_1620.76.wav, propagation has completely random weights in the layer above to the layer that you're trying to to learn and then we skip the random back propagation +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_299_2738.52_2749.9500000000003.wav, of the type of architecture we use there is that every time you have an acyclic graph like a Bayesian network for instance you can always convert this to a deep neural network by replacing +02. Learning in the Machine. Pierre Baldi_clip_186_1679.53_1689.7.wav," if it's one rank below the full rank, it will still sort of learn, there will be graceful degradation in performance, there will not be a..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_309_2825.55_2837.6400000000003.wav," This is sort of a Bayesian view, Bayesian network view of your prediction system, where your prediction at position t, which should be the probability of alpha helix, beta strand, or coil." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_8_73.5_85.94999999999999.wav," deep architectures and deep learning and show you one example of application towards the end. So as far as if we can tell, learning is essential for development." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_41_374.93_392.59999999999997.wav, is the size of my fist and then the diameter of a neuron is about 10 meters so this room is the neuron and then the tennis racket is in New York +02. Learning in the Machine. Pierre Baldi_clip_117_1049.06_1061.95.wav," completely different pathways. We definitely know that in the brain you have tons of connections going in the feedback direction. But again, two different possible notions of feedback." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_71_647.93_660.81.wav, people claim that they sort of paralyzed the AI and machine learning developments in the in the 70s I don't know if it's really that bad but but the fact is that the problem +02. Learning in the Machine. Pierre Baldi_clip_259_2401.48_2414.68.wav," You know, what kind of randomness you should be using? It's very robust. What process? Have you changed process? Yeah, we changed process. Again, we tried." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_95_861.35_876.89.wav, to use gradient descent. Yes? So I'm a little illuminating over this comment by Minsky and Papert. So I don't know this field. It's first the strange way of saying that there is not. +TheQuarksOfAttention1000000-1025000.wav," neurons, the attending neurons, they produce some outputs, and these outputs are added to the activation of some other neurons. Now, of course, this is nothing new. It's just part of the standard model. But the reason why this is important is because that is also one possible mechanism for inhibiting other neurons and doing the exclusion of other stimuli" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_291_2665.2_2677.6800000000003.wav," that's the ensemble average, it's very well approximated by applying the sigmoid to the average linear activity of the corresponding unit." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_202_1843.2_1855.3200000000002.wav," the targets, you know, the vector that is closest to the three targets. So this is general, can be applied to any Boolean circuit, not just the autoencoder circuit. Now let's look at the other way around." +02. Learning in the Machine. Pierre Baldi_clip_150_1346.53_1356.22.wav," above the current layer like backpropagation does. Backpropagation use all the derivatives above. You actually don't need all of them. If you have a skipped architecture, you can get rid of it." +02. Learning in the Machine. Pierre Baldi_clip_57_510.35_520.76.wav, learning problem when you think about it in biological terms. So that's just the rescaling. So this leads immediately. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_186_1689.649_1700.269.wav," some precise sense that you will see in a second. So the best way to show you that is let's try to understand what happens if you fix B, you try to optimize A, and vice versa. And let's start with" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_116_1045.35_1056.87.wav, biological neurons. So there was this backlash. It was very almost impossible to publish a paper at NIPS if you had neurometric in the title and you had to say artificial neurometric. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_197_1797.57_1808.3690000000001.wav," a single vector in the hidden space, that is the right output you should use for A. And you can see that you can study generalization in a very interesting way." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_361_3300.15_3311.79.wav, your system needs to be flexible and adapt to variable structure. These recursive networks are very good for that problem. The one we use for contact map prediction +TheQuarksOfAttention2550000-2575000.wav," with two colors, red and blue, how many such colorings are linearly separable? Right, that's the question. So it's a fundamental question about neural networks. It's not very well known, but I think it's one of the most important problems in neural network theory. And in 65, Kovar had proved an upper bound of N squared on the capacity of the single neuron. Moroga had..." +02. Learning in the Machine. Pierre Baldi_clip_6_54.109_66.29.wav," learn by looking at deep learning in a native neural network, in a physical system, rather than in the digital simulation. And by taking into account the..." +TheQuarksOfAttention2875000-2900000.wav," of attention to really try to identify fundamental basic mechanisms that are used to build attention. The interesting ones that I described to you are essentially output gating and synaptic gating, which are outside of standard models. So they extend the standard model towards using quadratic activations. You remember there were all those quadratic terms." +02. Learning in the Machine. Pierre Baldi_clip_178_1600.66_1610.74.wav, about all the weights below. And this is exactly what leads and is shown by random back propagation. Because random back propagation has completely run. +02. Learning in the Machine. Pierre Baldi_clip_91_812.75_822.8599999999999.wav," the activations, nonlinear activation functions of that layer. So it's reasonable to assume that the solution to these equations, you have one such equation" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_237_2184.43_2196.73.wav," using this deep target algorithm, you can see the error, both the training and the generalization error are going down and stay together in a nice way. This is an example of a 14-layer algorithm." +02. Learning in the Machine. Pierre Baldi_clip_198_1788.07_1798.45.wav, essentially this thing because it's very easy to see that because it's just the transpose of the of the stream coming from the forward pathway which is +02. Learning in the Machine. Pierre Baldi_clip_177_1592.26_1603.42.wav, should be the same for all the weights above. You really don't need to know everything about all the weights above in the same way that you don't need to know about all the weights below. And this. +02. Learning in the Machine. Pierre Baldi_clip_202_1821.22_1831.33.wav," is the covariance matrix of the input data. If your backward pathway is also adaptive, you get these equations for adapting the C. So you get a huge system." +02. Learning in the Machine. Pierre Baldi_clip_169_1519.0_1529.8600000000001.wav, know training at the same epoch it's a little bit behind and there are variations across the different algorithms this one doesn't seem to be doing very well but you know again +02. Learning in the Machine. Pierre Baldi_clip_59_527.69_538.7.wav," on local variables that are available in the neighborhood of the synapse. So using these high-level models that we're using, it means that you" +TheQuarksOfAttention2500000-2525000.wav," it into the weights of the neural network in order to select the red function of something similar to the red function, right? And so that's why the capacity is important for neural networks. And so the first thing you want to know is what is the capacity of a single neuron of a linear threshold gate. So there you are asking how many different linear threshold gates there are, how many Boolean functions are there that can" +TheQuarksOfAttention2825000-2850000.wav," And that's what we're doing with Roman and deriving all these results. And as I mentioned briefly already, the one surprising thing to me is that the key mathematical tool for proving some of these results is actually an attention mechanism. It's the first type of attention mechanism that I mentioned, which is inside the standard model, where you have a bunch of neurons that are inhibited." +02. Learning in the Machine. Pierre Baldi_clip_118_1058.39_1069.63.wav, two different possible notions of feedback. So let's discuss first where can this channel be in different neural systems. +TheQuarksOfAttention2325000-2350000.wav," in this prediction. Okay, I'm almost at the end now. Let me very quickly give you a sense of how you can try to build a mathematical theory of attention. And the tool I'm using to do that is called Capacity. It's a tool that we'll be using for quite some time, but the idea is very simple. If you have a class of functions, for instance, all the function" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_285_2610.74_2622.68.wav, the normalized geometric average because you have the geometric average but you have to normalize by this and the the prediction if you want of the opposite class here again taken over all possible +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_279_2558.93_2570.42.wav," So I'm using sigmoidal functions. Here's a function that computes a linear sum s, passes through the sigmoid to produce the output. If you look at all possible..." +TheQuarksOfAttention375000-400000.wav," signal X with the weights W, the synaptic weights of the neuron. So you have a weighted average, which is called the activation of the neuron. And then this activation is sent through a, an activation or transfer function to produce an output. And you have all kinds of activation functions, such as sigmoidal activation function, tanh and" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_315_2875.14_2885.9700000000003.wav," as a function of ut and ft minus 1. And you can, in order to keep the number of parameters small, you of course assume that the network here is the same as" +TheQuarksOfAttention1050000-1075000.wav," of inhibiting neurons, those that should not be part of the attention mechanism is by sending them a very large negative signal in the normal way within the standard model and shutting them down in that way. So that's why I'm including this additive mechanism in the list. It turns out that I'm not going to talk about it very much in the rest of the talk because it's." +02. Learning in the Machine. Pierre Baldi_clip_32_290.21_303.169.wav, group of neurons is removed etc and you keep repeating that. So dropout you could view it as a thinking in the machine type of thinking. +TheQuarksOfAttention300000-325000.wav," certain things and enhance, which is multiplied by say a factor of two or three, the thing that you're interested in. So already there, you get an intuition that there is something, one possible direction is to think that there is something multiplicative about attention where you can multiply things by zero and inhibit them, suppress them." +TheQuarksOfAttention275000-300000.wav," stimuli, this exclusion of all other stimuli means some kind of inhibition. It means that you are multiplying by zero, essentially, all the other stimuli so that you can concentrate on what you're interested in. And maybe you're also enhancing what you're concentrating in. So it means that you must be able to multiply by zero." +02. Learning in the Machine. Pierre Baldi_clip_40_358.55_370.43.wav, neural network that works well if you don't have exact weight sharing. Where you can show for instance that if you take a convolutional neural network and relax the weight sharing assumption but +TheQuarksOfAttention925000-950000.wav, by making the assumption that the origin of the signal comes from the output of some neurons. So I'm assuming that there are some neurons in the attention mechanism that produces an output and that's the attention signal. And this output then is gonna interact with either S or W variables. +02. Learning in the Machine. Pierre Baldi_clip_275_2569.73_2582.2000000000003.wav," the derivatives, right? You put random matrices or even the transpose of the main of the forward matrices but you don't multiply by derivatives then it doesn't work. That's an example." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_93_844.94_855.44.wav," deeply into a multi-layer architectures. So in the 80s it was applied to network with three layers, one in the layer, it worked nicely there and" +TheQuarksOfAttention850000-875000.wav," where the origin of the attending signal is both into in the output, maybe in the synaptic weights of some neurons, but that's a little bit strange and would of course create more cases. So I'm going to stick to these sort of homogeneous cases where the source of the signal is of one type and the target of the signal is of another types." +02. Learning in the Machine. Pierre Baldi_clip_166_1492.27_1504.75.wav," and these networks here have hidden layers of size 500 and there is maybe four or five hidden layers. And back propagation is here, you know, is able to learn very well the patterns. This is the data." +TheQuarksOfAttention1675000-1700000.wav," surprising for language, but as we shall see, very useful for applications where you need to be invariant to permutation of the inputs. So if your inputs are sets rather than sequences, that's exactly the kind of thing you want because you don't care about the order of the objects in the input. And so you want to sort of build that in." +02. Learning in the Machine. Pierre Baldi_clip_15_142.94_154.16.wav," of light, try to think how the world looks like if you are a photon. So here we're going to do the same thing. We're going to try to think that you are a neuron, or try to think that you are a photon." +TheQuarksOfAttention2575000-2600000.wav," a lower bound of one half n squared. So there is a gap and the gap was actually solved in the late eighties by a Russian mathematician called Zuev was able to prove that the capacity is n squared. This means that the total number of linear threshold function, Boolean function is about two to the n squared as opposed to the total." +02. Learning in the Machine. Pierre Baldi_clip_205_1844.47_1857.3990000000001.wav," systems. These are polynomial systems of differential equations and if you are in one dimension, if you have dx dt equal p of x, that we understand quite well." +02. Learning in the Machine. Pierre Baldi_clip_207_1864.12_1876.57.wav," to fixed points or divergence to infinity, but if you have two differential equations, dx, dt equal p of x, y, dy, dt equal q of x, y, just" +02. Learning in the Machine. Pierre Baldi_clip_23_213.23_223.76000000000002.wav," may think that this is a fairly simple task compared to parity, because parity, you have to look at all the bits and count whether there is an even or odd number of such bits. Whereas here, you just." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_90_820.35_829.8900000000001.wav," other nonlinear functions you are using in each layer. And if you are using logistic functions, after a little bit, after some learning, you are in the flat." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_82_744.72_758.64.wav," at UCSD that was led by David Ruebelhardt and other people that participate in that group that you probably recognize, Geoff Hinton, Francis Crick, and Terry Sinofsky. That's the group that introduced..." +02. Learning in the Machine. Pierre Baldi_clip_215_1938.01_1950.3400000000001.wav," The nonlinear case, for instance, if you have the case with three units like this, where you put a nonlinearity here, like a power function, for instance, that case we can solve and show that." +02. Learning in the Machine. Pierre Baldi_clip_185_1670.08_1682.41.wav," full rank matrix and it's five minutes left, it's about right, but it's not a sharp threshold. That is, if the random matrix is full rank, it works well. If it's one rank below the full rank..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_317_2892.6_2905.47.wav," and weight sharing in the output chain. So this is called the recursive neural network architectures. Architecture, it has been used for secondary structure. I won't go into the details and go, does very well." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_362_3309.45_3321.63.wav," So the one we use for contact map prediction, you have an input plane, which is the size of the protein. So if the protein is 100, this is gonna be 100 by 100. You're gonna have four hidden planes." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_329_2996.22_3006.84.wav," I mean, same ideas as what I've shown you before for the secondary structure. These are just examples of contact maps so that you see how they look like in case you have never seen a contact map." +02. Learning in the Machine. Pierre Baldi_clip_122_1092.1_1103.59.wav," when you're doing your digital fantasy in your computer. That's the way you think about it. Again, if you think about biology, many have pointed out it's very unlikely." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_306_2799.75_2810.9100000000003.wav, There is quaternary structure when you have proteins interacting with each other and forming protein complexes and you want to have the 3D coordinates of all the chains. +02. Learning in the Machine. Pierre Baldi_clip_102_911.5_924.41.wav, depends on the target. Okay? So there has to be this deep channel that conveys information about the targets and other things all the way from let's say the +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_280_2567.15_2578.52.wav," the output. If you look at all possible submetric of this function, that is all the possible submetric that are computing this S, you can take the" +TheQuarksOfAttention100000-125000.wav," knows at least in an intuitive way what attention is. It has been studied by psychologists for quite some time. So you see here the definition provided by, by Jaynes in the late 1800s. In fact, it's not obvious that, that there is something called attention, right? Unless you, you." +02. Learning in the Machine. Pierre Baldi_clip_217_1956.549_1966.5390000000002.wav, the skipped version versus the propagated version are equivalent. So let's stick with the skipped version. What you have here is a chain of linear neurons. Everything is linear. If I give. +02. Learning in the Machine. Pierre Baldi_clip_183_1646.05_1659.1899999999998.wav," use the precision on T minus O quite a bit, not down to one bit. If you do just one bit, the sign of T minus O, it doesn't seem to work. But a low precision version of T minus O times a random sparse matrix will work." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_128_1154.32_1164.1899999999998.wav," autoencoder, which compresses data a little bit more. And you do it a few times. So you stack autoencoders. You train the first. Then you use the hidden layer of the first." +02. Learning in the Machine. Pierre Baldi_clip_126_1127.47_1140.52.wav, which talks to the forward pathway and through different sets of weights and that's what I call the distinct case. +02. Learning in the Machine. Pierre Baldi_clip_208_1871.679_1886.289.wav, of xy dy dt equal q of xy just two equations with two polynomial that is extremely difficult in fact Hilbert 16 problem is the question of whether you can bound +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_253_2331.98_2342.15.wav," the lower layer, the discrimination has a small weight, and as you go up in the hierarchy, you crank up the weight so that the top layers have a very strong weight." +02. Learning in the Machine. Pierre Baldi_clip_236_2133.55_2144.049.wav," system, not in the digital fantasy that we use. Thinking about synapses and their environment." +02. Learning in the Machine. Pierre Baldi_clip_12_107.39_121.1.wav, some bookshelves and some books and this is where the Nazi burnt in 1933 burnt a lot of books from by Einstein and and many other great Jewish people. +02. Learning in the Machine. Pierre Baldi_clip_191_1720.15_1732.54.wav," a little bit, but you can see that the stable points are given by these hyperbolas here, where the products of the weights A and B is some constant, the right constant. And you can see in..." +02. Learning in the Machine. Pierre Baldi_clip_184_1659.19_1673.23.wav," work plus the derivative of the current layer. You may guess that if you multiply this by a matrix, it would have to be a full rank matrix. And it's five minutes." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_76_690.99_701.639.wav," is. And it has interesting properties, it is conversion, etc. That created a lot of excitement, brought many physicists into the field." +02. Learning in the Machine. Pierre Baldi_clip_190_1711.09_1722.04.wav, down the equations of such a system. In fact some of this is in the Lilly Krogh paper. We have extended the theorem a little bit. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_321_2929.07_2941.62.wav," a representation that doesn't depend on translations and rotation and the one we use is the contact map. So the contact map is a matrix, symmetric matrix," +02. Learning in the Machine. Pierre Baldi_clip_260_2410.09_2429.92.wav, process you know again we tried so of course Gaussian but then we tried sparse matrices with coin flips that's fine I'm not so much worried about convergence speeds but I would be interested if +02. Learning in the Machine. Pierre Baldi_clip_28_256.94_269.15.wav," out it's a very hard problem. And you get completely fooled by not thinking in the machine. Another example of thinking in the machine is dropout, because you could" +02. Learning in the Machine. Pierre Baldi_clip_239_2160.17_2171.39.wav," be able to learn anything interesting. You need a backward channel, the deep learning channel, to communicate information about the targets." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_110_994.98_1006.8.wav," doing. And it's another way of addressing Hebb's problem. How do you learn things without being told what to do? Here I just use my data. I have data. It's completely unsupervised learning, but I'm learning" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_148_1328.7_1341.1100000000001.wav," in the hidden layer, it doesn't change the overall solution. You want to know if the problem is how complex it is, is it NP-complete, etc. You would like to know something about the landscape of the distortion." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_250_2307.29_2317.4.wav, So the fact that you're putting this additional bit in this layer forces the representation in the hidden layer to be a little bit tuned to the task you're doing. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_177_1603.669_1614.86.wav," that same criterion would at least stay at 50 in the second place. That's a different issue. I'm not saying that you should do 150, 10. I'm not recommending that. When you should stop and accept." +02. Learning in the Machine. Pierre Baldi_clip_203_1828.659_1840.09.wav," for adopting the C's, so you get a huge system of differential equations. And just for comparison, these are the systems that you get for backpropagation. So can" +02. Learning in the Machine. Pierre Baldi_clip_72_646.52_657.05.wav, can extract simple statistics of the data such as the center of gravity or the principal component. So it's interesting to know that and which... +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_65_589.54_599.649.wav," until Minsky and Pappert came along. They wrote this book Perceptron in 69, proving a lot of interesting theorems about Rosenblatt's Perceptron." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_4_36.0_50.34.wav, Thank you. Can you hear me in the back? It's a pleasure to be here. Thank you for the invitation. And this is the roadmap for this presentation. I'm going to tell you a little bit about the project. +TheQuarksOfAttention1300000-1325000.wav," comes in and show you that it's exactly the type of mechanism that I just described, which is the multiplication of outputs by outputs or multiplication of synaptic weights by outputs. Okay. So if you read the Littleshore transformers, they're made of basically building blocks and co-order blocks, decoder blocks, but each one of these." +02. Learning in the Machine. Pierre Baldi_clip_71_636.95_649.6999999999999.wav," which is a quartic rule, actually, can extract the principal component of the data. So these rules that you can study can extract simple statistics of the." +TheQuarksOfAttention1800000-1825000.wav, layers depending how you count it. And all this gets compacted into a much shallower building block by having output gating mechanisms built in into your network. Right. OK. So let me now show you a few applications of transformers to problems that I've not. +TheQuarksOfAttention1525000-1550000.wav," in a few slides, you can get a circuit that is at least four or five layers deep in order to do that in the standard model. Here in one stage, in one layer, boom, you can compute dot products between vectors. And then these dot products go through a softmax. This is sort of not new, but the softmax the resulting weighting scheme" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_326_2971.53_2981.9700000000003.wav," The idea is how you can predict a contact map, and what is of course most challenging and most interesting is to predict this corner. That is the long range residues of the protein." +02. Learning in the Machine. Pierre Baldi_clip_138_1235.24_1245.62.wav," you like around sparse matrices, maybe we want to use sparse matrices in the backward channel, random sparse matrices. And what about these derivatives? Do you really?" +02. Learning in the Machine. Pierre Baldi_clip_132_1177.42_1190.08.wav," it works almost as well as plane backpropagation. So that's a remarkable result, and it opens the door for doing a lot of studies on this discipline." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_105_953.089_965.85.wav, already have in the input. You have your data. Why would you try to produce a corrupted version of the data in the app? But the reason why this is such an interesting and deep idea. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_66_597.579_613.41.wav," about Rosenblatt's perceptron learning theorem, showing that even if data is not linearly separable, you get something that behaves reasonably well, for instance. But they wrote this sentence. I don't know why the image is truncated here. But the sentence..." +TheQuarksOfAttention2650000-2675000.wav," in the 90s and more recently Roman Verschweining and I were able to prove the same thing, the generalization of the linear case where you have this, basically the capacity is n to the d plus one over d factorial. So the next question is how do you apply this to attention? So the most simple case, and I'm just going to show you this most simple case," +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_137_1233.779_1245.719.wav," take a general view of autoencoders, again, by playing on the type of functions and hardware that are used in this network, I think, helps a lot to understand them mathematically." +02. Learning in the Machine. Pierre Baldi_clip_77_692.33_704.6.wav," at least to 1980 with Fukushima, who came up with this architecture, which is nothing else than a convolutional neural network inspired by the work of UL Weasel, etc. But in his paper he said" +02. Learning in the Machine. Pierre Baldi_clip_226_2039.019_2049.46.wav," you replace each Ai as its function of A1, it's a large polynomial of degree, of even degree, and you end up with an equation that looks like this." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_350_3181.4_3194.329.wav," specific to learning that are activated during learning experiments, proteins that probably travel all the way to the synapses and by doing so modify those synapses ultimately so that you can..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_231_2123.4_2138.7000000000003.wav," the image of these vectors, but let's for now think you're going to produce a lot of samples in this layer. We're going to propagate them forward in the upper layer, so you get a sample in the upper layers. And now here we know what is the best of this sample, because we have the targets." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_366_3347.37_3359.25.wav," These are four hidden vectors in the four hidden lattices that are propagating contacts laterally in different directions. So you want, when you predict contact map at position ij, you want to know something." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_89_810.75_822.21.wav," the arrow terms by the transpose of the forward weights, that's fine, and then you have to multiply by the derivative of the logistic or whatever other nonlinear functions you're using." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_360_3291.15_3302.58.wav, So it's very different in that sense from the case where you have vectors of fixed length or image processing where all your images are the same size. So your system needs to be flexible and adaptable. +TheQuarksOfAttention2075000-2100000.wav," canonical about these two cues. If I exchange these two vectors, it's the same structure. So you have a permutation invariance of the level of the cues. And then you have also what is called the top symmetry, which is the symmetry between matter and antimatter. If I call this thing Q prime and replace this one by Q, it's still a valid tree. There is not a canonical." +TheQuarksOfAttention2375000-2400000.wav," notion of volume in a certain measure of theoretic sense if you want. But I'm going to work with Boolean neurons with, you know, I'm just going to use neuron that have a threshold function as their input. So their output is 0, 1 or minus 1, 1, right? So linear threshold functions. Then everything become Boolean and discrete." +TheQuarksOfAttention200000-225000.wav," scientists have been standing attention for a while. And the conclusion is that it's a very complex phenomenon. And in fact, it's not a single thing. It's not a singular term. It is a variety of different processes and mechanisms as described in this quote. So it is, there are several." +TheQuarksOfAttention2025000-2050000.wav," like this, where you have eight vectors of size four, these are called the jets, for instance, eight vectors of size four. And your problem is to match those eight vectors to these three structures. So you have to identify among these eight vectors, which one are sort of garbage vectors that you can throw away. And then you have to identify which one are the B." +02. Learning in the Machine. Pierre Baldi_clip_98_875.3_886.28.wav," neural network cannot learn complex functions. And so this leads to two new concepts, the concept of deep learning channel and local deep learning. So what?" +02. Learning in the Machine. Pierre Baldi_clip_45_405.349_417.20000000000005.wav," fast answer question like what exactly is abn learning? Abn learning is an important concept, but it's somewhat murky. You know, neurons that wire together, fire together. What does that mean?" +02. Learning in the Machine. Pierre Baldi_clip_19_177.2_187.70000000000002.wav," for a simple neuron. Imagine you're doing logistic regression, and I give you binary vectors to be classified into 0 and 1's. And the binary vector." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_198_1806.149_1817.07.wav, But I'd like to study generalization in a very interesting way because you can take the majority either on all the vectors that are mapped here by B or on the subset of vectors in the training set. The training set in B is the training set in C. +02. Learning in the Machine. Pierre Baldi_clip_223_2009.83_2023.6.wav," carefully you can see that any two consecutive equations are coupled in this way, which means that the evolution of Ai plus 1 is a quadratic function of Ai. So A2 is a quadratic function." +02. Learning in the Machine. Pierre Baldi_clip_39_350.0_360.529.wav," the weight sharing assumption. It's very unlikely that in biological networks you have exact weight sharing, for instance. So how can you have a convolutional neural network that works well?" +TheQuarksOfAttention825000-850000.wav," I'm going to assume that it could be in the activations of neurons. It could be in the outputs of neurons. Maybe it could be in the synaptic ways. So you have three possibilities. And then these attending signals have to reach their target. And again, the target could be of type S or W. You could even think about mixed schemes." +02. Learning in the Machine. Pierre Baldi_clip_261_2427.13_2440.03.wav, speed but I would be interested if you would use this tool not single networks but ensembles of such networks with random back propagation type weights whether these would have potential +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_290_2655.9_2668.56.wav," the expected value of the output of all the networks, which is really the quantity you're interested in. You're taking the expectation of all possible networks. That's the ensemble average. It's very well-known." +02. Learning in the Machine. Pierre Baldi_clip_233_2105.26_2117.2.wav," and end up here. So no matter where you start, this system is convergent and will converge to the right solution. So although you have completely random weights in the feedback channel." +TheQuarksOfAttention2600000-2625000.wav," number of Boolean functions, which is 2 to the 2 to the n, right, if you have n inputs, n is the number of inputs, right. It makes a lot of sense because n square means that you need n vectors of length n to specify a linear transfer function, and if you write the linear system, you know, you get a sense that this is about the right quantity. You can do the same thing for" +TheQuarksOfAttention950000-975000.wav," multiplicatively or additively. Okay, so we have six possibilities, we have reduced things to six possibility, and they are listed here, where you have two mechanisms, either it's through addition or multiplication, and then you have three targets, the activations of some neurons, or the outputs of some neurons, or the synapses of some neurons. Okay." +02. Learning in the Machine. Pierre Baldi_clip_68_607.97_619.9399999999999.wav," an interesting set of functions. But in any case, we can stratify all possible learning rules, and we can study them one by one. So we did that for polynomial." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_136_1225.589_1236.8690000000001.wav, you some other algorithms complementary to this one that can allow you to train deep architectures. So I'm going to take a general view of autoencoders again +02. Learning in the Machine. Pierre Baldi_clip_62_553.82_566.5699999999999.wav," That's a reasonable definition of what a local learning rule ought to be. You're welcome to have your own definition, but within this formalism, I think this is very reasonable. Now, if you are..." +TheQuarksOfAttention1850000-1875000.wav," C plus D. Now, whether it's A plus B or B plus A, from a chemistry point of view, it's the same thing. You are just at the same reactants, right? So the order is irrelevant when you're doing a chemical reaction, and so that's why transformer are a useful technology, a useful type of circuit for chemical prediction. We're using them in physics, in all kinds of..." +TheQuarksOfAttention1350000-1375000.wav," some embedding of words into vectors. So these are the different vectors representing the different words in the sequence. And then there is a circuit, let's say just a one layer of weights, that is transforming this vector here into three vectors, which are called Q, K, and V. The query," +02. Learning in the Machine. Pierre Baldi_clip_2_20.689_31.79.wav," of course is the brain or a neuromorphic chip. What I really mean here, it's a physical neural network. It's not the fantasy that you use in your computer." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_102_926.03_939.29.wav," you have a hidden layer of size P, the output layer of size N, and the goal is to adjust the parameters of this transfer function so that the output looks as close as possible to the input." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_28_252.51_265.83000000000004.wav," Hodgkin and Astley had studied action potentials, how neurons communicate with each other, had built their famous model. And on the theoretical side, I just put here Shannon, of course, had..." +02. Learning in the Machine. Pierre Baldi_clip_133_1187.5_1201.03.wav," a lot of studies on these different architectures, so you can do studies on these different architectures using random weights on the backward path, but not only that, you can ask all kinds of questions." +02. Learning in the Machine. Pierre Baldi_clip_151_1354.36_1367.89.wav," have a skipped architecture, you can get rid of all those derivatives, but you will need the derivative of the current layer. And also another thing that is important that you see also in when you do the..." +TheQuarksOfAttention400000-425000.wav," and the logistic function, or you can have a threshold function like the heavy side or the sine function, or you can have a piecewise linear function like real new and so forth, right? But this is what I call the standard model. Some of the mechanisms we're going to see are outside this definition of the standard model, are new additions to the standard model." +02. Learning in the Machine. Pierre Baldi_clip_158_1416.55_1427.32.wav, This is another set of experiments where we're looking at adaptive random back propagation. So we're adapting the weights both on the forward channel and on the deep learning channel using... +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_70_640.5_650.0999999999999.wav," that the extension to multi-layer system is derived. But anyway, this is the sentence for which they received a lot of flack. People claimed that they sort of." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_304_2784.03_2794.349.wav," that's called secondary structure prediction. You can try to predict 3D structure, which is the x, y, z coordinates of the atoms in the structure. You can do it for the backbone, the C alpha, C beta." +02. Learning in the Machine. Pierre Baldi_clip_52_468.74_480.73999999999995.wav, a million it's 10 to the minus one meter so about 10 centimeters the size of my fist and imagine Einstein is learning how to play the violin. Where is the bow of the violin? Well it's maybe a one meter +02. Learning in the Machine. Pierre Baldi_clip_251_2313.71_2325.16.wav," I guess it's answered already about the speed of convergence. So what happens when you try it on MNIST or one of these data sets? What you see in the curves. Oh, you did? Yeah." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_281_2574.41_2587.1600000000003.wav," computing this S, you can take the, not the expectation, not the normal average, but you take the geometric, the geometric mean if you want, of these different" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_34_307.02_321.479.wav," you learn how to play an instrument, etc. etc. And you can do a back of the envelope calculation that you cannot store bits in electrical signals. It would be way too expensive. You would lose a lot of weight very rapidly. So you would have to pay a lot of money to get it. So you would have to pay a lot of money to get it. So you would have to pay a lot of money to get it. So you would have to pay a lot of money to get it. So you would have to pay a lot of money to get it. So you would have to pay a lot of money to get it. So you would have to pay a lot of money to get it. So you would have to pay a lot of money to get it. So you would have to pay a lot of money to get it. So you would have to pay a lot of money to get it. So you would have to pay a lot of money to get it. So you would have to pay a lot of money to get it. So you would have to pay a lot of money to get it. So you would have to pay a lot of money to get it." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_161_1447.7_1462.1100000000001.wav, on to subspaces spanned by eigenvectors associated with eigenvalues that are not the top key eigenvalues. So very interesting landscape with a lot of subtle points and one global. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_67_609.899_624.24.wav," the image is truncated here, but the sentence says that there is no reason to suppose that any of these virtues, the virtues of the single-layer perceptron, carry over to the many-layered version." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_172_1549.05_1562.07.wav, complex. It's very difficult to do linear autoencoders over finite field. You can show that it's NP-complete and even optimizing one layer it's not clear how that can be done on finite fields. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_272_2496.21_2508.8399999999997.wav," point, why is it convergence, etc. Very briefly, the first thing you want to see is to look at the linear case. So you imagine you have a pure linear network. So you have something like this." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_348_3164.3_3174.859.wav," you look at the level of expression of the genes, for instance in the hippocampus, after the experiments and you compare it with the level of expression in a mice that has not been run in the maze." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_160_1437.97_1451.6599999999999.wav," the eigenvector associated with the top p eigenvalues. And then you have lots of other critical points where the gradient is zero, which corresponds to projection onto subspaces spanned by eigenvectors." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_248_2287.91_2300.39.wav," in the output two things, the image itself, but at the same time, whenever you have a label on the image, whenever you know if there is an elephant or not, you have to predict this bit, zero or one." +02. Learning in the Machine. Pierre Baldi_clip_231_2083.75_2097.28.wav," right? If you start here, the same thing, the derivative is positive, so you're going to end up here. Now, if you start here at minus infinity, or your derivative." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_21_188.66_200.83999999999997.wav, architectures and deep learning. So a little bit of the history of this starting in the 1950s and I'm sorry if you just had lunch this is a this is really the foundation +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_68_620.189_633.06.wav, carry over to the many-layered version so they were unable to see how a multi-layered perceptron can learn anything and of course they were edging their bet +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_356_3248.839_3261.8089999999997.wav," You'll have to go through it fairly quickly, but I'm curious for your built-in structure of how large the network of neurons would be." +02. Learning in the Machine. Pierre Baldi_clip_1_11.3_22.73.wav," Thank you, Gregoire. Good morning. So we're going to talk about deep learning in the machine, for lack of a better word. The machine, of course, is the brain or a neuromotor." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_264_2427.72_2439.93.wav, very interesting properties and so the question is why what is the system doing and why does it work well to try to understand this so the basic idea is that +02. Learning in the Machine. Pierre Baldi_clip_224_2020.71_2034.279.wav," So a2 is a quadratic function of a1, a3 is a quadratic function of a2, so it's a quadratic function of a1, etc. etc. So basically you can take" +TheQuarksOfAttention75000-100000.wav," of attentions and in particular of transformers to some interesting problems. And then I will finish by showing you how you can begin to develop a mathematical theory of attention. So let me start from the beginning. What is attention? Of course, every one of us." +02. Learning in the Machine. Pierre Baldi_clip_253_2331.41_2351.56.wav," The other variants may take 50 or 100 epochs, but you will get there in reasonable time. Yeah, Max. So as a follow up, what about the wall clock time? I guess with randomized weights, you kind of save some computation, but you need long time." +02. Learning in the Machine. Pierre Baldi_clip_90_802.85_812.75.wav, all the weights in a reverse direction in back propagation all the weights of the network in addition every time you traverse a layer you multiply by the derivative of +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_11_101.61_112.35.wav," It always requires a number of steps. And so the idea is that you have a system with many steps. You have learnable functions, functions that are." +02. Learning in the Machine. Pierre Baldi_clip_20_185.0_197.0.wav, into 0 and 1's. And the binary vectors that should be classified into 1's are those that are connected. That is where all the 0's are together and all the 1's are together. With wrap around or not. +02. Learning in the Machine. Pierre Baldi_clip_66_591.08_601.34.wav, in the learning rule which need to be local from the functional form of the learning rule. So I can decide what functional form the function f should have. +02. Learning in the Machine. Pierre Baldi_clip_100_893.24_905.3.wav," for instance, right? So there has to be a channel in a physical system, in the machine, there has to be a channel that conveys information about the targets all the way down to the" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_373_3410.4_3423.9900000000002.wav, the size of the model has definitely gone up due to data availability and computer power. Well we do cross validation so we train on +02. Learning in the Machine. Pierre Baldi_clip_175_1575.55_1586.53.wav, only thing you need is the activity of the presynaptic neurons. So all the information about all the weights below is subsumed by +TheQuarksOfAttention25000-50000.wav," that quarks are the fundamental building blocks of other particles. So this is the outline of my talk. First I'm going to give a general introduction to attention, the problem of attention, within the what I call the standard model, borrowing again some language from physics. You will see very shortly what I mean by standard model." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_328_2988.33_2998.95.wav," really you would have solved the protein structure prediction problem. So we use a recursive architecture, fairly similar, I mean same ideas as what I've shown here." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_156_1399.25_1410.83.wav," P is not a convex set. It's actually a very, very non-convex set. So this is not a convex optimization problem. However, if you fix A, it becomes convex in B." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_146_1310.639_1322.009.wav," using L2, you know, any rotation translation of the data usually in the input will leave the problem invariant. There is also invariance in the hidden layer. If you are, for instance, the linear case." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_222_2038.95_2051.22.wav," be complete by this reduction. So let me now shift gears, that's all I'll say about autoencoders, let me show you another possibility." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_22_197.3_210.32.wav," at lunch. This is really the foundation, the starting point I think for all the ideas in machine learning and in AI is the study of the human brain. So around 1950 a lot of the concepts" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_100_908.0_918.74.wav," in the talk, so I don't know of any such response. The other thing that the PDB group introduced, which is going to play an important role, is." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_15_137.99_148.79.wav," the input or the output targets. So in very big terms, that's the kind of problem that we're going to look at. And a question that comes up all the time." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_73_666.449_678.689.wav," places, not talking very much to each other that started the process. I think at the time the most influential one was the group by General Hoffeld at Caltech. Hoffeld actually got" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_42_387.79_399.13.wav, And then the tennis racket is in New York or maybe even in Florida something like that So how is it possible that this little sign out which is completely blank? +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_336_3057.5_3068.01.wav," These are some references that you can find on my website. And to finish, there are many, many students and postdocs." +02. Learning in the Machine. Pierre Baldi_clip_61_544.73_556.85.wav," weights, which is some function of local variables such as the presynaptic activity, the postsynaptic activity, and maybe the weight itself. That's a reasonable definition of what" +02. Learning in the Machine. Pierre Baldi_clip_97_864.89_877.28.wav," you're not sure. OK, so Hebbian learning, or more generally, deep local learning, stacked local learning in a feedforward neural network cannot learn complex functions." +02. Learning in the Machine. Pierre Baldi_clip_104_930.5_942.14.wav, know simulation fantasy you don't worry about it but in a physical system you have to worry about it and so we can ask for instance where is the channel located what kind of information does it carry +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_112_1011.99_1023.389.wav," In the 90s, it was all about graphical models, Bayesian networks, etc. Towards the end of the 90s, people started getting interested in kernel." +TheQuarksOfAttention1150000-1175000.wav," So here is the output gating. What I mean by that is you have an attending neuron, here's neuron i, which is being attended by neuron j. The output of neuron j is the attention signal, and you see this output comes here, and it multiplies the output of neuron i. So this is outside of the standard model. It's this new algebraic operation where you allow neurons to multiply their outputs." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_151_1355.9_1367.75.wav," then be and keep doing that and see what happens, right? So I'm going to tell you, give you examples of things that you can prove mathematically, starting with the most classical and simple case." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_331_3014.67_3026.3399999999997.wav," The last CASP experiment, this is an experiment that takes place every two years, where people do blind prediction on proteins that were solved by crystallographic methods, NMR methods." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_171_1541.04_1552.35.wav," Goldman Sachs likes GF2, to do accounting on GF2. But anyway, the problem turns out to be extremely complex. It's very difficult to do." +TheQuarksOfAttention2225000-2250000.wav," direction. Then you can sample neutron stars on this line and you can add Nuisance parameters such as, you know, where is the distance of the neutron star from the point of observation, the temperature, things about dust, etc. And then from there you can produce a spectrum. You can do a simulation that produces the corresponding" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_25_224.54_237.81.wav," Darwin that the brain has been built by evolution. They knew about synapses. This is Sherrington, who introduced the coined word synapse. Ramon y Cajal had done beautiful studies, stained" +02. Learning in the Machine. Pierre Baldi_clip_25_231.35_242.57.wav," your visual system. But if now you put yourself in the shoes of this neuron, of this little logistic regression, the world looks completely different. There is no sense that the first..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_367_3357.0_3367.7400000000002.wav, position ij you want to know something about the protein in regions that are further away than the input window so that's what the four hidden states are +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_363_3318.81_3331.08.wav," you're going to have four hidden planes, four hidden lattices, and one output at each position. The output is the probability whether there is contact or not between i and j. And this probability is going to" +02. Learning in the Machine. Pierre Baldi_clip_18_169.31_179.51.wav," where we're going to get, I think, some interesting results is when we think about synapses. So here's a first example of this kind of thinking for a simple neuron. Imagine you're doing." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_368_3365.7_3378.0.wav," So that's what the four hidden states are supposed to be. When you convert this Bayesian network, or the graph is acyclic into a neural networks, you're gonna end up with five neural networks." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_153_1373.93_1384.8799999999999.wav, linear so A and B are matrices. You probably know this is doing principal component analysis but there is a little bit more to the story. So what you're doing basically you're trying to find +02. Learning in the Machine. Pierre Baldi_clip_119_1065.98_1078.8999999999999.wav," this channel B in different neural systems. Again, you see immediately that there is a number of possibilities. You could have a system where signals can travel in both directions along axons." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_292_2674.98_2686.29.wav," of the corresponding unit. And so these are the equations that allow you to propagate the expectations from layer to layer with this approximation and to show that, yes, indeed, these networks work." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_200_1824.149_1836.1789999999999.wav," very interesting for that. If instead of doing, you know, mapping the data to itself, you add targets, everything I said remains the same because it would mean you have" +TheQuarksOfAttention2400000-2425000.wav," actually count how many functions are in that ball. And the log base two of the number of function that you get is what we call the capacity, the cardinal capacity. Now, measuring the volume of this ball is really, gives you a sense of how powerful the ball is because the bigger, the more powerful, but it's a very crude measure, right? Because we have a very crude measure." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_118_1063.11_1075.35.wav, and it's becoming I think more and more clear that this backlash was a sound thing at the time but it went the pendulum swung a little bit too far and the analogy I like to make +02. Learning in the Machine. Pierre Baldi_clip_222_2000.08_2011.5400000000002.wav," So if you write the differential equations, they look like this. That's a system of differential equations that is satisfied by this large set of weights. If you look carefully, you can see that any." +02. Learning in the Machine. Pierre Baldi_clip_14_125.9_139.34.wav, Einstein a few hundred meters from here and you would ask him how did he come up with the theory of special relativity everyone knows that he would have said well I just try to think that I was a ray of light +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_228_2098.41_2109.8999999999996.wav," So the question is how to give targets to deep layers. So I'm going to show you one way to do it. So you take your input and you propagate it forward to this layer, and now the question is what should it do?" +TheQuarksOfAttention2450000-2475000.wav," terms of neural network, it's because from Shannon theory, you know that this is the number of bits that you need to specify one of the functions within this ball, right? That's what the log 2 of the cardinal obey is, the average number of bits needed to select a function within this ball. And if you think about learning, learning is all about taking data." +02. Learning in the Machine. Pierre Baldi_clip_244_2225.81_2236.52.wav, you showed that this robustness is there in this learning rules. What I wonder is what is the gap in performance that you get if you go away from the classical? +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_276_2531.96_2542.55.wav," to be 0.05, if you're using 0.6 for deleting neurons, you're going to get 0.06 here. So in the linear case, you can see exactly what is happening." +02. Learning in the Machine. Pierre Baldi_clip_162_1454.56_1465.9.wav, interesting technique for some simulation that comes from paper by Sabatini et al. What you have at the top is your data. So there is a mathematical function that has a parameter k that allows you to +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_327_2979.36_2989.77.wav," long-range residues of the protein. The ones on the diagonal, close to the diagonal, we know how to predict. But if you can predict this corner here, that's really, you would have solved the protein." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_244_2247.88_2261.33.wav, So how do you know that the representation you're creating in these even layers is well suited to the task? So one thing you can do is to do a different type of training where you +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_230_2115.36_2125.68.wav," to do is sample. We're going to sample in this layer, create a lot of samples, and there are issues how do you do these samples. Maybe you should do them around the image of these vectors. But let's" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_344_3127.26_3142.0690000000004.wav," learning to develop silicon-based computing systems, computers, where we're now trying to implement deep learning into these systems and using that for analyzing data including genomic data." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_254_2339.54_2350.72.wav, so that the top layers have a very strong discrimination signal that influences the learning process So this is just to give you a sense of all kinds of new... +02. Learning in the Machine. Pierre Baldi_clip_241_2177.8_2189.72.wav," perturbation and variations in algorithms, in topology, etc. etc. We have sort of a corner what is the minimal information that is required to an" +TheQuarksOfAttention2275000-2300000.wav," universe sitting, right? And so again, your input is the spectrum of, let's say 20 neutron stars, and there is nothing canonical about the order of this 20 spectra. It's just a bag, a set of 20 spectra. And so again, we're using transformer to go to do the inference from the 20 spectra." +TheQuarksOfAttention675000-700000.wav," but now they're also making their way into other areas. And I'll give you example of that. I'll give you examples of application of transformers to problems, for instance, in physics and explain why now they are making their way into other areas in very interesting manner." +02. Learning in the Machine. Pierre Baldi_clip_149_1335.59_1346.53.wav," learn well, you do need those derivatives. In fact, you can show even more than that. You only need the derivative of the current layers. You don't need the derivatives" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_104_945.52_955.73.wav," Now, when you look at this, it looks completely stupid, because you're building a circuit and you're trying to produce in the output what you already have in the input. You have your data..." +TheQuarksOfAttention1100000-1125000.wav," And it's basically either the ability of some neurons to combine their outputs with the output of other neurons in a multiplicative way. So in the most simple case, a neuron produces an output and it has the ability of multiplying the value of the target of the attending neuron output with its value." +02. Learning in the Machine. Pierre Baldi_clip_271_2528.27_2540.8689999999997.wav," it. But... Um, in a way, so in a variational autoencoder for example, you will get a feedback, uh, which is exactly a quantity of information we can, you can..." +02. Learning in the Machine. Pierre Baldi_clip_247_2250.11_2262.23.wav, percent and skipped or random back propagation maybe at 95 or 96 so you see it's a little bit slower but ultimately it gets there. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_40_363.77_374.93.wav," and imagine you rescale everything by a factor of a million, then a synapse, imagine that you're trying to learn how to play tennis or play the violin, a synapse" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_338_3075.09_3086.9700000000003.wav, the topic of my of this of this talk which I think is the most interesting thing I can leave you with and it's the idea that deep learning is a +TheQuarksOfAttention700000-725000.wav," If you read a paper about transformer, you will see diagram of this kind and, you know, new vocabulary about query key and value vectors. If you're not in the NLP field, that will look a little bit strange. There will be a matrix operation, et cetera. So it's not clear if you read them." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_294_2691.81_2704.29.wav," something very close to this, which is the expectation over all possible subnetworks contained in the network. Let me finish by giving you an example of a" +02. Learning in the Machine. Pierre Baldi_clip_213_1921.48_1932.4289999999999.wav," unit, n units in the hidden layer, then one unit, this guy here we can solve, etc. There are interesting connections to complex ideas in algebraic geometry." +TheQuarksOfAttention1725000-1750000.wav," and the end with Xn. And then I allow a summation here. This is how I get a double product between X and V in a very compact form with this new mechanism. Well, let me, you can of course also combine this with softmax, but let me just skip this." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_154_1383.14_1392.95.wav," What you're doing, basically, you're trying to find a rank p approximation to the identity function. This is what this is doing. And you may think that this is a convex problem, because everything is linear." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_127_1144.66_1156.3.wav, representation. You do it again. For each input you get a value and activation here after training. You take this as your new training set for the next autoencoder which compresses data +02. Learning in the Machine. Pierre Baldi_clip_145_1300.179_1311.35.wav," And we've tried all of them essentially, maybe a hundred or two hundred simulations of all the combinations. And the main result is that the deep learning channel is very robust." +02. Learning in the Machine. Pierre Baldi_clip_276_2579.72_2590.67.wav," And that's an example. And in terms of applications, so the data sets you have tried, it always seems to work? The variations that work, yes. They work on cifar, they draw with." +02. Learning in the Machine. Pierre Baldi_clip_249_2272.07_2287.7599999999998.wav," gradients cost you something in performance and training time. Do you think that this can be related here? Possibly, possibly. I mean for a simple system like the one, the long chain, we sort of know how long it" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_265_2437.28_2449.05.wav, So the basic idea is that what the system is doing is using an ensemble for prediction. And we know from statistics and other things that using ensembles +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_106_963.089_973.4100000000001.wav," this is such an interesting and deep idea after all, is that you're not interested in the output, you're interested in what happens here in the hidden layer. And if the hidden layer is smaller, like..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_378_3473.8_3496.09.wav, deteriorating so it's not true that the more layers you have the better. We also know that everything can be done in a single layer but it may be of exponential size. There is no theory of how many layers is good as far as I know. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_185_1677.59_1691.119.wav," function, but you still have to address this problem of optimal compression. So I'm going to show you that this system is doing faster in some precise sense that you will see later." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_37_336.81_348.09.wav, people have made the hypothesis that learning or information storage is implemented by modifying the synapse in some complex ways that we still don't know. +02. Learning in the Machine. Pierre Baldi_clip_277_2588.15_2599.73.wav," that work, yes. They work on CIFAR, we tried on NIST, we tried on another data set that I didn't show. Yes. Some are more finicky, you know, they require more..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_49_449.45_462.15999999999997.wav," was a psychologist and wrote a book, The Organization of Behavior in 1949. And it is in this book where he has this famous sentence, which is sometimes paraphrased." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_149_1339.13_1349.3899999999999.wav," about the landscape of the distortion function, of the error function, does it have local minima, etc. And also there is an actual algorithm that is suggested." +02. Learning in the Machine. Pierre Baldi_clip_114_1023.41_1036.01.wav," to stabilize your perception, your percept of the world, right? That's the kind of feedback that is sort of dynamical and very fast, again, on the scale of tens to a hundred milliseconds." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_54_496.149_507.18899999999996.wav," a possible idea of how this could be happening, that synapses are looking at correlations between pre- and post-synaptic neurons. Now this doesn't explain how you get organized behavior." +02. Learning in the Machine. Pierre Baldi_clip_201_1812.82_1823.23.wav, is the covariance matrix of the targets with respect to the inputs. P is the product of all the matrices and this is the covariance matrix of the input data. +02. Learning in the Machine. Pierre Baldi_clip_42_376.49_390.199.wav," you can get them to learn provided you give them translated version of the examples so that every neuron, let's say in the first layer, sees roughly the same set of examples." +TheQuarksOfAttention650000-675000.wav," state of the art results in LLP problems, in translation and other problems. This is what is used by all the large companies, Googles and so forth. And these architectures are now implemented in the standard software frameworks like TensorFlow and PyTorch. So they are very widely used for natural language processing." +02. Learning in the Machine. Pierre Baldi_clip_88_783.8_796.58.wav, the sum of the presynaptic activity in layer H minus 1 multiplied by the postsynaptic backpropagated error. This backpropagated error starts at. +TheQuarksOfAttention725000-750000.wav," If you glance through such paper, it's not even clear that it's a neural network, right? They do not draw neural networks. And what I will try to do is to unpack these architectures for those of you who have not really studied them in detail and show you how you can draw them, in fact, as a neural network. And then we will identify where the so-called attention" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_33_298.2_309.09.wav," the question in 1950, where does the brain stores bits? Where are your memories? Where do you store your telephone numbers? How do you learn how to play an instrument, et cetera?" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_63_573.16_583.959.wav," you basically need the presynaptic intensity and you multiply it by a postsynaptic term, which is the error, the difference between the target, what you should have got." +02. Learning in the Machine. Pierre Baldi_clip_86_767.33_779.3.wav, the full training set so it's the average over the entire training set let's say of the for a weight W ij connecting neuron j to neuron i in linearity. +TheQuarksOfAttention975000-1000000.wav," Now, I'm not going to go all six cases because not all of them are interesting and some of them can be reduced to the others, but the three that are very important and that I'm going to use in the rest of the talk are what I call activation attention, where it's an additive mechanisms that is targeting the activations of some neuron. So this means that there are some." +02. Learning in the Machine. Pierre Baldi_clip_11_99.77_111.47.wav, across the street I recommend you go see there is a glass plate on the pavement through which you can see some bookshelves and some books. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_297_2721.869_2732.19.wav," the latest benchmarks on large data sets have been improved by several percentage points by these deep architectures. And one contribution, one data set" +02. Learning in the Machine. Pierre Baldi_clip_83_742.27_753.35.wav," A reasonable condition for that is to say you should be able to reach ideally global minima of your error function, but let's say at least critical points where the gradient is zero. So you run." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_83_756.0_767.28.wav," that's the group that introduced backpropagation, which is nothing else than gradient descent in a multi-layer neural network. So it's the chain rule" +02. Learning in the Machine. Pierre Baldi_clip_60_536.45_546.38.wav," that you were using, it means that you, one possible definition of local learning would be to say that you have a rule for adjusting a synaptic weights, which is some function" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_44_405.47_416.06.wav, How can it adjust itself so that you improve your ability to play tennis? How does it know what to do? That's very mysterious and that's a fun question. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_273_2506.01_2517.47.wav," So you have something like this, and the dropout here is represented by the selector function here, which is selecting neuron J in layer L." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_143_1284.2_1295.519.wav, nonlinear space of course you have very large numbers of different auto encoders so we would like to study these different classes and when you do that you you begin to see that the +02. Learning in the Machine. Pierre Baldi_clip_256_2374.51_2384.9500000000003.wav," to compute the gradients. Well, you still have to, if you use the random matrices, you still have to multiply by random matrices, multiply by derivative, multiply by random matrices. So if you do." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_164_1477.2_1487.61.wav," If you look at the complex case, it's exactly the same thing. The algebra goes through. You just have to change transposition into conjugate transposition. And you also understand..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_99_898.09_910.67.wav," I actually don't think that you require backpropagation, there is other ways to do it, and I'll show some of them later in the talk." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_364_3328.38_3340.26.wav, i and j and this probability is going to be a function of five vectors your input vector so what is the input vector is going to be a window around i a window by +02. Learning in the Machine. Pierre Baldi_clip_55_493.82_504.76.wav, know embedded in this deep circuits in the brain that has to decide whether to strengthen itself or not or weaken itself and then it has no notion +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_39_354.47_366.89000000000004.wav," If you start thinking about it, you should see that it's in fact raises a very difficult and profound question, which is the following. To see it, you have to rescale things. And imagine you rescale everything by" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_353_3214.16_3224.7799999999997.wav, And these chemical modifications are fairly stable and are also a form of memory. And it's not clear how far this analogy goes. It could be. It is not impossible. +02. Learning in the Machine. Pierre Baldi_clip_3_29.329_39.89.wav," the fantasy that you use in your computer when you're using TensorFlow and doing ResNet or something like that, that is not a real native neural network." +02. Learning in the Machine. Pierre Baldi_clip_143_1284.44_1294.1000000000001.wav," can have an architecture that has only skip connections, where basically you have connections running from the top layer back to all the different layers. So that's what we call a fully skip." +02. Learning in the Machine. Pierre Baldi_clip_80_718.25_729.11.wav," make this work as far as I know. And the reason is that it cannot work. So I'm going to tell you that if you stack things like this in a feedforward network, you have data, and you use it." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_242_2230.18_2241.7599999999998.wav," for training deep architectures, I showed you the trick by Hinton of stacking these autoencoders. And one question you may have is when you stack these autoencoders, they have no idea how to do it. So, I'm going to show you how to do it. So, I'm going to show you how to do it. So, I'm going to show you how to do it. So, I'm going to show you how to do it. So, I'm going to show you how to do it. So, I'm going to show you how to do it. So, I'm going to show you how to do it. So, I'm going to show you how to do it. So, I'm going to show you how to do it. So, I'm going to show you how to do it. So, I'm going to show you how to do it. So, I'm going to show you how to do it. So, I'm going to show you how to do it. So, I'm going to show you how to do it." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_262_2410.68_2421.21.wav," time, the claim is you divide all the weights by two if the probability was 0.5, otherwise you have to adjust this factor. And the claim is that it works very" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_125_1125.46_1137.85.wav," say image recognition, you want to detect whether there is an elephant or not in a given image. And what you do, you take tons of images, anything you want from Google, for instance, and you train it." +TheQuarksOfAttention175000-200000.wav," mathematical theorem, you need a lot of concentration and you have to focus your attention on internal representation of mathematical concepts and so on and so forth. So that's the intuitive idea of attention and of course there's a question of how does it really work. And one way to study this problem of course is to go into neuroscience and neuroscience" +TheQuarksOfAttention2050000-2075000.wav," vectors and which one are the q vectors. And same thing for b prime and q prime. Now you see immediately that first of all the order of these vectors means nothing here, so you have a permutation invariance with respect to the order. That's already a good reason for using transformer. And furthermore, in the final structure, you see that you can permute the two q's. There is no not" +02. Learning in the Machine. Pierre Baldi_clip_43_386.81_398.599.wav, same set of examples. So these are just examples of thinking in the machine from the point of view of neurons. Now I want to go to the point of view from +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_26_235.53_247.05.wav," done beautiful studies, sustaining studies of cells so they knew about periconchi cells in the cerebellum, pyramidal cell in the cortex, six-layer architecture of the cortex." +02. Learning in the Machine. Pierre Baldi_clip_148_1327.46_1338.649.wav," not work. For instance, if you get rid of all the derivatives, you don't multiply by any derivative in the deep learning channel, then you won't be able to learn well. You do need those derivatives." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_117_1054.35_1066.0200000000002.wav," you have to say artificial neural metrics. You didn't put the word artificial, you were really consider that person. And I think, and it's becoming, I think, more." +02. Learning in the Machine. Pierre Baldi_clip_144_1291.789_1302.59.wav," So that's what we call a fully escaped architectures. So you see that you end up with lots of possibilities, and we've tried all of them essentially." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_339_3084.0_3094.32.wav," is the idea that deep learning is at the center of this triangle, where on one hand you have evolution, which has used learning over billions of years." +TheQuarksOfAttention2675000-2700000.wav," is to imagine that you have a linear threshold gate here. It's the blue neuron. So this is just the sum of the WIXI and then you take the sign of that. So you get an output that is a plus one or minus one. You have the red neuron, which is also a linear threshold gate. It's the appending neuron, right? And then you take the product of the output of these two." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_108_980.16_989.6389999999999.wav," means understanding the data. If you want good compression, it means you have to understand the data. You have to find the right features, the right, the most important component, whatever." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_347_3156.41_3166.49.wav, because we're finding more and more that the genome plays an essential role in memory. If you run a mice through a maze and you look at the level of expression of +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_217_1990.51_2003.32.wav, the 2D lattice and you map the 2D lattice to the hypercube by assigning one component on the hypercube to each vertical direction on the lattice. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_181_1641.309_1655.03.wav," So, we started looking at the case of Boolean autoencoders, which are the most extreme form of autoencoder, of nonlinear autoencoder, where you imagine that you can have any Boolean function between..." +02. Learning in the Machine. Pierre Baldi_clip_219_1972.929_1987.4499999999998.wav," time the input. Let's call P the product of all these weights. Obviously you're trying to learn what's the right combination of weights, so you're adjusting a line. And very simple problem." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_78_709.589_721.44.wav," on graphical models and although it was not very known in the machine learning community at the time, and Les Valiant had written his paper on the theory of the learnable." +TheQuarksOfAttention1825000-1850000.wav," to do with language and I'm working now in a few problems in physics as well as in chemistry. I'm not, I don't have the time to go through these in detail but just give you the idea. And you see for instance in chemistry you want to predict chemical reactions so you have something like A plus B gives C plus V right. The reactants give some products A plus B gives" +TheQuarksOfAttention1500000-1525000.wav," add them together, right? So computing a dot product is an operation that naturally requires multiplying the outputs of two neurons or a bunch of neurons in a one-to-one fashion, right? So that's where attention mechanisms happens. As I told you, you can do it without adding anything to the standard model, but as I will show you..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_308_2816.52_2827.5299999999997.wav, but this is the kind of architecture you can build for instance for secondary structure prediction so here's your protein structure you take a window and this is sort of a Bayesian view +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_296_2712.24_2724.119.wav," all kinds of benchmark data sets in image recognition at Google, for instance, in speech recognition, natural language processing, you name it. All the latest benchmarks on large data sets." +02. Learning in the Machine. Pierre Baldi_clip_129_1153.84_1164.88.wav," One important result that was obtained by Lily Krupp et al. was that if you put completely random weights on the way back, back propagation still works." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_152_1364.63_1377.53.wav," the most classical and simple case, which is the case where you are using a square deuclidean distance as your distortion measure and everything is linear. So A and B are matrices." +02. Learning in the Machine. Pierre Baldi_clip_136_1218.02_1227.98.wav, a physical system use the same kind of hardware in both directions so you may try to have non-linear neurons in the learning channel. +02. Learning in the Machine. Pierre Baldi_clip_187_1687.39_1697.2600000000002.wav," performance, there will not be a complete collapse. So those are simulation results. Can we prove anything? Well, we can start with very simple networks." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_333_3032.97_3044.19.wav," prediction, the first two methods that got the best scores are both deep architectures. So that's another example of a recent success." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_215_1972.6_1983.3999999999999.wav," as soon as the number of clusters is large, scales with the data. And so the question is, can we use that to prove that clustering on the hypercube is a..." +TheQuarksOfAttention1325000-1350000.wav," blocks as roughly the architecture that is described here, which have been tried to lay out as a neural network. And the idea is this, you have inputs in this block, which you should think about as vectors. For instance, in the first layer, these vectors would be representing the words in the incoming sequence, using something like a word to vector." +02. Learning in the Machine. Pierre Baldi_clip_263_2445.4_2458.3300000000004.wav," I see maybe a little bit relationships, you know, random weights that convey information back to maybe human creativity where maybe you need to make an error to find a good solution." +02. Learning in the Machine. Pierre Baldi_clip_127_1136.53_1148.2.wav," the distinct case. But for any physical system, you can think about these different possibilities and what happens with learning, with rates, et cetera." +02. Learning in the Machine. Pierre Baldi_clip_116_1040.96_1050.59.wav," which can be much slower, could be hours, could be days, and could perhaps use the same pathways, but also possibly completely different pathways." +02. Learning in the Machine. Pierre Baldi_clip_220_1980.909_1994.49.wav, are adjusting a line and very simple problem it's even convex but each one of these little weights it's applying its own learning rule based on this random rule. +02. Learning in the Machine. Pierre Baldi_clip_156_1398.91_1409.9199999999998.wav," back propagation, random back propagation, this is without the derivatives, etc. You can see that they all converge at different speeds, but they all converge. If you remove the derivatives," +02. Learning in the Machine. Pierre Baldi_clip_221_1992.09_2001.669.wav, learning rule based on this random feedback weights CL. These weights are fixed but completely random. So if you write the differential equation +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_269_2472.18_2482.89.wav," So it's doing online training, stochastic gradient descent on the ensemble of all possible networks. Now why is this true or even plausible? Let me try to show you." +TheQuarksOfAttention550000-575000.wav," When you're trying to produce a word at position T in the output, you are looking at the words in the input but with some kind of waiting scheme where certain words are more important than others. Okay. Of course, when you're trying to produce the word journée which means day in French, the word day in English is the most important." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_375_3431.4_3443.4900000000002.wav, data to do the test and it's still very far I mean we got the best result of the CASP experiment but it's still very far from being very accurate so +02. Learning in the Machine. Pierre Baldi_clip_264_2454.58_2465.29.wav," make an error to find a good solution. Yeah, so I haven't tried to do an ensemble of back propagations, but we have done dropout on the way back, which is a little." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_342_3110.1_3120.75.wav," And the brain, which of course uses deep learning for all kinds of things, from perception all the way to skills like mathematics, learning how to..." +02. Learning in the Machine. Pierre Baldi_clip_124_1110.7_1121.71.wav, channel that has the same architecture as the forward but is completely separate but with the same architecture and then in my opinion the most plausible one is that you have +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_359_3283.05_3293.52.wav," as 100 amino acid, it's going to be 100 by 100. If it has 400 amino acid, it's 400 by 400. So it's variable size input and output. So it's very different in that." +02. Learning in the Machine. Pierre Baldi_clip_115_1033.55_1043.6599999999999.wav," on the scale of tens to a hundred milliseconds. Here we're talking about deep learning feedback, the feedback for learning which can be much slower, could be hours" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_199_1814.999_1828.309.wav, of vectors in the training set. The training set is a smaller set and so depending how you do it you're going to get generalization effect and you can study them in this system. It's very interesting for that. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_173_1562.07_1577.0.wav, it's a completely different story you mean here when you stack them? you're just +TheQuarksOfAttention425000-450000.wav," And it's important to keep in mind that the standard model, it's well known that the standard model has universal approximation properties. In the sense that for instance, every Boolean function is in the standard model. We're using linear threshold gates and every continuous function over a compact set, real valued function over a compact set can be approximated within EPS." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_267_2454.69_2465.04.wav," So this is a cheap way of training all the possible sub-networks of your network. Imagine you have the ensemble of all possible sub-networks, which is extremely simple." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_87_791.25_804.9300000000001.wav," the output of this neuron, and a postsynaptic term, which is the back-propagated error that comes from the output layer. And that's a term that is not local, not Hebbian, and is problematic because of." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_258_2372.84_2384.25.wav," that was introduced again by Hinton's group a few months ago. It's called Dropout. You take a neural network during training, and then with probability 0.5, you delete." +02. Learning in the Machine. Pierre Baldi_clip_35_317.24_326.69.wav," where you do dropout also at production time. And I think maybe you may gain a very small amount in accuracy by doing that. Nobody has done that, but it's possible." +TheQuarksOfAttention1550000-1575000.wav," and remember the intuitive picture I had for the translation from English to French, this is where it comes. You have a bunch of weights that are applied to these connections where maybe some V is enhanced and some Vs are suppressed by these weights here. And so you have multiplication of synaptic weights by the output of these neurons, which is the synaptic gaining mechanism, right?" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_282_2585.03_2594.69.wav," mean, if you want, of these different networks. So here is the different networks with some probability p, which can be produced by this Bernoulli..." +TheQuarksOfAttention1875000-1900000.wav," problems in physics, I'm going to give you just two examples very quickly. One is in the problems that come from collider physics of the large Hadron collider, for instance, where you are colliding protons at very high speeds close to the speed of light. And you get a shower of particle that is produced around the" +02. Learning in the Machine. Pierre Baldi_clip_16_152.33_162.56.wav, that you are a neuron or try to think you are a synapse or an axon and ask yourself how would the world around you look like. So that's what we're going to do. +02. Learning in the Machine. Pierre Baldi_clip_89_792.38_805.9100000000001.wav," This backpropagated error starts at the top of the network, depends on target minus output, and then gets multiplied by all the weights in the reverse direction." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_277_2540.12_2552.75.wav," can see exactly what is going on is that you're computing this expectation, this average over all possible network is indeed computed by this expectation. But why should any..." +02. Learning in the Machine. Pierre Baldi_clip_107_962.18_972.23.wav," the brain, if you think that supervised learning is sort of a reasonable approximation to some form of biological learning, what I'm telling you is that there has to be a channel." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_303_2774.99_2785.2000000000003.wav," protein sequence or the position of the beta sheets or beta strands, these arrows that you see here, coils, that's called secondary structure." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_372_3401.55_3412.6099999999997.wav," to give you a sort of ballpark number. People are doing image recognition today with one billion parameters at Google. So the range, the size of the model has definitely gone up." +TheQuarksOfAttention2625000-2650000.wav," polynomial threshold function, where you're taking a polynomial of degree D and then thresholding it to plus one or minus one, for instance, the upper bound there and D plus one over D factorial, D is the degree of the polynomial. This upper bound was actually my PhD thesis in the 80s. There was a lower bound derived by Sachs." +02. Learning in the Machine. Pierre Baldi_clip_123_1101.37_1112.5.wav, have pointed out it's it's very unlikely that you have exact weights in the opposite direction right. You could have a twin situation where you have a deep learning channel that has the same architecture +02. Learning in the Machine. Pierre Baldi_clip_194_1754.049_1765.4499999999998.wav, trajectories tend to diverge from those points but they will converge on some other points on those hyperbolas. So for that very simple system you can understand what happens. +02. Learning in the Machine. Pierre Baldi_clip_49_441.44_454.64000000000004.wav," a few algorithms. So if we put ourselves in the shoes, imagine that you are a synapse, the important thing I want to impress on you is that to understand" +TheQuarksOfAttention2000000-2025000.wav," representing for instance, the momentum of the particles, vectors typically, let's say of dimension four. So at the level of the observation, you may get a bunch of vector of length four, ideally it should be six, but very often you have more than that because you have other things, you have garbage, you have noise, whatever. So the input may look." +02. Learning in the Machine. Pierre Baldi_clip_159_1425.1_1436.71.wav," and on the deep learning channel using the same rule, product of presynaptic time, postsynaptic error, if you want, so to speak. Training set, test set." +02. Learning in the Machine. Pierre Baldi_clip_274_2561.869_2572.369.wav," give some example where it fails. For instance, if you don't have, if on the learning channel, you completely forget the derivatives, right? You put random matrix." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_92_836.16_847.8399999999999.wav," by zero essentially, very rapidly you run into machine precision problems and that's why learning cannot propagate, the gradient doesn't propagate very deeply into a multi-layer architecture." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_330_3005.37_3016.9199999999996.wav," I've never seen a contact map. This is the recursive approach we take and I don't have time to go into details, but to make a long story short, at the last CASP experiment, this is a..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_319_2910.39_2921.5800000000004.wav," using that, but of course the difficult problem is how do you go through 3D structure, right? And you have to think about this problem because the structure of the protein is invariant to rotation." +02. Learning in the Machine. Pierre Baldi_clip_74_662.66_675.64.wav," these rules in a deep network. So here you have a deep feed-forward network and imagine that you're using local rules in the first layer, in the second layer, etc. all the way to the top layer." +TheQuarksOfAttention225000-250000.wav," been progress, but it's a very complex biological phenomenon. So what we're going to do instead is to study attention within artificial neural networks, which is deep learning. And most of all, I'm going to focus on what should be the fundamental building blocks of attention, regardless of less" +TheQuarksOfAttention350000-375000.wav," the basic model for artificial neural networks, where an artificial neural network is a network of very simple computing devices, which go back to McCulloch and Pitts. Very simple model neurons, if you want, where a neuron is a computing device that operates by first taking the dot product of the incoming data." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_351_3194.329_3207.319.wav, your memories and store your telephone number or other things. In addition there are chemical modifications that are applied to the DNA double helix itself which are +02. Learning in the Machine. Pierre Baldi_clip_242_2187.319_2198.2099999999996.wav, information that is required to enable learning in deep synapses and in some cases we can build a mathematical theory but ultimately this leads this area +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_266_2446.38_2457.12.wav, statistics and other things that using ensembles training many many models is a good idea in general to have robust prediction So this is a cheap way of training all the +02. Learning in the Machine. Pierre Baldi_clip_93_829.64_840.83.wav," because this term depends on the targets. If you do this local learning in feedforward mode, this Abyan learning applied layer by layer, you see immediately that the deep layer will never depend on the target." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_157_1408.07_1418.42.wav," If you fix A, it becomes convex in B and vice versa. And so that's how you get your equations for the critical points or for the solutions and how you solve the linear." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_5_48.09_60.09.wav," for this presentation. I'm going to tell you very briefly what the basic problem is, and then go a little bit into an overview of the history of the problem. I don't plan to be exhaustive. I don't plan to be very long." +TheQuarksOfAttention800000-825000.wav," one to one, right? But let's imagine you have three variable types, three types of variables, activation outputs and synaptic weights. I'm going to try to classify all possible signals, whatever attention signal, whatever they are, according to the origin of the signal. So when you have attention, you have an attention signal that is generated somewhere." +02. Learning in the Machine. Pierre Baldi_clip_111_996.14_1007.8399999999999.wav," be separated. There is one type of feedback that is relatively fast that may occur, let's say in biological neurons on a scale of 10 to 100 milliseconds." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_341_3102.42_3112.5899999999997.wav, development interaction with the world to build extremely sophisticated carbon based computing system like the brain which of course is using +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_140_1258.529_1269.629.wav, the output delta again I'll use L2 metrics and Hamming distance in a specific case but that's that's the general framework and so if you do that you'll see that +02. Learning in the Machine. Pierre Baldi_clip_209_1884.28_1896.61.wav," the question of whether you can bound the number of limit cycles of such a system. And that question is completely unsolved. Steve Smale wrote a paper 15 years ago, the new version of Hilbert's problem." +02. Learning in the Machine. Pierre Baldi_clip_30_274.64_285.44.wav," come up with the idea that neurons are quite faulty, maybe they don't work 50% of the time, so let's do that during learning and that's exactly what dropout does. You remove 50% or some other..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_310_2835.24_2845.23.wav," of alpha helix, beta strand, or coil is a function of the input window, what's in the input window, and then on the hidden values that are on the backward chain." +02. Learning in the Machine. Pierre Baldi_clip_37_333.199_345.08.wav, rather than doing the pseudo quick average that you get by assuming that all the neurons are working properly. So that's dropout. +02. Learning in the Machine. Pierre Baldi_clip_243_2195.839_2227.97.wav," but ultimately this leads, this area leads to systems of polynomial differential equations which are quite difficult to solve. Thank you. Other questions? Hi. I'm very interested in that basically you showed that this robustness is there." +02. Learning in the Machine. Pierre Baldi_clip_63_563.54_573.89.wav," this is very reasonable. Now, if you are, let's say you have a feedforward network, you are in the output layer, then you may have targets. So maybe the targets could also be considered." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_94_852.92_869.15.wav," a layer, it worked nicely there, and that's what you could do with the computers at the time. But as soon as you went to deeper architecture, it was impossible to use gradient descent. Yes? A little illuminating over this comment by Minsky and Capra." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_270_2480.49_2490.63.wav, or even plausible. Let me try to show you that in a more mathematical way. And what happens if you use different values of p? What if you apply dropouts to +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_332_3023.99_3035.67.wav," crystallographic methods, NMR methods in the last few months and there is different categories. This is the contact map prediction, residue, residue, contact prediction. The first two methods" +TheQuarksOfAttention2175000-2200000.wav," end of the spectrum, which is dealing with the neutron stars, where you have, you know, mathematical models of the universe, which in this drawing have two parameters, let's say, so you have the equation of states with two parameters or four parameters, whatever. And then from the theory of neutron star or nuclear theory, you can derive." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_61_558.069_568.5690000000001.wav," which is nothing else than gradient descent, which generalize the perceptron learning rule, which all these rules, they sort of look abyant because to modify the way" +02. Learning in the Machine. Pierre Baldi_clip_262_2436.91_2448.4300000000003.wav, whether these would have potentially a better performance than say an average of simply back propagated neural networks. I see maybe a little bit relationships +02. Learning in the Machine. Pierre Baldi_clip_101_903.2_917.12.wav," the targets all the way down to the deep weights. There is no other way, otherwise you cannot solve those critical equations and have the hidden weights depend on the target." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_240_2211.599_2224.1499999999996.wav, quite nicely and we've done a fair number of experiments. This is another one. So the deep targets algorithm is another possible approach for training deep architectures without doing any gradient. +02. Learning in the Machine. Pierre Baldi_clip_267_2489.42_2499.71.wav," ad esempio, computa posteriori distribuzione, divido l'input, computa posteriori distribuzione, divido il'obieto, e poi provociamo divido le due distribuzioni." +02. Learning in the Machine. Pierre Baldi_clip_172_1549.78_1560.6399999999999.wav," of information that is needed. From the critical equation, you get the impression that you need to transmit the targets, the output, all the weights above, all the weights below, and all the..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_10_93.21_105.0.wav," to do a difficult task. And when trying to do a difficult task, this system never does them in a single step. It always requires a number of steps." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_27_244.8_255.66.wav," layer architecture of the cortex, a lot of these fundamental anatomical ideas were in place. And of course, Hodgkin and Astley had studied actually the anatomy of the cortex." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_17_154.28_165.44.wav," there is not a precise answer to that. The short answer is more than one layer. If you think about vision in the human visual system, we can recognize..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_80_727.83_739.17.wav," shows that machine learning has come a long way over the last 30 years. But in the 80s, it was the word machine learning actually didn't really exist. But the group that had the greatest" +02. Learning in the Machine. Pierre Baldi_clip_246_2243.39_2253.86.wav, the top curve is back propagation so this may be omnis. So in 20 epoch back propagation is essentially a hundred percent and skipped or random +02. Learning in the Machine. Pierre Baldi_clip_197_1780.6_1790.679.wav," in the propagation fraction, it's essentially equivalent. And if you write the learning equation for the matrices A, you get essentially this thing, because it's a." +02. Learning in the Machine. Pierre Baldi_clip_250_2300.09_2315.15.wav," we can get some scaling there. But I don't expect that there is any fundamental difference. Okay, thank you. So my first question I guess is answered already." +02. Learning in the Machine. Pierre Baldi_clip_103_921.74_933.02.wav," other things, all the way from, let's say, the output back to the deep weights. In a physical system, in your digital simulation fantasy, you don't worry." +02. Learning in the Machine. Pierre Baldi_clip_79_709.22_720.3199999999999.wav," using HEB's rule, some local learning rule. HEB is a special case of local learning. Well, no one has ever been able to make this work, as far as I know." +02. Learning in the Machine. Pierre Baldi_clip_163_1463.62_1474.6599999999999.wav," as a parameter k that allows you to adjust the complexity of the data. So if k equals 1, this is your data. k equals 2, it's like this, et cetera. So as k grows." +02. Learning in the Machine. Pierre Baldi_clip_176_1583.23_1594.03.wav, the weights below is subsumed by the activity of the presynaptic neurons. This by the way suggests that it should be the same for all the weights above. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_322_2937.21_2949.7200000000003.wav," map is a matrix, symmetric matrix, very sparse of 0 and 1's. You put a 1 here if the i and j elements are close to each other in 3D. So if you do it" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_2_9.75_21.0.wav, of Computer Science at UC Irvine. He's done a lot of work in machine learning and in the interface between machine learning and the life science. +02. Learning in the Machine. Pierre Baldi_clip_266_2480.63_2492.21.wav," So you can use, for example, message passing to train the layers of network, or more generally, you can use variation on inference. For example, you compute a posterior data." +02. Learning in the Machine. Pierre Baldi_clip_137_1225.309_1237.669.wav, the learning channel. You like to use dropout on the forward channel. Why not use dropout on the backward channel? You like sparse matrices? +02. Learning in the Machine. Pierre Baldi_clip_105_939.31_952.73.wav, what kind of information does it carry or what is the minimal amount of information that it has to carry and what is the rate of the channel etc. All classical Shannon theory. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_211_1933.48_1948.03.wav," try this alternate optimization problem and see how well it does. And on real data it does quite well, but you can show that the problem isn't incomplete. The optimization problem is" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_260_2393.82_2403.7799999999997.wav," you delete another set of neurons randomly, and you train the weights. And you transfer the weights at each epoch. You do weight sharing. The weights are transferred from one case to the other." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_48_439.31_452.69.wav," do. So the first person that wrote about this fundamental problem and came up with some ideas is of course Hebb, who was a psychologist and wrote a book" +TheQuarksOfAttention2900000-2925000.wav," Both output gating and synaptic gating are the fundamental building blocks of the transformer architectures, which have been very useful for NLP problems. But I've shown you that because they have this permutation invariance property, they're also very good for other kinds of problems, for instance, in physics or of chemistry. And then I've tried to give you a sense of how you can." +TheQuarksOfAttention2425000-2450000.wav, you really want to know is what are the functions that are inside this ball etc and try to characterize them which of course is a very complex mathematical problem for say a deep architecture nobody's able to do that this very very efficiently but still the reason why the log base two of the volume or the number of function is particularly important in the in the in in +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_6_57.57_68.7.wav," I don't plan to be exhaustive, I don't claim to be exhaustive, but I'll try to connect a few important dots, starting from the 1950s up to today, and then moving to the present." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_288_2639.07_2650.77.wav," same thing as taking the sigmoid and applying it to the expectation of the sum which is linear. Right? So that's an exact inequality. Furthermore, if you take" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_208_1905.97_1917.25.wav," the entire cell that is around one center should be mapped to that center in the layer and this is why the system is doing clustering. It's grouping all the vectors, all the vectors that are centered" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_43_396.98_408.47.wav," this little synapse, which is completely blind, only recognizes its immediate physical, chemical environment, how can it adjust itself so that you" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_188_1706.45_1717.489.wav, right? So that means that I give you a hidden vector here and you have to tell me what should be the output. That's what it means to determine A and it can be determined by the output. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_120_1080.57_1093.09.wav," with cell phones. It is true at some levels, they don't have GPS, they don't have Facebook, etc., but at some other level, they are fundamental for understanding processing in cell phones or computers. I think it's a little bit" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_287_2628.47_2641.109.wav," that you can prove is that the normalized weighted geometric average over all possible networks is exactly equal, is exactly the same thing as taking the sigmoid." +TheQuarksOfAttention2200000-2225000.wav," a curve, depending on where you are in this space, you obtain a curve that tells you that in the universe, all the neutron star have to be on this curve relating mass and radius, right? So for each point in this space, you get a curve in the mass radius space that corresponds to the universe you live in. Of course, I'm describing things in the form." +02. Learning in the Machine. Pierre Baldi_clip_34_309.56_319.55.wav," by the probabilities of dropping and that's it. And so that maybe opens the door for having a better form of dropout, where you do dropout also at production." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_271_2488.65_2499.2599999999998.wav," be, what if you apply dropouts to connections rather than units? You delete connections rather than deleting neurons, if you want. Why is it convergence, etc.?" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_219_2008.59_2024.4.wav," I'm changing the first four bits, each step is one of the four bits, and then when you move vertically, you're changing one of the three bits. And you can see that the L1 distance in the lattice goes exactly onto the half-step." +02. Learning in the Machine. Pierre Baldi_clip_31_282.229_295.21999999999997.wav," part does. You remove 50% or some other fraction of your neurons during learning, you adjust the synapses and then another group of neurons is removed etc." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_96_873.2_885.3199999999999.wav," It's first the strange way of saying that there is no reason to believe X, which is not equivalent to saying there is reason not to believe X." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_307_2808.63_2818.2.wav," coordinates of all the chains in the complex. So there's all kinds of sub-problems within protein structure, but this is the kind of architecture you can use." +TheQuarksOfAttention1775000-1800000.wav," logarithm of everything. Then here you add the logarithms. So you would add the logarithm of u1 with the logarithm of v1 to get these things. Then you would have a neuron with an exponential transfer function that would give you back u1 v1. And then you would add everything at the top to get the dot product, right? So you see you have a circuit with, say, one, two, three layers or four." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_259_2384.25_2395.95.wav," you delete neurons in the network. And you train, you take an example, you train the corresponding weights, and then you do it again. With probability zero five, you delete another set of neuron random." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_207_1895.2_1908.13.wav," It's obviously A of H1. It's gonna be H1, right? That's the natural thing to do. So the entire Voronoi space, so the entire cell that is around one center." +02. Learning in the Machine. Pierre Baldi_clip_170_1527.22_1542.85.wav," be doing very well, but again, tweaking learning rate, et cetera, you can get even this one after a while to look exactly like this. So now I want to tell you about what needs to be communicated." +TheQuarksOfAttention1750000-1775000.wav," as I told you, you can do dot products within the standard model, but this is the circuit that you need in the SM, in the standard model, if you wanted to do the dot product between u1, u2, u3, let's say, and the vector v of v1, v2, v3, you have to be able to do these kinds of things where you take the logarithm of u1 and etc. In this first layer, you take the" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_234_2153.079_2168.02.wav, which is another way that doesn't require propagation of gradients. This requires only forward propagations and keeping track of which sample in this layer gives a sample in that layer. This is an example. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_36_327.27_339.47.wav, place to think about storing this information is in the synapses which are the points of contact between the neurons. So already at that time people have made the hypothesis that learning +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_346_3149.089_3158.8999999999996.wav," If you think that genomes have nothing to do with learning in the brain, you better look at that more carefully because we're finding more and more that..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_371_3393.3_3403.98.wav," one hidden layer and one input layer. So we end up with models that are from 10,000 to 100,000 parameters to give you a sort of ballpark number." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_298_2729.13_2740.44.wav," one contribution, one data set on which we worked is in protein structure prediction and just to give you a flavor of the type of architecture we used there" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_57_523.839_535.769.wav," strong learning algorithms. So again, here is this very simple neuron model with a threshold gate and he found a very simple, if you have input-output training data, for instance classification of a..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_180_1633.13_1643.6899999999998.wav," more mathematical ways. And up to recently, there was no such solution until we started looking at the." +02. Learning in the Machine. Pierre Baldi_clip_278_2597.72_2608.47.wav," more finicky, you know, they require more hyper parameter tuning, but... Did you try just adapting the last layer? I mean, there's this echo state idea. If you adapt only the last layer on a difficult..." +TheQuarksOfAttention1700000-1725000.wav," into your architecture. All right. So here you see just the dot product mechanisms. You see a bunch of neurons. The attending neurons produce these output V1, V2, VN. These are the attended neurons with output X1, X2, XN. If I allow this new multiplication of V1 with X1, V2 with X2," +TheQuarksOfAttention1125000-1150000.wav," you have synaptic attention, where again, the output of some neuron can be used to multiply now the synapses of some other neurons. And this is very much in the framework in the, you know, language of electrical engineering, it's really gating, right? It's gating the output or gating the synaptic weights of other neurons. I'm going to show them in sort of enlarging things." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_225_2067.33_2079.27.wav," look at it is can you get targets for the weights in this layer? Can you tell this layer what the activity here should be? What is the right thing to do? Because if you give me targets, you have" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_268_2463.18_2474.3999999999996.wav," possible subnetwork which is extremely large and what this system is doing is picking one at random, training it and then picking another one at random so it's doing online training." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_204_1865.19_1879.72.wav," at the tessellation, if you want, of the Boolean hypercube that is created by this output. That is, I look at all the binary vectors that are closest to this output for the Hamming distance, and all the ones" +TheQuarksOfAttention2250000-2275000.wav," in the X-ray channels spectrum for the neutron stars. So of course, in reality, we're going in the reverse. We are observing, we have data about some neutron star, noisy data about neutron star in the universe. And you want to go in the reverse direction to try to see where in this parameter space is our universe." +02. Learning in the Machine. Pierre Baldi_clip_212_1912.9_1923.49.wav, of a very deep chain of units that are all linear. I'll show you this at the very end. If you have a system with one unit and units in the hidden layer then one +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_194_1771.32_1783.889.wav," these three vectors. It turns out it's the majority. You can show that it's the majority. So it's the vector that has a one in the first component, a zero in the second component, etc." +TheQuarksOfAttention125000-150000.wav," you start focusing on it. And also you see here two other definitions, for instance, the concentration of awareness on some phenomenon to the exclusion of other stimuli. So broadly speaking, it's this idea that the brain somehow has this amazing ability to concentrate its computational power for." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_312_2850.45_2860.26.wav," take this and transform it to a deep neural network architecture by using essentially only three neural networks, one that computes the output probabilities as a function of" +02. Learning in the Machine. Pierre Baldi_clip_53_478.61_488.69.wav," the violin? Well, it's maybe a one meter away, which when you rescale by 10 to the 6, that's a thousand kilometers away, so maybe in Paris, right? Or Rome if you are trying." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_261_2401.95_2413.08.wav," are transferred from one case to the other. And you keep doing that until it stabilizes. And then at prediction time, the claim is you divide all the way." +02. Learning in the Machine. Pierre Baldi_clip_58_517.82_530.5400000000001.wav," So this leads immediately to the notion of local learning because Synapse, in order to learn whatever the learning rule is, it has to depend on local variables that are available at the..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_275_2523.53_2535.65.wav, the product is the product of the expectations and that indeed you get the expectation of the selector variable which if you're using 0.5 is going to be 0.5 if you're using you know 0.6 +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_209_1914.7_1928.5.wav," vectors, all the vectors that are sent to the same activity level in the hidden layer form a cluster of points and then they are mapped to the center of gravity of that cluster. So you can understand" +02. Learning in the Machine. Pierre Baldi_clip_134_1197.97_1208.2.wav," But not only that, you can ask all kinds of questions. On the backward path, typically you have a linear network. All the operations you do are matrix multiplication. You multiply maybe by." +TheQuarksOfAttention1975000-2000000.wav," see that whatever the meaning is for bq and b prime q prime, on one branch of the tree you have two q's which are interchangeable and you have on the other branch you have two symmetric q primes that are also interchangeable. Now the data that you observe, what these bq's etc are, in fact are vectors. So what you are observing are vectors." +TheQuarksOfAttention2475000-2500000.wav," information from the training set and using it to choose a function in the bowl, the function that does the best approximation right, you want to choose this from this red function that is the closest to your target function, h, which may or may not be inside the ball but that's not important. So, learning in some way it's all about extracting information from the data and pushing it to the goal." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_206_1885.96_1898.679.wav," by the images of these vectors. And now if you take an input, let's say an input which is gonna be inside this sphere, what should be its image in the hidden layer? It's obviously A of H1. It's gonna be H1." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_251_2315.48_2325.17.wav," be a little bit tuned to the task you're interested in, which in this case would be elephant recognition. And you can imagine making, so you have an arrow function here that has two terms, it has a function of two. And you can see that it's a function of two. And you can see that it's a function of two. And you can see that it's a function of two. And you can see that it's a function of two. And you can see that it's a function of two. And you can see that it's a function of two. And you can see that it's a function of two. And you can see that it's a function of two. And you can see that it's a function of two. And you can see that it's a function of two. And you can see that it's a function of two. And you can see that it's a function of two. And you can see that it's a function of two. And you can see that it's a function of two. And you can see that it's a function of two." +02. Learning in the Machine. Pierre Baldi_clip_211_1903.45_1916.23.wav," It's a little bit like p equal np. So these problems are very difficult. But in some restricted cases, we can solve them. For instance, if you have a long chain of a very deep chain of units that are." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_379_3493.24_3512.8.wav," no theory of how many layers is good as far as I know. It's all empirical and trying different numbers of layers. There are a few Boolean circuit, you know, results that show that certain function..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_9_83.78_96.39.wav," learning is essential for building intelligent systems, whether it's carbon based systems or silicon based systems, they all use learning to try to do difficult tasks." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_334_3040.53_3052.5.wav, example of a recent success. And we have built a suite of programs for predicting different properties of protein structures and 3D structures. They are all available on the internet. +02. Learning in the Machine. Pierre Baldi_clip_155_1390.27_1401.07.wav," of simulation, Omnist or CIFAR. So these are example of this is back propagation, this is skipped back propagation, skipped random back propagation, random back propagation." +02. Learning in the Machine. Pierre Baldi_clip_161_1442.19_1456.87.wav, experiment done with sparse random matrices with different level of sparsity etc. Same thing. Same thing on CIFAR. This is just to show you an interesting technique for some simulation that comes. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_18_163.79_174.2.wav," the human visual system, we can recognize images in about 200 milliseconds, and it takes about 5 milliseconds to traverse a synaptic cleft." +TheQuarksOfAttention325000-350000.wav," and then you can also multiply what you're interested in, enhance it by some other factor. So that's the sort of thinking or idea we're going to develop. Now we're going to do this in artificial neural networks, in particular in what I'm going to call the standard model. And what is the standard model? Well, if you attended my tutorial yesterday, the standard model is just..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_192_1752.72_1764.059.wav," think what should be the output. Once you map all these vectors onto this vector, the information about these vectors is lost. That's what the bottleneck does. So you have to produce a single vector here." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_229_2107.44_2117.55.wav," And now the question is, what should it do here in order to do well on the function? Well, we don't know. What we're going to do is sample. We're going to sample..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_55_504.879_518.889.wav," doesn't explain how you get organized behavior on a larger scale, but at least it gives some idea about a synapse to decide whether to strengthen itself or weaken itself." +TheQuarksOfAttention250000-275000.wav," whether it is say visual attention, auditory attention, or some other kind of attention. I think all these ideas, different types of attention at their core have a certain basic mechanisms that we're going to try to identify. In particular, when we say that it is at the exclusion of all others." +TheQuarksOfAttention900000-925000.wav," also going to look at additive interaction. Let's see what happens if we allow addition also to be one of the interaction, the two interaction mechanisms. And so if you look at all these possible cases, you get 18 cases, right? That you can study one by one and it's an interesting things, but already I'm going to shrink it down to six possible." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_166_1493.58_1507.05.wav, first P1 principal components of the data and then in the second stage I extract the top P principal component from that. So projection onto projections is where we are. +02. Learning in the Machine. Pierre Baldi_clip_9_81.23_93.86.wav," on computers. So how can we do this learning in the machine? Well, the solution was found a long time ago by Albert Einstein. If you walk a few hundred" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_274_2513.0_2524.82.wav," selecting neuron J in layer L. And if you compute the expectation of this output, you can see that all these terms being independent, the expectation of the product is the product of" +02. Learning in the Machine. Pierre Baldi_clip_210_1893.97_1906.48.wav," ago, the new version of Hilbert's problem for the 21st century, it's in there and basically no progress has been made on this question for many decades. It's a little bit like P equal NP." +TheQuarksOfAttention875000-900000.wav," Okay, and then you have to specify how the signal, the attending signal interacts with this target. And already in the introduction, I suggested that multiplication is likely to be a fundamental mechanism for attention. So we're going to look at multiplication, but in order to be complete, so systematic in some way," +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_233_2144.5_2155.7799999999997.wav, here that produce the best sample here and use this as the target for adjusting these weights. So that's what we call the deep targets algorithm which is another way that doesn't require +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_38_345.78_356.24.wav, complex ways that we still don't understand very well today. So that's a very nice model but if you start thinking about it you should see +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_314_2867.4_2878.38.wav," as a function of the vector ut and the vector bt plus 1, and one that computes the vector ft at time c as a function of ut and ft minus 1." +02. Learning in the Machine. Pierre Baldi_clip_229_2065.96_2077.7799999999997.wav," coefficient. So it is something that looks like this, right? And so it should start anywhere. Suppose you start here." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_352_3203.24_3216.2200000000003.wav," to the DNA double helix itself, which are called epigenetic modifications, throughout the life of a neuron, for instance during differentiation, and these chemical modifications are fairly stable." +02. Learning in the Machine. Pierre Baldi_clip_92_820.79_831.6800000000001.wav," these equations, you have one such equation for each weight, so you may have a billion equations, right? The solutions have to depend, for instance, on the targets, because this term depends on the target." +02. Learning in the Machine. Pierre Baldi_clip_85_759.47_769.16.wav, that this is just writing backpropagation equals zero. So you can do it with large batches or just the full training set. So it's. +02. Learning in the Machine. Pierre Baldi_clip_41_367.669_380.15.wav," the weight sharing assumption, but you initialize the weight sort of from the same, typically from this zero mean Gaussian with small standard deviation, you can get them to learn provided" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_16_146.75_157.88.wav," A question that comes up all the time is, how deep has the network to be in order to be deep learning? Well, there is not a precise answer to that." +02. Learning in the Machine. Pierre Baldi_clip_188_1695.37_1705.15.wav," We can start with very simple networks. This is a simple linear network, for instance, with two layers, in this case three layers. You have weights A and B on both sides." +02. Learning in the Machine. Pierre Baldi_clip_56_501.62_512.479.wav," in itself. And then it has no notion of music, of violin, etc. So how can it do that? This is really the deep learning problem when you think about it." +02. Learning in the Machine. Pierre Baldi_clip_180_1618.81_1630.78.wav," Then we skip the random back propagation. We see that we don't need all the derivatives of the layers above. You just need the derivative of the current layer. So basically, what it seems." +02. Learning in the Machine. Pierre Baldi_clip_7_63.98_74.18.wav," And by taking into account the physical constraints of the real world on the real system, I think we can get new insights on the foundation of religion." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_12_110.549_123.58999999999999.wav," functions, functions that have parameters between the different layers and you want to learn a certain input-output function from examples that are given to you. And that's a" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_113_1021.56_1031.88.wav, started getting interested in in kernel methods SVM etc and so neural network sort of disappeared for for 10 or 15 years and it was sort of a backlash +02. Learning in the Machine. Pierre Baldi_clip_146_1308.86_1320.5.wav, learning channel is very robust. That is most of these combinations they work or you can get them to work. They may be a little harder to get to work than plain back propagation but if +02. Learning in the Machine. Pierre Baldi_clip_195_1763.35_1773.49.wav," can understand what happens. But of course, you would like to understand more complex system. Even in the linear case, you could have a multi-layer linear network. All these are matrices." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_239_2202.43_2215.15.wav," this character recognition data set. You can see that gradient descent cannot do anything when you have 40 layers. The arrows stay flat, and this learns quite nicely, and we've done fair enough." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_243_2239.0_2250.0989999999997.wav," these autoencoders, they have no idea of the final task. They don't know if you want to recognize elephants or zebras, or maybe something completely different. So how do you know that" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_158_1418.42_1430.0600000000002.wav," autoencoders, it turns out that it has a very interesting landscape that looks like this, where the global optimum is principal component analysis or singular value decomposition, whichever way you want to put it." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_377_3459.65_3475.84.wav, in the deep architecture I see consistently improving performance because that's what the MNIST data says. It is not true in general. Usually you will see some increase at the beginning and then it will plateau or even start deteriorating. So it's not true that... +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_170_1531.86_1543.3799999999999.wav," GF2 is the field where everything is like normal numbers, but 1 plus 1 is equal to 0. So very good for accounting. Goldman Sachs likes GF2." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_58_532.899_543.7299999999999.wav," instance classification of a bit string or some kind of image, there is an algorithm and if things are linearly inseparable, the algorithm works very well." +02. Learning in the Machine. Pierre Baldi_clip_94_838.85_850.28.wav," immediately that the deep layer will never depend on the targets. And so you cannot learn such function. By the way, in this term, there is also information about all" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_223_2049.72_2061.4799999999996.wav," let me show you another possible algorithm for training deep architectures, which is not backpropagations to answer the question that was asked in the audience. Take a deep architecture, take some input out." +02. Learning in the Machine. Pierre Baldi_clip_121_1084.75_1094.74.wav, are sort of identical. You use the transpose of the forward weights in the reverse. This is sort of what you think when you're doing your digital fantasy. +02. Learning in the Machine. Pierre Baldi_clip_113_1012.64_1026.14.wav, a bottom-up sensory stream that meets a top-down expectation or modeling stream and together these two streams combine to stabilize your +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_354_3222.589_3233.599.wav," It could be, it is not impossible that when you are storing your telephone, ultimately there are chemical modifications that are very important for that storage that are happening" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_111_1004.459_1016.79.wav," unsupervised learning, but I'm learning to build somehow some kind of model or representation of the data in the hidden layer. In the 90s it was all about" +02. Learning in the Machine. Pierre Baldi_clip_140_1255.69_1268.09.wav, You adjust the weights in the forward channel by HEB. HEB and back propagation become essentially the same once you have the backward learning channel. But why not adopt also the weights in the forward channel? +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_238_2194.02_2204.98.wav," This is an example of a 14-layer network, so quite a deep network trained on the standard NIST dataset. This is a character recognition dataset." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_31_280.26_292.13899999999995.wav," introduced the idea of artificial neurons, those very simple neurons that take a weighted linear sum of their inputs and then use a threshold or a sigmoidal function to produce an output." +02. Learning in the Machine. Pierre Baldi_clip_135_1206.309_1219.76.wav, multiplication you multiply maybe by the derivatives etc. Why should the backward channel be linear and the forward path channel be nonlinear? Right? You may want in a physical system use the same kind +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_212_1946.049_1957.51.wav," The optimization problem in the Boolean case isn't incomplete. And just to give you a sense of how to do that, you have to, of course, do this reduction between incomplete problem." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_142_1276.169_1286.7.wav," You can do them over the complex numbers, real numbers, finite fields, etc. Every time you have a linear space and in the nonlinear space, of course, you have a" +TheQuarksOfAttention2100000-2125000.wav," decision on which one is Q and which one is Q prime and the same for the, for the, for the, for the B's. So plenty of permutations in these problems that are essential. And again, something that can be handled very well with, with transformers. There is different levels of symmetry. So you really have to go through the details of our architecture to see how we handle that." +02. Learning in the Machine. Pierre Baldi_clip_10_91.82_101.53999999999999.wav, Einstein. If you walk a few hundred meters from here there is Humboldt University and that's where Einstein spent some time. In fact if you walk across the street I recommend you go +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_97_881.09_892.3100000000001.wav," is reason not to believe X. And so what I'm curious about is, has anybody responded to their challenge in the sense of showing that without that propagation," +TheQuarksOfAttention575000-600000.wav," one in the sentence and then the other ones have less importance. In this case, you know, it's the same position, it's the last word in the sentence, but of course, as you change languages or sentence types, you don't have a one-to-one correspondence between the location of words in the input sequence, of course, and the same position in the output sequence." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_60_550.18_560.8.wav," general by using, instead of having a threshold gate, by putting a sigmoidal function here and they found a more general learning rule which is nothing else than gradient descent." +TheQuarksOfAttention2725000-2750000.wav," So it's like doing an edge. If instead you're using a minus one, one, four, my zone, if you have minus minus or plus plus, you get a plus. And if you have a mixed minus plus or plus minus, you get a minus. So it's more like an X or, or, or the negation of annex. So, so there is a little different there, but it creates two nice, interesting problems. You know that for the first, for the blue," +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_257_2364.35_2374.8799999999997.wav, supervised learning in different ways and using multitask approach. Let me show you one last interesting algorithm that was introduced again by Hinton. +02. Learning in the Machine. Pierre Baldi_clip_131_1169.74_1181.38.wav," weight on the deep learning channel, you can have completely random matrices. And if you do the simulation, you see that it works almost as well as plain." +TheQuarksOfAttention1450000-1475000.wav," weights like you do in a neural network. But these weights, again, are modulated by this softmax operation coming from here. So you see where the basic mechanisms come in. First of all, you have to compute the dot products. And when you want to compute, I hope it's in my next slide. Oops, let's see. Well, in order to compute the dot products, you have to compute the dot products." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_220_2020.86_2031.0.wav," the lattice goes exactly onto the Hamming distance on the hypercube through this transformation. So when you apply this transformation, if you could do" +02. Learning in the Machine. Pierre Baldi_clip_254_2356.87_2369.65.wav," So is there some, do I get some speed improvements if I don't? If you use random weights, no, you'll be slower. You don't improve your speed. You mean your, your speed of conversion in terms of." +02. Learning in the Machine. Pierre Baldi_clip_82_734.54_745.01.wav," able to learn interesting functions. And the reason is actually quite simple. If you want to be able to learn things, a reasonable condition for that is to say." +02. Learning in the Machine. Pierre Baldi_clip_257_2383.03_2394.25.wav," by random matrices. So if you do standard back propagation with random weights, the number of calculation is the same. It's just that you're using random weights instead of using, you know." +02. Learning in the Machine. Pierre Baldi_clip_168_1511.17_1521.79.wav, you see that at low complexity it matches the data and back propagation very well. At high complexity at the same you know training at the same epoch it's +02. Learning in the Machine. Pierre Baldi_clip_258_2390.47_2404.0.wav," using random weights instead of using the transpose of the forward matrices. And Pierre, have you studied what kind of randomness you should?" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_221_2029.41_2038.95.wav," this transformation, if you could do the clustering on the hypercube, you would be able to solve the clustering problem for the Manhattan distance on the 2D lattice, and so the problem is then solved." +02. Learning in the Machine. Pierre Baldi_clip_54_485.96_496.22.wav," be in Paris, right, or Rome if you are learning how to ride a bicycle. So you have this synapse which is, you know, embedded in these deep circuits in the brain." +02. Learning in the Machine. Pierre Baldi_clip_84_751.49_760.94.wav," where the gradient is zero. So you write the equation of the gradient is equal to zero. Those of you who know these things well, of course, they understand that this is just writing." +02. Learning in the Machine. Pierre Baldi_clip_73_655.34_666.23.wav," It's interesting to know that and which rules converge, et cetera. But really, what you care about is learning by combining these rules in a deep network." +TheQuarksOfAttention1275000-1300000.wav," model. And this is exactly what happens in transformers. So that's what I'm going to do now. I'm going to move to transformers. As I told you, this is the sort of crème de la crème of attention architectures currently. And I'm going to unpack them and show you how is the layout from a neural network point of view and show you where attention." +TheQuarksOfAttention1225000-1250000.wav," of the attending neurons, right? Note that when you reach the neuron k, what gets there is the same thing. It's the same thing in both cases, this new quadratic terms, but of course this mechanism is different. And if you look at what happens on the different axons emanating from neuron i, or at least a different connection, I should say, emanating from neuron i," +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_374_3421.77_3435.45.wav," Well, we do cross-validation. So we train on, say, 2,000 protein structures from the PDB, sort of 2,000, 4,000, and then we have holdout data sets, or we use CAS data to do the test. And it's." +02. Learning in the Machine. Pierre Baldi_clip_272_2539.01_2551.96.wav," of information we can, you can actually measure in knots and you use that quantity of information to correct and update your layers. So it feels very much like what you're trying to do here. Yeah." +02. Learning in the Machine. Pierre Baldi_clip_142_1274.779_1286.149.wav," channels, in the forward channel and the deep learning channel. And if you look at this architecture, you can also have skipped connections like this. In fact, you can have an architecture that has only skipped connections." +TheQuarksOfAttention150000-175000.wav," lack of a better word, we don't know exactly how it works, but to concentrate its resources on a particular stimulus in the sensory system, whether it's a visual system or visual stimulus or auditory stimulus, for instance, or also on some internal representation, on some thought. Obviously, if you're trying, let's say, to prove" +02. Learning in the Machine. Pierre Baldi_clip_8_71.3_85.49.wav, insights on the foundation of learning and occasionally even find algorithms that can improve deep learning on computers. So how can we do this learning? +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_51_467.27_482.349.wav, is correlation in the firing and that is what is used by the synapses somehow to adjust themselves. This is a very simple form of what today would be called the Hebbian learning rule. There are many other forms. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_232_2136.069_2146.299.wav," of this sample, because we have the targets. So we choose the best, and look where it came from here, what was the best sample here that produced the best sample here." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_155_1391.12_1402.28.wav," problem because everything is linear, this is L2 squared, so it should be convex etc. except that matrices of rank P is not a convex set. It's actually one." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_56_514.93_525.97.wav," or weaken itself. A few years later, Rosenblatt introduced the perceptron learning algorithm. So again, here is this very" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_53_488.439_499.089.wav, some idea about this very mysterious problem of how deep synapses could adjust themselves. This is a possible idea of how this could be solved. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_3_18.84_36.0.wav," and the life science, bioinformatics, chemoinformatics. He's won a number of awards and he's also a fellow of the ACM, AAAI, and IEEE. So, thank you." +TheQuarksOfAttention1400000-1425000.wav," Then here you will have the, what they call the attention mechanisms, which is just taking all possible pairwise dot products between all Q vectors and all K vectors, right? So if you have N words, if the sequence is length N, you are taking N squared dot products between all the Q and all the K vectors." +TheQuarksOfAttention1925000-1950000.wav," in any of the details of the physics. This is a case where at the end of the decay, you get in this fine mind diagram, you get six possibilities marked by BQQ and B prime QQ prime. This corresponds to matter and antimatter because" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_145_1301.669_1313.009.wav," class of autoencoders. The first one is group invariances, whether there are any invariances in the input that leave the problem unchanged. If you are using L2, you know, any rotation transformation." +02. Learning in the Machine. Pierre Baldi_clip_46_415.31_427.91.wav," together, what does that mean exactly? What is the relation between Abian learning and backpropagation? Is backpropagation Abian, for instance, a question that may seem somewhat..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_284_2601.56_2613.35.wav," of all the outputs weighted by the probability of the corresponding network. Now, this formula is a little bit more complicated. It's called the normalized geometric average." +02. Learning in the Machine. Pierre Baldi_clip_255_2366.47_2377.54.wav," I mean, your speed of conversion in terms of epochs... But I need to do less computation, right? I guess, because I don't need to compute the gradients." +TheQuarksOfAttention775000-800000.wav," there is three types of variables. You have the activation of the neurons, you have the output of the neurons and you have the synaptic weights. So you have S, O and W. That's the only variables that are used in this indescended model. You could even say that the activation and the output are redundant if the activation function is wrong." +02. Learning in the Machine. Pierre Baldi_clip_26_239.72_252.01899999999998.wav," There is no sense that the first beat is to the left of the second beat to the left of the third beat etc. That comes only from your visual system. In reality, this neuron has to learn the right way to learn the right beat." +TheQuarksOfAttention2150000-2175000.wav," because the existing methods are looking at all possible assignments of jets to those three structures. So they are very slow and transformers are actually much faster than the, some of the current approaches. So that's just to give you an idea without getting into the details. I'll show you another example at the completely, at the other." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_227_2086.2_2100.45.wav," right, or SVM type of optimization algorithm. So we know how to do shallow learning, perceptron algorithm is another shallow learning algorithm. The question is we need targets. So the question is how to give targets to..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_187_1697.539_1710.7389999999998.wav," optimize A and vice versa. And let's start with the easy part, which is we fix the D player, we fix B, let's try to optimize A, right? So that means that I give you" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_168_1511.67_1526.04.wav," linear case, when you do stacking you're just compressing the space onto smaller and smaller subspaces spanned by optimal eigenvectors." +TheQuarksOfAttention750000-775000.wav," mechanisms that they use are inside these neural networks. All right. So let's try to organize now the fundamental building block of attention mechanisms, whatever attention may be. And what I'm going to do to do in order to do that, I'm going to think in the following way, in the standard model that I described," +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_46_423.23_434.12.wav, the periphery either on the visual perception let's say or maybe on the motor side you can have some idea of what this the synapses are how it could get a signal for what to do but if the synapse +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_72_657.8_669.149.wav," But the fact is that the problem came back in the 80s, so that's really when machine learning started. And there were different groups in different places, not talking very much to each other." +02. Learning in the Machine. Pierre Baldi_clip_196_1771.45_1782.669.wav," network, all these are matrices, forward matrices, you have random matrices on the way back, whether you do it in the skip fashion as drawn here or in the propagation faction, it's essentially a loop." +02. Learning in the Machine. Pierre Baldi_clip_22_204.01_214.79.wav, etc. How does it compare to parity for instance? And if you're not used to this you may look at this and you may think that this is a fairly simple +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_316_2884.2_2895.57.wav," that the network here is the same as the network here, etc. That is, you do weight sharing in this forward chain and weight sharing in the backward chain and weight sharing in the output chain. So..." +TheQuarksOfAttention625000-650000.wav," a series of important publications on this topic. I've just listed a few of them here. I have no time to go through them. But the important thing is that the sort of pinnacle of this movement, of this trend in NLP, is what are called transformer architectures, which are widely used today, which have led to the" +02. Learning in the Machine. Pierre Baldi_clip_218_1964.08_1975.3600000000001.wav," neurons, everything is linear. If I give you an input it gets multiplied by a1, a2, al. So the output is a1, a2, al times the input, let's call p the product." +02. Learning in the Machine. Pierre Baldi_clip_109_979.7_990.38.wav," each one of these synapses. Otherwise, they cannot learn. And this is important also because it shows that." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_255_2348.3_2359.25.wav," give you a sense of all kinds of new ideas, fairly empirical, I admit that certainly, that are being used today to train these deep architectures in." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_81_737.19_747.96.wav, But the group that had the greatest practical influence and that took on the Minsky-Papert challenge is the PDP group at UCSD that was led by David Rubin. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_139_1250.969_1262.759.wav, a and b here that belong to certain classes and I want to be flexible for now on the classes and you have an overall distortion function in the output delta again I'll use L2 matrix +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_345_3138.74_3151.069.wav," that for analyzing data, including genomic data and protein data, and closing this loop in this very strange way. And if you think that genomes have nothing to do with the genetic" +02. Learning in the Machine. Pierre Baldi_clip_50_451.15_463.46.wav, impress on you is that to understand the world of the synapse which is such a small object you need to rescale things so that they become more more palatable to you. So I'm going to rescale things +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_138_1242.629_1252.8590000000002.wav, to understand them mathematically. So I'm going to define our encoder as being a circuit of this kind with functions a and b here that belong to circuit a. +02. Learning in the Machine. Pierre Baldi_clip_139_1243.88_1255.6000000000001.wav," What about these derivatives? Do you really need to multiply by the derivatives of the forward channel in the backward channel? Do you need all the derivatives, just the derivatives of the current layers?" +02. Learning in the Machine. Pierre Baldi_clip_228_2056.419_2069.1690000000003.wav," polynomial is of degree 2L minus 1, so it's an odd polynomial with an odd degree and a negative leading coefficient. So it is something" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_30_271.169_281.60999999999996.wav," built the first computer. By the way, von Neumann wrote a little book about the brain around that time. It's a very interesting book to read if you find it. And McCulloch and Pitts had already introduced the idea of artificial intelligence." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_64_582.1_592.42.wav, target what you should have gotten and your actual output. So all that is nice until Minsky and Pappert came along +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_62_566.41_577.3.wav," of look abiant because to modify the weights between neuron or perceptron i and j, you basically need the presynaptic intensity." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_122_1099.39_1110.82.wav, other papers came out which restarted interest and interest in neural networks and deep architectures and the paper was built using +02. Learning in the Machine. Pierre Baldi_clip_147_1318.13_1330.1589999999999.wav," than plain back propagation, but if you spend some time tweaking the learning rate, etc., you can get most of them to work. There is a couple of them that do not work. For instance, if you get rid" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_150_1346.57_1357.76.wav," actual algorithm that is suggested just by the shape of this circuit, which is, well, optimize A first, then B, then A, then B, and keep doing that, and see what happens." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_343_3117.84_3130.64.wav," skills like mathematics, learning how to do complex mathematics. This brain has been able, through deep learning, to develop silicon-based" +02. Learning in the Machine. Pierre Baldi_clip_44_395.93_408.409.wav," to go to the point of view from the point of view of synapses, which I think is even more interesting. And this is, among other things, is going to help us answer questions like what exactly..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_103_935.38_947.81.wav," as close as possible to the input. For instance, for L2 square norm or Hamming distance, that depends on the problem, but that's the basic idea of an autoencoder. Now when you look at this, it looks like this." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_224_2059.11_2070.929.wav," architecture, pick some input output targets, the question is how do you set the weights in these layers? One way to look at it is can you get targets for the" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_114_1028.549_1038.539.wav, or 15 years and there was a sort of backlash against neural network especially because in the 80s some people claimed they were good models of a +02. Learning in the Machine. Pierre Baldi_clip_234_2114.92_2127.94.wav," weights in the feedback channel. Although this could have a million layers, by magic this system will always converge to a correct solution." +02. Learning in the Machine. Pierre Baldi_clip_27_249.68_261.29.wav, this neuron has to learn the right permutation of all the n bits in order to solve this problem. And so it turns out it's a very hard problem. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_85_772.88_785.67.wav," neural metrics, but it was done in 1985. And when you look at the rule at the end of the day, if you take again a deep weight in the architecture and you want to change this weight, you get" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_109_987.36_997.259.wav," most important component, whatever the exact mathematics of the problem is, but that's what this way, this circuit is doing. And it's another way of..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_98_889.13_901.55.wav, that without that propagation these virtues don't convey to the multi-layer and it requires that propagation to make progress in this field. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_174_1574.539_1585.309.wav," back then. You're just, you're training first autoencoder, so it's projecting on a subspace of the P optimal eigenvectors. You're training..." +02. Learning in the Machine. Pierre Baldi_clip_252_2321.39_2333.75.wav, these data sets? What you see in the curves. Yeah. So back propagation may converge in 20 epochs. And one of the other variants may take 50 or 100 epochs. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_144_1293.57_1304.3690000000001.wav," When you do that, you begin to see that there are general properties that are important for autoencoders that you should study every time you look at a particular class of autoencoders. The first one is group-based. The first one is group-based." +02. Learning in the Machine. Pierre Baldi_clip_38_340.539_351.889.wav, So that's dropout. Other example of such thinking when you're looking at neurons would be for instance relaxing the weight sharing assumption. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_134_1204.45_1218.2089999999998.wav," the interest that we have in this deep learning problem. So I'm going to spend a few, if you want to try to understand this a little bit more mathematically, the first thing you have to do is to understand how to" +02. Learning in the Machine. Pierre Baldi_clip_232_2094.339_2105.2599999999998.wav, at minus infinity or your derivative is positive so you're going to move and end up here and the same thing here if you start here your derivative is negative so you're going to move to the left +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_19_170.09_182.29000000000002.wav," to traverse a synaptic cleft. So even in the rapid visual recognition, we're not dealing with millions of layers, something like 10, 20." +TheQuarksOfAttention1575000-1600000.wav," So in some sense, the transformer use both output gating to compute the dot products, the similarity. If you want, it can be viewed as a similarity if the vectors are normalized between all the Q, the query vectors and the key vectors. And then it uses synaptic gating to gate these connections and combine the value vectors in a dynamic." +02. Learning in the Machine. Pierre Baldi_clip_189_1702.57_1715.0500000000002.wav," layers. You have weights A and B on the forward channel, weights C in the deep reverse channel and you can write down the equations of such a system." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_286_2619.8_2631.4.wav," class here, again, taken over all possible metrics. So that's the normalized geometric average. And the theorem that you can prove is that the normalized" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_295_2702.31_2714.9700000000003.wav," Let me finish by giving you an example of an application. So in the past year, these deep architectures of one kind or the other have been able to improve all kinds of benchmark data sets in images." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_77_699.54_711.9300000000001.wav," many physicists into the field and that's when NIPS and Snowbird Conference were started, etc. Judah Pearl was starting to work on graphical models and although" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_203_1855.32_1869.539.wav," Now, suppose I fix A. So I fix the transformation A. It means that for every even vector here, I get an output. And I can look at the tessellation, if you want," +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_335_3050.73_3060.78.wav, all available on the internet. You can download them. You can submit a protein and get your prediction back via email. These are some references that +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_201_1834.83_1844.999.wav," the same because it will mean you have a target Y for this vector, for this vector, and for this vector, and so you now take the majority of the targets, you know, the vector that you have. And you can see that the target Y is now a positive Y. So, you know, you can see that the target Y is now a positive Y. So, you know, you can see that the target Y is now a positive Y. So, you know, you can see that the target Y is now a positive Y. So, you know, you can see that the target Y is now a positive Y. So, you know, you can see that the target Y is now a positive Y. So, you know, you can see that the target Y is now a positive Y. So, you know, you can see that the target Y is now a positive Y. So, you know, you can see that the target Y is now a positive Y. So, you know, you can see that the target Y is now a positive Y. So, you know, you can see that the target Y is now a positive Y." +02. Learning in the Machine. Pierre Baldi_clip_36_325.28_335.599.wav," that, nobody has done that, but it's probably a very small effect. It would require at production time to just average over a large number of networks rather than doing the pseudo-quick" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_241_2221.299_2232.309.wav, architectures without doing any gradient descent. Let me show you another set of ideas that are being used today for training deep architectures. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_179_1624.22_1636.3300000000002.wav, learning in other areas you're interested in nonlinear autoencoders and so the question is can we solve a nonlinear autoencoder in a precise more mathematical ways and up to recently +02. Learning in the Machine. Pierre Baldi_clip_192_1729.9_1741.6899999999998.wav," the right constant. And you can see in this phase space as all these points are attractors, all the arrows are converging. If you start here, you have a parabolic trajectory that ends up here. And here." +02. Learning in the Machine. Pierre Baldi_clip_174_1566.37_1578.7.wav," in fact, to send T minus O. You don't need to send T and O separately. You don't need all the weights below. In fact, the only thing you need is the activity of" +02. Learning in the Machine. Pierre Baldi_clip_130_1161.22_1172.44.wav," way back, back propagation still works, which is somewhat amazing. You don't need to have the transpose of the forward weight on the deep learning channel." +TheQuarksOfAttention2850000-2875000.wav," and other neurons. I don't have time to show you that, but we're going to post the technical report on archive in a few days, it's almost ready. And if you're interested, you can email me or you will see in our archive in a few days. So very rapidly, I'm out of time. So my conclusion, I've tried to show you that it's possible to produce a taxonomy of," +02. Learning in the Machine. Pierre Baldi_clip_110_987.91_998.9.wav, important also because it shows that the notion of feedback that you know the word feedback is actually two completely different meanings that have to be separated. +TheQuarksOfAttention2350000-2375000.wav," that be computed by a neuron or by an architecture, a neural architecture, you define the capacity as being the volume, the log base two of the volume of all the functions that can be computed by your architecture, right? So if you're working with continuous neurons, you have, of course, to define." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_50_458.6_469.34.wav, sentence which is sometimes summarized by neurons that wire together fire together. This idea that there is correlation in the in the firing +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_357_3258.39_3275.16.wav," How large a network of neurons were you using and how does that map onto the physical structure? So there is, let's talk about contact maps which is close to, so if you're trying to predict contact map," +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_131_1180.179_1190.47.wav," is that, so you have a completely unsupervised training phase where you just use your input data to extract this, you know, increasingly refined..." +02. Learning in the Machine. Pierre Baldi_clip_87_775.52_786.17.wav," i, j connecting neuron j to neuron i in layer h, neuron j in layer h minus 1. It's the sum of the presynaptic activity." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_167_1503.03_1514.79.wav," So projection onto projections is well understood, and so you can understand what happens in the linear case, real linear case, when you do stocking." +02. Learning in the Machine. Pierre Baldi_clip_269_2506.16_2517.2.wav," structure to the one you proposed with the encoding network, the coding network and skip connections between the two. So I was wondering is there any way of making a formal connection between variation" +02. Learning in the Machine. Pierre Baldi_clip_70_627.26_640.97.wav," all these rules and their properties. And occasionally, you can find rules that have some interesting capabilities. For instance, Oja's rule, which is a quartic rule, actually, can extract." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_119_1072.11_1083.1499999999999.wav, too far. And the analogy I like to make is to say that neural networks have nothing to do with the brain. It's like saying Turing machines have nothing to do with cell phones. It is true at some levels. +TheQuarksOfAttention1025000-1050000.wav," operation that is essential for attention. Now this happens when you have, let's say sigmoidal neurons. If the attending neurons send a very large negative signal to the attended neurons that have sigmoidal activation function, of course, if you get a very large negative input, let's say you have a logistic, the output is going to be zero, right? So one way." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_29_262.71_273.03000000000003.wav," I just put here Shannon, of course, who developed the information theory a few years before. This is von Neumann, who had built the first computer. By the way," +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_195_1779.6_1792.4399999999998.wav, the second component etc. Of course if you have an even number of vectors etc. you can have tie you flip a coin it doesn't matter but basically it's the majority vector. So the majority vector +02. Learning in the Machine. Pierre Baldi_clip_165_1483.87_1495.3.wav," Basically the task of your network is you give it as input two values, x and y, and the output is the prediction, the classification to black and white. And these networks here have hidden layers." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_302_2767.95_2778.839.wav," very difficult problem which has many facets. You can predict secondary structure, the position of alpha helices along the protein sequence or the position of." +TheQuarksOfAttention1600000-1625000.wav," shifting way controlled by these attention mechanism, these attention weights, okay? So transformer is built out of the fundamental building blocks out of the quarks that I just described to you. One thing I want to impress on you that will be important for the applications is a little bit surprising is that transformers." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_313_2858.21_2870.069.wav," output probabilities as a function of the vector b, the vector f, and the vector u. One then perputes the vector b at time t as a function of the vector u t and" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_84_763.68_777.0.wav," neural network. So it's the chain rule, if you apply the chain rule you get back propagation, something that Newton could have done easily if he had known about neural networks, but it was done in 1985." +TheQuarksOfAttention1650000-1675000.wav," the inputs, you will get the same permutation in the first even layer because there is weight sharing, so the results will be the same but permuted in the same way. You will get the same permutation in the dot products, in the softmax, and so the output will be identical, right? So you see that this whole block is invariant to permutation of the inputs. A little bit surprised for" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_123_1108.33_1119.07.wav," The paper was built using restricted Boltzmann machines, which are a particular type of random Markov field that I don't need to describe to you. I'm going to describe the same idea using neural networks because." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_213_1955.44_1965.19.wav," between NP-complete problem. We know that clustering endpoints on a planar lattice, if you have endpoints on a 2D lattice and you want to cluster..." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_147_1320.089_1330.649.wav," If you are, for instance, in the linear case, if you're doing A times B, if you put CC minus one between A and B, the problem is unchanged. So you change coordinates in the hidden layer. It doesn't change." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_278_2550.2_2561.36.wav, by this expectation. But why should anything like this be true in the nonlinear case where you're using sigmoidal things? So I'm using sigmoidal functions. +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_236_2173.54_2186.5.wav," So you cannot do gradient descent, strictly speaking. But with this algorithm, you can do it. So this is an autoencoder, 130, 10, 30, 100, that was trained using this deep target algorithm." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_301_2758.56_2769.78.wav, structure you can do weight sharing and use the same network in different places. So for protein structure prediction is a well-known very difficult problem which has many +TheQuarksOfAttention1375000-1400000.wav," key and the value vector, but these are just names, so this vector here is transformed in one layer into three vectors Q, K, and V, and then there is weight sharing, so the same circuit, the same weights are reused at every position to produce these three vectors. Right. So very simple initial stage." +TheQuarksOfAttention1075000-1100000.wav," of the standard model, it's nothing new. But in the mathematical proofs of the theorems, very strangely, in a way that you don't completely understand, this mechanism comes up in the proof themselves to prove the theorems about the other two mechanisms, which are new. So the other two mechanisms that I'm going to talk about are multiplicative, just like our intuition sort of suggested." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_35_318.18_329.61.wav, would lose a lot of weight very rapidly so it has bits have to be stored ultimately biochemically in the brain and the natural place to think about storing +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_376_3440.46_3451.89.wav, very far from being very accurate so the problem is far from solved how to predict the 3d structure of a protein is not a solved problem by any structure +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_249_2297.21_2309.2099999999996.wav," to predict this bit, 0 or 1. So the hidden layer has to learn these two tasks at the same time. It's what's called transfer learning. And so the fact that you're putting this addition" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_218_2000.86_2011.08.wav," to each vertical direction on the lattice and one component for each horizontal. So when I'm moving from this point to here, I'm changing the first four bits each side." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_323_2947.05_2957.4.wav," each other in 3D. So if you do it at the level of amino acids, I and J are amino acids in the sequence, are letters in the sequence, the protein falls." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_75_683.879_694.98.wav," where he took perceptrons, connected them with symmetric connections and applied Hebb rule. That's basically what the Hopfield model is. And it has interesting projects." +TheQuarksOfAttention450000-475000.wav," along by a circuit, by a network that belongs to the standard model. It's very easy to show that. So whatever attention is or what we're going to do attention, it's not about being able to compute functions, new functions that you cannot do with the standard model. Everything can be done within the standard model. It's all about doing things in more efficient ways with less." +TheQuarksOfAttention525000-550000.wav," NLP is represented in this picture, where you have at the bottom a sentence in English, how was your day? And then a translation in French, which actually is not very good one, but I downloaded this from the web, commence la passage journée, right? And the idea is that whatever the processing you're doing to translate from English to French," +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_210_1924.27_1935.76.wav," of that class. So you can understand in detail what happens, what the Boolean autoencoder is trying to do, and you can try this alternate optimization problem." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_32_289.949_300.99.wav," a sigmoidal function to produce an output. So all these ideas were already in place, and so you could start asking the question in 1950, where does the block go?" +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_318_2902.47_2912.88.wav, go into the details and does very well. There is a predictor called SSPro that you can use to predict secondary structure using that. But of course the difficult... +TheQuarksOfAttention2300000-2325000.wav," or whatever number of spectra you have back to the parameter of states in these equations. And you can see here the prediction of the first parameter, true value versus predicted value, and then the second, which is quite good. The second parameter, the prediction is still pretty good, but there is more noise and we're trying to reduce the noise." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_252_2322.92_2334.11.wav, function here that has two terms. It has a reconstruction term plus a discrimination term and you can of course put a weight there so that in the lower layer the discrimination has +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_159_1428.41_1440.59.wav," decomposition, whichever way you want to look at it, where in the hidden layer, you're basically projecting the data on the subspace that is spanned by the eigenvector associated with the top." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_247_2278.16_2290.46.wav, but I'm going to go directly to the last one which combines all these ideas. So what you can do is you take your images and you train a hidden layer to reproduce in the output two things. The image itself... +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_311_2842.74_2852.5499999999997.wav," hidden values that are on the backward chain and the forward Markov chain of this Bayesian network. And again, you can take this and transform it into a deep network." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_14_129.89_141.95000000000002.wav, layers that are deep in the architectures that do not see exactly what goes on in the outside world that do not have access to the input or the output targets. So inventing... +TheQuarksOfAttention2525000-2550000.wav," that are linear separable, right? A Boolean function is just the coloring of the cube of vectors of zero and one components into two colors, the plus one class and the minus one class. And if it's a linear threshold gate, it means that there is a hyperplane that separates the red dots from the blue dots, right? So you're asking of all possible coloring of the cubes," +TheQuarksOfAttention2800000-2825000.wav," and it turns out that the output, it doesn't matter which one you're using has also capacity, as capacity equal to the sum. So the capacity, the answer to my question is 2N squared up to a smaller, smaller terms. That's the capacity of this very simple circuit. You can do the same thing with polynomial gate. You can study all kinds of other circuit, as I said." +02. Learning in the Machine. Pierre Baldi_clip_216_1948.179_1958.26.wav," that case we can solve and show that it converge. So just to finish, let me show you what happens in this case. So these two problems are equivalent. Again, the skipped version versus." +CAM Colloquium - Pierre Baldi: Deep Architectures and Deep Learning_clip_69_630.839_642.48.wav," And of course, they were edging their bet, if you look at the following sentence, nevertheless, we consider it to be an important research problem to elucidate or reject our intuitive judgment that the extension to multilayer systems is not."