{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# VAE: Creating new handwritten numbers based on MNIST" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Imports" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "from dataset import Dataset\n", "from nn import MLP\n", "from vae import VAE, Sampler\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "np.random.seed(3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Theory" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The main motivation behind variational autoencoders is to construct a generator that produces new meaningful data from scratch. So how does it work? Simply put, it takes the structure of an autoencoder, i.e. it takes an input x, computes a lower dimensional representation of x which can then be reconstructed to an outuput that is very similar to x and additionally the lower dimensional representation of the whole dataset is well organized such that the different classes of the data are concentrated in distinct heap points. This ensures that when trying to generate new data one can just sample in the region of those heap points in the lower dimensional space and use the decoder to transform the samples to the shape of our data. Similar samples in the lower dimensional space should result in the same class of data which means that our new synthetic data is meaningful and not just random noise. \n", "Thus a variational autoencoder satisfies two main conditions: the autoencoder property and an organized lower dimensional space. Those aspects can be directly observed in the Loss function:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
$C\\|x - \\hat x\\| + D_{KL}\\Big(\\mathcal{N}(g(x),h(x)),\\mathcal{N}(0,I)\\Big)$
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here the first term calculates the error for input and output pairs and thus ensures the autoencoder property. The second term is composed of the Kullback-Leibler divergence of two normal distributions which means some sort of distance or error is calculated for those two. Hence it is ensured that the lower dimensional space follows a multivariate standard normal distirbution and is thus well organized." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here is a schematic visualization of a VAE:" ] }, { "attachments": { "575c2b17-21e6-4255-9092-48cfde3f4869.jpg": { "image/jpeg": 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} }, "cell_type": "markdown", "metadata": {}, "source": [ "![Variational Autoencoder-5.jpg](attachment:575c2b17-21e6-4255-9092-48cfde3f4869.jpg)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Demo" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Firstly we load our pre-trained variational autoencoder model:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "scrolled": true, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-------------------- VARIATIONAL AUTOENCODER (VAE) --------------------\n", "\n", "TOTAL PARAMETERS = 427344 \n", "\n", "###############\n", "# ENCODER #\n", "###############\n", "\n", " *** 1. Layer: *** \n", "------------------------\n", "DENSE 784 -> 256 [ReLU]\n", "------------------------\n", "Total parameters: 200960 \n", "---> WEIGHTS: (256, 784)\n", "---> BIASES: (256,)\n", "------------------------\n", "\n", "###############\n", "# SAMPLER #\n", "###############\n", "\n", " *** MEAN Layer: *** \n", "---------------------------\n", "DENSE 256 -> 32 [Identity]\n", "---------------------------\n", "Total parameters: 8224 \n", "---> WEIGHTS: (32, 256)\n", "---> BIASES: (32,)\n", "---------------------------\n", "\n", " *** LOG_VAR Layer: *** \n", "---------------------------\n", "DENSE 256 -> 32 [Identity]\n", "---------------------------\n", "Total parameters: 8224 \n", "---> WEIGHTS: (32, 256)\n", "---> BIASES: (32,)\n", "---------------------------\n", "\n", "###############\n", "# DECODER #\n", "###############\n", "\n", " *** 1. Layer: *** \n", "-----------------------\n", "DENSE 32 -> 256 [ReLU]\n", "-----------------------\n", "Total parameters: 8448 \n", "---> WEIGHTS: (256, 32)\n", "---> BIASES: (256,)\n", "-----------------------\n", "\n", " *** 2. Layer: *** \n", "---------------------------\n", "DENSE 256 -> 784 [Sigmoid]\n", "---------------------------\n", "Total parameters: 201488 \n", "---> WEIGHTS: (784, 256)\n", "---> BIASES: (784,)\n", "---------------------------\n", "\n", "----------------------------------------------------------------------\n", "\n" ] } ], "source": [ "#load model\n", "vae = VAE()\n", "vae.load(\"mnist_variational_autoencoder\")\n", "print(vae)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we load our MNIST dataset" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "#load dataset\n", "dataset = Dataset(name = \"mnist\", train_size = 60000, test_size = 10000, batch_size = 1)\n", "original = next(dataset.batches())[1][0] #load a random handwritten image\n", "output = vae.feedforward(original)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we can see, what a forward pass through our model does. It looks quite similar to what we'd expect form a normal Autoencoder." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#example of feedforward pass\n", "f, ax = plt.subplots(1,2)\n", "ax[0].imshow(original.reshape(28,28))\n", "ax[0].set_title(\"Original\")\n", "ax[1].imshow(output.reshape(28,28))\n", "ax[1].set_title(\"VAE\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we can observe, what VAEs are all about. We extrapolate from \"new\" objects in our latent space an image, which is simmilar to it's two parent images. Thereby we can create new digit-like images." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#extrapolating from latent space:\n", "n = 11\n", "\n", "latent1 = vae.sampler.sample\n", "vae.feedforward(next(dataset.batches())[1][0])\n", "latent2 = vae.sampler.sample\n", "\n", "\n", "f, ax = plt.subplots(1, n, figsize = (20,20))\n", "\n", "for i in range(n):\n", " z = (latent1 * (n-1-i) + latent2 * i) / (n-1)\n", " ax[i].imshow(vae.decoder.feedforward(z).reshape(28,28))\n", " ax[i].set_title(f\"{i/(n-1) * 100}%\")\n", " ax[i].axis(\"off\")\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "1. Diederik P Kingma and Max Welling. Auto-Encoding Variational Bayes. 2013. arXiv: 1312.6114 [stat.ML]\n", "\n", "2. https://towardsdatascience.com/understanding-variational-autoencoders-vaes-f70510919f73\n", "\n", "3. https://github.com/pometa0507/Variational-Autoencoder-Numpy" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.5" } }, "nbformat": 4, "nbformat_minor": 4 }