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To understand this equation first you need to understand the context in which it is first introduced. We have two neural networks (i.e. $D$ and $G$) that are playing a minimax game. This means that they have competing goals. Let's look at each one separately: Generator Before we start, you should note that throughout the whole paper the notion of the data-...

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The Focus of This Question "How can ... we process the data from the true distribution and the data from the generative model in the same iteration? Analyzing the Foundational Publication In the referenced page, Understanding Generative Adversarial Networks (2017), doctoral candidate Daniel Sieta correctly references Generative Adversarial Networks, ...

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The key is: VAE usually use a small latent dimension, the information of input is so hard to pass through this bottleneck, meanwhile it tries to minimize the loss with the batch of input data, you should know the result -- VAE can only have a mean and blurry output. If you increase the bandwidth of the bottleneck, i.e. the size of latent vector, VAE can get ...

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There are several generative models that have been proposed before or roughly at the same time of the GAN (2014). For example, the deep Boltzman machine (2009), deep generative stochastic network (2014) or variational auto-encoder (2014).

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In deep networks there is actually a wide variety of solutions to the problem, but if you need to find one, any easy way to do this is just through normal optimization schemes $$\hat x = argmin_x \ L(y,x)$$ where $L(y,x)$ is your loss function. Since ANN's are generally differentiable you can optimize this iteratively with some form gradient descent scheme: $... 4 Probably the simplest way to search for an image with the highest probability of being a cat is to use a technique similar to Deep Dream: Load the network for training, but freeze all the network weights Create a random input image, and connect it to the network as a "variable" i.e. data that can be changed through training Set a loss function based on ... 4 I guess the issue is you lost track of where the samples came from and since you requested a math explanation I'll try to go step by step using my notation and without checking other material to avoid being biased by how other authors present it So we start from $$L(D,G) = E_{x \sim p_{r}(x)} \log(D(x)) + E_{x \sim p_{g}(x)}\log(1 - D(x))$$ then you apply ... 4 You can already do this with some neural networks, such as GANs and VAEs, which are generative models that learn a probability distribution over the inputs, so they learn how to produce e.g. images that are similar to the images they were trained with. Now, if you're interested in whether there is a black-box method, i.e. a method that, for every possible ... 3 We can already observe information bubbles on social media, where the circle is that the ML algorithms learn what content people like and give more similar content based on clicks and so on. From a single wrong click, you could enter a bubble and never come out if you don't take care or be aware. This happens with humans, so the same may apply to computers. ... 3 In essence, Variational Autoencoders learn an "explicit" distribution of the data by trying to fit the data via a multi-dimensional Gaussian/Normal distribution. However, Generative Adversarial Networks learn an "implicit" distribution of data meaning that you cannot directly sample them. Also, due to the deterministic nature of neural networks GANs tend to ... 3 From the theoretical foundations one can look into the Chapter 20: Deep Generative Models of the classic DL book by Goodfellow, Bengio https://amzn.to/2MmZNbH. Not the most recent reference, but written by the professionals in simple and accessible way. There is a nice book Generative Deep Learning by D.Foster with some simple heuristics and probability ... 3 Due to subjective nature, quantitative evaluation of synthetic images is difficult in general. However, there are metrics like Inception Score or FID score that are used for evaluation of generative models like GANs or VAEs. Technically, it considers two aspects of the generated data: Similarity with training data Diversity within itself Even though such ... 2 Let's start at the beginning. GANs are models that can learn to create data that is similar to the data that we give them. When training a generative model other than a GAN, the easiest loss function to come up with is probably the Mean Squared Error (MSE). Kindly allow me to give you an example (Trickot L 2017): Now suppose you want to generate cats ; you ... 2 GANs were invented in a bar somewhere in Montreal, Canada. At said bar, the idea was that neural networks could be used for generating new examples from an existing distribution. This was the problem: Given an input set$X$, can we make a new$x'$that looks like it should be in$X$? The classic description of a GAN is a counterfeiter (generator) and a cop ... 2 Now I have a network trained to get an output value from an random set of attributes but, can I use this trained network to get the input attributes using only the desired output? It depends: If you are happy to find any inputs, even non-realistic ones, that get your desired output, then you can use your trained network, with a minor modification. Freeze ... 2 Use of Transposed Convolution can lead to checkerboard artifacts. So we prefer to up-sample and then apply convolution. You can check this article for more information https://distill.pub/2016/deconv-checkerboard/. 2 The problem isn't the GAN but the implementation of its discriminator which is typically a convolutional neural network (CNN). CNNs have trouble with sparse data. They require dense data to learn well. There are ways to work around this. See the following for some ideas: Sparse and Dense Data with CNNs: Depth Completion and Semantic Segmentation Sparse ... 2 It looks like you're asking about the difference between using conditional and joint probabilities. The joint probability $$D(x,y)$$ is the probability of x and y both happening together. The conditional probability $$D(x | y)$$ is the probability that x happens, given that y has already happened. So, $$D(x,y) = D(y) * D(x | y)$$. Notice that, in a C-GAN,... 2 Can AI provide a more reliable analysis of the gross effects of carbon emissions on extinctions of species ice-cap melting, and other effects? Yes. The work of Judea Pearl and others over the last 20 years began out of a desire to address uncertainty within AI. Eventually, this led Pearl to become fascinated by the need to quantifiably determine when one ... 2 Model means you can say a Prototype we make regarding to our task. As we first train our model on some observed or you can say bench-marked data ; called as TRaining phase of model. Then we apply that model to our problem (test data) you can say in order to evaluate how much well you have trained your model. Training data we use related to our task or use ... 2 I'll answer your questions one by one: In this equation are the$E_{z \sim p_z(z)}$and$E_{x \sim p_{data}(x)}$the means of the distributions of the mini batch samples? So let's take the first part$E_{x \sim p_{data}(x)}[log \,D(x)]$. This is read as the "expected value of$log \, D(x)$, where$x$is sampled from$p_{data}(x)$". So, in simpler terms ... 2 GANs are notably hard to train and it is not uncommon to have large bumps in the losses. The learning rate is a good start but the instability may come from a wide variety of reasons. I'm assuming that you have no bug in your code or data. For one, gradient descent is not well suited to the 2-player game we're playing. I've personally found ExtraAdam to ... 2 Generally, text generators work by modeling the joint distribution of the text by its Bayesian forward decomposition$ \begin{align*} p(w_1, w_2, ..., w_n) &= p(w_1) * p(w_2|w_1) * p(w_3|w_2, w_1) *\ ...\ * p(w_n|\{w_i\}_{i<n})\\ &= \prod_{i=1}^n p(w_i|\{w_k\}_{k<i})\\ \end{align*} $From a modeling perspective, this looks right up ... 2 [Answering my own question after 5 months of studying VAE models] The point of the MMD-VAE or InfoVAE is not exactly to emphasise on the visual quality of generated samples. It is to preserve greater amount of information through the encoding process. The MMD formulation stems from introducing a mutual coefficient factor into the Evidence Lower BOund (ELBO) ... 2 I just came across this piece of news yesterday: "This week, Microsoft Research threw down the gauntlet with the launch of a competition challenging researchers around the world to develop AI agents that can solve text-based games." This seems to be an AI competition announced by Microsoft with the aim to create AI that can solve text-based games. This ... 2 The terminologies can be confusing because of the different ways authors use them. The bottom line is this The Synthesis task basically refers to creating or synthesizing new data. Creation of data can be purely deterministic, e.g. .. we provide a written sentence .. to emit an audio waveform containing a spoken version of that sentence But, a vast ... 1 Your goal is to model a distribution when constructing a GAN, therefore you need a way to be able to sample that distribution. The noise's purpose is so you can do this. Generally, it's drawn from a distribution that is computationally easy to draw from (like a gaussian). You are modeling the generator$G(X)$where$X \sim N(\mu, \sigma^2)$. this means$...

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Image Caption Generation is an interesting problem to work on. I think your question was to know if there are any open-source libraries with built-in functions for Image Captioning. You can build Image Caption Generation models using Frameworks like Tensorflow, PyTorch, and Trax. I'd also recommend you to read the following papers: Show and Tell: A Neural ...

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If you're building a straight "vanilla" generative adversarial network, it's best to understand the network as a statistical engine: You are training the generator on samples of a statistical distribution. (And you're training the discriminator to distinguish between "ground truth" images, and images from that generator.) Once you replace the input noise ...

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With a Google Cloud V100 GPU the GAN would run a week to two with default parameters. Does this sound realistic time for this kind of dataset? It's definitely not feasible for me. Yes, V100s are quite beefy. You shouldn't even need a week. Obviously this is based on my experience with various problems, rather than a concrete calculation. Is 4000 ...

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