Patent Publication Number: US-11663483-B2

Title: Latent space and text-based generative adversarial networks (LATEXT-GANs) for text generation

Description:
TECHNICAL FIELD 
     The present disclosure relates generally to generative adversarial networks (GANs) and, in particular, to methods and systems for latent space and text-based GANs (LATEXT-GANs) for text generation. 
     BACKGROUND 
     Deep learning has shown great success in various domains such as natural language processing (NLP), autonomous driving, gaming, and unsupervised learning. Generative adversarial networks (GANs) have been developed to generate realistic-looking synthetic images. GANs correspond to a mini-max two-player game where two models (e.g., two artificial neural networks) are trained simultaneously: a generative model G that captures data distribution, and a discriminative model D that computes a probability that describe whether a sample comes from the training data rather than from the generator. GAN solutions can be useful when there is a scarcity of training samples. 
     GANs have achieved substantial success in the field of computer vision for generating realistic-looking images. However, applying a GAN to NLP applications can be technically challenging because of the discrete nature of natural languages (e.g., text in a language does not map to real numbers with an inherent mapping function). For example, one technical problem relates to backpropagation. In NLP applications, text is a sequence of discrete words, and the output of the generator would be a discrete representation of the sequence of words. The discrete nature of the representation of the sequence of words output by the generator makes the backpropagation procedure, which is used in training the GAN, difficult. 
     Accordingly, more efficient and robust techniques for training a GAN for NLP applications are desirable. 
     SUMMARY 
     Technical advantages are generally achieved, by embodiments of this disclosure which describe methods and systems for training a latent space and text-based generative adversarial networks (LATEXT-GANs) for text generation. 
     In accordance to embodiments, an encoder neural network may receive a one-hot representation of a real text. The real text may comprise a sequence of words. The encoder neural network may also output a latent space representation of the real text generated from the one-hot representation of the real text. A decoder neural network may receive artificial code generated by a generator neural network of the GAN from random noise data. The decoder neural network may output softmax representation of artificial text generated from the artificial code. The decoder neural network may receive the latent space representation of the real text. The decoder neural network may output a reconstructed softmax representation of the real text generated from the latent space representation of the real text. The reconstructed softmax representation of the real text may comprise a soft-text that is a continuous representation of the real text. A hybrid discriminator neural network may receive a combination of the soft-text and the latent space representation of the real text and a combination of the softmax representation of artificial text and the artificial code. The hybrid discriminator neural network may output a probability indicating whether the combination of the softmax representation of artificial text and the artificial code received by the hybrid discriminator neural network is similar to the combination of the soft-text and the latent space representation of the real text. 
     In accordance to embodiments, an encoder neural network may receive a one-hot representation of a real text. The real text comprising a sequence of words. The encoder neural network may output a latent space representation of the real text generated from the one-hot representation of the real text. A decoder neural network may receive artificial code generated by a generator neural network of the GAN from random noise data. The decoder neural network may output softmax representation of artificial text generated from the artificial code. The decoder neural network may receive the latent space representation of the real text. The decoder neural network may output a reconstructed softmax representation of the real text generated from the latent space representation of the real text. The reconstructed softmax representation of the real text may comprise a soft-text that is a continuous representation of the real text. A first discriminator neural network (e.g., a text-based discriminator neural network) may receive the soft-text and the softmax representation of artificial text. The first discriminator neural network may output a first probability indicating whether the softmax representation of artificial text received by the first discriminator neural network is similar to the soft-text. A second discriminator neural network (e.g., a code-based discriminator neural network) may receive the latent space representation of the real text and the artificial code. The second discriminator neural network may output a second probability indicating whether the artificial code received by the second discriminator neural network is similar to the latent space representation of the real text. 
     In accordance to embodiments, an encoder neural network may receive a one-hot representation of a real text. The real text comprising a sequence of words. The encoder neural network may output a latent space representation of the real text generated from the one-hot representation of the real text. A decoder neural network may receive random noise data. The decoder neural network may output softmax representation of artificial text generated from the random noise data. The decoder neural network may receive the latent space representation of the real text. The decoder neural network may output a reconstructed softmax representation of the real text generated from the latent space representation of the real text. The reconstructed softmax representation of the real text may comprise a soft-text that is a continuous representation of the real text. A first discriminator neural network (e.g., a text-based discriminator neural network) may receive the soft-text and the softmax representation of artificial text. The first discriminator neural network may output a first probability indicating whether the softmax representation of artificial text received by the first discriminator neural network is similar to the soft-text. A second discriminator neural network (e.g., a code-based discriminator neural network) may receive the latent space representation of the real text and the random noise data. The second discriminator neural network may output a second probability indicating whether the random noise data received by the second discriminator neural network is similar to the latent space representation of the real text. 
     Apparatuses, as well as computer program products, for performing the methods are also provided. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of the present invention, and the advantages thereof, reference is now made to the following description taken in conjunction with the accompanying drawings, in which: 
         FIG.  1    is a block diagram of an example generative adversarial network (GAN); 
         FIG.  2    illustrates a block diagram of a conventional GAN with a text-based generator; 
         FIG.  3    shows the locus of the input vectors to a discriminator of a conventional GAN for a two-word language; 
         FIG.  4    illustrates a diagram of a LATEXT-GAN for text generation, according to some embodiments; 
         FIG.  5    illustrates a diagram of a LATEXT-GAN II for text generation, according to some embodiments; 
         FIG.  6    illustrates a diagram of a LATEXT-GAN III for text generation, according to some embodiments; 
         FIG.  7    illustrates a flowchart of a method for raining a LATEXT-GAN I for text generation, according to some embodiments; 
         FIG.  8    illustrates a flowchart of a method for training a LATEXT-GAN II for text generation, according to some embodiments; 
         FIG.  9    illustrates a flowchart of a method for training a LATEXT-GAN III for text generation, according to some embodiments; and 
         FIG.  10    is a block diagram of a processing system that can be used to implement the LATEXT-GANs, according to example embodiments. 
     
    
    
     Corresponding numerals and symbols in the different figures generally refer to corresponding parts unless otherwise indicated. The figures are drawn to clearly illustrate the relevant aspects of the embodiments and are not necessarily drawn to scale. 
     DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS 
     The making and using of embodiments of this disclosure are discussed in detail below. It should be appreciated, however, that the present invention provides many applicable inventive concepts that can be embodied in a wide variety of specific contexts. The specific embodiments discussed are merely illustrative of specific ways to make and use the invention, and do not limit the scope of the invention. These and other inventive aspects are described in greater detail below. 
     The operating of the current example embodiments and the structure thereof are discussed in detail below. It should be appreciated, however, that the present disclosure provides many applicable inventive concepts that can be embodied in a wide variety of specific contexts. The specific embodiments discussed are merely illustrative of specific structures of the embodiments and ways to operate the embodiments disclosed herein, and do not limit the scope of the disclosure. 
     A generative adversarial network (GAN) includes two separate deep artificial neural networks: a generator artificial neural network (generally referred to as a generator) and a discriminator artificial neural network (generally referred to as a discriminator). During training of the GAN, the generator receives random variables, z, with a probability distribution P z (z) and generates artificial samples (e.g., images or text) based on the received random variables, z. The discriminator receives real samples (e.g., real or observed images or text) and the artificial samples generated by the generator, and the discriminator predicts whether the artificial samples generated by the generator are real samples or artificial samples. The discriminator outputs a probability value of 1 when the discriminator predicts that the artificial samples are real samples, and a probability value of 0 when the discriminator predicts that the artificial samples are artificial samples. In the GAN training process, the generator and the discriminator are trained together to improve the performance of each other in an adversarial manner. A GAN implements a two-player mini-max game with the objective of deriving a Nash-equilibrium. The generator and the discriminator are trained together until the following adversarial loss function for the GAN is optimized: 
     
       
         
           
             
               
                 
                   
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       FIG.  1    illustrates a block diagram of a generative adversarial network (GAN)  100 . The GAN  100  may execute on one or more processing units. Examples of the processing units include, but are not limited to, graphics processing units (GPUs), tensor processing units (TPUs), application-specific integrated circuits (ASCIs), field-programmable gate arrays (FPGAs), artificial intelligence (AI) accelerators, or combinations thereof. The GAN  100  includes a generator  102 , configured to receive random variables z and generate, from random variables z, artificial samples {circumflex over (x)} that are similar or close to the content of real samples x taken from a set of training samples comprising real samples once GAN is trained. The GAN  100  also includes a discriminator  104 . The discriminator  104  is configured to receive both real samples x taken from the set of training samples and the artificial samples {circumflex over (x)} generated by the generator  102  and predict a probability D(x) of whether the artificial sample   is a real sample x (i.e., the artificial sample matches real sample x in the set of training samples). 
     GANs have achieved substantial success in the field of computer vision for generating realistic artificial images. Such success has motivated utilization of GANs in NLP applications as well. However, utilizing GANs in NLP applications has been challenging because of the discrete nature of natural languages (e.g., text in a language does not map to real numbers with an inherent mapping function). NLP applications utilize a natural language dictionary in all aspects of natural languages processing. The natural language dictionary includes K unique words in which each word is mapped to a K-dimensional representation.  FIG.  2    illustrates a block diagram of a conventional GAN  200  with a text-based generator  202 . The GAN  200  may execute on one or more processing units described above. The GAN  200  includes the text-based generator  202 , configured to receive random variables z and generate artificial samples {circumflex over (x)} based on random variables z. In the example shown in  FIG.  2   , the generator  202  is configured to receive random variables z, and generate and output a K-dimensional vector of arbitrary real numbers. A softmax function is applied to the K-dimensional vector of arbitrary real numbers output by the generator  202  to generate a representation of an artificial sample {circumflex over (x)}. The softmax function is a generalization of the logistic function that “squashes” a K-dimensional vector of arbitrary real numbers to a K-dimensional vector of real numbers, in which each entry of the vector is a real number in the range (0, 1), and all the real numbers add up to 1. The K-dimensional vector of real numbers, in Which each entry of the vector is a real number in the range (0, 1), that is output by the softmax function can be used to represent a categorical distribution. That is, a probability distribution over K different possible real numbers. Thus, in the example shown in  FIG.  2   , the artificial sample {circumflex over (x)} output from the softmax function is the K-dimensional vector of real numbers in which each entry is a real number the range (0, 1), and is referred to as a softmax representation of artificial text. The arg-max function is applied to the softmax representation of artificial text during inference (e.g., after training the GAN is completed) to obtain a representation that maps to words in the natural language dictionary. 
     The GAN  200  also includes a discriminator  204 , Which is configured to receive both an artificial sample {circumflex over (x)} (e.g., a softmax representation of artificial text output by the generator  202 ) and a real sample x from a training set of real samples and output a probability value that the artificial sample {circumflex over (x)} matches the real sample x in the training set of real samples. The real sample x is a one-hot representation of real text from a set of real texts. A one-hot representation is a group of bits among which the allowable combinations of values are only those with a single high (1) bit and all the others low (0). For example, when text is words and the natural language dictionary comprises four words, x1, x2, x3, and x4, the word x1 may have a one-hot representation of 0001. The word x2 may have a one-hot representation of 0010. The word x3 may have a one-hot representation of 0100. The word x4 may have a one-hot representation of 1000. In  FIG.  2   , the box labelled with “ONE-HOT” encodes the real text into the one-hot representation. 
     For each artificial sample {circumflex over (x)} received by the discriminator  204  from the generator  202 , the discriminator  204  predicts and outputs a probability D(x) of whether the artificial sample {circumflex over (x)} received by the discriminator  204  is real (i.e., the softmax representation of artificial text matches a one-hot representation of real text in a set of real texts) or fake (i.e., the softmax representation of artificial text generated by the generator  202  does not match a one-hot representation of real text in a set of real texts). 
     In conventional GAN systems with text-based discriminators, such as GAN  200 , the discriminator  204  is responsible for distinguishing between the one-hot representation of the real text and the softmax representation of artificial text received from the generator  202 . A technical disadvantage of this conventional technique is that the discriminator is able to easily tell apart the one-hot representation of the real text from the softmax representation of artificial text. In other words, the generator  202  would have a hard time fooling the discriminator  204 . This results in poor training of the GAN  200  and a vanishing gradient is highly likely to occur.  FIG.  3    shows a graphical representation of the GAN  200  in which the natural language dictionary includes two-words. The example shows a locus of the softmax representation of two words to the discriminator  204  of the conventional GAN  200  for a two-word language. The two-word language includes one-hot representations of two real words: the one-hot representation of real word x 1  ( 302 ) and the one-hot representation of real word x 2  ( 304 ). The discriminator  204  receives the one-hot representations of real word x 1  ( 302 ) and the real word x 2  ( 304 ). The discriminator  204  also receives a softmax representation of artificial text {circumflex over (x)} ( 306 ) generated by the generator  202 .  FIG.  3    depicts the one-hot representations of these two real words as the two discrete points  302  and  304  in the Cartesian space.  FIG.  3    also shows the span of the softmax representation of artificial words over the one-hot representations of the two words (i.e., the line segment  306  connecting the points x 1    302  and x 2    304 ). As  FIG.  3    illustrates, the task of the discriminator  204  is to discriminate the points  302  and  304  from the line  306  connecting these two points, which would be an easy task for the discriminator  204 . 
     Additionally, the discrete nature of the text of natural languages presents technical problems in training a GAN for text generation. For the GAN training, the representation of softmax representation of artificial text generated from the generator  202  needs to be differentiable for back-propagating the gradient from the discriminator. Therefore, the arg-max function cannot be applied. 
     The conventional systems, such as the GAN  200 , use the discriminator to discriminate the softmax representation of artificial text from the one-hot representation of real text, in which there is a clear downside as the discriminator receives two different types of the inputs: a one-hot representation of the real text and a softmax representation of artificial text. The consequence is that the discrimination task performed by the discriminator  204  becomes too easy. Particularly, to the discriminators in some conventional GAN systems, the one-hot representations of real text can be easily discriminated from the softmax representations of artificial text, which leads to vanishing gradient. Consequently, the softmax representation of artificial text generated by the generator  202  is less realistic. 
     To solve these technical problems, embodiments of this application use technical solutions that utilize autoencoders to learn continuous representations of the real text rather than the one-hot representations of real text. A continuous representation of real text is a K-dimensional vector of real numbers in which each entry of the K-dimensional vector is a probability (which is a continuous function that has a value between 0 and 1), and the probabilities of the K-dimensional vector sum to 1. Each entry of the K-dimensional vector maps to a word in a natural language dictionary of K unique words. An autoencoder is a type of artificial neural network used to learn efficient representations of text. The purpose of an autoencoder is to learn representations for a set of real text from a natural language dictionary that includes K-words, typically for the goal of dimensionality reduction. An autoencoder includes two networks: an encoder artificial neural network (hereinafter encoder neural network) and a decoder artificial neutral network (hereinafter decoder neural network). The encoder neural network of the autoencoder learns to map a one-hot representation of real text into a latent representation, and then the decoder neutral network of the autoencoder learns to decode the latent representation into a representation that closely matches the original one-hot representation of real text, referred to hereinafter as a reconstructed representation. 
     In example embodiments, the LATENT-GAN may learn a softmax representation of real text (i.e., soft-text), which is a continuous representation of the real text. In contrast to the conventional GAN  200 , the soft-text is input into the discriminator of a GAN. Inputting the soft-text into the discriminator as opposed to a one-hot representation of real text makes the discrimination task of the discriminator more difficult. Consequently, the soft-text approach provides a richer signal to the generator. At the time of training, the generator of the LATENT GAN may try to learn continuous representations that are similar to the soft-text, which can later on be mapped to the real text by applying the arg-max function. 
       FIG.  4    illustrates a block diagram of a LATEXT-GAN for text generation, according to an embodiment. The LATEXT-GAN (hereinafter referred to as LATEX-GAN I  400 ) shows embodiments in which the discriminator of the GAN discriminates between a combined latent code and soft-text as described in further detail below. The LATEXT-GAN I  400  may be implemented in software comprising computer-readable code or instructions, which may be executed by one or more processing devices of a processing system, such as processing devices  1002  ( FIG.  10   ) of the processing system  1000  ( FIG.  10   ) described below. The LATEXT-GAN I  400  includes a generator artificial neural network  402  (hereinafter generator neural network  402 ) and a hybrid discriminator artificial neural network  404  (hereinafter hybrid discriminator neural network  404 ). The generator neural network  402  is deep neural network comprising neural network parameters θ. The hybrid discriminator neural network  404  is also a deep neural network comprising neural network parameters w. The LATEXT-GAN I  400  further includes an autoencoder  420 , which comprises a one-hot operator  403 , an encoder artificial neural network  408  (hereinafter encoder neural network  408 ) and a decoder artificial neural network  410 , and a softmax operator  412 A.  FIG.  4    depicts the decoder neural network  410  as if there are two decoder neural networks  410 A and  410 B and the softmax operator  412  as if there are two softmax operators  412 A and  412 B. This is for illustration purposes only. The decoder neural networks  410 A and  410 B are the same decoder neural network  410 . That is, the decoder neural networks  410 A and  410 B are the same deep neural network comprising the same parameters ψ. The softmax operators  412 A and  412 B are also the same softmax operator  412 . That is, the softmax operators  412 A and  412 B apply the same softmax function. 
     The encoder neural network is a deep neural network comprising neural network parameters ϕ. The encoder neural network  408  is configured to receive a one-hot representation of the real text (x), generate a latent representation (c) of the real text, and output the latent representation. (c). In  FIG.  4   , the one hot operator  403  encodes the real text into the one-hot representation based on the K-word natural language dictionary. The latent representation captures the semantic closeness of words and is a condensed representation of the one-hot representation of text. The latent representation is an N-dimensional vector of real numbers, N is less than K, the number of words in the natural language dictionary. 
     The decoder neural network  410 A is configured to receive the latent representation (c) of the real text, decode the latent representation (c) into a reconstructed representation of the real text from the latent representation of the real text, and output a reconstructed representation of the real text. The softmax operator  412 A is configured to perform a softmax function on the reconstructed representation of real text output by the decoder  410 A to generate a reconstructed softmax representation of the real text. The autoencoder  420  outputs the reconstructed softmax representation of the real text, which is referred to as soft-text ({tilde over (x)}). The reconstructed softmax representation of the real text (e.g., soft-text   is a continuous representation of the real text (e.g., a K-dimensional vector of real numbers in which each entry of the K-dimensional vector is a probability (which is a continuous function that has a value between 0 and 1), and the probabilities of the K-dimensional vector sum to 1). 
     In the LATEXT-GAN I  400 , the soft-text ({tilde over (x)}) and the latent representation (c) of the real text generated by the autoencoder  120  are combined to generate a combination ({tilde over (x)}, c) including the soft-text ({tilde over (x)}) and the latent representation c of the real text from the autoencoder  420 . In some embodiments, the LATEXT-GAN I  400  combines the soft-text ({tilde over (x)}) and the latent representation (c) of the real text generated by the autoencoder  120  using concatenation. 
     The generator neural network  402  is configured to generate the artificial code (ĉ), generated from random noise data (z). The decoder neural network  410 B is also configured to receive the artificial code (ĉ), generate a representation of artificial text (from the artificial code (ĉ), and output the representation of artificial text. The softmax operator  412 B is configured to perform a softmax function on the representation of artificial text output from decoder neural network  410 B to generate a softmax representation of artificial text ({circumflex over (x)}). In the LATEXT-GAN I  400 , the softmax representation of artificial text ({circumflex over (x)}) and the artificial code (ĉ) are combined using, for example, concatenation, to generate the combination ({circumflex over (x)}, ĉ) including the softmax representation of artificial text ({circumflex over (x)}) and the artificial code (ĉ). 
     The hybrid discriminator neural network  404  is configured to receive the combinations ({circumflex over (x)}, ĉ) and ({tilde over (x)}, c), predict and output a probability D(x) of whether the input combination ({tilde over (x)}, c), is a real (i.e., a probability that the input combination ({circumflex over (x)}, ĉ) of the softmax representation of artificial text ({circumflex over (x)}) and the artificial code ĉ matches the combination ({tilde over (x)}, c) of the soft-text ({tilde over (x)}) and the latent representation c of the real text) or a fake (i.e., a probability that the input combination ({circumflex over (x)}, ĉ) of the softmax representation of artificial text ({circumflex over (x)}) and the artificial code (ĉ) does not match the input combination ({tilde over (x)}, c) of the soft-text ({tilde over (x)}) and the latent representation (c) of the real text). 
     The LATEXT-GAN I  400  is trained to learn to generate artificial samples (e.g. softmax representations of artificial text ({circumflex over (x)})) that mimic the real samples (e.g., the reconstructed softmax representation of real text ({tilde over (x)}).) using the following training process. In an epoch, the autoencoder  420  is trained by initializing the parameters φ of the encoder neural network  408  and the parameters ψ of the decoder neural network  410 , and using backpropagation and a reconstruction loss function L AE (φ,ψ) which is evaluated by solving the following optimization problem:
 
 L   AE (φ,ψ)=min (φ,ψ) (∥ x −softmax(dec ψ (enc φ ( x )))∥ 2 )
 
     Here, x is the one-hot representation of the real text. φ denotes parameters of the encoder neural network  408 . ψ denotes parameters of the decoder neural network  410 . 
     The LATEXT-GAN I  400 , in the same epoch, then uses backpropagation and the discriminator loss function L critic−ALI  with a gradient penalty to train the hybrid discriminator neural network  404 , the encoder neural network  408 , and the decoder neural network  410 . The discriminator loss function L critic−ALI  with a gradient penalty is evaluated by solving the following optimization problem: 
     
       
         
           
             
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     Here, {tilde over (x)} is the softmax representation of the decoder output (e.g., soft-text). ĉ is the artificial code. {circumflex over (x)} is the softmax representation of artificial text. c is the latent representation of the real text.  x  denotes random samples obtained by sampling uniformly along a line connecting pairs of softmax representation of artificial text and real text.  c  denotes random latent code samples obtained by sampling uniformly along a line connecting pairs of the artificial code and the latent representation of the real text. λ is a gradient penalty coefficient. w denotes parameters of the hybrid discriminator neural network  404 . φ denotes parameters of the encoder neural network  408 . ψ denotes parameters of the decoder neural network  410 . 
     The LATEXT-GAN I  400 , in the same epoch, also uses backpropagation and the generator loss function L Gen−ALI  to train the generator neural network  402  and the decoder neural network  410 . The generator loss function L Gen−ALI  is evaluated by solving the following optimization problem:
 
 L   Gen−ALI =min (θ,ψ) ( −E   ({circumflex over (x)},ĉ)˜P     {circumflex over (x)}     ,P     ĉ   [ f   w   t+c ( {circumflex over (x)},ĉ )] +E   ({tilde over (x)},c)˜P     {tilde over (x)}     ,P     c   [ f   w   t+c ( {tilde over (x)},c )])
 
     Here, {circumflex over (x)} is the softmax representation of artificial text. c is the latent representation of the real text. {tilde over (x)} is the soft-text. ĉ is the artificial code. θ denotes parameters of the generator neural network  402 . ψ denotes parameters of the decoder neural network  410 . 
     The training process is repeated for several epochs until the LATENT GAN I  400  is trained (e.g., the neural network parameters φ of the encoder neural network  408 , the neural network parameters ψ of the decoder neural network  410 , the neural network parameters θ of the generator neural network  402 , and the neural network parameters w of the hybrid discriminator  404 ) are learned. After the LATENT GAN I  400  is trained, the generator  402  may be used to generate artificial codes which is decoded by the decoder neural network  410 B and softmax operator  412 B to generate artificial samples (e.g. softmax representations of artificial text ({circumflex over (x)})) that mimic the real samples (e.g., the reconstructed softmax representation of real text ({tilde over (x)}).). The artificial samples (e.g., softmax representations of artificial text ({circumflex over (x)})) may be decoded to generate one-hot representations of the text using the K-word natural language dictionary. The one-hot representations of text may be converted into text and output for display on an output device, such as output device  1016  ( FIG.  10   ) of the processing system  1000  ( FIG.  10   ) described below. 
       FIG.  5    illustrates a diagram of a block diagram of a LATEXT-GAN according to another embodiment. The LATEXT-GAN depicted in  FIG.  5    is referred to hereinafter as LATEXT-GAN II  500 . The LATEXT-GAN II  500  shows embodiments with multiple critics for the latent code and soft-text discrimination. The LATEXT-GAN II  500  may be implemented in software comprising computer-readable code or instructions, which may be executed on one or more processing devices of a processing system, such as processing devices  1002  of the processing system  1000  described below. The LATEXT-GAN II  500  includes a generator artificial neural network  502  (hereinafter generator neural network  502 ), a text-based discriminator artificial neural network  504  (hereinafter text-based discriminator neural network  504 ), and a code-based discriminator artificial neural network  505  (hereinafter code-based discriminator neural network  505 ). The generator neural network  502  is deep neural network comprising neural network parameters θ. The text-based neural network  504  is also a deep neural network comprising neural network parameters w 1  and the code-based discriminator neural network  505  is a deep neural network comprising neural network parameters w 2 . The LATEXT-GAN II  500  further includes an autoencoder  520 , which comprises an encoder artificial neural network  508  (hereinafter encoder neural network  508 ) and a decoder artificial neural network  510  (hereinafter decoder neural network  510 ). The encoder neural network  508  is a deep neural network comprising neural network parameters ϕ and the decoder neural network  510  is a deep neural network comprising neural network parameters ψ.  FIG.  5    depicts the decoder neural network  510  as if there are two decoder neural networks  510 A and  510 B and the softmax operator  512  as if there are two softmax operators  512 A and  512 B. This is for illustration purposes only. The decoder neural networks  510 A and  510 B are the same decoder neural network  510 . That is, the decoder neural networks  510 A and  510 B are the same deep neural network comprising the same neural network parameters ψ. In some embodiments, the decoder neural networks  510 A and  510 B may be two different decoder neural networks having different neural network parameters. The softmax operators  512 A and  512 B are also the same softmax operator  512 . That is, the softmax operators  512 A and  512 B apply the same softmax function. 
     The encoder neural network  508  is configured to receive the one-hot representation of the real text (x) and output a latent space representation (c) of the real text in the latent space. In  FIG.  5   , the one-hot operator  503  encodes the real text into the one-hot representation based on the K-word dictionary. The latent representation captures the semantic closeness of words and is a condensed representation of the one-hot representation of text. The latent representation is an N-dimensional vector of real numbers. N is less than K, the number of words in the natural language dictionary. 
     The decoder neural network  510  (shown as the decoder  510 A) is configured to receive the latent representation (c) of the real text and output a reconstructed representation of the real text generated from the latent representation of the real text. The softmax operator  512 A is configured to receive the reconstructed representation of the real text and perform a softmax function on the reconstructed representation of real text output by the decoder  510 A to generate a reconstructed softmax representation of the real text ({tilde over (x)}), which is referred to as soft-text ({tilde over (x)}). The reconstructed softmax representation of the real text (e.g., soft-text ({tilde over (x)})) is a continuous representation of the real text (e.g., a K-dimensional vector of real numbers in which each entry of the K-dimensional vector is a probability (which is a continuous function that has a value between 0 and 1), and the probabilities of the K-dimensional vector sum to 1). 
     In the LATEX-GAN II  500 , the text-based discriminator neural network  504  receives the soft-text ({tilde over (x)}). The soft-text ({tilde over (x)}) is obtained from the decoder neural network  510 . The code-based discriminator neural network  505  receives the latent representation (c) of the real text. The latent representation (c) is obtained from the encoder neural network  508 . 
     The generator neural network  502  is configured to receive random noise data and generate an artificial code (ĉ) from random noise data (z), and output the artificial code (ĉ). The decoder neural network  510 B is also configured to receive the artificial code (ĉ), and decode the artificial code (ĉ) into a representation of artificial text, and output the representation of artificial text. The softmax operator  512 B is configured to receive the representation of artificial text and perform a softmax function on the representation of artificial text to generate a softmax representation of artificial text (e.g., soft-text ({circumflex over (x)})). The text-based discriminator neural network  504  is configured to also receive the softmax representation of artificial text ({circumflex over (x)}). The softmax representation of artificial text ({circumflex over (x)}) is received from the softmax operator  512 B. The code-based discriminator neural network  505  is also configured to receive the artificial code (ĉ). The artificial code (ĉ) is received from the generator neural network  502 . 
     The text-based discriminator neural network  504  is configured to predict and output a probability D1(x) of whether the input sample is a real (i.e., a probability that the softmax representation of artificial text ({circumflex over (x)}) matches the soft-text ({tilde over (x)})) or a fake (i.e., a probability that the softmax representation of artificial text ({circumflex over (x)}) does not match the soft-text ({tilde over (x)})). 
     The code-based discriminator neural network  505  is configured to predict and output a probability D2(x) of whether the input sample is a real (i.e., the artificial code (ĉ) matches the latent representation (c) of the real text) or a fake (i.e., the artificial code (ĉ) does not match the latent space representation (c) of the real text). 
     The LATEXT-GAN II  500  is trained to learn to generate artificial samples (e.g. softmax representations of artificial text ({circumflex over (x)})) that mimic the real samples (e.g., the reconstructed softmax representation of real text ({tilde over (x)}).) using the following training process. In an epoch, the autoencoder  520  is trained by initializing the parameters φ of the encoder neural network  408  and the parameters ψ of the decoder neural network, and using backpropagation and the reconstruction loss function L AE (φ,ψ) which is evaluated by solving the following optimization problem.
 
 L   AE (φ,ψ)=min (φ,ψ) (∥ x −softmax(dec ψ (enc φ ( x )))∥ 2 )  Formula (4):
 
     Here, x is the one-hot representation of the real text. φ denotes parameters of the encoder neural network  508 , and ψ denotes parameters of the decoder neural network  510 . 
     The LATEXT-GAN II  500 , in the same epoch, then uses backpropagation and the text-based discriminator loss function L critic1  to train the text-based discriminator neural network  504  and the decoder neural network  510 , which is evaluated by solving the following optimization problem. 
     
       
         
           
             
               
                 
                   
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     Here, {tilde over (x)} is the soft-text. {circumflex over (x)} is the softmax representation of artificial text.  x  denotes random data samples obtained by sampling uniformly along a line connecting pairs of generated and soft-text samples. λ 1  is a gradient penalty coefficient. w 1  denotes the neural network parameters of the text-based discriminator neural network  504 . ψ denotes the neural network parameters of the decoder neural network  510 . 
     The LATEXT-GAN II  500 , in the same epoch, also uses backpropagation and the code-based discriminator loss function L critic2  to train the code-based discriminator neural network  505  and the encoder neural network  508 , which is evaluated by solving the following optimization problem:
 
 L   critic2 =min (w     2     ,φ) ( E   ĉ˜P     ĉ   [ f   w     2     c ( ĉ )] −E   c˜P     c   [ f   w     2     c ( c )]+λ 2   E     c ˜P       c     [(∥∇ ( c )   f   w     2     c (   c   )∥ 2 −1) 2 ])  Formula (6):
 
     Here, c is the latent space representation of the real text. ĉ is the artificial code.  c  denotes random latent code samples obtained by sampling uniformly along a line connecting pairs of the artificial code and the latent space representation of the real text. λ 2  is a gradient penalty coefficient. w 2  denotes the neural network parameters of the code-based discriminator neural network  505 . φ denotes the neural network parameters of the encoder neural network  508 . 
     The LATENT-GAN II  500 , in the same epoch, also uses backpropagation and the generator loss function L Gen−ARAE−mul  to train the generator neural network  502  and the decoder neural network  510 , which is evaluated by solving the following optimization problem: 
     
       
         
           
             
               
                 
                   
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     Here, {circumflex over (x)} is the softmax representation of artificial text. c is the latent space representation of the real text. ĉ is the artificial code. {tilde over (x)} is the soft-text. θ denotes the neural network parameters of the generator neural network  502 . ψ denotes the neural network parameters of the decoder neural network  510 . 
     The training process is repeated for several epochs until the LATENT GAN II  500  is trained (e.g., the neural network parameters φ of the encoder neural network  508 , the neural network parameters ψ of the decoder neural network  510 , the neural network parameters θ of the generator neural network  502 , and the neural network parameters w 1  of the text-based discriminator neural network  504 , and the neural network parameters w 2  of the code-based discriminator neural network  505 ) are learned. After the LATENT GAN II  500  is trained, the generator  502  may be used to generate artificial codes which is decoded by the decoder neural network  510 B and softmax operator  512 B to generate artificial samples (e.g. softmax representations of artificial text ({circumflex over (x)})) that mimic the real samples (e.g., the reconstructed softmax representation of real text ({tilde over (x)}).). The artificial samples (e.g., softmax representations of artificial text ({circumflex over (x)})) may be decoded to generate one-hot representations of the text using the K-word natural language dictionary. The one-hot representations of text may be converted into text and output for display on an output device  1016  ( FIG.  10   ), such as output device  1016  ( FIG.  10   ) of the processing system  1000  ( FIG.  10   ) described below. 
       FIG.  6    illustrates a block diagram of a LATEXT-GAN for text generation, according to another embodiment. The LATEXT-GAN depicted in  FIG.  6    is referred to hereinafter as LATEXT-GAN III  600 . The LATEXT-GAN III  600  shows additional embodiments with multiple critics for the latent code and soft-text discrimination. The LATEXT-GAN III  600  may be implemented in software that includes computer-readable code or instructions, which may be execute on one or more processing devices of a processing system, such as processing devices  1002  ( FIG.  10   ) of the processing system  1000  ( FIG.  10   ) described below. The LATEXT-GAN III  600  includes a text-based discriminator artificial neural network  604  (hereinafter text-based discriminator neural network  604 ) and a code-based discriminator artificial neural network  605  (hereinafter code-based discriminator neural network  605 ). The text-based neural network  604  is also a deep neural network comprising neural network parameters w 1  and the code-based discriminator neural network  605  is a deep neural network comprising neural network parameters w 2 . The LATEXT-GAN III  600  further includes an autoencoder  620 , which comprises an encoder artificial neural network  608  (hereinafter encoder neural network  608 ) and a decoder artificial neural network  610  (decoder neural network  610 ). The encoder neural network  608  is a deep neural network comprising neural network parameters ϕ and the decoder neural network  610  is a deep neural network comprising neural network parameters ψ.  FIG.  6    depicts the decoder neural network  610  as if there are two decoder neural networks  610 A and  610 B and the softmax operator  612  as if there are two softmax operators  612 A and  612 B. This is for illustration purposes only. The decoder neural networks  610 A and  610 B are the same decoder neural network  610 . That is, the decoder neural networks  610 A and  610 B are the same deep neural network comprising the same neural network parameters ψ. The softmax operators  612 A and  612 B are also the same softmax operator  612 . That is, the softmax operators  612 A and  612 B apply the same softmax function. The encoder neural network  608  is configured to receive the one-hot representation of the real text (x), generate a latent space representation (c) of the real text, and output the latent space representation (c). In  FIG.  6   , the one-hot operator  603  encodes the real text into the one-hot representation. The latent representation captures the semantic closeness of words and is a condensed representation of the one-hot representation of text. The latent representation is an N-dimensional vector of real numbers. N is less than K, the number of words in the natural language dictionary. 
     The decoder neural network  610 A is configured to receive the latent representation (c) of the real text, decode the latent space representation (c) into a reconstructed representation of the real text from the latent representation of the real text, and output the reconstructed representation of the real text. The softmax operator  612 A of the autoencoder  620  is configured to perform a softmax function on the reconstructed representation of real text output by the decoder  610 A to generate a reconstructed softmax representation of the real text. The autoencoder  620  outputs the reconstructed softmax representation of the real text, which is referred to as soft-text ({tilde over (x)}). The reconstructed softmax representation of the real text (e.g., soft-text ({tilde over (x)})) is a continuous representation of the real text (e.g., a K-dimensional vector of real numbers in which each entry of the K-dimensional vector is a probability (which is a continuous function that has a value between 0 and 1), and the probabilities of the K-dimensional vector sum to 1). 
     In the LATEXT-GAN III  600 , the text-based discriminator neural network  604  receives the soft-text ({tilde over (x)}). The soft-text ({tilde over (x)}) is received from the decoder neural network  610 A. The code-based discriminator neural network  605  receives the latent representation (c) of the real text. The latent representation (c) is received from the encoder neural network  608 . 
     The decoder neural network  610 B is further configured to receive random noise data (z) and output a representation of artificial text from random noise data (z). The softmax operator  612 B is configured to receive the representation of the artificial text and perform a softmax operation on the representation of the artificial text output by the decoder neural network  610 B to generate a softmax representation of the representation of artificial text ({circumflex over (x)}). The text-based discriminator neural network  604  is configured to receive the softmax representation of artificial text ({circumflex over (x)}). The softmax representation of artificial text ({circumflex over (x)}) is received from the decoder neural network  610 B. The code-based discriminator neural network  605  is also configured to receive the random noise data (z). 
     The text-based discriminator neural network  604  is configured to predict and output a probability D1(x) of whether the input sample is a real (i.e., a probability that the softmax representation of artificial text ({circumflex over (x)})) matches the soft-text ({tilde over (x)})) or a fake (i.e., a probability that the softmax representation of artificial text ({circumflex over (x)})) does not match the soft-text ({tilde over (x)})). 
     The code-based discriminator neural network  605  is configured to predict and output a probability D2(x) of whether the input sample is a real (i.e., a probability that the random noise data (z) matches the latent space representation (c) of the real text) or a fake (i.e., a probability that the random noise data (z) does not match the latent representation (c) of the real text). 
     The autoencoder  620  is trained using the reconstruction loss function L AE (φ,ψ), which is evaluated by solving the following optimization problem.
 
 L   AE (φ,ψ)=min (φ,ψ) (∥ x −softmax(dec ψ (enc φ ( x )))∥ 2 )  Formula (8):
 
     Here, x is the one-hot representation of the real text. φ denotes the neural network parameters of the encoder neural network  608 , and ψ denotes the neural network parameters of the decoder neural network  610 . 
     The LATEXT-GAN III  600  is trained to learn to generate artificial samples (e.g. softmax representations of artificial text ({circumflex over (x)})) that mimic the real samples (e.g., the reconstructed softmax representation of real text ({tilde over (x)}).) using the following training process. In an epoch, the LATEXT-GAN III  600  uses backpropagation and the text-based discriminator loss function L critic1  to train the text-based discriminator neural network  604  and the decoder neural network  610 , which is evaluated by solving the following optimization problem.
 
 L   critic1 =min (w     1     ,ψ) ( −E   ({tilde over (x)})˜P     {tilde over (x)}   [ f   w     1     t ( {tilde over (x)} )] +E   ({circumflex over (x)})˜P     {circumflex over (x)}   [ f   w     1     t ( {circumflex over (x)} )]+λ 1   E     x ˜P       x     [(∥∇ ( x )   f   w     1     t (   x   )∥ 2 −1) 2 ])  Formula (9):
 
     Here, {tilde over (x)} is the soft-text. {circumflex over (x)} is the softmax representation of artificial text.  x  denotes random samples obtained by sampling uniformly along a line connecting pairs of softmax representation of artificial text and real text. λ 1  is a gradient penalty coefficient. w 1  denotes the neural network parameters of the text-based discriminator neural network  604 . ψ denotes the neural network parameters of the decoder neural network  610 . 
     The LATEXT-GAN III  600 , in the same epoch, uses backpropagation and the code-based discriminator loss L critic2  function to train the code-based discriminator neural network  605 , which is evaluated by solving the following optimization problem.
 
 L   critic2 =min w     2   ( E   c˜P     c   [ f   w     2     c ( c ) −E   z˜P     z   [ f   w     2     c ( z )]+λ 2   E     c1 ˜P       c1     [(∥∇ ( c1 )   f   w     2     c (   c 1 )∥ 2 −1) 2 ])  Formula (10):
 
     Here, z is the random noise data.  c 1    is random latent code samples obtained by sampling uniformly along a line connecting pairs of the random noise data and the latent representation of the real text. λ 2  is a gradient penalty coefficient. w 2  denotes the neural network parameters of the code-based discriminator neural network  605 . 
     The LATEXT-GAN III  600 , in the same epoch, also uses backpropagation and the generator loss function L Gen−AAE−mul  to train the encoder neural network  608  and the decoder neural network  610  by solving the following optimization problem.
 
 L   Gen−AAE−mul =min φ,ψ ( −E   {circumflex over (x)}˜P     {circumflex over (x)}   [ f   w     1     t ( {circumflex over (x)} )] +E   ({tilde over (x)})˜P     {tilde over (x)}   [ f   w     1     t ( {tilde over (x)} )] +E   z˜P     z   [ f   w     2     c ( z )] −E   c˜P     c   [ f   w     2     c ( c )])  Formula (11):
 
     Here, {circumflex over (x)} is the softmax representation of artificial text. c is the latent representation of the real text. {tilde over (x)} is the soft-text. φ denotes the neural network parameters of the encoder neural network  608 . ψ denotes the neural network parameters of the decoder neural network  610 . 
     The training process is repeated for several epochs until the LATENT GAN III  600  is trained (e.g., the neural network parameters of the encoder neural network  608 , the neural network parameters ψ of the decoder neural network  610 , the neural network parameters w 1  of the text-based discriminator neural network  604 , and the neural network parameters w 2  of the code-based discriminator neural network  605 ) are learned. After the LATENT GAN III  600  is trained, a random generator (not used) may be used to generate random noise data which is decoded by the decoder neural network  510 B and softmax operator  512 B to generate artificial samples (e.g. softmax representations of artificial text ({circumflex over (x)})) that mimic the real samples (e.g., the reconstructed softmax representation of real text ({tilde over (x)}).). The artificial samples (e.g., softmax representations of artificial text ({circumflex over (x)})) may be decoded to generate one-hot representations of the text using the K-word natural language dictionary. The one-hot representations of text may be converted into text and output for display on an output device  1016  ( FIG.  10   ), such as output device  1016  ( FIG.  10   ) of the processing system  1000  ( FIG.  10   ) described below. 
     The LATEXT-GANs I, II, III  400 ,  500 , or  600  in  FIGS.  4 - 6    may define the encoder and decoder neural networks for the autoencoder. These networks may be the long short term memory (LSTM) networks. 
     The decoder neural networks  410 ,  510 ,  610  are shared as described above. The LATEXT-GANs may also define generator and discriminator neural network(s). These networks may be a stack of convolutional neural network (CNN) layers. 
     The LATEXT GANs  400 ,  500 ,  600  may derive the graph in TensorFlow. TensorFlow is an open-source software library for dataflow programming across a range of tasks. TensorFlow is a symbolic math library. TensorFlow can be used for machine learning applications such as neural networks. 
     The LATEXT-GANs  400 ,  500 ,  600  may define the loss function for the autoencoder, which is a mean-squared difference of the one-hot representations of the real text and the reconstructed output from the decoder neural networks  410 ,  510 ,  610 . The LATEXT-GANs  400 ,  500 ,  600  may also define the gradient penalty loss function for the generator  402 ,  502 ,  602  and discriminator neural networks  404 ,  504 ,  604 . In addition, the LATEXT-GANs  400 ,  500 ,  600  may define Adam optimizers for the autoencoder  420 ,  520 ,  620 , the generator neural network(s)  402 ,  502 , and the discriminator neural network(s)  404 ,  504 ,  505 ,  604 ,  605 . Adam optimization is an optimization algorithm that can be used instead of the classical stochastic gradient descent procedure to learn the neural network parameters of all the neural networks iteratively. 
     For training, the LATEXT-GANs  400 ,  500 ,  600  first initialize all TensorFlow variables (e.g., variables for loss functions, network parameters, and placeholder variables) for the generator neural network, the discriminator neural network(s), the encoder neural network, and the decoder neural network. Then, for a number of training iterations, the LATEXT-GANs  400 ,  500 ,  600  may train the autoencoder (i.e., the encoder neural network  408 ,  508 ,  608  and the decoder neural network  410 ,  510 ,  610 ) to learn the neural network parameters φ and ψ and for reconstructing the real text train the discriminator neural network(s) for k times to learn the neural network parameters w for LATENT GAN I  400 , and to learn the neural network parameters w 1  and w 2  for LATENT-GANs II  500 ,  600 , and perform additional training. 
     To train the autoencoder  420 ,  520 ,  620 , the LATEXT-GANs  400 ,  500 ,  600  receives one-hot representations of real text {x i } i=1   m ˜P x , computes latent representations c i =enc φ (x i ), reconstructs a representation of the real text, and applies a softmax function to the reconstructed representation of the real text to generate a reconstructed softmax representation of the real text (e.g., soft-text) {{tilde over (x)} i } i=1   m . The LATEXT-GANs  400 ,  500 ,  600  then use backpropagation and the reconstruction loss L AE (φ,ψ) to update the neural network parameters φ of the encoder neural network  408 ,  508 ,  608  and the neural network parameters ψ of the decoder neural network  410 ,  510 ,  610 . 
     To train the discriminator neural network(s) k times, the LATEXT-GANs receives random noise variables {z i } i=1   m ˜N(0, I) and generates a representation of an artificial sample based on the random noise variables. The LATEXT-GANs  400 ,  500 ,  600  also computes a representation of artificial text, and applies a softmax function to the representation of the artificial text to generate a softmax representation of the artificial text {{circumflex over (x)} i } i=1   m ˜G θ (z). For the LATEXT-GAN I  400 , the LATEXT-GAN I backpropagates the discriminator loss based on the Wasserstein GAN-Gradient penalty (WGAN-GP) to update the neural network parameters w of the discriminator neural network. For the LATEXT-GAN II  500 , the LATEXT-GAN II backpropagates the text-based and the code-based discriminator losses to update the neural networks parameters w 1  and w 2  of the text-based and the code-based neural networks. For the LATEXT-GAN III  600 , the LATEXT-GAN III backpropagates the text-based and code-based discriminators losses to update the neural network parameters w 1  and w 2  of the text-based and code-based neural networks. 
     To perform additional training, the LATEXT-GANs samples {x i } i=1   m ˜P x  and sample {z i } i=1   m ˜N(0, I). For the LATEXT-GAN I  400 , the LATEXT-GAN I may backpropagate the discriminator loss to update the neural network parameters φ of the encoder neural network  408  and the neural network parameters ψ of the decoder neural network  410  The LATEXT-GAN I also backpropagate the generator loss to update the neural network parameters θ of the generator neural network  402  and the neural network parameters ψ of the decoder neural network  410 . 
     For the LATEXT-GAN II  500 , the LATEXT-GAN II backpropagates the text-based discriminator loss to update the neural network parameter ψ of the decoder neural network  510 . The LATEXT-GAN II also backpropagate the code-based discriminator loss to update the neural network parameters of the encoder neural network  508 . The LATEXT-GAN II further backpropagate the generator loss to update the neural network parameters θ of the generator neural network  502  and the neural network parameters ψ of the decoder neural network  510 . 
     For the LATEXT-GAN III  600 , the LATEXT-GAN III backpropagates the text-based discriminator loss to update the neural network parameters ψ of the decoder neural network  610 . The LATEXT-GAN III also backpropagate the generator loss L Gen−AAE−mul  to update the neural network parameters φ of the encoder neural network  608  and the neural network ψ parameters decoder neural networks, respectively. 
       FIG.  7    illustrates a flowchart of a method  700  for training a latent space and text-based generative adversarial network (LATEXT-GAN) for text generation, according to some embodiments. The method  700  may be carried out or performed by the LATEXT-GAN I, such as the LATEXT-GAN I  400 , which includes computer-readable code or instructions executing on one or more processing devices of a processing system, such as processing devices  1000  ( FIG.  10   ) of the processing unit  1000  ( FIG.  10   ). Coding of the software for carrying out or performing the method  700  is well within the scope of a person of ordinary skill in the art having regard to the present disclosure. The method  700  may include additional or fewer operations than those shown and described and may be carried out or performed in a different order. Computer-readable code or instructions of the software executable by the one or more processing units may be stored on a non-transitory computer-readable medium, such as for example, the memory of a computing device. 
     The method  700  starts at the operation  701  where the neural network parameters φ, ψ, θ, and w of the encoder neural network  408 , the decoder neural network  410 , the generator neural network  402 , and the hybrid discriminator neural network  404 , respectively are initialized, and proceeds to the operation  702 , where an encoder neural network  408  receives a one-hot representation of a real text. The real text comprises a sequence of words. The encoder neural network  408  outputs a latent representation of the real text generated from the one-hot representation of the real text. 
     At the operation  704 , the decoder neural network  410 B receives the latent representation of the real text. The decoder neural network  410 B outputs a reconstructed representation of the real text generated from the latent representation of the real text. A softmax operator  412 A performs a softmax function of the output of the decoder neural network  410 A to generate a reconstructed softmax representation of the real text. The reconstructed softmax representation of the real text (e.g., a soft-text) is a continuous representation of the real text 
     At the operation  706 , the decoder neural network  410 B receives artificial code generated by a generator neural network  402  of the GAN (e.g., the generator neural network  402  and the hybrid discriminator neural network  404 ) from random noise data. The decoder neural network  410  outputs softmax representation of artificial text generated from the artificial code. 
     At the operation  708 , the hybrid discriminator neural network  404  receives a combination of the soft-text and the latent representation of the real text and a combination of the softmax representation of artificial text and the artificial code. The combination of the soft-text and the latent representation of the real text comprise a concatenation of the soft-text and the latent representation of the real text. The combination of the softmax representation of artificial text and the artificial code comprises a concatenation of the softmax representation of artificial text and the artificial code. 
     At the operation  710 , the hybrid discriminator neural network  404  outputs a probability indicating whether the combination of the softmax representation of artificial text and the artificial code received by the hybrid discriminator neural network  404  is similar to the combination of the soft-text and the latent representation of the real text. 
     The LATEXT-GAN I  400  calculates a reconstruction loss for the autoencoder  420  based on a difference between the one-hot representation of the real text and the soft-text output from the decoder neural network  410 . The LATEXT-GAN I  400  uses backpropagation and a reconstruction loss function L AE (φ,ψ) to update the neural network parameters φ of the encoder neural network  408  and the neural network parameters ψ of the decoder neural network  410 . In one embodiment, the LATEXT-GAN  400  may solve the following optimization problem 
     
       
         
           
             
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     to minimize the reconstruction loss for the autoencoder  420 . Here, x denotes the one-hot representation of the real text. φ denotes the neural network parameters of the encoder neural network  408 . ψ denotes the neural network parameters of the decoder neural network  410 . 
     The LATEXT-GAN I  400  calculates a discriminator loss based on the soft-text, the artificial code, the softmax representation of artificial text, and the latent representation of the real text. The LATEXT-GAN I  400  uses backpropagation and a discriminator loss function L critic−ALI  to update the neural network parameters w of the hybrid discriminator neural network, the neural network parameters φ of the encoder neural network  408 , and the neural network parameters ψ of the decoder neural network based on the discriminator loss. In one embodiment, the LATEXT-GAN I may solve the following optimization problem 
     
       
         
           
             
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     to minimize the discriminator loss. Here, {tilde over (x)} denotes the soft-text. ĉ denotes the artificial code. {circumflex over (x)} denotes the softmax representation of artificial text. c denotes the latent representation of the real text.  x  denotes random samples obtained by sampling uniformly along a line connecting pairs of generated and soft-text samples.  c  denotes random latent code samples obtained by sampling uniformly along a line connecting pairs of the artificial code and the latent representation of the real text. λ denotes a gradient penalty coefficient, w denotes the neural network parameters of the hybrid discriminator neural network  404 , φ denotes neural network parameters of the encoder neural network  408 , and ψ denotes neural network parameters of the decoder neural network  410 . 
     The LATEXT-GAN I  400  calculates a generator loss that maximizes the probability output by the hybrid discriminator neural network  404 . The LATEXT-GAN I  400  uses backpropagation and a generator loss function L Gen−ALI  to update the neural network parameters θ of the generator neural network  402  and the neural network parameters ψ of the decoder neural network  410 . In one embodiment, the LATEXT-GAN I  400  solves the following optimization problem
 
 L   Gen−ALI =min (θ,ψ) ( +E   ({circumflex over (x)},ĉ)˜P     {circumflex over (x)}     ,P     ĉ   [ f   w   t+c ( {circumflex over (x)},ĉ )] +E   ({tilde over (x)},c)˜P     {tilde over (x)}     ,P     c   [ f   w   t+c ( {tilde over (x)},c )])
 
     to minimize the generator loss. Here, {circumflex over (x)} denotes the softmax representation of artificial text. c denotes the latent space representation of the real text. {tilde over (x)} denotes the soft-text. ĉ denotes the artificial code. θ denotes the neural network parameters of the generator neural network  402 . ψ denotes the neural network parameters of the decoder neural network  410 . 
     At the operation  712 , the LATEXT-GAN I  400  determines whether the combination of the soft-text and the latent representation of the real text can be discriminated with the combination of the artificial text and the artificial code by the hybrid discriminator neural network. If so, the LATEXT-GAN I  400  further perform the training by repeating the operations  702 - 710 . Otherwise, the neural network parameters neural network parameters φ, ψ, θ, and w of the encoder neural network  408 , the decoder neural network  410 , the generator neural network  402 , and the hybrid discriminator neural network  404  are learned and the LATENT-GAN I  400  may be used to generate artificial text that mimics real text. The method  700  ends at the operation  714 . 
       FIG.  8    illustrates a flowchart of a method  800  for training a latent space and text-based generative adversarial network (LATEXT-GAN) for text generation, according to some embodiments. The method  800  may be carried out or performed by the LATEXT-GAN II  500 , which includes computer-readable code or instructions executing on one or more processing devices of a processing system, such as processing devices  1000  ( FIG.  10   ) of the processing unit  1000  ( FIG.  10   ). The method  800  may further be carried out or performed by a combination of hardware and software. Coding of the software for carrying out or performing the method  800  is well within the scope of a person of ordinary skill in the art having regard to the present disclosure. The method  800  may include additional or fewer operations than those shown and described and may be carried out or performed in a different order. Computer-readable code or instructions of the software executable by the one or more processing units may be stored on a non-transitory computer-readable medium, such as for example, the memory of a computing device. 
     Method  800  starts at the operation  801  where the neural network parameters φ, ψ, θ, w 1  and w 2  of the encoder neural network  508 , the decoder neural network  510 , the generator neural network  502 , and the text-based discriminator neural network  504  and the code-based discriminator neural network  505 , respectively are initialized and proceeds to the operation  802 , where an encoder neural network  508  receives a one-hot representation of a real text. The real text comprising a sequence of words. The encoder neural network  508  outputs a latent representation of the real text generated from the one-hot representation of the real text. 
     At the operation  804 , the decoder neural network  510 A receives the latent representation of the real text. The decoder neural network  510 A outputs a reconstructed representation of the real text generated from the latent representation of the real text. The softmax operator  512 A performs a softmax function on the reconstructed representation of the real text to generate a reconstructed softmax representation of the real text. The reconstructed softmax representation of the real text (e.g. a soft-text) is a continuous representation of the real text. 
     At the operation  806 , the decoder neural network  510 B receives artificial code generated by a generator neural network  502  from random noise data. The decoder neural network  510 B outputs softmax representation of artificial text generated from the artificial code. 
     At the operation  808 , a first discriminator neural network (e.g., a text-based discriminator neural network  504 ) receives the soft-text and the softmax representation of artificial text. The text-based discriminator neural network  504  outputs a first probability indicating whether the softmax representation of artificial text received by the text-based discriminator neural network  504  is similar to the soft-text. 
     At the operation  810 , a second discriminator neural network (e.g., a code-based discriminator neural network  505 ) receives the latent representation of the real text and the artificial code. The text-based discriminator neural network  505  outputs a second probability indicating whether the artificial code received by the text-based discriminator neural network  505  is similar to the latent representation of the real text. 
     The LATEXT-GAN II  500  calculates a reconstruction loss for the autoencoder  520  based on a difference between the one-hot representation of the real text and the soft-text output from the autoencoder  420 . The LATEXT-GAN II  500  uses backpropagation and a reconstruction loss function L AE (φ,ψ) to update the neural network parameters φ of the encoder neural network  508  and the neural network parameters ψ of the decoder neural network  510  based on the reconstruction loss. In one embodiment, the LATEXT-GAN II  500  solves the following optimization problem
 
 L   AE (φ,ψ)=min (φ,ψ) (∥ x −softmax(dec ψ (enc φ ( x )))∥ 2 )
 
     to minimize the reconstruction loss. Here, x denotes the one-hot representation of the real text. φ denotes the neural network parameters of the encoder neural network  508 . ψ denotes the neural network parameters of the decoder neural network  510 . 
     The LATEXT-GAN II  500  calculates a first discriminator loss for the text-based discriminator neural network  504  based on the soft-text and the softmax representation of artificial text. The LATEXT-GAN II  500  uses backpropagation and a first discriminator loss function ψ to update the neural network parameter w 1  of the text-based discriminator neural network  504  and the neural network parameters ψ of the decoder neural network  510 . In one embodiment, the LATEXT-GAN II  500  solves the following optimization problem.
 
 L   critic1 =min (w     1     ,ψ) ( −E   ({tilde over (x)})˜P     {tilde over (x)}   [ f   w     1     t ( {tilde over (x)} )] +E   ({circumflex over (x)})˜P     {circumflex over (x)}   [ f   w     1     t ( {circumflex over (x)} )]+λ 1   E     x ˜P       x     [(∥∇ ( x )   f   w     1     t (   x   )∥ 2 −1) 2 ])
 
     to minimize the first discriminator loss. Here, {tilde over (x)} denotes the soft-text. {circumflex over (x)} denotes the softmax representation of artificial text.  x  denotes random samples obtained by sampling uniformly along a line connecting pairs of softmax representation of artificial text and real text. λ 1  denotes a gradient penalty coefficient. w 1  denotes the neural network parameters of the text-based discriminator neural network  504 . ψ denotes the neural network parameters of the decoder neural network. 
     The LATEXT-GAN II  500  calculates a second discriminator loss for the code-based discriminator neural network  504  based on the artificial code and the latent representation of the real text. The LATEXT-GAN II  500  uses backpropagation and a second discriminator loss function L critic2  to update the neural network parameters w 2  of the code-based discriminator neural network  505  and the neural network parameters φ of the encoder neural network  505 . In one embodiment, the LATEXT-GAN II  500  solves the following optimization problem.
 
 L   critic2 =min (w     2     ,φ) ( E   ĉ˜P     ĉ   [ f   w     2     c ( ĉ )] −E   c˜P     c   [ f   w     2     c ( c )]+λ 2   E     c ˜P       c     [(∥∇ ( c )   f   w     2     c (   c   )∥ 2 −1) 2 ])
 
     to minimize second discriminator loss. Here, c denotes the latent representation of the real text. ĉ denotes the artificial code.  c  denotes random latent code samples obtained by sampling uniformly along a line connecting pairs of the artificial code and the latent space representation of the real text. λ 2  denotes a gradient penalty coefficient. w 2  denotes neural network parameters of the second discriminator neural network. φ denotes neural network parameters of the encoder neural network. 
     The LATEXT-GAN II  500  calculates a generator loss that maximizes the first probability and the second probability. The LATEXT-GAN II  500  uses backpropagation and a generator loss function to update the neural network parameters θ of the generator neural network and the neural network parameters ψ of the decoder neural network based on the generator loss. In one embodiment, the LATEXT-GAN II solves the following optimization problem
 
min (θ,ψ) ( −E   {circumflex over (x)}˜P     {circumflex over (x)}   [ f   w     1     t ( {circumflex over (x)} )] +E   ({tilde over (x)})˜P     {tilde over (x)}   [ f   w     1     t ( {tilde over (x)} )] −E   ĉ˜P     ĉ   [ f   w     2     c ( ĉ )] +E   c˜P     c   [ f   w     2     c ( c )])
 
     To minimize the generator loss. Here, {circumflex over (x)} denotes the softmax representation of artificial text. c denotes the latent space representation of the real text. ĉ denotes the artificial code. {tilde over (x)} denotes the soft-text. θ denotes parameters of the generator neural network. ψ denotes parameters of the decoder neural network. 
     At the operation  812 , the LATEXT-GAN II  500  determines a first condition of whether the soft-text and the softmax representation of artificial text can be discriminated by the first discriminator neural network. The LATEXT-GAN II  500  determines a second condition of whether the latent representation of the real text and the artificial code can be discriminated by the second discriminator neural network. In one embodiment, if at least one of the two conditions is satisfied, the LATEXT-GAN II  500  further perform the training by repeating the operations  802 - 810 . Otherwise, the method  800  ends at the operation  814 . In another embodiment, if both of the two conditions are satisfied, the LATEXT-GAN II may further perform the training by repeating the operations  802 - 810 . Otherwise, the neural network parameters neural network parameters φ, ψ, θ, w 1  and w 2  of the encoder neural network  508 , the decoder neural network  510 , the generator neural network  502 , and the text-based discriminator neural network  504 , and the code-based discriminator network  505  are learned and the LATENT-GAN II  500  may be used to generate artificial text that mimics real text and method  800  ends at the operation  814 . 
       FIG.  9    illustrates a flowchart of a method  900  for training a latent space and text-based generative adversarial network (LATEXT-GAN) for text generation, according to some additional embodiments. The method  900  may be carried out or performed by the LATEXT-GAN III, such as the LATEXT-GAN III  600  in  FIG.  6   , which includes computer-readable code or instructions executing on one or more processing devices of a processing system, such as processing devices  1000  ( FIG.  10   ) of the processing unit  1000  ( FIG.  10   ). The method  900  may also be carried out or performed by routines, subroutines, or modules of software executed by the one or more processing units. The method  900  may further be carried out or performed by a combination of hardware and software. Coding of the software for carrying out or performing the method  900  is well within the scope of a person of ordinary skill in the art having regard to the present disclosure. The method  900  may include additional or fewer operations than those shown and described and may be carried out or performed in a different order. Computer-readable code or instructions of the software executable by the one or more processing units may be stored on a non-transitory computer-readable medium, such as for example, the memory of a computing device. 
     Method  900  starts at the operation  901 , where the neural network parameters φ, ψ, θ, w 1  and w 2  of the encoder neural network  608 , the decoder neural network  610 , and the text-based discriminator neural network  604  and the code-based discriminator neural network  605 , respectively are initialized and proceeds to the operation  902 , where the encoder neural network  608  receives a one-hot representation of a real text. The real text comprising a sequence of words. The encoder neural network  608  outputs a latent representation of the real text generated from the one-hot representation of the real text. 
     At the operation  904 , the decoder neural network  610 A receives the latent representation of the real text. The decoder neural network outputs a reconstructed representation of the real text generated from the latent representation of the real text. The autoencoder  420  outputs the reconstructed softmax representation of the real text comprising a soft-text that is a continuous representation of the real text. 
     At the operation  906 , the decoder neural network  610 B receives random noise data. The decoder neural network  610 B outputs representation of artificial text generated from the random noise data to the softmax operator  612 B, which performs a softmax function on the representation of artificial text and outputs a softmax representation of artificial text. 
     At the operation  908 , a first discriminator neural network (e.g., a text-based discriminator neural network  604 ) receives the soft-text and the softmax representation of artificial text. The text-based discriminator neural network  604  outputs a first probability indicating whether the softmax representation of artificial text received by the text-based discriminator neural network  604  is similar to the soft-text. 
     At the operation  910 , a second discriminator neural network (e.g., a code-based discriminator neural network  605 ) receives the latent representation of the real text and the random noise data. The code-based discriminator neural network outputs a second probability indicating whether the random noise data received by the text-based discriminator neural network  605  is similar to the latent representation of the real text. 
     The LATEXT-GAN III  600  calculate a reconstruction loss for an autoencoder based on a difference between the one-hot representation of the real text and the soft-text output from the decoder neural network. The LATEXT-GAN III  600  also uses backpropagation and a reconstruction loss function L AE (φ,ψ)=to update the neural network parameters. φ of the encoder neural network  408  and the neural network parameters ψ of the decoder neural network  610 . In one embodiment, the LATEXT-GAN III solves the following optimization problem
 
 L   AE (φ,ψ)=min (φ,ψ) (∥ x −softmax(dec ψ (enc φ ( x )))∥ 2 )
 
     to minimize the reconstruction loss. Here, x denotes the one-hot representation of the real text. φ denotes parameters of the encoder neural network. ψ denotes parameters of the decoder neural network. 
     The LATEXT-GAN III  600  calculates a first discriminator loss for the text-based discriminator neural network  604  based on the soft-text and the softmax representation of artificial text. The LATEXT-GAN III  600  uses backpropagation and the first discriminator loss function L critic1  to update the neural network parameters w 1  of the text-based discriminator neural network and the neural network parameters ψ of the decoder neural network  610 . In one embodiment, the LATEXT-GAN III  600  solves the following optimization problem
 
min (w     1,ψ)   ( −E   ({tilde over (x)})˜P     {tilde over (x)}   [ f   w     1     t ( {tilde over (x)} )] +E   ({circumflex over (x)})˜P     {circumflex over (x)}   [ f   w     1     t ( {circumflex over (x)} )]+λ 1   E     x ˜P       x     [(∥∇ ( x )   f   w     1     t (   x   )∥ 2 −1) 2 ])
 
     minimize the first discriminator loss. Here, {tilde over (x)} denotes the soft-text. {circumflex over (x)} denotes the softmax representation of artificial text.  x  denotes random samples obtained by sampling uniformly along a line connecting pairs of softmax representation of artificial text and real text. λ 1  denotes a gradient penalty coefficient, w 1  denotes the neural network parameters of the first discriminator neural network. ψ denotes the neural network parameters of the decoder neural network. 
     The LATEXT-GAN III calculates a second discriminator loss for the code-based discriminator neural network  605  based on the random noise data and the latent representation of the real text. The LATEXT-GAN III  600  uses backpropagation and the second discriminator loss function L critic2  update the neural network parameters w 2  of the code-based discriminator neural network  605 . In one embodiment, the LATEXT-GAN solves the following optimization problem
 
 L   critic2 =min w     2   ( E   c˜P     c   [ f   w     2     c ( c ) −E   z˜P     z   [ f   w     2     c ( z )]+λ 2   E     c1 ˜P       c1     [(∥∇ ( c   1 )   f   w     2     c (   c 1     )∥ 2 −1) 2 ])
 
     to minimize the second discriminator loss. Here, z denotes the random noise data.  c 1    denotes random latent code samples obtained by sampling uniformly along a line connecting pairs of the random noise data and the latent space representation of the real text. λ 2  denotes a gradient penalty coefficient w 2  denotes parameters of the second discriminator neural network. 
     The LATEXT-GAN III  600  calculates a generator loss that maximizes the first probability and the second probability. The LATEXT-GAN III uses backpropagation and a generator loss function L Gen−AAE−mul  to update the neural network parameters φ of the encoder neural network  608  and the neural network parameters ψ the decoder neural network  610 . In one embodiment, the LATEXT-GAN III solves the following optimization problem.
 
 L   Gen−AAE−mul =min φ,ψ ( −E   {circumflex over (x)}˜P     {circumflex over (x)}   [ f   w     1     t ( {circumflex over (x)} )] +E   ({tilde over (x)})˜P     {tilde over (x)}   [ f   w     1     t ( {tilde over (x)} )] +E   z˜P     z   [ f   w     2     c ( z )] −E   c˜P     c   [ f   w     2     c ( c )])
 
     to minimize the generator loss Here, {circumflex over (x)} denotes the softmax representation of artificial text. c denotes the latent representation of the real text. {tilde over (x)} denotes the soft-text. φ denotes the neural network parameters of the encoder neural network. ψ denotes the neural network parameters of the decoder neural network. 
     At the operation  912 , the LATEXT-GAN III  600  determines a first condition of whether the soft-text and the softmax representation of artificial text can be discriminated by the first discriminator neural network. The LATEXT-GAN III  600  determines a second condition of whether the latent space representation of the real text and the random noise data can be discriminated by the second discriminator neural network. In one embodiment, if at least one of the two conditions is satisfied, the LATEXT-GAN III  600  may further perform the training by repeating the operations  902 - 910 . Otherwise, the neural network parameters neural network parameters φ, ψ, θ, w 1  and w 2  of the encoder neural network  508 , the decoder neural network  510 , and the text-based discriminator neural network  504 , and the code-based discriminator network  505  are learned and the LATENT-GAN III  600  may be used to generate artificial text that mimics real text and the method  900  ends at the operation  914 . In another embodiment, if both of the two conditions are satisfied, the LATEXT-GAN III may further perform the training by repeating the operations  902 - 910 . Otherwise, the method  900  ends at the operation  814 . 
     In sum, embodiments of this disclosure address the main bottleneck of text generation using a GAN in dealing with discrete data and provide three embodiment approaches of using the latent code and the soft-text in the GAN training. The combined code-based and text-based discriminator(s) become more powerful than the discriminators in the traditional approaches. The generator also becomes more successful in fooling the discriminator(s) than the generators in the traditional approaches. Consequently, after the adversarial training between the generator and the discriminator(s), the softmax representation of artificial text samples generated by the generator would be more realistic than the softmax representation of artificial text samples generated by the generators of the conventional systems. The disclosed techniques result in better performance for generating more accurate artificial text samples than conventional techniques. More realistic and more understandable texts can be produced by the generator of the GAN using the disclosed techniques. 
     The disclosed techniques in the embodiments of this disclosure can be applied to other technical areas. The disclosed techniques can be applied directly to other applications such as bilingual machine translation (or the Bilingual GAN) and generating conversations. 
     The disclosed techniques can be applied to text-to-text generation systems, such as machine translation, dialog models, chatbots, and question answering, etc. For example, the disclosed techniques can be employed in natural language processing (NLP) related applications. 
     The disclosed techniques can be applied to summarization applications where textual summaries of the data set are generated. Examples of such applications include, but are not limited to, producing textual weather forecasts from weather data, summarizing financial and business data, summarizing electronic medical records, and describing graphs and data sets to blind people, etc. 
       FIG.  10    is a block diagram of an example simplified processing system  1000 , which may be used to implement embodiments disclosed herein, and provides a higher level implementation example. The LATEXT GANs I, II, and III  400 ,  500 , and  600  of  FIGS.  4 - 6    and the methods  700 ,  800 , and  900  of  FIGS.  7 - 9    may be implemented using the example processing system  1000 , or variations of the processing system  1000 . The processing system  1000  could be a server or a desktop terminal, for example, or any suitable processing system. Other processing systems suitable for implementing embodiments described in the present disclosure may be used, which may include components different from those discussed below. Although  FIG.  10    shows a single instance of each component, there may be multiple instances of each component in the processing system  1000 . 
     The processing system  1000  may include one or more processing devices  1002 , such as a processor, graphics processing unit (GPU), a microprocessor, an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), a dedicated logic circuitry, a tensor processing units (TPU), an artificial intelligence (AI) accelerator, or combinations thereof. The processing system  1000  may also include one or more input/output (I/O) interfaces  1004 , which may enable interfacing with one or more appropriate input devices  1014  and/or output devices  1016 . The processing system  1000  may include one or more network interfaces  1006  for wired or wireless communication with a network (e.g., an intranet, the Internet, a P2P network, a WAN and/or a LAN) or other node. The network interfaces  1006  may include wired links (e.g., Ethernet cable) and/or wireless links (e.g., one or more antennas) for intra-network and/or inter-network communications. 
     The processing system  1000  may also include one or more storage units  1008 , which may include a mass storage unit such as a solid state drive, a hard disk drive, a magnetic disk drive and/or an optical disk drive. The processing system  1000  may include one or more memories  1010 , which may include a volatile or non-volatile memory (e.g., a flash memory, a random access memory (RAM), and/or a read-only memory (ROM)). The non-transitory memory(ies)  1010  may store instructions for execution by the processing device(s)  1002 , such as to carry out examples described in the present disclosure, for example to perform encoding or decoding. The memory(ies)  1010  may include other software instructions, such as for implementing an operating system and other applications/functions. In some examples, one or more data sets and/or modules may be provided by an external memory (e.g., an external drive in wired or wireless communication with the processing system  1000 ) or may be provided by a transitory or non-transitory computer-readable medium. Examples of non-transitory computer readable media include a RAM, a ROM, an erasable programmable ROM (EPROM), an electrically erasable programmable ROM (EEPROM), a flash memory, a CD-ROM, or other portable memory storage. There may be a bus  1012  providing communication among components of the processing system  1000 , including the processing device(s)  1002 , I/O interface(s)  1004 , network interface(s)  1006 , storage unit(s)  1008 , and/or memory(ies)  1010 . The bus  1012  may be any suitable bus architecture including, for example, a memory bus, a peripheral bus or a video bus. 
     In  FIG.  10   , the input device(s)  1014  (e.g., a keyboard, a mouse, a microphone, a touchscreen, and/or a keypad) and output device(s)  1016  (e.g., a display, a speaker and/or a printer) are shown as external to the processing system  1000 . In other examples, one or more of the input device(s)  1014  and/or the output device(s)  1016  may be included as a component of the processing system  1000 . In other examples, there may not be any input device(s)  1014  and output device(s)  1016 , in which case the I/O interface(s)  1004  may not be needed. 
     The memory(ies)  1010  may include instructions for a regression module  1018  that, when executed, cause the processing system  1000  to perform a method such as the method  700 ,  800 , and  900  of  FIGS.  7 - 9   . The memory(ies)  1010  may further store training dataset (e.g., real text data samples) and generated text data samples in a databank  1028 . 
     Although the present disclosure may describe methods and processes with steps in a certain order, one or more steps of the methods and processes may be omitted or altered as appropriate. One or more steps may take place in an order other than that in which they are described, as appropriate. 
     Although the present disclosure may be described, at least in part, in terms of methods, a person of ordinary skill in the art will understand that the present disclosure is also directed to the various components for performing at least some of the aspects and features of the described methods, be it by way of hardware components, software or any combination of the two. Accordingly, the technical solution of the present disclosure may be embodied in the form of a software product. A suitable software product may be stored in a pre-recorded storage device or other similar non-volatile or non-transitory computer readable medium, including DVDs, CD-ROMs, USB flash disk, a removable hard disk, or other storage media, for example. The software product includes instructions tangibly stored thereon that enable a processing device (e.g., a personal computer, a server, or a network device) to execute examples of the methods disclosed herein. 
     Although this invention has been described with reference to illustrative embodiments, this description is not intended to be construed in a limiting sense. Various modifications and combinations of the illustrative embodiments, as well as other embodiments of the invention, will be apparent to persons skilled in the art upon reference to the description. It is therefore intended that the appended claims encompass any such modifications or embodiments.