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##tive learning algorithms, but they are still deservedly recognized for their important role in deep learning history. deep belief networks are generative models with several layers of latent variables. the latent variables are typically binary, while the visible units may be binary or real. there are no intralayer co... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 675 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
##n is given by p ( h ( ) l, h ( 1 ) l− ) exp [UNK] b ( ) l h ( ) l + b ( 1 ) l− h ( 1 ) l− + h ( 1 ) l− w ( ) l h ( ) l, ( 20. 17 ) p h ( ( ) k i = 1 | h ( + 1 ) k ) = σ b ( ) k i + w ( + 1 ) k :, i h ( + 1 ) k [UNK] ∈ − i, k 1,..., l 2, ( 20. 18 ) p v ( i = 1 | h ( 1 ) ) = σ b ( 0 ) i + w ( 1 ) :, i h ( 1 ) [UNK]. ( ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 675 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models with β diagonal for tractability. generalizations to other exponential family visible units are straightforward, at least in theory. a dbn with only one hidden layer is just an rbm. to generate a sample from a dbn, we first run several steps of gibbs sampling on the top two hidden laye... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 676 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
to the network width. evaluating or maximizing the log - likelihood requires not just confronting the problem of intractable inference to marginalize out the latent variables, but also the problem of an intractable partition function within the undirected model of the top two layers. to train a deep belief network, one... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 676 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
units of the first rbm, when the first rbm is driven by the data. this procedure can be repeated indefinitely, to add as many layers to the dbn as desired, with each new rbm modeling the samples of the previous one. each rbm defines another layer of the dbn. this procedure can be justified as increasing a variational lower ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 676 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models the trained dbn may be used directly as a generative model, but most of the interest in dbns arose from their ability to improve classification models. we can take the weights from the dbn and use them to define an mlp : h ( 1 ) = σ b ( 1 ) + v w ( 1 ). ( 20. 22 ) h ( ) l = σ b ( ) l i ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 677 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
. this mlp 19 is a heuristic choice that seems to work well in practice and is used consistently in the literature. many approximate inference techniques are motivated by their ability to find a maximally variational lower bound on the log - likelihood tight under some set of constraints. one can construct a variational... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 677 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
it may be approximated with ais ( salakhutdinov and murray 2008, ). this permits evaluating its quality as a generative model. the term “ deep belief network ” is commonly used incorrectly to refer to any kind of deep neural network, even networks without latent variable semantics. the term “ deep belief network ” shou... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 677 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models h ( 1 ) 1 h ( 1 ) 1 h ( 1 ) 2 h ( 1 ) 2 h ( 1 ) 3 h ( 1 ) 3 v1 v1 v2 v2 v3 v3 h ( 2 ) 1 h ( 2 ) 1 h ( 2 ) 2 h ( 2 ) 2 h ( 2 ) 3 h ( 2 ) 3 h ( 1 ) 4 h ( 1 ) 4 figure 20. 2 : the graphical model for a deep boltzmann machine with one visible layer ( bottom ) and two hidden layers. connec... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 678 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
variables ( rbms have just one ). but like the rbm, within each layer, each of the variables are mutually independent, conditioned on the variables in the neighboring layers. see figure for the graph structure. deep boltzmann 20. 2 machines have been applied to a variety of tasks including document modeling ( srivastava... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 678 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
) = 1 z ( ) θ exp −e, ( v h ( 1 ), h ( 2 ), h ( 3 ) ; ) θ. ( 20. 24 ) to simplify our presentation, we omit the bias parameters below. the dbm energy function is then defined as follows : e, ( v h ( 1 ), h ( 2 ), h ( 3 ) ; ) = θ −vw ( 1 ) h ( 1 ) −h ( 1 ) w ( 2 ) h ( 2 ) −h ( 2 ) w ( 3 ) h ( 3 ). ( 20. 25 ) 663 | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 678 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models h ( 1 ) 1 h ( 1 ) 1 h ( 1 ) 2 h ( 1 ) 2 h ( 1 ) 3 h ( 1 ) 3 v1 v1 v2 v2 h ( 2 ) 1 h ( 2 ) 1 h ( 2 ) 2 h ( 2 ) 2 h ( 2 ) 3 h ( 2 ) 3 h ( 3 ) 1 h ( 3 ) 1 h ( 3 ) 2 h ( 3 ) 2 v1 v2 h ( 2 ) 1 h ( 2 ) 1 h ( 2 ) 2 h ( 2 ) 2 h ( 2 ) 3 h ( 2 ) 3 h ( 1 ) 1 h ( 1 ) 1 h ( 1 ) 2 h ( 1 ) 2 h ( 1 )... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 679 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
the rbm energy function ( equation ), the dbm energy 20. 5 function includes connections between the hidden units ( latent variables ) in the form of the weight matrices ( w ( 2 ) and w ( 3 ) ). as we will see, these connections have significant consequences for both the model behavior as well as how we go about perform... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 679 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
even layers also become conditionally independent. the bipartite structure of the dbm means that we can apply the same equa - tions we have previously used for the conditional distributions of an rbm to determine the conditional distributions in a dbm. the units within a layer are conditionally independent from each ot... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 679 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models p h ( ( 1 ) i = 1 | v h, ( 2 ) ) = σ vw ( 1 ) :, i + w ( 2 ) i, : h ( 2 ) ( 20. 27 ) and p h ( ( 2 ) k = 1 | h ( 1 ) ) = σ h ( 1 ) w ( 2 ) :, k. ( 20. 28 ) the bipartite structure makes gibbs sampling in a deep boltzmann machine [UNK]. the naive approach to gibbs sampling is to update... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 680 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
, one including all even layers ( including the visible layer ) and the other including all odd layers. due to the bipartite dbm connection pattern, given the even layers, the distribution over the odd layers is factorial and thus can be sampled simultaneously and independently as a block. likewise, given the odd layer... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 680 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
units can be provided by an upward pass through the network in an mlp that uses sigmoid activation functions and the same weights as the original dbn. distribution any q ( h ) may be used to obtain a variational lower bound on the log - likelihood. this heuristic procedure therefore allows us to obtain such a bound. ho... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 680 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models from optimal. in dbms, all of the hidden units within a layer are conditionally independent given the other layers. this lack of intralayer interaction makes it possible to use fixed point equations to actually optimize the variational lower bound and find the true optimal mean field exp... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 681 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
used only at the end of the sampling process, in one [UNK] ancestral sampling pass. to generate a sample from a dbm, it is necessary to use mcmc across all layers, with every layer of the model participating in every markov chain transition. 20. 4. 2 dbm mean field inference the conditional distribution over one dbm la... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 681 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
dbn, we are left to seek out methods to approximate the dbm posterior distribution. however, unlike the dbn, the dbm posterior distribution over their hidden units — while complicated — is easy to approximate with a variational approximation ( as discussed in section ), specifically a 19. 4 mean field approximation. the ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 681 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models mating a particular target distribution — in our case, the posterior distribution over the hidden units given the visible units — by some reasonably simple family of dis - tributions. in the case of the mean field approximation, the approximating family is the set of distributions wher... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 682 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
). importantly, the inference process must be run again to find a [UNK] distribution q every time we use a new value of. v one can conceive of many ways of measuring how well q ( h v | ) fits p ( h v | ). the mean field approach is to minimize kl ( ) = q p h q ( h ( 1 ), h ( 2 ) | v ) log q ( h ( 1 ), h ( 2 ) | v ) p ( h ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 682 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
we parametrize q as a product of bernoulli distributions, that is we associate the probability of each element of h ( 1 ) with a parameter. specifically, for each j, [UNK] ( 1 ) j = q ( h ( 1 ) j = 1 | v ), where [UNK] ( 1 ) j ∈ [ 0, 1 ] and for each k, [UNK] ( 2 ) k = q ( h ( 2 ) k = 1 | v ), where [UNK] ( 2 ) k ∈ [ 0 ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 682 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
k ( 1 [UNK] ( 2 ) k ) ( 1−h ( 2 ) k ). ( 20. 32 ) of course, for dbms with more layers the approximate posterior parametrization can be extended in the obvious way, exploiting the bipartite structure of the graph 667 | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 682 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models to update all of the even layers simultaneously and then to update all of the odd layers simultaneously, following the same schedule as gibbs sampling. now that we have specified our family of approximating distributions q, it remains to specify a procedure for choosing the member of t... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 683 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
( 2 ) j, [UNK] ( 1 ) j, k. [UNK] ( 20. 34 ) at a fixed point of this system of equations, we have a local maximum of the variational lower bound l ( q ). thus these fixed point update equations define an iterative algorithm where we alternate updates of [UNK] ( 1 ) j ( using equation ) and 20. 33 updates of [UNK] ( 2 ) k ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 683 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
distribution, using the techniques from chapter. 19 as described in section, variational inference allows the construction of 20. 4. 2 a distribution q ( h v | ) that approximates the intractable p ( h v | ). learning then proceeds by maximizing l ( v θ, q, ), the variational lower bound on the intractable log - likeli... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 683 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models for a deep boltzmann machine with two hidden layers, is given by l l ( ) = q, θ i j viw ( 1 ) i, [UNK] ( 1 ) j + j k [UNK] ( 1 ) j w ( 2 ) j, [UNK] ( 2 ) k− h log ( ) + z θ ( ) q. ( 20. 35 ) this expression still contains the log partition function, log z ( θ ). because a deep boltzma... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 684 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
other techniques described in chapter are not applicable. techniques such as pseudolikelihood require the 18 ability to evaluate the unnormalized probabilities, rather than merely obtain a variational lower bound on them. contrastive divergence is slow for deep boltzmann machines because they do not allow [UNK] samplin... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 684 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
, the model fails to learn to represent the distribution adequately. in other cases, the dbm may represent the distribution well, but with no higher likelihood than could be obtained with just an rbm. a dbm with very small weights in all but the first layer represents approximately the same distribution as an rbm. vario... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 684 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models algorithm 20. 1 the variational stochastic maximum likelihood algorithm for training a dbm with two hidden layers. set, the step size, to a small positive number set k, the number of gibbs steps, high enough to allow a markov chain of p ( v h, ( 1 ), h ( 2 ) ; θ + ∆θ ) to burn in, sta... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 685 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
model ’ s marginals. while not converged ( mean field inference loop ) do [UNK] h ( 1 ) ←σ v w ( 1 ) + [UNK] h ( 2 ) w ( 2 ). [UNK] h ( 2 ) ←σ [UNK] h ( 1 ) w ( 2 ). end while ∆w ( 1 ) ←1 mv [UNK] h ( 1 ) ∆w ( 2 ) ←1 m [UNK] h ( 1 ) [UNK] ( 2 ) for do l k = 1 to ( gibbs sampling ) gibbs block 1 : [UNK], j, [UNK] i, j sa... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 685 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
i, j = 1 ) = σ [UNK], : w ( 1 ) :, j + [UNK] h ( 2 ) i, : w ( 2 ) j, :. end for ∆w ( 1 ) ←∆w ( 1 ) −1 mv [UNK] h ( 1 ) ∆w ( 2 ) ←∆w ( 2 ) −1 m [UNK] h ( 1 ) [UNK] h ( 2 ) w ( 1 ) ←w ( 1 ) + ∆w ( 1 ) ( this is a cartoon illustration, in practice use a more [UNK] algorithm, such as momentum with a decaying learning rate ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 685 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models rbms have been trained in this way, they can be combined to form a dbm. the dbm may then be trained with pcd. typically pcd training will make only a small change in the model ’ s parameters and its performance as measured by the log - likelihood it assigns to the data, or its ability... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 686 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
##ed before inclusion in the dbm. a layer in the middle of the stack of rbms is trained with only bottom - up input, but after the stack is combined to form the dbm, the layer will have both bottom - up and top - down input. to account for this [UNK], salakhutdinov and hinton 2009a ( ) advocate dividing the weights of ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 686 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
( salakhutdinov and hinton 2009a, ). specifically, the expectation of the energy gradient should be computed with respect to the mean field distribution in which all of the units are independent from each other. the parameters of this mean field distribution should be obtained by running the mean field fixed point equations... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 686 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models d ) a ) b ) c ) figure 20. 4 : the deep boltzmann machine training procedure used to classify the mnist dataset ( salakhutdinov and hinton 2009a srivastava 2014, ; et al., ). train an rbm ( a ) by using cd to approximately maximize log p ( v ). train a second rbm that models ( b ) h (... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 687 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
2 ) that are obtained by running mean field inference in the model lacking y. use these features as input to an mlp whose structure is the same as an additional pass of mean field, with an additional output layer for the estimate of y. initialize the mlp ’ s weights to be the same as the dbm ’ s weights. train the mlp to... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 687 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models are working until quite late in the training process. software implementations of dbms need to have many [UNK] components for cd training of individual rbms, pcd training of the full dbm, and training based on back - propagation through the mlp. finally, the mlp on top of the boltzman... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 688 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
. unfortunately, it remains unable to compete with appropriately regularized mlps as a classifier. the second way to jointly train a deep boltzmann machine is to use a multi - prediction deep boltzmann machine ( goodfellow 2013b et al., ). this model uses an alternative training criterion that allows the use of the back... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 688 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
[UNK] sparsity patterns in the weight matrix u, we can implement structures of boltzmann machines, such as rbms, or dbms with [UNK] numbers of layers. this is accomplished by partitioning x into visible and hidden units and zeroing out elements of u for units that do not interact. the centered boltzmann machine introdu... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 688 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models in a hessian matrix that is better conditioned. ( ) experimentally melchior et al. 2013 confirmed that the conditioning of the hessian matrix improves, and observed that the centering trick is equivalent to another boltzmann machine learning technique, the enhanced gradient (, ). the i... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 689 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
consists of randomly sampling a 20. 5 training example, randomly sampling a subset of inputs to the inference network, and then training the inference network to predict the values of the remaining units. this general principle of back - propagating through the computational graph for approximate inference has been app... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 689 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
used — with approximate inference. this means that approximate inference, for example, to fill in missing inputs, or to perform classification despite the presence of missing inputs, is more accurate in the mp - dbm than in the original dbm. the original dbm does not make an accurate classifier on its own ; the best class... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 689 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models figure 20. 5 : an illustration of the multi - prediction training process for a deep boltzmann machine. each row indicates a [UNK] example within a minibatch for the same training step. each column represents a time step within the mean field inference process. for each example, we sam... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 690 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models dbms may be trained jointly while dbms require a greedy layer - wise pretraining. the disadvantage of back - propagating through the approximate inference graph is that it does not provide a way to optimize the log - likelihood, but rather a heuristic approximation of the generalized ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 691 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
##ete it entirely as dropout does. instead, the mp - dbm treats it as a latent variable to be inferred. one could imagine applying dropout to the mp - dbm by additionally removing some units rather than making them latent. 20. 5 boltzmann machines for real - valued data while boltzmann machines were originally develope... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 691 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
not a particularly theoretically satisfying approach, and binary images sampled independently in this way have a noisy appearance. in this section, we present boltzmann machines that define a probability density over real - valued data. 20. 5. 1 gaussian - bernoulli rbms restricted boltzmann machines may be developed fo... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 691 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models there are many ways of parametrizing gaussian - bernoulli rbms. one choice is whether to use a covariance matrix or a precision matrix for the gaussian distribution. here we present the precision formulation. the modification to obtain the covariance formulation is straightforward. we ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 692 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
, and the partition function of whatever energy function we choose will carry out that role. if we include all of the terms ( with their sign flipped ) involving v from equa - tion in our energy function and do not add any other terms involving 20. 39 v, then our energy function will represent the desired conditional. p... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 692 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
have a choice about whether to include the terms involving only a single hi. if we assume a diagonal precision matrix, we find that for each hidden unit hi we have a term 1 2hi j βjw 2 j, i. ( 20. 41 ) in the above, we used the fact that h2 i = hi because hi ∈ { 0, 1 }. if we include this term ( with its sign flipped ) i... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 692 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models we include bias parameters for the hidden units ) but it does [UNK] the learning dynamics of the model. including the term may help the hidden unit activations remain reasonable even when the weights rapidly increase in magnitude. one way to define the energy function on a gaussian - b... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 693 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
also be a scalar times the identity matrix, or it may be a diagonal matrix. typically we do not allow the precision matrix to be non - diagonal in this context, because some operations on the gaussian distribution require inverting the matrix, and a diagonal matrix can be inverted trivially. in the sections ahead, we w... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 693 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
words, it is the relationships between pixels and not their absolute values where most of the useful information in images resides. since the gaussian rbm only models the conditional mean of the input given the hidden units, it cannot capture conditional covariance information. in response to these criticisms, alternat... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 693 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models mean and covariance rbm the mcrbm uses its hidden units to indepen - dently encode the conditional mean and covariance of all observed units. the mcrbm hidden layer is divided into two groups of units : mean units and covariance units. the group that models the conditional mean is sim... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 694 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
where em is the standard gaussian - bernoulli rbm energy function : 2 em ( x h, ( ) m ) = 1 2 xx − j xw :, jh ( ) m j − j b ( ) m j h ( ) m j, ( 20. 44 ) and ec is the crbm energy function that models the conditional covariance information : ec ( x h, ( ) c ) = 1 2 j h ( ) c j xr ( ) j 2 − j b ( ) c j h ( ) c j. ( 20. ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 694 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
46 ) and a corresponding conditional distribution over the observations given h ( ) m and h ( ) c as a multivariate gaussian distribution : pmc ( x h | ( ) m, h ( ) c ) = n x c ; mc x h | j w :, jh ( ) m j, c mc x h |. ( 20. 47 ) note that the covariance matrix cmc x h | = j h ( ) c j r ( ) j r ( ) j + i −1 is non - di... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 694 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models conditional means. it is [UNK] to train the mcrbm via contrastive divergence or persistent contrastive divergence because of its non - diagonal conditional covariance structure. cd and pcd require sampling from the joint distribution of x h, ( ) m, h ( ) c which, in a standard rbm, is... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 695 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
mean - product of student ’ s t - distribution ( mpot ) model (, ) extends the pot model ( ranzato et al. 2010b welling et al., ) in a manner similar to how the mcrbm extends the crbm. this 2003a is achieved by including nonzero gaussian means by the addition of gaussian rbm - like hidden units. like the mcrbm, the pot... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 695 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
c ) ( 20. 48 ) = em ( x h, ( ) m ) + j h ( ) c j 1 + 1 2 r ( ) j x 2 + ( 1 −γj ) log h ( ) c j ( 20. 49 ) where r ( ) j is the covariance weight vector associated with unith ( ) c j and em ( x h, ( ) m ) is as defined in equation. 20. 44 just as with the mcrbm, the mpot model energy function specifies a mul - tivariate g... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 695 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models spike and slab restricted boltzmann machines spike and slab restricted boltzmann machines (, ) or ssrbms provide another means courville et al. 2011 of modeling the covariance structure of real - valued data. compared to mcrbms, ssrbms have the advantage of requiring neither matrix in... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 696 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
determines the intensity of that component, if it is present. when a spike variable is active, the corresponding slab variable adds variance to the input along the axis defined by w :, i. this allows us to model the covariance of the inputs. fortunately, contrastive divergence and persistent contrastive divergence with ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 696 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
variable si. the parameter φi is a non - negative diagonal matrix that defines an h - modulated quadratic penalty on x. each µi is a mean parameter for the slab variable si. with the joint distribution defined via the energy function, it is relatively straightforward to derive the ssrbm conditional distributions. for exa... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 696 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models where c ss x h | = λ + iφihi − i α−1 i hiw :, iw :, i −1. the last equality holds only if the covariance matrix css x h | is positive definite. gating by the spike variables means that the true marginal distribution over h s is sparse. this is [UNK] from sparse coding, where samples fr... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 697 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
##j > 0 to enforce constraints on the conditional covariance in the direction r ( ) j. in contrast, the ssrbm specifies the conditional covariance of the observations using the hidden spike activations hi = 1 to pinch the precision matrix along the direction specified by the corresponding weight vector. the ssrbm conditi... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 697 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
to the overcomplete setting. the primary disadvantage of the spike and slab restricted boltzmann machine is that some settings of the parameters can correspond to a covariance matrix that is not positive definite. such a covariance matrix places more unnormalized probability on values that are farther from the mean, cau... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 697 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models term to the energy function that prevents the partition function from becoming undefined results in a sparse coding model, spike and slab sparse coding ( goodfellow et al., ), also known as s3c. 2013d 20. 6 convolutional boltzmann machines as seen in chapter, extremely high dimensional... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 698 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
##ize this to the setting of energy - based models. we could introduce a binary pooling unit p over n binary detector units d and enforce p = maxi di by setting the energy function to be ∞whenever that constraint is violated. this does not scale well though, as it requires evaluating 2n [UNK] energy configurations to co... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 698 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
an additional state corresponding to all of the detector units being [UNK] ). the pooling unit is on if and only if one of the detector units is on. the state with all units [UNK] assigned energy zero. we can think of this as describing a model with a single variable that has n + 1 states, or equivalently as a model th... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 698 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models machines. lee 2009 et al. ( ) demonstrated that probabilistic max pooling could be used to build convolutional deep boltzmann machines. 3 this model is able to perform operations such as filling in missing portions of its input. while intellectually appealing, this model is challenging... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 699 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
fixed number of pooling units and dynamically increase the size of their pooling regions in order to obtain a fixed - size representation of a variable - sized input. for boltzmann machines, large pooling regions become too expensive for the naive approach. the approach of ( ) of making lee et al. 2009 each of the detect... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 699 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
##fies that each of these edges may only appear once in a 3 × 3 region. as we grow a model ’ s input image in this way, the model generates edges with less density. of course, these issues only arise when the model must use variable amounts of pooling in order to emit a fixed - size output vector. models that use probabi... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 699 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models well because they lie in the receptive field of fewer hidden units. however, if we do implicitly zero - pad the input, then the hidden units at the boundary are driven by fewer input pixels, and may fail to activate when needed. 20. 7 boltzmann machines for structured or sequential out... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 700 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
also for sequence modeling. in the latter case, rather than mapping an input x to an output y, the model must estimate a probability distribution over a sequence of variables, p ( x ( 1 ),..., x ( ) τ ). conditional boltzmann machines can represent factors of the form p ( x ( ) t | x ( 1 ),..., x ( 1 ) t− ) in order to... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 700 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
− ) for small m. the model is an rbm over p ( x ( ) t ) whose bias parameters are a linear function of the preceding m values of x. when we condition on [UNK] values of x ( 1 ) t− and earlier variables, we get a new rbm over x. the weights in the rbm over x never change, but by conditioning on [UNK] past values, we can... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 700 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models of musical notes used to compose songs. boulanger - lewandowski 2012 et al. ( ) introduced the rnn - rbm sequence model and applied it to this task. the rnn - rbm is a generative model of a sequence of frames x ( ) t consisting of an rnn that emits the rbm parameters for each time ste... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 701 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
approximate gradient may then be back - propagated through the rnn using the usual back - propagation through time algorithm. 20. 8 other boltzmann machines many other variants of boltzmann machines are possible. boltzmann machines may be extended with [UNK] training criteria. we have focused on boltzmann machines trai... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 701 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
such a term is viwi, jhj. it is also possible to train higher - order boltzmann machines (, ) whose energy function terms sejnowski 1987 involve the products between many variables. three - way interactions between a hidden unit and two [UNK] images can model spatial transformations from one frame of video to the next ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 701 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models some hidden units to learn to model the input using features that are relevant to the class but also to learn extra hidden units that explain nuisance details that are necessary for the samples of v to be realistic but do not determine the class of the example. another use of higher -... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 702 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
[UNK] to find an energy function that maintains tractability of all of the [UNK] conditional distributions needed to use the boltzmann machine, but despite this required [UNK] the field remains open to innovation. 20. 9 back - propagation through random operations traditional neural networks implement a deterministic tra... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 702 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
with mean and variance µ σ2 : y [UNK] ( µ, σ2 ). ( 20. 54 ) because an individual sample of y is not produced by a function, but rather by a sampling process whose output changes every time we query it, it may seem counterintuitive to take the derivatives of y with respect to the parameters of its distribution, µ and σ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 702 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models transforming an underlying random value z [UNK] ( z ; 0, 1 ) to obtain a sample from the desired distribution : y µ σz = + ( 20. 55 ) we are now able to back - propagate through the sampling operation, by regard - ing it as a deterministic operation with an extra input z. crucially, t... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 703 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
or the parameters of the sampling operation. for example, we could build a larger graph with µ = f ( x ; θ ) and σ = g ( x ; θ ). in this augmented graph, we can use back - propagation through these functions to derive ∇θj y ( ). the principle used in this gaussian sampling example is more generally appli - cable. we c... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 703 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
traditional tools such as the back - propagation algorithm applied to f, so long as f is continuous and [UNK] almost everywhere. crucially, ω must not be a function of z, and z must not be a function of ω. this technique is often called the reparametrization trick, stochastic back - propagation or perturbation analysis... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 703 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models in neural network applications, we typically choose z to be drawn from some simple distribution, such as a unit uniform or unit gaussian distribution, and achieve more complex distributions by allowing the deterministic portion of the network to reshape its input. the idea of propagat... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 704 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
dropout, are also naturally designed to take noise as an input without requiring any special reparametrization to make the noise independent from the model. 20. 9. 1 back - propagating through discrete stochastic operations when a model emits a discrete variable y, the reparametrization trick is not applicable. suppose... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 704 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
reward increment = non - negative factor × [UNK] reinforcement × characteristic eligibility ) provides a framework defining a family of simple but powerful solutions (, ). the core idea is that williams 1992 even though j ( f ( z ; ω ) ) is a step function with useless derivatives, the expected cost ez z [UNK] ( ) j f (... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 704 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models the simplest version of reinforce can be derived by simply [UNK] the expected cost : ez [ ( ) ] = j y y j p ( ) y ( ) y ( 20. 59 ) ∂ j e [ ( ) ] y ∂ω = y j ( ) y ∂p ( ) y ∂ω ( 20. 60 ) = y j p ( ) y ( ) y ∂ p log ( ) y ∂ω ( 20. 61 ) ≈1 m m y ( ) i [UNK], i ( ) y = 1 j ( y ( ) i ) ∂ p ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 705 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
an unbiased monte carlo estimator of the gradient. anywhere we write p ( y ) in this section, one could equally write p ( y x | ). this is because p ( y ) is parametrized by ω, and ω contains both θ and x, if x is present. one issue with the above simple reinforce estimator is that it has a very high variance, so that ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 705 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
). note that any [UNK] b ( ω ) that does not depend on y would not change the expectation of the estimated gradient because ep ( ) y ∂ p log ( ) y ∂ω = y p ( ) y ∂ p log ( ) y ∂ω ( 20. 63 ) = y ∂p ( ) y ∂ω ( 20. 64 ) = ∂ ∂ω y p ( ) = y ∂ ∂ω1 = 0, ( 20. 65 ) 690 | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 705 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models which means that ep ( ) y ( ( ) ( ) ) j y −b ω ∂ p log ( ) y ∂ω = ep ( ) y j ( ) y ∂ p log ( ) y ∂ω −b e ( ) ω p ( ) y ∂ p log ( ) y ∂ω ( 20. 66 ) = ep ( ) y j ( ) y ∂ p log ( ) y ∂ω. ( 20. 67 ) furthermore, we can obtain the optimal b ( ω ) by computing the variance of ( j ( y ) − b ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 706 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
log ( ) y ∂ωi 2. ( 20. 68 ) the gradient estimator with respect to ωi then becomes ( ( ) ( ) j y −b ω i ) ∂ p log ( ) y ∂ωi ( 20. 69 ) where b ( ω ) i estimates the above b∗ ( ω ) i. the estimate b is usually obtained by adding extra outputs to the neural network and training the new outputs to estimate ep ( ) y [ j ( ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 706 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
use a single shared output 20. 68 mnih and gregor 2014 ( across all elements i of ω ) trained with the target j ( y ), using as baseline b ( ω ) ≈ ep ( ) y [ ( ) ] j y. variance reduction methods have been introduced in the reinforcement learning context (, ; sutton et al. 2000 weaver and tao 2001, ), generalizing prev... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 706 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models magnitude of this quantity. ( ) called this heuristic mnih and gregor 2014 variance normalization. reinforce - based estimators can be understood as estimating the gradient by correlating choices of y with corresponding values of j ( y ). if a good value of y is unlikely under the cur... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 707 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
described sparse coding models, which can be thought of as shallow directed generative models. they are often used as feature learners in the context of deep learning, though they tend to perform poorly at sample generation and density estimation. we now describe a variety of deep, fully directed models. 20. 10. 1 sigm... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 707 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models the sampling process are independent from each other, rather than sampled from a restricted boltzmann machine. such a structure is interesting for a variety of reasons. one reason is that the structure is a universal approximator of probability distributions over the visible units, in... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 708 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
bound that is specialized for sigmoid belief networks (, saul et al. 1996 ). this approach has only been applied to very small networks. another approach is to use learned inference mechanisms as described in section. the 19. 5 helmholtz machine ( dayan 1995 dayan and hinton 1996 et al., ;, ) is a sigmoid belief networ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 708 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
bornschein 2015, ) and bidirectional helmholtz machines ( et al., ) make it possible to quickly train sigmoid belief networks and reach state - of - the - art performance on benchmark tasks. a special case of sigmoid belief networks is the case where there are no latent variables. learning in this case is [UNK], becaus... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 708 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 20. deep generative models 20. 10. 2 [UNK] generator nets many generative models are based on the idea of using a [UNK] generator network. the model transforms samples of latent variables z to samples x or to distributions over samples x using a [UNK] function g ( z ; θ ( ) g ) which is typically represented by... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 709 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
network contains just one [UNK] layer : x z lz = ( g ) = + µ ( 20. 71 ) where is given by the cholesky decomposition of. l σ pseudorandom number generators can also use nonlinear transformations of simple distributions. for example, inverse transform sampling ( devroye 2013, ) draws a scalar z from u ( 0, 1 ) and appli... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 709 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
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