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phenomena. we have not yet described precisely what these individual cells detect. in a deep, nonlinear network, it can be [UNK] to understand the function of individual cells. simple cells in the first layer are easier to analyze, because their responses are driven by a linear function. in an artificial neural network, ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 383 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
weights that are described by gabor functions. the gabor function describes the weight at a 2 - d point in the image. we can think of an image as being a function of 2 - d coordinates, i ( x, y ). likewise, we can think of a simple cell as sampling the image at a set of locations, defined by a set of x coordinates x and... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 383 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
##xx2 −βyy2 cos ( fx + ) φ, ( 9. 16 ) where x = ( x x − 0 ) cos ( ) + ( τ y y − 0 ) sin ( ) τ ( 9. 17 ) 368 | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 383 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 9. convolutional networks and y = ( −x x − 0 ) sin ( ) + ( τ y y − 0 ) cos ( ) τ. ( 9. 18 ) here, α, βx, βy, f, φ, x0, y0, and τ are parameters that control the properties of the gabor function. figure shows some examples of gabor functions with 9. 18 [UNK] settings of these parameters. the parameters x0, y0, a... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 384 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
is a gaussian function and the other is a cosine function. the gaussian factor α exp −βxx2 −βyy2 can be seen as a gating term that ensures the simple cell will only respond to values near where x and yare both zero, in other words, near the center of the cell ’ s receptive field. the scaling factor α adjusts the total m... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 384 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
the image has the same phase as the weights. this occurs when the image is bright where the weights are positive and dark where the weights are negative. simple cells are most inhibited when the wave of brightness is fully out of phase with the weights — when the image is dark where the weights are positive and bright ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 384 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
##yy 2 ) contains a high amplitude sinusoidal wave with frequency f in direction τ near ( x0, y0 ), regardless of the phase [UNK] of this wave. in other words, the complex cell is invariant to small translations of the image in direction τ, or to negating the image 369 | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 384 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 9. convolutional networks figure 9. 18 : gabor functions with a variety of parameter settings. white indicates large positive weight, black indicates large negative weight, and the background gray corresponds to zero weight. ( left ) gabor functions with [UNK] values of the parameters that control the coordinat... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 385 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
β values are fixed to 1. 5× the image width. gabor functions with [UNK] sinusoid parameters ( right ) f and φ. as we move top to bottom, f increases, and as we move left to right, φ increases. for the other two plots, is fixed to 0 and is fixed to 5 the image width. φ f × ( replacing black with white and vice versa ). som... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 385 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
examples. because so many [UNK] learning algorithms learn edge detectors, it is [UNK] to conclude that any specific learning algorithm is the “ right ” model of the brain just based on the features that it learns ( though it can certainly be a bad sign if an algorithm does learn some sort of edge detector not when appli... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 385 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 9. convolutional networks figure 9. 19 : many machine learning algorithms learn features that detect edges or specific colors of edges when applied to natural images. these feature detectors are reminiscent of the gabor functions known to be present in primary visual cortex. ( left ) weights learned by an unsupe... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 386 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
networks were also some of the first neural networks to solve important commercial applications and remain at the forefront of commercial applications of deep learning today. for example, in the 1990s, the neural network research group at at & t developed a convolutional network for reading checks (, ). by the end of th... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 386 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 9. convolutional networks had been used to win other machine learning and computer vision contests with less impact for years earlier. convolutional nets were some of the first working deep networks trained with back - propagation. it is not entirely clear why convolutional networks succeeded when general back -... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 387 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
networks ). whatever the case, it is fortunate that convolutional networks performed well decades ago. in many ways, they carried the torch for the rest of deep learning and paved the way to the acceptance of neural networks in general. convolutional networks provide a way to specialize neural networks to work with dat... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 387 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10 sequence modeling : recurrent and recursive nets recurrent neural networks or rnns (, ) are a family of rumelhart et al. 1986a neural networks for processing sequential data. much as a convolutional network is a neural network that is specialized for processing a grid of values x such as an image, a recurren... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 388 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
sharing parameters across [UNK] parts of a model. parameter sharing makes it possible to extend and apply the model to examples of [UNK] forms ( [UNK] lengths, here ) and generalize across them. if we had separate parameters for each value of the time index, we could not generalize to sequence lengths not seen during t... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 388 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets word or the second word of the sentence. suppose that we trained a feedforward network that processes sentences of fixed length. a traditional fully connected feedforward network would have separate parameters for each input feature, so it would need to learn ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 389 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
sharing manifests in the application of the same convolution kernel at each time step. recurrent networks share parameters in a [UNK] way. each member of the output is a function of the previous members of the output. each member of the output is produced using the same update rule applied to the previous outputs. this... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 389 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
and even when applied to data involving time, the network may have connections that go backwards in time, provided that the entire sequence is observed before it is provided to the network. this chapter extends the idea of a computational graph to include cycles. these cycles represent the influence of the present value... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 389 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets 10. 1 unfolding computational graphs a computational graph is a way to formalize the structure of a set of computations, such as those involved in mapping inputs and parameters to outputs and loss. please refer to section for a general introduction. in this s... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 390 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
time steps τ, the graph can be unfolded by applying the definition τ −1 times. for example, if we unfold equation for 10. 1 τ = 3 time steps, we obtain s ( 3 ) = ( f s ( 2 ) ; ) θ ( 10. 2 ) = ( ( f f s ( 1 ) ; ) ; ) θ θ ( 10. 3 ) unfolding the equation by repeatedly applying the definition in this way has yielded an expr... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 390 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
f figure 10. 1 : the classical dynamical system described by equation, illustrated as an 10. 1 unfolded computational graph. each node represents the state at some timet and the function f maps the state at t to the state at t + 1. the same parameters ( the same value of used to parametrize ) are used for all time step... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 390 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets where we see that the state now contains information about the whole past sequence. recurrent neural networks can be built in many [UNK] ways. much as almost any function can be considered a feedforward neural network, essentially any function involving recur... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 391 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
the network typically learns to use h ( ) t as a kind of lossy summary of the task - relevant aspects of the past sequence of inputs up to t. this summary is in general necessarily lossy, since it maps an arbitrary length sequence ( x ( ) t, x ( 1 ) t−, x ( 2 ) t−,..., x ( 2 ), x ( 1 ) ) to a fixed length vector h ( ) t... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 391 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
##coder frameworks ( chapter ). 14 f h x h ( t−1 ) h ( t−1 ) h ( ) t h ( ) t h ( + 1 ) t h ( + 1 ) t x ( t−1 ) x ( t−1 ) x ( ) t x ( ) t x ( + 1 ) t x ( + 1 ) t h ( )... h ( )... h ( )... h ( )... f unfold f f f figure 10. 2 : a recurrent network with no outputs. this recurrent network just processes information from t... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 391 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets physical implementation of the model, such as a biological neural network. in this view, the network defines a circuit that operates in real time, with physical parts whose current state can influence their future state, as in the left of figure. 10. 2 throughou... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 392 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
the figure to a computational graph with repeated pieces as in the right side. the unfolded graph now has a size that depends on the sequence length. we can represent the unfolded recurrence after steps with a function t g ( ) t : h ( ) t = g ( ) t ( x ( ) t, x ( 1 ) t−, x ( 2 ) t−,..., x ( 2 ), x ( 1 ) ) ( 10. 6 ) = ( ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 392 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
1. regardless of the sequence length, the learned model always has the same input size, because it is specified in terms of transition from one state to another state, rather than specified in terms of a variable - length history of states. 2. it is possible to use the transition function same f with the same parameters ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 392 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets information flow forward in time ( computing outputs and losses ) and backward in time ( computing gradients ) by explicitly showing the path along which this information flows. 10. 2 recurrent neural networks armed with the graph unrolling and parameter sharin... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 393 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
+ 1 ) t x ( t−1 ) x ( t−1 ) x ( ) t x ( ) t x ( + 1 ) t x ( + 1 ) t w w w w h ( )... h ( )... h ( )... h ( )... v v v u u u unfold figure 10. 3 : the computational graph to compute the training loss of a recurrent network that maps an input sequence of x values to a corresponding sequence of output o values. a loss l m... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 393 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
by a weight matrix v. equation defines forward propagation in this model. 10. 8 ( left ) the rnn and its loss drawn with recurrent connections. ( right ) the same seen as an time - unfolded computational graph, where each node is now associated with one particular time instance. some examples of important design pattern... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 393 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets • recurrent networks that produce an output at each time step and have recurrent connections between hidden units, illustrated in figure. 10. 3 • recurrent networks that produce an output at each time step and have recurrent connections only from the output at... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 394 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
##ymptotically linear in the number of time steps used by the turing machine and asymptotically linear in the length of the input ( siegelmann and sontag 1991 siegelmann 1995 siegelmann and sontag 1995, ;, ;, ; hyotyniemi 1996, ). the functions computable by a turing machine are discrete, so these results regard exact ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 394 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
##ed stack by representing its activations and weights with rational numbers of unbounded precision. we now develop the forward propagation equations for the rnn depicted in figure. the figure does not specify the choice of activation function for the 10. 3 hidden units. here we assume the hyperbolic tangent activation f... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 394 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets u v w o ( t−1 ) o ( t−1 ) h o y l x o ( ) t o ( ) t o ( + 1 ) t o ( + 1 ) t l ( t−1 ) l ( t−1 ) l ( ) t l ( ) t l ( + 1 ) t l ( + 1 ) t y ( t−1 ) y ( t−1 ) y ( ) t y ( ) t y ( + 1 ) t y ( + 1 ) t h ( t−1 ) h ( t−1 ) h ( ) t h ( ) t h ( + 1 ) t h ( + 1 ) t x (... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 395 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
##fold figure 10. 4 : an rnn whose only recurrence is the feedback connection from the output to the hidden layer. at each time step t, the input is xt, the hidden layer activations are h ( ) t, the outputs are o ( ) t, the targets are y ( ) t and the loss is l ( ) t. ( left ) circuit diagram. ( right ) unfolded comput... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 395 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
, via the predictions it was used to produce. unless o is very high - dimensional and rich, it will usually lack important information from the past. this makes the rnn in this figure less powerful, but it may be easier to train because each time step can be trained in isolation from the others, allowing greater paralle... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 395 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets t t τ = 1 to =, we apply the following update equations : a ( ) t = + b w h ( 1 ) t− + ux ( ) t ( 10. 8 ) h ( ) t = tanh ( a ( ) t ) ( 10. 9 ) o ( ) t = + c v h ( ) t ( 10. 10 ) [UNK] ( ) t = softmax ( o ( ) t ) ( 10. 11 ) where the parameters are the bias ve... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 396 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
if l ( ) t is the negative log - likelihood of y ( ) t given x ( 1 ),..., x ( ) t, then l { x ( 1 ),..., x ( ) τ } {, y ( 1 ),..., y ( ) τ } ( 10. 12 ) = t l ( ) t ( 10. 13 ) = − t log pmodel y ( ) t | { x ( 1 ),..., x ( ) t }, ( 10. 14 ) where pmodel y ( ) t | { x ( 1 ),..., x ( ) t } is given by reading the entry for... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 396 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
a backward propagation pass 10. 3 moving right to left through the graph. the runtime is o ( τ ) and cannot be reduced by parallelization because the forward propagation graph is inherently sequential ; each time step may only be computed after the previous one. states computed in the forward pass must be stored until ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 396 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets because it lacks hidden - to - hidden recurrent connections. for example, it cannot simulate a universal turing machine. because this network lacks hidden - to - hidden recurrence, it requires that the output units capture all of the information about the pas... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 397 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
the training set provides the ideal value of that output. h ( t−1 ) h ( t−1 ) w h ( ) t h ( ) t...... x ( t−1 ) x ( t−1 ) x ( ) t x ( ) t x ( )... x ( )... w w u u u h ( ) τ h ( ) τ x ( ) τ x ( ) τ w u o ( ) τ o ( ) τ y ( ) τ y ( ) τ l ( ) τ l ( ) τ v...... figure 10. 5 : time - unfolded recurrent neural network with a... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 397 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
modules. models that have recurrent connections from their outputs leading back into the model may be trained with teacher forcing. teacher forcing is a procedure that emerges from the maximum likelihood criterion, in which during training the model receives the ground truth output y ( ) t as input at time t + 1. we ca... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 397 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets o ( t−1 ) o ( t−1 ) o ( ) t o ( ) t h ( t−1 ) h ( t−1 ) h ( ) t h ( ) t x ( t−1 ) x ( t−1 ) x ( ) t x ( ) t w v v u u o ( t−1 ) o ( t−1 ) o ( ) t o ( ) t l ( t−1 ) l ( t−1 ) l ( ) t l ( ) t y ( t−1 ) y ( t−1 ) y ( ) t y ( ) t h ( t−1 ) h ( t−1 ) h ( ) t h ( )... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 398 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
time step. ( left ) at train time, we feed the correct outputy ( ) t drawn from the train set as input to h ( + 1 ) t. when the model is deployed, the true output is generally ( right ) not known. in this case, we approximate the correct output y ( ) t with the model ’ s output o ( ) t, and feed the output back into th... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 398 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets likelihood criterion is log p y ( 1 ), y ( 2 ) | x ( 1 ), x ( 2 ) ( 10. 15 ) = log p y ( 2 ) | y ( 1 ), x ( 1 ), x ( 2 ) + log p y ( 1 ) | x ( 1 ), x ( 2 ) ( 10. 16 ) in this example, we see that at time t = 2, the model is trained to maximize the conditional... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 399 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
hidden connections. teacher forcing may still be applied to models that have hidden - to - hidden connections so long as they have connections from the output at one time step to values computed in the next time step. however, as soon as the hidden units become a function of earlier time steps, the bptt algorithm is ne... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 399 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
to take into account input conditions ( such as those it generates itself in the free - running mode ) not seen during training and how to map the state back towards one that will make the network generate proper outputs after a few steps. another approach ( bengio et al., ) to mitigate the gap between the inputs seen ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 399 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets to the unrolled computational graph. no specialized algorithms are necessary. gradients obtained by back - propagation may then be used with any general - purpose gradient - based techniques to train an rnn. to gain some intuition for how the bptt algorithm b... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 400 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
in this derivation we assume that the outputs o ( ) t are used as the argument to the softmax function to obtain the vector [UNK] of probabilities over the output. we also assume that the loss is the negative log - likelihood of the true target y ( ) t given the input so far. the gradient ∇o ( ) t l on the outputs at t... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 400 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
) we can then iterate backwards in time to back - propagate gradients through time, from t = τ −1 down to t = 1, noting that h ( ) t ( for t < τ ) has as descendents both o ( ) t and h ( + 1 ) t. its gradient is thus given by ∇h ( ) t l = ∂h ( + 1 ) t ∂h ( ) t ( ∇h ( + 1 ) t l ) + ∂o ( ) t ∂h ( ) t ( ∇o ( ) t l ) ( 10.... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 400 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets once the gradients on the internal nodes of the computational graph are obtained, we can obtain the gradients on the parameter nodes. because the parameters are shared across many time steps, we must take some care when denoting calculus operations involving ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 401 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
##cl = t ∂o ( ) t ∂c ∇o ( ) t l = t ∇o ( ) t l ( 10. 22 ) ∇bl = t ∂h ( ) t ∂b ( ) t ∇h ( ) t l = t diag 1 − h ( ) t 2 ∇h ( ) t l ( 10. 23 ) ∇v l = t i ∂l ∂o ( ) t i ∇v o ( ) t i = t ( ∇o ( ) t l ) h ( ) t ( 10. 24 ) ∇wl = t i ∂l ∂h ( ) t i ∇w ( ) t h ( ) t i ( 10. 25 ) = t diag 1 − h ( ) t 2 ( ∇h ( ) t l ) h ( 1 ) t− (... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 401 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
t 2 ( ∇h ( ) t l ) x ( ) t ( 10. 28 ) we do not need to compute the gradient with respect to x ( ) t for training because it does not have any parameters as ancestors in the computational graph defining the loss. 386 | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 401 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets 10. 2. 3 recurrent networks as directed graphical models in the example recurrent network we have developed so far, the losses l ( ) t were cross - entropies between training targetsy ( ) t and outputs o ( ) t. as with a feedforward network, it is in principl... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 402 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
next 10. 12 sequence element y ( ) t given the past inputs. this may mean that we maximize the log - likelihood log ( p y ( ) t | x ( 1 ),..., x ( ) t ), ( 10. 29 ) or, if the model includes connections from the output at one time step to the next time step, log ( p y ( ) t | x ( 1 ),..., x ( ) t, y ( 1 ),..., y ( 1 ) ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 402 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
independent given the sequence of x values. when we do feed the actual y values ( not their prediction, but the actual observed or generated values ) back into the network, the directed graphical model contains edges from all y ( ) i values in the past to the current y ( ) t value. as a simple example, let us consider ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 402 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
( 2 ) t−,..., y ( 1 ) ) ( 10. 31 ) where the right - hand side of the bar is empty for t = 1, of course. hence the negative log - likelihood of a set of values { y ( 1 ),..., y ( ) τ } according to such a model 387 | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 402 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets y ( 1 ) y ( 1 ) y ( 2 ) y ( 2 ) y ( 3 ) y ( 3 ) y ( 4 ) y ( 4 ) y ( 5 ) y ( 5 ) y ( )... y ( )... figure 10. 7 : fully connected graphical model for a sequencey ( 1 ), y ( 2 ),..., y ( ) t,... : every past observation y ( ) i may influence the conditional dist... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 403 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
10. 32 ) where l ( ) t = log ( − p y ( ) t = y ( ) t | y ( 1 ) t−, y ( 2 ) t−,..., y ( 1 ) ). ( 10. 33 ) y ( 1 ) y ( 1 ) y ( 2 ) y ( 2 ) y ( 3 ) y ( 3 ) y ( 4 ) y ( 4 ) y ( 5 ) y ( 5 ) y ( )... y ( )... h ( 1 ) h ( 1 ) h ( 2 ) h ( 2 ) h ( 3 ) h ( 3 ) h ( 4 ) h ( 4 ) h ( 5 ) h ( 5 ) h ( )... h ( )... figure 10. 8 : intr... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 403 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
every stage in the sequence ( for 10. 5 h ( ) t and y ( ) t ) involves the same structure ( the same number of inputs for each node ) and can share the same parameters with the other stages. the edges in a graphical model indicate which variables depend directly on other variables. many graphical models aim to achieve ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 403 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets example, it is common to make the markov assumption that the graphical model should only contain edges from { y ( ) t k −,..., y ( 1 ) t− } to y ( ) t, rather than containing edges from the entire past history. however, in some cases, we believe that all past... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 404 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
figure. the complete 10. 7 graph interpretation of the rnn is based on ignoring the hidden units h ( ) t by marginalizing them out of the model. it is more interesting to consider the graphical model structure of rnns that results from regarding the hidden units h ( ) t as random variables. 1 including the hidden units ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 404 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
scale with sequence length. equation shows that the rnn parametrizes 10. 5 long - term relationships between variables [UNK], using recurrent applications of the same function f and same parameters θ at each time step. figure 10. 8 illustrates the graphical model interpretation. incorporating the h ( ) t nodes in the g... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 404 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets values in the middle of the sequence. the price recurrent networks pay for their reduced number of parameters is that the parameters may be [UNK]. optimizing the parameter sharing used in recurrent networks relies on the assumption that the same parameters ca... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 405 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
describe how to draw samples from the model. the main operation that we need to perform is simply to sample from the conditional distribution at each time step. however, there is one additional complication. the rnn must have some mechanism for determining the length of the sequence. this can be achieved in various way... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 405 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
for example, it may be applied to an rnn that emits a sequence of real numbers. the new output unit is usually a sigmoid unit trained with the cross - entropy loss. in this approach the sigmoid is trained to maximize the log - probability of the correct prediction as to whether the sequence ends or continues at each ti... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 405 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets time steps. without this extra input, the rnn might generate sequences that end abruptly, such as a sentence that ends before it is complete. this approach is based on the decomposition p ( x ( 1 ),..., x ( ) τ ) = ( ) ( p τ p x ( 1 ),..., x ( ) τ | τ. ) ( 10... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 406 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
extension of the graphical model view to represent not only a joint distribution over the y variables but also a conditional distribution over y given x. as discussed in the context of feedforward networks in section, any model representing a variable 6. 2. 1. 1 p ( y ; θ ) can be reinterpreted as a model representing ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 406 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
of the rnn that generates the y sequence. some common ways of providing an extra input to an rnn are : 1. as an extra input at each time step, or 2. as the initial state h ( 0 ), or 3. both. the first and most common approach is illustrated in figure. the interaction 10. 9 between the input x and each hidden unit vector ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 406 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets of xr that is [UNK] a new bias parameter used for each of the hidden units. the weights remain independent of the input. we can think of this model as taking the parameters θ of the non - conditional model and turning them into ω, where the bias parameters wi... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 407 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
s ( )... h ( )... h ( )... v v v u u u x y ( )... y ( )... r r r r r figure 10. 9 : an rnn that maps a fixed - length vectorx into a distribution over sequences y. this rnn is appropriate for tasks such as image captioning, where a single image is used as input to a model that then produces a sequence of words describin... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 407 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
..., x ( ) τ ) that makes a conditional independence assumption that this distribution factorizes as t p ( y ( ) t | x ( 1 ),..., x ( ) t ). ( 10. 35 ) to remove the conditional independence assumption, we can add connections from the output at time t to the hidden unit at time t + 1, as shown in figure. the 10. 10 mode... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 407 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets o ( t−1 ) o ( t−1 ) o ( ) t o ( ) t o ( + 1 ) t o ( + 1 ) t l ( t−1 ) l ( t−1 ) l ( ) t l ( ) t l ( + 1 ) t l ( + 1 ) t y ( t−1 ) y ( t−1 ) y ( ) t y ( ) t y ( + 1 ) t y ( + 1 ) t h ( t−1 ) h ( t−1 ) h ( ) t h ( ) t h ( + 1 ) t h ( + 1 ) t w w w w h ( )... h ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 408 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
conditional recurrent neural network mapping a variable - length sequence of x values into a distribution over sequences of y values of the same length. compared to figure, this rnn contains connections from the previous output to the current state. 10. 3 these connections allow this rnn to model an arbitrary distributi... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 408 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets sequence still has one restriction, which is that the length of both sequences must be the same. we describe how to remove this restriction in section. 10. 4 o ( t−1 ) o ( t−1 ) o ( ) t o ( ) t o ( + 1 ) t o ( + 1 ) t l ( t−1 ) l ( t−1 ) l ( ) t l ( ) t l ( +... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 409 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
( ) t g ( ) t g ( + 1 ) t g ( + 1 ) t figure 10. 11 : computation of a typical bidirectional recurrent neural network, meant to learn to map input sequences x to target sequences y, with loss l ( ) t at each step t. the h recurrence propagates information forward in time ( towards the right ) while the g recurrence pro... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 409 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
##−, and the present input x ( ) t. some of the models we have discussed also allow information from past y values to [UNK] the current state when the y values are available. however, in many applications we want to output a prediction of y ( ) t which may 394 | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 409 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets depend on the whole input sequence. for example, in speech recognition, the correct interpretation of the current sound as a phoneme may depend on the next few phonemes because of co - articulation and potentially may even depend on the next few words because... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 410 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
, ;, ), speech recogni - tion ( graves and schmidhuber 2005 graves 2013 baldi, ; et al., ) and bioinformatics ( et al., ). 1999 as the name suggests, bidirectional rnns combine an rnn that moves forward through time beginning from the start of the sequence with another rnn that moves backward through time beginning fro... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 410 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
##lutional network, or a regular rnn with a fixed - size look - ahead [UNK] ). this idea can be naturally extended to 2 - dimensional input, such as images, by having rnns, each one going in one of the four directions : up, down, left, four right. at each point ( i, j ) of a 2 - d grid, an output oi, j could then comput... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 410 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets 10. 4 encoder - decoder sequence - to - sequence architec - tures we have seen in figure how an rnn can map an input sequence to a fixed - size 10. 5 vector. we have seen in figure how an rnn can map a fixed - size vector to a 10. 9 sequence. we have seen in figur... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 411 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
) c figure 10. 12 : example of an encoder - decoder or sequence - to - sequence rnn architecture, for learning to generate an output sequence ( y ( 1 ),..., y ( n y ) ) given an input sequence ( x ( 1 ), x ( 2 ),..., x ( nx ) ). it is composed of an encoder rnn that reads the input sequence and a decoder rnn that gener... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 411 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets answering, where the input and output sequences in the training set are generally not of the same length ( although their lengths might be related ). we often call the input to the rnn the “ context. ” we want to produce a representation of this context, c. t... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 412 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
these authors respectively called this architecture, illustrated in figure, the encoder - decoder or sequence - to - sequence architecture. the 10. 12 idea is very simple : ( 1 ) an encoder or reader or input rnn processes the input sequence. the encoder emits the context c, usually as a simple function of its final hidd... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 412 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
, y ( ny ) | x ( 1 ),..., x ( nx ) ) over all the pairs of x and y sequences in the training set. the last state hnx of the encoder rnn is typically used as a representation c of the input sequence that is provided as input to the decoder rnn. if the context c is a vector, then the decoder rnn is simply a vector - to -... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 412 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
has a dimension that is too small to properly summarize a long sequence. this phenomenon was observed by ( ) in the context bahdanau et al. 2015 of machine translation. they proposed to make c a variable - length sequence rather than a fixed - size vector. additionally, they introduced an attention mechanism that learns... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 412 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets sequence. see section for more details. 12. 4. 5. 1 10. 5 deep recurrent networks the computation in most rnns can be decomposed into three blocks of parameters and associated transformations : 1. from the input to the hidden state, 2. from the previous hidde... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 413 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
al., ) strongly suggests so. the experimental evidence is in agreement with the idea that we need enough depth in order to perform the required mappings. see also schmidhuber 1992 ( ), el hihi and bengio 1996 jaeger 2007a ( ), or ( ) for earlier work on deep rnns. graves 2013 et al. ( ) were the first to show a significa... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 413 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
representational 10. 13 capacity suggest to allocate enough capacity in each of these three steps, but doing so by adding depth may hurt learning by making optimization [UNK]. in general, it is easier to optimize shallower architectures, and adding the extra depth of figure b makes the shortest path from a variable in t... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 413 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets h y x z ( a ) ( b ) ( c ) x h y x h y figure 10. 13 : a recurrent neural network can be made deep in many ways ( pascanu et al., ). the hidden recurrent state can be broken down into groups organized 2014a ( a ) hierarchically. deeper computation ( e. g., an ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 414 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets can be mitigated by introducing skip connections in the hidden - to - hidden path, as illustrated in figure c. 10. 13 10. 6 recursive neural networks x ( 1 ) x ( 1 ) x ( 2 ) x ( 2 ) x ( 3 ) x ( 3 ) v v v y l x ( 4 ) x ( 4 ) v o u w u w u w figure 10. 14 : a re... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 415 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
recursive neural networks2 represent yet another generalization of recurrent networks, with a [UNK] kind of computational graph, which is structured as a deep tree, rather than the chain - like structure of rnns. the typical computational graph for a recursive network is illustrated in figure. recursive neural 10. 14 2w... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 415 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets networks were introduced by pollack 1990 ( ) and their potential use for learning to reason was described by ( ). recursive networks have been successfully bottou 2011 applied to processing data structures as input to neural nets ( frasconi 1997 et al.,, 1998... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 416 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
can suggest the appropriate tree structure. for example, when processing natural language sentences, the tree structure for the recursive network can be fixed to the structure of the parse tree of the sentence provided by a natural language parser (,, ). ideally, one would like the learner itself to socher et al. 2011a ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 416 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
, which have previously been found useful to model relationships between concepts ( weston 2010 bordes 2012 et al., ; et al., ) when the concepts are represented by continuous vectors ( embeddings ). 10. 7 the challenge of long - term dependencies the mathematical challenge of learning long - term dependencies in recur... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 416 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets − − − 60 40 20 0 20 40 60 input coordinate −4 −3 −2 −1 0 1 2 3 4 projection of output 0 1 2 3 4 5 figure 10. 15 : when composing many nonlinear functions ( like the linear - tanh layer shown here ), the result is highly nonlinear, typically with most of the v... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 417 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
et al., ). in this section, we describe the problem in more detail. the remaining sections describe approaches to overcoming the problem. recurrent networks involve the composition of the same function multiple times, once per time step. these compositions can result in extremely nonlinear behavior, as illustrated in fi... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 417 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 10. sequence modeling : recurrent and recursive nets with orthogonal, the recurrence may be simplified further to q h ( ) t = qλtqh ( 0 ). ( 10. 39 ) the eigenvalues are raised to the power of t causing eigenvalues with magnitude less than one to decay to zero and eigenvalues with magnitude greater than one to e... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 418 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
t. suppose that the w ( ) t values are generated randomly, independently from one another, with zero mean and variance v. the variance of the product is o ( vn ). to obtain some desired variance v∗we may choose the individual weights with variance v = n√ v∗. very deep feedforward networks with carefully chosen scaling ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 418 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
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