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a model that can accommodate variable length inputs and variable length outputs. an rnn provides this ability. section describes several ways 10. 2. 4 of constructing an rnn that represents a conditional distribution over a sequence given some input, and section describes how to accomplish this conditioning 10. 4 when ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 489 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
of an encoder - decoder framework for machine translation is illustrated in figure. 12. 5 in order to generate an entire sentence conditioned on the source sentence, the model must have a way to represent the entire source sentence. earlier models were only able to represent individual words or phrases. from a represent... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 489 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 12. applications learning point of view, it can be useful to learn a representation in which sentences that have the same meaning have similar representations regardless of whether they were written in the source language or the target language. this strategy was explored first using a combination of convolution... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 490 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
c × × × + figure 12. 6 : a modern attention mechanism, as introduced by ( ), is bahdanau et al. 2015 essentially a weighted average. a context vectorc is formed by taking a weighted average of feature vectors h ( ) t with weights α ( ) t. in some applications, the feature vectorsh are hidden units of a neural network, ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 490 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
a smooth, [UNK] approximation that can be trained with existing optimization algorithms. using a fixed - size representation to capture all the semantic details of a very long sentence of say 60 words is very [UNK]. it can be achieved by training a [UNK] large rnn well enough and for long enough, as demonstrated by cho ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 490 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 12. applications is being expressed ), then produce the translated words one at a time, each time focusing on a [UNK] part of the input sentence in order to gather the semantic details that are required to produce the next output word. that is exactly the idea that ( ) first introduced. the attention mechanism u... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 491 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
the content of the memory to sequentially perform exploits a task, at each time step having the ability put attention on the content of one memory element ( or a few, with a [UNK] weight ). the third component generates the translated sentence. when words in a sentence written in one language are aligned with correspon... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 491 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
2014 12. 4. 6 historical perspective the idea of distributed representations for symbols was introduced by rumelhart et al. ( ) in one of the first explorations of back - propagation, with symbols 1986a corresponding to the identity of family members and the neural network capturing the relationships between family memb... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 491 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 12. applications might represent which family tree colin was in, what branch of that tree he was in, what generation he was from, etc. one can think of the neural network as computing learned rules relating these attributes together in order to obtain the desired predictions. the model can then make predictions... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 492 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
al. ( ) returned the focus to modeling words and introduced neural language models, which produce interpretable word embeddings. these neural models have scaled up from defining representations of a small set of symbols in the 1980s to millions of words ( including proper nouns and misspellings ) in modern applications.... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 492 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
labeling, chunking, etc, sometimes using a single multi - task learning architecture ( collobert and weston, 2008a collobert 2011a ; et al., ) in which the word embeddings are shared across tasks. two - dimensional visualizations of embeddings became a popular tool for an - alyzing language models following the develop... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 492 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 12. applications 12. 5 other applications in this section we cover a few other types of applications of deep learning that are [UNK] from the standard object recognition, speech recognition and natural language processing tasks discussed above. part of this book will expand that iii scope even further to tasks ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 493 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
forms of online advertising. there are major parts of the economy that rely on online shopping. companies including amazon and ebay use machine learning, including deep learning, for their product recommendations. sometimes, the items are not products that are actually for sale. examples include selecting posts to disp... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 493 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
early work on recommender systems relied on minimal information as inputs for these predictions : the user id and the item id. in this context, the only way to generalize is to rely on the similarity between the patterns of values of the target variable for [UNK] users or for [UNK] items. suppose that user 1 and user 2... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 493 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 12. applications user 2 have similar tastes. if user 1 likes item d, then this should be a strong cue that user 2 will also like d. algorithms based on this principle come under the name of collaborative filtering. both non - parametric approaches ( such as nearest - neighbor methods based on the estimated simil... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 494 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
a matrix with item embeddings in its columns. let b and c be vectors that contain respectively a kind of bias for each user ( representing how grumpy or positive that user is in general ) and for each item ( representing its general popularity ). the bilinear prediction is thus obtained as follows : [UNK], i = bu + ci ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 494 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
variant ) into the product of two factors, the lower rank matrices a = ud and b = v. one problem with the svd is that it treats the missing entries in an arbitrary way, as if they corresponded to a target value of 0. instead we would like to avoid paying any cost for the predictions made on missing entries. fortunately... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 494 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 12. applications presented by most of the competitors, including the winners (, ; toscher et al. 2009 koren 2009, ). beyond these bilinear models with distributed representations, one of the first uses of neural networks for collaborative filtering is based on the rbm undirected probabilistic model ( salakhutdino... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 495 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
, that new user and existing items. this is called the problem of cold - start recommendations. a general way of solving the cold - start recommendation problem is to introduce extra information about the individual users and items. for example, this extra information could be user profile information or features of eac... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 495 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
##ding for a user is then used to predict whether a user will listen to the song. 12. 5. 1. 1 exploration versus exploitation when making recommendations to users, an issue arises that goes beyond ordinary supervised learning and into the realm of reinforcement learning. many recom - mendation problems are most accurat... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 495 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 12. applications ad was below a minimum price threshold, or does not win the auction, so the ad is not shown at all ). more importantly, we get no information about what outcome would have resulted from recommending any of the other items. this would be like training a classifier by picking one class [UNK] for e... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 496 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
in general, reinforcement learning can involve a sequence of many actions and many rewards. the bandits scenario is a special case of reinforcement learning, in which the learner takes only a single action and receives a single reward. the bandit problem is easier in the sense that the learner knows which reward is ass... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 496 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
from the current, best version of the learned policy — actions that we know will achieve a high reward. exploration refers to taking actions specifically in order to obtain more training data. if we know that given context x, action a gives us a reward of 1, we do not know whether that is the best possible reward. we ma... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 496 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 12. applications many factors determine the extent to which we prefer exploration or exploitation. one of the most prominent factors is the time scale we are interested in. if the agent has only a short amount of time to accrue reward, then we prefer more exploitation. if the agent has a long time to accrue rew... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 497 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
that it is not straightforward to evaluate the learner ’ s performance using a fixed set of test set input values. the policy itself determines which inputs will be seen. ( ) present dudik et al. 2011 techniques for evaluating contextual bandits. 12. 5. 2 knowledge representation, reasoning and question an - swering dee... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 497 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
be trained to capture the relations between two entities. these relations allow us to formalize facts about objects and how objects interact with each other. in mathematics, a binary relation is a set of ordered pairs of objects. pairs that are in the set are said to have the relation while those who are not in the set... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 497 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 12. applications do not. for example, we can define the relation “ is less than ” on the set of entities { 1, 2, 3 } by defining the set of ordered pairs s = { ( 1, 2 ), ( 1, 3 ), ( 2, 3 ) }. once this relation is defined, we can use it like a verb. because ( 1, 2 ) ∈s, we say that 1 is less than 2. because ( 2, 1... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 498 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
and object. these sentences take the form of a triplet of tokens ( subject verb object ),, ( 12. 21 ) with values ( entityi, relationj, entityk ). ( 12. 22 ) we can also define an attribute, a concept analogous to a relation, but taking only one argument : ( entityi, attribute j ). ( 12. 23 ) for example, we could define... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 498 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
expert knowledge about an application area to an artificial intelligence system, we call the database a knowledge base. knowledge bases range from general ones like freebase, opencyc, wordnet, or wikibase, 1 etc. to more specialized knowledge bases, like geneontology. 2 representations for entities and relations can be ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 498 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 12. applications in addition to training data, we also need to define a model family to train. a common approach is to extend neural language models to model entities and relations. neural language models learn a vector that provides a distributed representation of each word. they also learn about interactions b... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 499 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
posited highly constrained parametric forms ( “ linear relational embeddings ” ), often using a [UNK] form of representation for the relation than for the entities. for example, paccanaro and hinton 2000 bordes 2011 ( ) and et al. ( ) used vectors for entities and matrices for relations, with the idea that a relation a... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 499 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
( ) and ( ) for examples of such an 2014b lin et al. 2015 garcia - duran et al. 2015 application. evaluating the performance of a model on a link prediction task is [UNK] because we have only a dataset of positive examples ( facts that are known to be true ). if the model proposes a fact that is not in the dataset, we ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 499 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 12. applications another application of knowledge bases and distributed representations for them is word - sense disambiguation ( navigli and velardi 2005 bordes, ; et al., 2012 ), which is the task of deciding which of the senses of a word is the appropriate one, in some context. eventually, knowledge of relat... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 500 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
an extension that uses gru recurrent nets to read 2015 the input into the memory and to produce the answer given the contents of the memory. deep learning has been applied to many other applications besides the ones described here, and will surely be applied to even more after this writing. it would be impossible to de... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 500 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
part iii deep learning research 486 | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 501 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
this part of the book describes the more ambitious and advanced approaches to deep learning, currently pursued by the research community. in the previous parts of the book, we have shown how to solve supervised learning problems — how to learn to map one vector to another, given enough examples of the mapping. not all ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 502 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
unsupervised learning problems, but none have truly solved the problem in the same way that deep learning has largely solved the supervised learning problem for a wide variety of tasks. in this part of the book, we describe the existing approaches to unsupervised learning and some of the popular thought about how we ca... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 502 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
that grow exponentially with the number of dimensions. with probabilistic models, this computational challenge arises from the need to perform intractable inference or simply from the need to normalize the distribution. • intractable inference : inference is discussed mostly in chapter. it regards 19 the question of gu... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 502 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
a, b and c. in order to even compute such conditional probabilities one needs to sum over the values of the variables c, as well as compute a normalization constant which sums over the values of a and c. • intractable normalization constants ( the partition function ) : the partition function is discussed mostly in cha... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 503 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
- separated, especially in high - dimensional spaces ( section ). 17. 5 one way to confront these intractable computations is to approximate them, and many approaches have been proposed as discussed in this third part of the book. another interesting way, also discussed here, would be to avoid these intractable computa... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 503 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 13 linear factor models many of the research frontiers in deep learning involve building a probabilistic model of the input, pmodel ( x ). such a model can, in principle, use probabilistic inference to predict any of the variables in its environment given any of the other variables. many of these models also ha... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 504 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
models ( et al., ). they also show many of the basic approaches necessary to build generative models that the more advanced deep models will extend further. a linear factor model is defined by the use of a stochastic, linear decoder function that generates by adding noise to a linear transformation of. x h these models ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 504 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 13. linear factor models sample from. next we sample the real - valued observable variables given the factors : x w h b = + + noise ( 13. 2 ) where the noise is typically gaussian and diagonal ( independent across dimensions ). this is illustrated in figure. 13. 1 h1 h1 h2 h2 h3 h3 x1 x1 x2 x2 x3 x3 x h n ois e ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 505 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
##a ( principal components analysis ), factor analysis and other linear factor models are special cases of the above equations ( and ) and only 13. 1 13. 2 [UNK] in the choices made for the noise distribution and the model ’ s prior over latent variables before observing. h x in factor analysis (, ;, ), the latent vari... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 505 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 13. linear factor models in order to cast pca in a probabilistic framework, we can make a slight modification to the factor analysis model, making the conditional variances σ2 i equal to each other. in that case the covariance of x is just ww + σ2i, where σ2 is now a scalar. this yields the conditional distribut... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 506 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
##bilistic pca becomes pca as σ →0. in that case, the conditional expected value of h given x becomes an orthogonal projection of x b − onto the space spanned by the columns of, like in pca. d w as σ →0, the density model defined by probabilistic pca becomes very sharp around these d dimensions spanned by the columns of... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 506 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
scaled and added together to form the observed data. these signals are intended to be fully independent, rather than merely decorrelated from each other. 1 many [UNK] specific methodologies are referred to as ica. the variant that is most similar to the other generative models we have described here is a variant (, ) th... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 506 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 13. linear factor models nonlinear change of variables ( using equation ) to determine 3. 47 p ( x ). learning the model then proceeds as usual, using maximum likelihood. the motivation for this approach is that by choosing p ( h ) to be independent, we can recover underlying factors that are as close as possib... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 507 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
for recording electrical signals originating in the brain. many electrode sensors placed on the subject ’ s head are used to measure many electrical signals coming from the body. the experimenter is typically only interested in signals from the brain, but signals from the subject ’ s heart and eyes are strong enough to... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 507 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
variants of ica avoid this problematic operation by constraining to be orthogonal. w all variants of ica require that p ( h ) be non - gaussian. this is because if p ( h ) is an independent prior with gaussian components, then w is not identifiable. we can obtain the same distribution over p ( x ) for many values of w. ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 507 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 13. linear factor models many variants of ica are not generative models in the sense that we use the phrase. in this book, a generative model either represents p ( x ) or can draw samples from it. many variants of ica only know how to transform between x and h, but do not have any way of representing p ( h ), a... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 508 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
generate the observed data. see hyvarinen and pajunen 1999 ( ) for the initial work on nonlinear ica and its successful use with ensemble learning by ( ) and ( ). roberts and everson 2001 lappalainen et al. 2000 another nonlinear extension of ica is the approach of nonlinear independent components estimation, or nice (... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 508 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
##ization of ica is to learn groups of features, with statistical dependence allowed within a group but discouraged between groups ( hyvarinen and hoyer 1999 hyvarinen 2001b, ; et al., ). when the groups of related units are chosen to be non - overlapping, this is called independent subspace analysis. it is also possib... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 508 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 13. linear factor models time signals to learn invariant features (, ). wiskott and sejnowski 2002 slow feature analysis is motivated by a general principle called the slowness principle. the idea is that the important characteristics of scenes change very slowly compared to the individual measurements that mak... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 509 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
bergstra and bengio 2009, ). in general, we can apply the slowness principle to any [UNK] model trained with gradient descent. the slowness principle may be introduced by adding a term to the cost function of the form λ t l f ( ( x ( + 1 ) t ) (, f x ( ) t ) ) ( 13. 7 ) where λ is a hyperparameter determining the stren... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 509 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
se, in the sense that it defines a linear map between input space and feature space but does not define a prior over feature space and thus does not impose a distribution on input space. p ( ) x the sfa algorithm ( wiskott and sejnowski 2002, ) consists of defining f ( x ; θ ) to be a linear transformation, and solving th... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 509 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 13. linear factor models the constraint that the learned feature have zero mean is necessary to make the problem have a unique solution ; otherwise we could add a constant to all feature values and obtain a [UNK] solution with equal value of the slowness objective. the constraint that the features have unit var... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 510 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
due to the linearity of sfa features. the sfa problem may be solved in closed form by a linear algebra package. sfa is typically used to learn nonlinear features by applying a nonlinear basis expansion to x before running sfa. for example, it is common to replace x by the quadratic basis expansion, a vector containing ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 510 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
in rat brains that are used for navigation ( franzius 2007 et al., ). sfa thus seems to be a reasonably biologically plausible model. a major advantage of sfa is that it is possibly to theoretically predict which features sfa will learn, even in the deep, nonlinear setting. to make such theoretical predictions, one mus... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 510 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 13. linear factor models this is in comparison to other learning algorithms where the cost function depends highly on specific pixel values, making it much more [UNK] to determine what features the model will learn. deep sfa has also been used to learn features for object recognition and pose estimation ( franzi... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 511 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
has olshausen and field 1996 been heavily studied as an unsupervised feature learning and feature extraction mechanism. strictly speaking, the term “ sparse coding ” refers to the process of inferring the value of h in this model, while “ sparse modeling ” refers to the process of designing and learning the model, but ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 511 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
or factorized student - t distributions. for example, the laplace prior parametrized in terms of the sparsity penalty [UNK] is given by λ p h ( i ) = laplace ( hi ; 0, 2 λ ) = λ 4e−1 2 λ h | i | ( 13. 13 ) and the student - prior by t p h ( i ) [UNK] 1 ( 1 + h2 i ν ) ν + 1 2. ( 13. 14 ) 496 | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 511 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 13. linear factor models training sparse coding with maximum likelihood is intractable. instead, the training alternates between encoding the data and training the decoder to better reconstruct the data given the encoding. this approach will be justified further as a principled approximation to maximum likelihoo... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 512 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
) = arg max h log ( ) p h x | ( 13. 17 ) = arg min h λ | | | | h 1 + β | | − | | x wh 2 2, ( 13. 18 ) where we have dropped terms not depending on h and divided by positive scaling factors to simplify the equation. due to the imposition of an l1 norm on h, this procedure will yield a sparse h∗ ( see section ). 7. 1. 2 ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 512 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
β. to learn β, these terms must be included, or β will collapse to. 0 not all approaches to sparse coding explicitly build a p ( h ) and a p ( x h | ). often we are just interested in learning a dictionary of features with activation values that will often be zero when extracted using this inference procedure. if we sa... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 512 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 13. linear factor models inference in a [UNK] model family, the spike and slab sparse coding model, for which samples from the prior usually contain true zeros. the sparse coding approach combined with the use of the non - parametric encoder can in principle minimize the combination of reconstruction error and ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 513 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
unfamiliar points, but this is due to generalization error in the decoder weights, rather than generalization error in the encoder. the lack of generalization error in sparse coding ’ s optimization - based encoding process may result in better generalization when sparse coding is used as a feature extractor for a clas... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 513 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
iterative algorithm. the parametric autoencoder approach, developed in chapter, uses only a fixed number of layers, often only one. another 14 disadvantage is that it is not straight - forward to back - propagate through the non - parametric encoder, which makes it [UNK] to pretrain a sparse coding model with an unsuper... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 513 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 13. linear factor models figure 13. 2 : example samples and weights from a spike and slab sparse coding model trained on the mnist dataset. ( left ) the samples from the model do not resemble the training examples. at first glance, one might assume the model is poorly fit. the ( right ) weight vectors of the mode... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 514 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
, ). we can view probabilistic pca as hinton et al. 1997 defining a thin pancake - shaped region of high probability — a gaussian distribution that is very narrow along some axes, just as a pancake is very flat along its vertical axis, but is elongated along other axes, just as a pancake is wide along its horizontal axes... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 514 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 13. linear factor models the encoder computes a low - dimensional representation of h. with the autoencoder view, we have a decoder computing the reconstruction [UNK] h b v h = ( g ) = +. ( 13. 20 ) figure 13. 3 : flat gaussian capturing probability concentration near a low - dimensional manifold. the figure sho... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 515 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
form an orthonormal basis which spans the same subspace as the principal eigenvectors of the covariance matrix c x µ x µ = [ ( e − ) ( − ) ]. ( 13. 22 ) in the case of pca, the columns of w are these eigenvectors, ordered by the magnitude of the corresponding eigenvalues ( which are all real and non - negative ). one c... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 515 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 13. linear factor models optimal reconstruction error ( choosing,, and as above ) is µ b v w min [ e | | − x [UNK] | | 2 ] = d i d = + 1 λi. ( 13. 23 ) hence, if the covariance has rank d, the eigenvalues λd + 1 to λd are 0 and recon - struction error is 0. furthermore, one can also show that the above solution... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 516 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 14 autoencoders an autoencoder is a neural network that is trained to attempt to copy its input to its output. internally, it has a hidden layer h that describes a code used to represent the input. the network may be viewed as consisting of two parts : an encoder function h = f ( x ) and a decoder that produces... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 517 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
##coder and a de - coder beyond deterministic functions to stochastic mappings pencoder ( h x | ) and pdecoder ( ) x h |. the idea of autoencoders has been part of the historical landscape of neural networks for decades (, ;, ;, lecun 1987 bourlard and kamp 1988 hinton and zemel 1994 ). traditionally, autoencoders were... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 517 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 14. autoencoders to the activations on the reconstructed input. recirculation is regarded as more biologically plausible than back - propagation, but is rarely used for machine learning applications. x r h f g figure 14. 1 : the general structure of an autoencoder, mapping an input to an output x ( called recon... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 518 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
dimension is less than the input dimension is called undercomplete. learning an undercomplete representation forces the autoencoder to capture the most salient features of the training data. the learning process is described simply as minimizing a loss function l, g f ( x ( ( ) ) ) x ( 14. 1 ) where l is a loss functio... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 518 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 14. autoencoders nately, if the encoder and decoder are allowed too much capacity, the autoencoder can learn to perform the copying task without extracting useful information about the distribution of the data. theoretically, one could imagine that an autoencoder with a one - dimensional code but a very powerfu... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 519 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
have seen that these autoencoders fail to learn anything useful if the encoder and decoder are given too much capacity. a similar problem occurs if the hidden code is allowed to have dimension equal to the input, and in the overcomplete case in which the hidden code has dimension greater than the input. in these cases,... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 519 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
##ity of the representation, smallness of the derivative of the representation, and robustness to noise or to missing inputs. a regularized autoencoder can be nonlinear and overcomplete but still learn something useful about the data distribution even if the model capacity is great enough to learn a trivial identity fu... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 519 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 14. autoencoders autoencoder ( section ) and the generative stochastic networks ( section ). 20. 10. 3 20. 12 these models naturally learn high - capacity, overcomplete encodings of the input and do not require regularization for these encodings to be useful. their encodings are naturally useful because the mod... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 520 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
task such as classification. an autoencoder that has been regularized to be sparse must respond to unique statistical features of the dataset it has been trained on, rather than simply acting as an identity function. in this way, training to perform the copying task with a sparsity penalty can yield a model that has lea... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 520 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
probability distribution over the model parameters. in this view, regularized maximum likelihood corresponds to maximizing p ( θ x | ), which is equivalent to maximizing log p ( x θ | ) + log p ( θ ). the log p ( x θ | ) term is the usual data log - likelihood term and the log p ( θ ) term, the log - prior over paramet... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 520 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 14. autoencoders maximum likelihood training of a generative model that has latent variables. suppose we have a model with visible variables x and latent variables h, with an explicit joint distribution pmodel ( x h, ) = p model ( h ) pmodel ( x h | ). we refer to pmodel ( h ) as the model ’ s prior distributio... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 521 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
coding generative model ( section ), but with 13. 4 h being the output of the parametric encoder rather than the result of an optimization that infers the most likely h. from this point of view, with this chosen, we are maximizing h log pmodel ( ) = log h x, pmodel ( ) + log h pmodel ( ) x h |. ( 14. 4 ) the log pmodel... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 521 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
term depends only on λ and not h. we typically treat λ as a hyperparameter and discard the constant term since it does not [UNK] the parameter learning. other priors such as the student - t prior can also induce sparsity. from this point of view of sparsity as resulting from the [UNK] of pmodel ( h ) on approximate max... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 521 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 14. autoencoders why the features learned by the autoencoder are useful : they describe the latent variables that explain the input. early work on sparse autoencoders (,, ) explored ranzato et al. 2007a 2008 various forms of sparsity and proposed a connection between the sparsity penalty and the log z term that... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 522 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
h | is more mathematically straightforward. one way to achieve actual zeros in h for sparse ( and denoising ) autoencoders was introduced in ( ). the idea is to use rectified linear units to glorot et al. 2011b produce the code layer. with a prior that actually pushes the representations to zero ( like the absolute valu... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 522 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
to be merely an identity function if they have the capacity to do so. a or dae instead minimizes denoising autoencoder l, g f ( x ( ( [UNK] ) ) ), ( 14. 9 ) where [UNK] is a copy of x that has been corrupted by some form of noise. denoising autoencoders must therefore undo this corruption rather than simply copying the... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 522 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 14. autoencoders autoencoders thus provide yet another example of how useful properties can emerge as a byproduct of minimizing reconstruction error. they are also an example of how overcomplete, high - capacity models may be used as autoencoders so long as care is taken to prevent them from learning the identi... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 523 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
applied only at training examples, it forces the autoencoder to learn features that capture information about the training distribution. an autoencoder regularized in this way is called a contractive autoencoder or cae. this approach has theoretical connections to denoising autoencoders, manifold learning and probabili... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 523 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
these components of the autoencoder can individually benefit from depth. one major advantage of non - trivial depth is that the universal approximator theorem guarantees that a feedforward neural network with at least one hidden layer can represent an approximation of any function ( within a broad class ) to an 508 | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 523 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 14. autoencoders arbitrary degree of accuracy, provided that it has enough hidden units. this means that an autoencoder with a single hidden layer is able to represent the identity function along the domain of the data arbitrarily well. however, the mapping from input to code is shallow. this means that we are ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 524 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
##akhutdinov 2006, ). a common strategy for training a deep autoencoder is to greedily pretrain the deep architecture by training a stack of shallow autoencoders, so we often encounter shallow autoencoders, even when the ultimate goal is to train a deep autoencoder. 14. 4 stochastic encoders and decoders autoencoders a... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 524 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
well as the input. however, we can still apply the same machinery as before. given a hidden code h, we may think of the decoder as providing a conditional distribution p decoder ( x h | ). we may then train the autoencoder by minimizing −log pdecoder ( ) x h |. the exact form of this loss function will change depending... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 524 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 14. autoencoders typically, the output variables are treated as being conditionally independent given h so that this probability distribution is inexpensive to evaluate, but some techniques such as mixture density outputs allow tractable modeling of outputs with correlations. x r h pencoder ( ) h x | pdecoder (... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 525 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
model pmodel ( ) h x, defines a stochastic encoder pencoder ( ) = h x | pmodel ( ) h x | ( 14. 12 ) and a stochastic decoder pdecoder ( ) = x h | pmodel ( ) x h |. ( 14. 13 ) in general, the encoder and decoder distributions are not necessarily conditional distributions compatible with a unique joint distribution pmodel... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 525 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 14. autoencoders [UNK] l h f g x c ( [UNK] x | ) figure 14. 3 : the computational graph of the cost function for a denoising autoencoder, which is trained to reconstruct the clean data point x from its corrupted version [UNK]. this is accomplished by minimizing the loss l = −log pdecoder ( x h | = f ( [UNK] ) )... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 526 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
. 3. use ( x, [UNK] ) as a training example for estimating the autoencoder reconstruction distribution preconstruct ( x | [UNK] ) = pdecoder ( x h | ) with h the output of encoder f ( [UNK] ) and pdecoder typically defined by a decoder. g ( ) h typically we can simply perform gradient - based approximate minimization ( ... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 526 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
chapter 14. autoencoders x [UNK] g f [UNK] [UNK] c ( [UNK] x | ) x figure 14. 4 : a denoising autoencoder is trained to map a corrupted data [UNK] back to the original data point x. we illustrate training examples x as red crosses lying near a low - dimensional manifold illustrated with the bold black line. we illustra... | /home/ricoiban/GEMMA/mnlp_chatsplaining/RAG/Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org).pdf | 527 | Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville (z-lib.org) | 0 |
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