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generative adversarial nets were recently introduced as an alternative framework for training generative models in order to sidestep the difficulty of approximating many intractable probabilistic computations .
adversarial nets have the advantages that markov chains are never needed , only backpropagation is used to obtain gradients , no inference is required during learning , and a wide variety of factors and interactions can easily be incorporated into the model .
furthermore , as demonstrated in @xcite , it can produce state of the art log - likelihood estimates and realistic samples .    in an unconditioned generative model
, there is no control on modes of the data being generated .
however , by conditioning the model on additional information it is possible to direct the data generation process .
such conditioning could be based on class labels , on some part of data for inpainting like @xcite , or even on data from different modality .    in this work
we show how can we construct the conditional adversarial net . and
for empirical results we demonstrate two set of experiment .
one on mnist digit data set conditioned on class labels and one on mir flickr 25,000 dataset @xcite for multi - modal learning .
despite the many recent successes of supervised neural networks ( and convolutional networks in particular ) @xcite , it remains challenging to scale such models to accommodate an extremely large number of predicted output categories .
a second issue is that much of the work to date has focused on learning one - to - one mappings from input to output .
however , many interesting problems are more naturally thought of as a probabilistic one - to - many mapping .
for instance in the case of image labeling there may be many different tags that could appropriately applied to a given image , and different ( human ) annotators may use different ( but typically synonymous or related ) terms to describe the same image .    one way to help address the first issue is to leverage additional information from other modalities : for instance , by using natural language corpora to learn a vector representation for labels in which geometric relations are semantically meaningful .
when making predictions in such spaces , we benefit from the fact that when prediction errors we are still often ` close ' to the truth ( e.g. predicting table instead of chair ) , and also from the fact that we can naturally make predictive generalizations to labels that were not seen during training time . works such as @xcite
have shown that even a simple linear mapping from image feature - space to word - representation - space can yield improved classification performance .    one way to address
the second problem is to use a conditional probabilistic generative model , the input is taken to be the conditioning variable and the one - to - many mapping is instantiated as a conditional predictive distribution .
@xcite take a similar approach to this problem , and train a multi - modal deep boltzmann machine on the mir flickr 25,000 dataset as we do in this work .
additionally , in @xcite the authors show how to train a supervised multi - modal neural language model , and they are able to generate descriptive sentence for images .
generative adversarial nets were recently introduced as a novel way to train a generative model .
they consists of two ` adversarial ' models : a generative model @xmath1 that captures the data distribution , and a discriminative model @xmath2 that estimates the probability that a sample came from the training data rather than @xmath1 .
both @xmath1 and @xmath2 could be a non - linear mapping function , such as a multi - layer perceptron .    to learn a generator distribution @xmath3 over data data @xmath4 ,
the generator builds a mapping function from a prior noise distribution @xmath5 to data space as @xmath6 .
and the discriminator , @xmath7 , outputs a single scalar representing the probability that @xmath4 came form training data rather than @xmath3 .
@xmath1 and @xmath2 are both trained simultaneously : we adjust parameters for @xmath1 to minimize @xmath8 and adjust parameters for @xmath9 to minimize @xmath10 , as if they are following the two - player min - max game with value function @xmath11 :    @xmath12 + \mathbb{e}_{\bm{z } \sim p_z(\bm{z})}[\log ( 1 - d(g(\bm{z})))].\ ] ]      generative adversarial nets can be extended to a conditional model if both the generator and discriminator are conditioned on some extra information @xmath13 .
@xmath13 could be any kind of auxiliary information , such as class labels or data from other modalities .
we can perform the conditioning by feeding @xmath13 into the both the discriminator and generator as additional input layer .    in the generator
the prior input noise @xmath14 , and @xmath13 are combined in joint hidden representation , and the adversarial training framework allows for considerable flexibility in how this hidden representation is composed .    in the discriminator @xmath4 and @xmath13 are presented as inputs and to a discriminative function ( embodied again by a mlp in this case ) .
the objective function of a two - player minimax game would be as eq [ eq : minimaxgame - definition - conditioned ] @xmath15 + \mathbb{e}_{\bm{z } \sim p_z(\bm{z})}[\log ( 1 - d(g(\bm{z } | \bm{y})))].\ ] ]    fig [ fig : diagram ] illustrates the structure of a simple conditional adversarial net .
we trained a conditional adversarial net on mnist images conditioned on their class labels , encoded as one - hot vectors .    in the generator net ,
a noise prior @xmath16 with dimensionality 100 was drawn from a uniform distribution within the unit hypercube .
both @xmath16 and @xmath13 are mapped to hidden layers with rectified linear unit ( relu ) activation @xcite , with layer sizes 200 and 1000 respectively , before both being mapped to second , combined hidden relu layer of dimensionality 1200 .
we then have a final sigmoid unit layer as our output for generating the 784-dimensional mnist samples .
the discriminator maps @xmath4 to a maxout @xcite layer with 240 units and 5 pieces , and @xmath13 to a maxout layer with 50 units and 5 pieces . both of the hidden layers mapped to a joint maxout layer with 240 units and 4 pieces before being fed to the sigmoid layer .
( the precise architecture of the discriminator is not critical as long as it has sufficient power ; we have found that maxout units are typically well suited to the task . )
the model was trained using stochastic gradient decent with mini - batches of size 100 and initial learning rate of @xmath17 which was exponentially decreased down to @xmath18 with decay factor of @xmath19 .
also momentum was used with initial value of @xmath20 which was increased up to @xmath21 .
dropout @xcite with probability of 0.5 was applied to both the generator and discriminator . and
best estimate of log - likelihood on the validation set was used as stopping point .
table [ table : parzen ] shows gaussian parzen window log - likelihood estimate for the mnist dataset test data .
1000 samples were drawn from each 10 class and a gaussian parzen window was fitted to these samples .
we then estimate the log - likelihood of the test set using the parzen window distribution .
( see @xcite for more details of how this estimate is constructed . )
the conditional adversarial net results that we present are comparable with some other network based , but are outperformed by several other approaches  including non - conditional adversarial nets .
we present these results more as a proof - of - concept than as demonstration of efficacy , and believe that with further exploration of hyper - parameter space and architecture that the conditional model should match or exceed the non - conditional results .
fig [ fig : mnist ] shows some of the generated samples .
each row is conditioned on one label and each column is a different generated sample .    .
parzen window - based log - likelihood estimates for mnist .
we followed the same procedure as @xcite for computing these values . [ cols="^,^",options="header " , ]
photo sites such as flickr are a rich source of labeled data in the form of images and their associated user - generated metadata ( ugm )  in particular user - tags .
user - generated metadata differ from more ` canonical ' image labelling schems in that they are typically more descriptive , and are semantically much closer to how humans describe images with natural language rather than just identifying the objects present in an image .
another aspect of ugm is that synoymy is prevalent and different users may use different vocabulary to describe the same concepts  consequently , having an efficient way to normalize these labels becomes important .
conceptual word embeddings @xcite can be very useful here since related concepts end up being represented by similar vectors .    in this section
we demonstrate automated tagging of images , with multi - label predictions , using conditional adversarial nets to generate a ( possibly multi - modal ) distribution of tag - vectors conditional on image features .    for image features we pre - train a convolutional model similar to the one from @xcite on the full imagenet dataset with 21,000 labels @xcite .
we use the output of the last fully connected layer with 4096 units as image representations .    for the world representation
we first gather a corpus of text from concatenation of user - tags , titles and descriptions from yfcc100 m dataset metadata .
after pre - processing and cleaning of the text we trained a skip - gram model @xcite with word vector size of 200 .
and we omitted any word appearing less than 200 times from the vocabulary , thereby ending up with a dictionary of size 247465 .
we keep the convolutional model and the language model fixed during training of the adversarial net . and leave the experiments when we even backpropagate through these models as future work .    for our experiments we use mir flickr 25,000 dataset @xcite , and extract the image and tags features using the convolutional model and language model we described above .
images without any tag were omitted from our experiments and annotations were treated as extra tags .
the first 150,000 examples were used as training set .
images with multiple tags were repeated inside the training set once for each associated tag .    for evaluation , we generate 100 samples for each image and find top 20 closest words using cosine similarity of vector representation of the words in the vocabulary to each sample .
then we select the top 10 most common words among all 100 samples .
table [ table : samples ] shows some samples of the user assigned tags and annotations along with the generated tags .
the best working model s generator receives gaussian noise of size 100 as noise prior and maps it to 500 dimension relu layer .
and maps 4096 dimension image feature vector to 2000 dimension relu hidden layer .
both of these layers are mapped to a joint representation of 200 dimension linear layer which would output the generated word vectors .
the discriminator is consisted of 500 and 1200 dimension relu hidden layers for word vectors and image features respectively and maxout layer with 1000 units and 3 pieces as the join layer which is finally fed to the one single sigmoid unit .
the model was trained using stochastic gradient decent with mini - batches of size 100 and initial learning rate of @xmath17 which was exponentially decreased down to @xmath18 with decay factor of @xmath19 .
also momentum was used with initial value of @xmath20 which was increased up to @xmath21 .
dropout with probability of 0.5 was applied to both the generator and discriminator .
the hyper - parameters and architectural choices were obtained by cross - validation and a mix of random grid search and manual selection ( albeit over a somewhat limited search space . )
l | b3.7 cm | b3.7 cm & user tags + annotations & generated tags +   & montanha , trem , inverno , frio , people , male , plant life , tree , structures , transport , car & taxi , passenger , line , transportation , railway station , passengers , railways , signals , rail , rails +   & food , raspberry , delicious , homemade & chicken , fattening , cooked , peanut , cream , cookie , house made , bread , biscuit , bakes +   & water , river & creek , lake , along , near , river , rocky , treeline , valley , woods , waters +   & people , portrait , female , baby , indoor & love , people , posing , girl , young , strangers , pretty , women , happy , life +    [ table : samples ]
the results shown in this paper are extremely preliminary , but they demonstrate the potential of conditional adversarial nets and show promise for interesting and useful applications .      also , in the current experiments we only use each tag individually . but by using multiple tags at the same time ( effectively posing generative problem as one of ` set generation ' ) we hope to achieve better results .    another obvious direction left for future
work is to construct a joint training scheme to learn the language model .
works such as @xcite has shown that we can learn a language model for suited for the specific task .
this project was developed in pylearn2  @xcite framework , and we would like to thank pylearn2 developers . we also like to thank ian goodfellow for helpful discussion during his affiliation at university of montreal .
the authors gratefully acknowledge the support from the vision & machine learning , and production engineering teams at flickr ( in alphabetical order : andrew stadlen , arel cordero , clayton mellina , cyprien noel , frank liu , gerry pesavento , huy nguyen , jack culpepper , john ko , pierre garrigues , rob hess , stacey svetlichnaya , tobi baumgartner , and ye lu ) .
* generative adversarial nets * @xcite were recently introduced as a novel way to train generative models . in this work 
 we introduce the conditional version of generative adversarial nets , which can be constructed by simply feeding the data , @xmath0 , we wish to condition on to both the generator and discriminator . 
 we show that this model can generate mnist digits conditioned on class labels . 
 we also illustrate how this model could be used to learn a multi - modal model , and provide preliminary examples of an application to image tagging in which we demonstrate how this approach can generate descriptive tags which are not part of training labels .