Morten Hjorth-Jensen
946 lines
31 KiB
Plaintext
946 lines
31 KiB
Plaintext
{
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"cells": [
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{
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"# Generative Models\n",
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"**Generative models** describe a class of statistical models that are a contrast\n",
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"to **discriminative models**. Informally we say that generative models can\n",
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"generate new data instances while discriminative models discriminate between\n",
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"different kinds of data instances. A generative model could generate new photos\n",
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"of animals that look like 'real' animals while a discriminative model could tell\n",
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"a dog from a cat. More formally, given a data set $x$ and a set of labels /\n",
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"targets $y$. Generative models capture the joint probability $p(x, y)$, or\n",
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"just $p(x)$ if there are no labels, while discriminative models capture the\n",
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"conditional probability $p(y | x)$. Discriminative models generally try to draw\n",
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"boundaries in the data space (often high dimensional), while generative models\n",
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"try to model how data is placed throughout the space.\n",
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"\n",
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"\n",
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"## Generative Adversarial Networks\n",
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"**Generative Adversarial Networks** are a type of unsupervised machine learning\n",
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"algorithm proposed by [Goodfellow et. al](https://arxiv.org/pdf/1406.2661.pdf)\n",
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"in 2014 (Read the paper first it's only 6 pages). The simplest formulation of\n",
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"the model is based on a game theoretic approach, *zero sum game*, where we pit\n",
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"two neural networks against one another. We define two rival networks, one\n",
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"generator $g$, and one discriminator $d$. The generator directly produces\n",
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"samples"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"<!-- Equation labels as ordinary links -->\n",
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"<div id=\"_auto1\"></div>\n",
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"\n",
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"$$\n",
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"\\begin{equation}\n",
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" x = g(z; \\theta^{(g)})\n",
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"\\label{_auto1} \\tag{1}\n",
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"\\end{equation}\n",
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"$$"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"The discriminator attempts to distinguish between samples drawn from the\n",
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"training data and samples drawn from the generator. In other words, it tries to\n",
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"tell the difference between the fake data produced by $g$ and the actual data\n",
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"samples we want to do prediction on. The discriminator outputs a probability\n",
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"value given by"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"<!-- Equation labels as ordinary links -->\n",
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"<div id=\"_auto2\"></div>\n",
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"\n",
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"$$\n",
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"\\begin{equation}\n",
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" d(x; \\theta^{(d)})\n",
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"\\label{_auto2} \\tag{2}\n",
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"\\end{equation}\n",
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"$$"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"indicating the probability that $x$ is a real training example rather than a\n",
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"fake sample the generator has generated. The simplest way to formulate the\n",
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"learning process in a generative adversarial network is a zero-sum game, in\n",
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"which a function"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"<!-- Equation labels as ordinary links -->\n",
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"<div id=\"_auto3\"></div>\n",
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"\n",
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"$$\n",
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"\\begin{equation}\n",
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" v(\\theta^{(g)}, \\theta^{(d)})\n",
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"\\label{_auto3} \\tag{3}\n",
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"\\end{equation}\n",
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"$$"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"determines the reward for the discriminator, while the generator gets the\n",
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"conjugate reward"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"<!-- Equation labels as ordinary links -->\n",
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"<div id=\"_auto4\"></div>\n",
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"\n",
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"$$\n",
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"\\begin{equation}\n",
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" -v(\\theta^{(g)}, \\theta^{(d)})\n",
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"\\label{_auto4} \\tag{4}\n",
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"\\end{equation}\n",
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"$$"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"During learning both of the networks maximize their own reward function, so that\n",
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"the generator gets better and better at tricking the discriminator, while the\n",
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"discriminator gets better and better at telling the difference between the fake\n",
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"and real data. The generator and discriminator alternate on which one trains at\n",
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"one time (i.e. for one epoch). In other words, we keep the generator constant\n",
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"and train the discriminator, then we keep the discriminator constant to train\n",
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"the generator and repeat. It is this back and forth dynamic which lets GANs\n",
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"tackle otherwise intractable generative problems. As the generator improves with\n",
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" training, the discriminator's performance gets worse because it cannot easily\n",
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" tell the difference between real and fake. If the generator ends up succeeding\n",
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" perfectly, the the discriminator will do no better than random guessing i.e.\n",
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" 50\\%. This progression in the training poses a problem for the convergence\n",
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" criteria for GANs. The discriminator feedback gets less meaningful over time,\n",
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" if we continue training after this point then the generator is effectively\n",
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" training on junk data which can undo the learning up to that point. Therefore,\n",
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" we stop training when the discriminator starts outputting $1/2$ everywhere.\n",
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" At convergence we have"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"<!-- Equation labels as ordinary links -->\n",
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"<div id=\"_auto5\"></div>\n",
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"\n",
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"$$\n",
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"\\begin{equation}\n",
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" g^* = \\underset{g}{\\mathrm{argmin}}\\hspace{2pt}\n",
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" \\underset{d}{\\mathrm{max}}v(\\theta^{(g)}, \\theta^{(d)})\n",
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"\\label{_auto5} \\tag{5}\n",
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"\\end{equation}\n",
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"$$"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"The default choice for $v$ is"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"<!-- Equation labels as ordinary links -->\n",
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"<div id=\"_auto6\"></div>\n",
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"\n",
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"$$\n",
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"\\begin{equation}\n",
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" v(\\theta^{(g)}, \\theta^{(d)}) = \\mathbb{E}_{x\\sim p_\\mathrm{data}}\\log d(x)\n",
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" + \\mathbb{E}_{x\\sim p_\\mathrm{model}}\n",
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" \\log (1 - d(x))\n",
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"\\label{_auto6} \\tag{6}\n",
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"\\end{equation}\n",
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"$$"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"The main motivation for the design of GANs is that the learning process requires\n",
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"neither approximate inference (variational autoencoders for example) nor\n",
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"approximation of a partition function. In the case where"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"<!-- Equation labels as ordinary links -->\n",
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"<div id=\"_auto7\"></div>\n",
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"\n",
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"$$\n",
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"\\begin{equation}\n",
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" \\underset{d}{\\mathrm{max}}v(\\theta^{(g)}, \\theta^{(d)})\n",
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"\\label{_auto7} \\tag{7}\n",
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"\\end{equation}\n",
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"$$"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"is convex in $\\theta^{(g)} then the procedure is guaranteed to converge and is\n",
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"asymptotically consistent\n",
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"( [Seth Lloyd on QuGANs](https://arxiv.org/pdf/1804.09139.pdf) ). This is in\n",
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"general not the case and it is possible to get situations where the training\n",
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"process never converges because the generator and discriminator chase one\n",
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"another around in the parameter space indefinitely. A much deeper discussion on\n",
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"the currently open research problem of GAN convergence is available\n",
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"[here](https://www.deeplearningbook.org/contents/generative_models.html). To\n",
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"anyone interested in learning more about GANs it is a highly recommended read.\n",
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"Direct quote: \"In this best-performing formulation, the generator aims to\n",
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"increase the log probability that the discriminator makes a mistake, rather than\n",
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"aiming to decrease the log probability that the discriminator makes the correct\n",
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"prediction.\" [Another interesting read](https://arxiv.org/abs/1701.00160)\n",
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"\n",
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"\n",
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"## Writing Our First Generative Adversarial Network\n",
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"Let us now move on to actually implementing a GAN in tensorflow. We will study\n",
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"the performance of our GAN on the MNIST dataset. This code is based on and\n",
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"adapted from the\n",
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"[google tutorial](https://www.tensorflow.org/tutorials/generative/dcgan)\n",
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"\n",
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"First we import our libraries"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false,
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"editable": true
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},
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"outputs": [],
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"source": [
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"%matplotlib inline\n",
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"\n",
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"import os\n",
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"import time\n",
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"import numpy as np\n",
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"import tensorflow as tf\n",
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"import matplotlib.pyplot as plt\n",
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"from tensorflow.keras import layers\n",
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"from tensorflow.keras.utils import plot_model"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Next we define our hyperparameters and import our data the usual way"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false,
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"editable": true
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},
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"outputs": [],
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"source": [
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"BUFFER_SIZE = 60000\n",
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"BATCH_SIZE = 256\n",
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"EPOCHS = 30\n",
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"\n",
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"data = tf.keras.datasets.mnist.load_data()\n",
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"(train_images, train_labels), (test_images, test_labels) = data\n",
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"train_images = np.reshape(train_images, (train_images.shape[0],\n",
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" 28,\n",
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" 28,\n",
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" 1)).astype('float32')\n",
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"\n",
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"# we normalize between -1 and 1\n",
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"train_images = (train_images - 127.5) / 127.5\n",
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"training_dataset = tf.data.Dataset.from_tensor_slices(\n",
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" train_images).shuffle(BUFFER_SIZE).batch(BATCH_SIZE)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Let's have a quick look"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false,
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"editable": true
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},
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"outputs": [],
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"source": [
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"plt.imshow(train_images[0], cmap='Greys')\n",
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"plt.show()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Now we define our two models. This is where the 'magic' happens. There are a\n",
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"huge amount of possible formulations for both models. A lot of engineering and\n",
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"trial and error can be done here to try to produce better performing models. For\n",
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"more advanced GANs this is by far the step where you can 'make or break' a\n",
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"model.\n",
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"\n",
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"We start with the generator. As stated in the introductory text the generator\n",
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"$g$ upsamples from a random sample to the shape of what we want to predict. In\n",
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"our case we are trying to predict MNIST images ($28\\times 28$ pixels)."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false,
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"editable": true
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},
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"outputs": [],
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"source": [
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"def generator_model():\n",
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" \"\"\"\n",
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" The generator uses upsampling layers tf.keras.layers.Conv2DTranspose() to\n",
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" produce an image from a random seed. We start with a Dense layer taking this\n",
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" random sample as an input and subsequently upsample through multiple\n",
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" convolutional layers.\n",
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" \"\"\"\n",
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"\n",
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" # we define our model\n",
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" model = tf.keras.Sequential()\n",
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"\n",
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"\n",
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" # adding our input layer. Dense means that every neuron is connected and\n",
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" # the input shape is the shape of our random noise. The units need to match\n",
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" # in some sense the upsampling strides to reach our desired output shape.\n",
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" # we are using 100 random numbers as our seed\n",
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" model.add(layers.Dense(units=7*7*BATCH_SIZE,\n",
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" use_bias=False,\n",
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" input_shape=(100, )))\n",
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" # we normalize the output form the Dense layer\n",
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" model.add(layers.BatchNormalization())\n",
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" # and add an activation function to our 'layer'. LeakyReLU avoids vanishing\n",
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" # gradient problem\n",
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" model.add(layers.LeakyReLU())\n",
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" model.add(layers.Reshape((7, 7, BATCH_SIZE)))\n",
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" assert model.output_shape == (None, 7, 7, BATCH_SIZE)\n",
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" # even though we just added four keras layers we think of everything above\n",
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" # as 'one' layer\n",
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"\n",
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" # next we add our upscaling convolutional layers\n",
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" model.add(layers.Conv2DTranspose(filters=128,\n",
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" kernel_size=(5, 5),\n",
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" strides=(1, 1),\n",
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" padding='same',\n",
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" use_bias=False))\n",
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" model.add(layers.BatchNormalization())\n",
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" model.add(layers.LeakyReLU())\n",
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" assert model.output_shape == (None, 7, 7, 128)\n",
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"\n",
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" model.add(layers.Conv2DTranspose(filters=64,\n",
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" kernel_size=(5, 5),\n",
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" strides=(2, 2),\n",
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" padding='same',\n",
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" use_bias=False))\n",
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" model.add(layers.BatchNormalization())\n",
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" model.add(layers.LeakyReLU())\n",
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" assert model.output_shape == (None, 14, 14, 64)\n",
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"\n",
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" model.add(layers.Conv2DTranspose(filters=1,\n",
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" kernel_size=(5, 5),\n",
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" strides=(2, 2),\n",
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" padding='same',\n",
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" use_bias=False,\n",
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" activation='tanh'))\n",
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" assert model.output_shape == (None, 28, 28, 1)\n",
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"\n",
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" return model"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"And there we have our 'simple' generator model. Now we move on to defining our\n",
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"discriminator model $d$, which is a convolutional neural network based image\n",
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"classifier."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
|
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"metadata": {
|
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"collapsed": false,
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"editable": true
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},
|
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"outputs": [],
|
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"source": [
|
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"def discriminator_model():\n",
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" \"\"\"\n",
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" The discriminator is a convolutional neural network based image classifier\n",
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" \"\"\"\n",
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"\n",
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" # we define our model\n",
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" model = tf.keras.Sequential()\n",
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" model.add(layers.Conv2D(filters=64,\n",
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" kernel_size=(5, 5),\n",
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" strides=(2, 2),\n",
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" padding='same',\n",
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" input_shape=[28, 28, 1]))\n",
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" model.add(layers.LeakyReLU())\n",
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" # adding a dropout layer as you do in conv-nets\n",
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" model.add(layers.Dropout(0.3))\n",
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"\n",
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"\n",
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" model.add(layers.Conv2D(filters=128,\n",
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" kernel_size=(5, 5),\n",
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" strides=(2, 2),\n",
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" padding='same'))\n",
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" model.add(layers.LeakyReLU())\n",
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" # adding a dropout layer as you do in conv-nets\n",
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" model.add(layers.Dropout(0.3))\n",
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"\n",
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" model.add(layers.Flatten())\n",
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" model.add(layers.Dense(1))\n",
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"\n",
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" return model"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Let us take a look at our models. **Note**: double click images for bigger view."
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]
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},
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{
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"cell_type": "code",
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|
"execution_count": null,
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"metadata": {
|
|
"collapsed": false,
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"editable": true
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},
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"outputs": [],
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"source": [
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"generator = generator_model()\n",
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"plot_model(generator, show_shapes=True, rankdir='LR')"
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]
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},
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{
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"cell_type": "code",
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|
"execution_count": null,
|
|
"metadata": {
|
|
"collapsed": false,
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"editable": true
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},
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"outputs": [],
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"source": [
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"discriminator = discriminator_model()\n",
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"plot_model(discriminator, show_shapes=True, rankdir='LR')"
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]
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},
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{
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"cell_type": "markdown",
|
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"metadata": {},
|
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"source": [
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"Next we need a few helper objects we will use in training"
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]
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},
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{
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"cell_type": "code",
|
|
"execution_count": null,
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|
"metadata": {
|
|
"collapsed": false,
|
|
"editable": true
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"cross_entropy = tf.keras.losses.BinaryCrossentropy(from_logits=True)\n",
|
|
"generator_optimizer = tf.keras.optimizers.Adam(1e-4)\n",
|
|
"discriminator_optimizer = tf.keras.optimizers.Adam(1e-4)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"The first object, *cross_entropy* is our loss function and the two others are\n",
|
|
"our optimizers. Notice we use the same learning rate for both $g$ and $d$. This\n",
|
|
"is because they need to improve their accuracy at approximately equal speeds to\n",
|
|
"get convergence (not necessarily exactly equal). Now we define our loss\n",
|
|
"functions"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"collapsed": false,
|
|
"editable": true
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def generator_loss(fake_output):\n",
|
|
" loss = cross_entropy(tf.ones_like(fake_output), fake_output)\n",
|
|
"\n",
|
|
" return loss"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"collapsed": false,
|
|
"editable": true
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def discriminator_loss(real_output, fake_output):\n",
|
|
" real_loss = cross_entropy(tf.ones_like(real_output), real_output)\n",
|
|
" fake_loss = cross_entropy(tf.zeros_liks(fake_output), fake_output)\n",
|
|
" total_loss = real_loss + fake_loss\n",
|
|
"\n",
|
|
" return total_loss"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"Next we define a kind of seed to help us compare the learning process over\n",
|
|
"multiple training epochs."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"collapsed": false,
|
|
"editable": true
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"noise_dimension = 100\n",
|
|
"n_examples_to_generate = 16\n",
|
|
"seed_images = tf.random.normal([n_examples_to_generate, noise_dimension])"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"Now we have everything we need to define our training step, which we will apply\n",
|
|
"for every step in our training loop. Notice the @tf.function flag signifying\n",
|
|
"that the function is tensorflow 'compiled'. Removing this flag doubles the\n",
|
|
"computation time."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"collapsed": false,
|
|
"editable": true
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"@tf.function\n",
|
|
"def train_step(images):\n",
|
|
" noise = tf.random.normal([BATCH_SIZE, noise_dimension])\n",
|
|
"\n",
|
|
" with tf.GradientTape() as gen_tape, tf.GradientTape() as disc_tape:\n",
|
|
" generated_images = generator(noise, training=True)\n",
|
|
"\n",
|
|
" real_output = discriminator(images, training=True)\n",
|
|
" fake_output = discriminator(generated_images, training=True)\n",
|
|
"\n",
|
|
" gen_loss = generator_loss(fake_output)\n",
|
|
" disc_loss = discriminator_loss(real_output, fake_output)\n",
|
|
"\n",
|
|
" gradients_of_generator = gen_tape.gradient(gen_loss,\n",
|
|
" generator.trainable_variables)\n",
|
|
" gradients_of_discriminator = disc_tape.gradient(disc_loss,\n",
|
|
" discriminator.trainable_variables)\n",
|
|
" generator_optimizer.apply_gradients(zip(gradients_of_generator,\n",
|
|
" generator.trainable_variables))\n",
|
|
" discriminator_optimizer.apply_gradients(zip(gradients_of_discriminator,\n",
|
|
" discriminator.trainable_variables))\n",
|
|
"\n",
|
|
" return gen_loss, disc_loss"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"Next we define a helper function to produce an output over our training epochs\n",
|
|
"to see the predictive progression of our generator model. **Note**: I am including\n",
|
|
"this code here, but comment it out in the training loop."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"collapsed": false,
|
|
"editable": true
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def generate_and_save_images(model, epoch, test_input):\n",
|
|
" # we're making inferences here\n",
|
|
" predictions = model(test_input, training=False)\n",
|
|
"\n",
|
|
" fig = plt.figure(figsize=(4, 4))\n",
|
|
"\n",
|
|
" for i in range(predictions.shape[0]):\n",
|
|
" plt.subplot(4, 4, i+1)\n",
|
|
" plt.imshow(predictions[i, :, :, 0] * 127.5 + 127.5, cmap='gray')\n",
|
|
" plt.axis('off')\n",
|
|
"\n",
|
|
" plt.savefig(f'./images_from_seed_images/image_at_epoch_{str(epoch).zfill(3)}.png')\n",
|
|
" plt.close()\n",
|
|
" #plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"Setting up checkpoints to periodically save our model during training so that\n",
|
|
"everything is not lost even if the program were to somehow terminate while\n",
|
|
"training."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"collapsed": false,
|
|
"editable": true
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Setting up checkpoints to save model during training\n",
|
|
"checkpoint_dir = './training_checkpoints'\n",
|
|
"checkpoint_prefix = os.path.join(checkpoint_dir, 'ckpt')\n",
|
|
"checkpoint = tf.train.Checkpoint(generator_optimizer=generator_optimizer,\n",
|
|
" discriminator_optimizer=discriminator_optimizer,\n",
|
|
" generator=generator,\n",
|
|
" discriminator=discriminator)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"Now we define our training loop"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"collapsed": false,
|
|
"editable": true
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def train(dataset, epochs):\n",
|
|
" generator_loss_list = []\n",
|
|
" discriminator_loss_list = []\n",
|
|
"\n",
|
|
" for epoch in range(epochs):\n",
|
|
" start = time.time()\n",
|
|
"\n",
|
|
" for image_batch in dataset:\n",
|
|
" gen_loss, disc_loss = train_step(image_batch)\n",
|
|
" generator_loss_list.append(gen_loss.numpy())\n",
|
|
" discriminator_loss_list.append(disc_loss.numpy())\n",
|
|
"\n",
|
|
" #generate_and_save_images(generator, epoch + 1, seed_images)\n",
|
|
"\n",
|
|
" if (epoch + 1) % 15 == 0:\n",
|
|
" checkpoint.save(file_prefix=checkpoint_prefix)\n",
|
|
"\n",
|
|
" print(f'Time for epoch {epoch} is {time.time() - start}')\n",
|
|
"\n",
|
|
" #generate_and_save_images(generator, epochs, seed_images)\n",
|
|
"\n",
|
|
" loss_file = './data/lossfile.txt'\n",
|
|
" with open(loss_file, 'w') as outfile:\n",
|
|
" outfile.write(str(generator_loss_list))\n",
|
|
" outfile.write('\\n')\n",
|
|
" outfile.write('\\n')\n",
|
|
" outfile.write(str(discriminator_loss_list))\n",
|
|
" outfile.write('\\n')\n",
|
|
" outfile.write('\\n')"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"To train simply call this function. **Warning**: this might take a long time so\n",
|
|
"there is a folder of a pretrained network already included in the repository."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"collapsed": false,
|
|
"editable": true
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"train(train_dataset, EPOCHS)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"And here is the result of training our model for 100 epochs\n",
|
|
"\n",
|
|
"<!-- dom:MOVIE: [images_from_seed_images/generation.gif] -->\n",
|
|
"<!-- begin movie -->"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"collapsed": false,
|
|
"editable": true
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"from IPython.display import HTML\n",
|
|
"_s = \"\"\"\n",
|
|
"<embed src=\"images_from_seed_images/generation.gif\" autoplay=\"false\" loop=\"true\"></embed>\n",
|
|
"<p><em></em></p>\n",
|
|
"\"\"\"\n",
|
|
"HTML(_s)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"<!-- end movie -->\n",
|
|
"\n",
|
|
"\n",
|
|
"Now to avoid having to train and everything, which will take a while depending\n",
|
|
"on your computer setup we now load in the model which produced the above gif."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"collapsed": false,
|
|
"editable": true
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"checkpoint.restore(tf.train.latest_checkpoint(checkpoint_dir))\n",
|
|
"restored_generator = checkpoint.generator\n",
|
|
"restored_discriminator = checkpoint.discriminator\n",
|
|
"\n",
|
|
"print(restored_generator)\n",
|
|
"print(restored_discriminator)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Exploring the Latent Space\n",
|
|
"\n",
|
|
"So we have successfully loaded in our latest model. Let us now play around a bit\n",
|
|
"and see what kind of things we can learn about this model. Our generator takes\n",
|
|
"an array of 100 numbers. One idea can be to try to systematically change our\n",
|
|
"input. Let us try and see what we get"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"collapsed": false,
|
|
"editable": true
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def generate_latent_points(number=100, scale_means=1, scale_stds=1):\n",
|
|
" latent_dim = 100\n",
|
|
" means = scale_means * tf.linspace(-1, 1, num=latent_dim)\n",
|
|
" stds = scale_stds * tf.linspace(-1, 1, num=latent_dim)\n",
|
|
" latent_space_value_range = tf.random.normal([number, number],\n",
|
|
" means,\n",
|
|
" stds,\n",
|
|
" dtype=tf.float64)\n",
|
|
"\n",
|
|
" return latent_space_value_range\n",
|
|
"\n",
|
|
"def generate_images(latent_points):\n",
|
|
" # notice we set training to false because we are making inferences\n",
|
|
" generated_images = restored_generator(latent_space_value_range,\n",
|
|
" training=False)\n",
|
|
"\n",
|
|
" return generated_images"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"collapsed": false,
|
|
"editable": true
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def plot_result(generated_images, number):\n",
|
|
" # obviously this assumes sqrt number is an int\n",
|
|
" fig, axs = plt.subplots(int(np.sqrt(number)), int(np.sqrt(number)),\n",
|
|
" figsize=(10, 10))\n",
|
|
"\n",
|
|
" for i in range(int(np.sqrt(number))):\n",
|
|
" for j in range(int(np.sqrt(number))):\n",
|
|
" axs[i, j].imshow(generated_images[i*j], cmap='Greys')\n",
|
|
" axs[i, j].axis('off')\n",
|
|
"\n",
|
|
" plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"collapsed": false,
|
|
"editable": true
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"generated_images = generate_images(generate_latent_points())\n",
|
|
"plot_result(generated_images, number)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"Interesting! We see that the generator generates images that look like MNIST\n",
|
|
"numbers: $1, 4, 7, 9$. Let's try to tweak it a bit more to see if we are able\n",
|
|
"to generate a similar plot where we generate every MNIST number. Let us now try\n",
|
|
"to 'move' a bit around in the latent space. **Note**: decrease the plot number if\n",
|
|
"these following cells take too long to run on your computer."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"collapsed": false,
|
|
"editable": true
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"plot_number = 225\n",
|
|
"\n",
|
|
"generated_images = generate_images(generate_latent_points(number=plot_number,\n",
|
|
" scale_means=5,\n",
|
|
" scale_stds=1))\n",
|
|
"plot_result(generated_images, plot_number)\n",
|
|
"\n",
|
|
"generated_images = generate_images(generate_latent_points(number=plot_number,\n",
|
|
" scale_means=-5,\n",
|
|
" scale_stds=1))\n",
|
|
"plot_result(generated_images, plot_number)\n",
|
|
"\n",
|
|
"generated_images = generate_images(generate_latent_points(number=plot_number,\n",
|
|
" scale_means=1,\n",
|
|
" scale_stds=5))\n",
|
|
"plot_result(generated_images, plot_number)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"Again, we have found something interesting. *Moving* around using our means\n",
|
|
"takes us from digit to digit, while *moving* around using our standard\n",
|
|
"deviations seem to increase the number of different digits! In the last image\n",
|
|
"above, we can barely make out every MNIST digit. Let us make on last plot using\n",
|
|
"this information by upping the standard deviation of our Gaussian noises."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"collapsed": false,
|
|
"editable": true
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"plot_number = 400\n",
|
|
"generated_images = generate_images(generate_latent_points(number=plot_number,\n",
|
|
" scale_means=1,\n",
|
|
" scale_stds=10))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"A pretty cool result! We see that our generator indeed has learned a\n",
|
|
"distribution which qualitatively looks a whole lot like the MNIST dataset.\n",
|
|
"\n",
|
|
"## Interpolating Between MNIST Digits\n",
|
|
"Another interesting way to explore the latent space of our generator model is by\n",
|
|
"interpolating between the MNIST digits. This section is largely based on\n",
|
|
"\"this excellent blogpost\": <https://machinelearningmastery.com/how-to-interpolate-and-perform-vector-arithmetic-with-faces-using-a-generative-adversarial-network/>\n",
|
|
"by Jason Brownlee.\n",
|
|
"\n",
|
|
"So let us start"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 4
|
|
}
|