learning_and_relational_spaces.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Learning and relational spaces"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Levan Tsinadze"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Head of AI - MaxinAI\n",
    "<br>\n",
    "\n",
    "Head of School of AI / MaxinAI Education\n",
    "<br>\n",
    "\n",
    "Machine learning researcher - \n",
    "eyeo GmbH\n",
    "<br>\n",
    "\n",
    "PhD student of Tbilisi State University"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Macheine learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Machine learning (ML) is the study of computer algorithms that improve automatically through experience\n",
    "<br>\n",
    "In another words it is called statistical learning:\n",
    "<br>\n",
    "$$\n",
    "(X, P)\n",
    "$$\n",
    "We need approximation to this distribution\n",
    "<br>\n",
    "Generalization:\n",
    "We have sample of data and we need to approximate to the distribution for entire population"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"images/ssl_1/linear_regression_1.png\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Types of machine learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Classification when $X$ belongs to the particular class:\n",
    "<img src=\"images/ssl_1/classification_1.png\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Regression $X$ has complicated distribution:\n",
    "<img src=\"images/ssl_1/regression_1.png\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"images/ssl_1/classification_2.png\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"images/ssl_1/classification_3.jpg\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Learning types"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Supervised learning $(y, \\bar{y})$ and we calculate error by true labels $||y - \\bar{y}||$\n",
    "- Unsupervised learning only input features $X$ and error calculated by this features (clustering)\n",
    "- Reinforcement learning\n",
    "- Self-supervised learning $m:X \\to Y$ and we can consider $m(x) = \\bar{y}$ as labels"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Relational space"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Space $(X, \\mathcal{R}_X)$ where $\\mathcal{R}_X = \\{R_X \\in X \\times X\\}$ is relation on $X$\n",
    "<br>\n",
    "Also we can conside that $R_X = (R_X^i)_{i \\in I}$ or more often $R_X = (R_X^1, R_X^2, \\dots, R_X^k)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's for two spaces $(X, \\mathcal{R}_X)$ and $(Z, \\mathcal{R}_Z)$ and mapping $f:X \\to Z$ define:\n",
    "$$\n",
    "\\mathcal{R}_X \\times_f \\mathcal{R}_Z = \\{(R_X, R_Z) \\in \\mathcal{R}_X \\times \\mathcal{R}_Z | (f \\times f)(R_X) \\subset R_Z\\}\n",
    "$$\n",
    "<br>\n",
    "we define:\n",
    "$$\n",
    "f(R_X) = (f \\times f)(R_X) = \\{(f(x), f(y)) | (x, y) \\in R_X\\} \\text{ or } (f \\times f) (R_X)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "For instance we can define \n",
    "- $R_U = \\{ x, y \\in U  | U \\in \\tau_X\\}$ for topological space $(X, \\tau_X)$\n",
    "- $R_X = U$ for (locally) (quasi) uniform space $(X, U_X)$\n",
    "- $R_\\epsilon = \\{(x, y) \\in X \\times X | d(x, y) < \\epsilon \\}$ for (locally) (quasi) (pseudo) metric space\n",
    "-etc\n",
    "<br>\n",
    "All this above cases $f$ would be continous function if for every $R_Z \\in \\mathcal{R}_Z$ there exists $R_X \\in \\mathcal{R}_X$ such that \n",
    "$$\n",
    "(R_X, R_Z) \\in \\mathcal{R}_X \\times_f \\mathcal{R_Z}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Apply to machine learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Image classification\n",
    "- Text classification\n",
    "- Graph classification\n",
    "- Node classification"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "This kind of data somehow deeds to be \"vectorized\" in order to run them is an input for different machine learning models:\n",
    "<img src=\"images/ssl_1/dl_images_1.gif\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Apply on features level"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Deep neural networks / deep learning:\n",
    "<img src=\"images/ssl_1/deep_learning_1.png\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Deep models as general feature extractors - input data\n",
    "<img src=\"images/ssl_1/dl_features_1.gif\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Deep models as general feature extractors - weights\n",
    "<img src=\"images/ssl_1/dl_features_2.gif\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Low level features might be enough for different tasks\n",
    "<img src=\"images/ssl_1/dl_features_3.png\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "There are many approaches to measure the information in hidden - representation layers:\n",
    "$$\n",
    "I(X, T_i)\n",
    "$$\n",
    "<br>\n",
    "But mostly they are black-boxes and there is no clear and formal picture of extracted information\n",
    "<br>\n",
    "Similarity distance (angular, Euclidean, etc)\n",
    "<br>\n",
    "Different topological spaces\n",
    "<br>\n",
    "Enriched structures (quasi-metric, quasi-uniforms / locally quasi-uniform, approach spaces)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Demo time !!!!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Re-use this features if we only change and retrain classifier layer\n",
    "<img src=\"images/ssl_1/dl_features_4.png\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Transfer learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Recall architecture of deep learning models on images (convolutional neural network - ConvNet):\n",
    "<img src=\"images/ssl_1/dl_feature_extractor_1.jpg\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "So this features are mostly the same / or we enrich them and make them as informative as possible\n",
    "<img src=\"images/ssl_1/dl_features_5.png\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"images/ssl_1/transfer_1.png\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "ImageNet dataset:\n",
    "<img src=\"images/ssl_1/imagenet_1.jpeg\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "ImageNet dataset informativeness:\n",
    "<img src=\"images/ssl_1/imagenet_2.png\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"images/ssl_1/transfer_2.png\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Fine-tuning with discriminative learning rate\n",
    "<img src=\"images/ssl_1/ft_1.png\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Labeling and data preparation for deep models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Deep models are data hungry\n",
    "- They need millions of labeled data\n",
    "- For classification\n",
    "- For object detection\n",
    "- For semantic segmentation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"images/cnn/detection_segmentation.jpg\" height=\"1000\" width=\"1000\" />"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Down-sampling plus up-sampling (Encoder decoder architecture)\n",
    "<img src=\"images/od/encoder_decoder_1.png\" height=\"1000\" width=\"1000\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "In all this models we have so called backbones:\n",
    "<br>\n",
    "Representation part of deep models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Labeling data is expensive:\n",
    "- Labeling images for classification\n",
    "- Tend to be biased and has an errors\n",
    "- ImageNet is one of the\n",
    "- Labeling images for detection and segmentation is at least twice expensive and biased"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "There are many approaches to measure the information in hidden - representation layers:\n",
    "$$\n",
    "I(X, T_i)\n",
    "$$\n",
    "<br>\n",
    "But mostly they are black-boxes and there is no clear and formal picture of extracted information"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "ImageNet dataset informativeness - less informative:\n",
    "<img src=\"images/ssl_1/imagenet_2.png\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Self-supervised learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Self supervised learning is ML learning when labels are simple generated by the modification of the original data, without human-in-the loop:\n",
    "- Generative models:\n",
    " - Auto-encoders when labels are the original images\n",
    "- Discriminative models:\n",
    " - When labels are the meta information about original data modification"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Pretext tasks and downstream tasks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Pretext tasks task on which model is trained for better representation:\n",
    "- Auto encoders\n",
    "- Context encoders\n",
    "- One view from another\n",
    "- Contrastive learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Downstream task on which features learned from downstream task is used as input or fine-tuned entire model:\n",
    "- Classification\n",
    "- Localization\n",
    "- Backbone for object detection or semantic segmentation models\n",
    "- Feature extractor for image retrieval, image captioning etc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## ImageNet vs custom data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "ImageNet - over the one million labeled images\n",
    "- Size range and three channels\n",
    "- Object are in central area\n",
    "- Limited brightness, contours, etc (augmentation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Our custom dataset might be completely different:\n",
    "- Grayscale images (X-ray, old images, etc)\n",
    "- Multi-channel images (MRI with eight channels, etc)\n",
    "- Objects located in different corners\n",
    "- Satellite images\n",
    "- Images from drones\n",
    "- Images from microscope\n",
    "- etc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Center crop\n",
    "<img src=\"images/ssl/mic_1.jpeg\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"images/ssl/mic_2.jpg\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"images/ssl/sat_1.jpg\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"images/ssl/sat_2.jpg\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"images/ssl/xr_1.jpg\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"images/ssl/xr_2.jpeg\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Pluses of self-supervised learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Labeling is expensive and time-consuming, mistakes are almost inevitable.\n",
    "- Labeled data for classification contains small amount of information in comparison with images which has other different objects\n",
    "- Multi-task learning adds more difficulties and hyper-parameters\n",
    "- Multi object classifiers need more labeling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "ImageNet pre-trained models perform pretty well on even different domains, but if we have an alternative:\n",
    "- Pre-trained images for the similar domain\n",
    "- Train images on custom domain \n",
    "- and put it in public\n",
    "- Different model architectures (All of them are trained on ImageNet)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "For deep learning:\n",
    "<img src=\"images/ssl/dl_cacke_1.png\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Autoecoders"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Auto-encoders learn from the original images, they encode and reconstruct data\n",
    "<img src=\"images/ssl/ae_1.png\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Denoising auto-encoders"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "If we add augmentation and make the model extract features from images:\n",
    "<img src=\"images/ssl/dae_1.png\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Context encoders"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Deepak Pathak Philipp Krahenbuhl Jeff Donahue Trevor Darrell Alexei A. Efros\n",
    "\n",
    "Context Encoders: Feature Learning by Inpainting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"images/ssl/ce_1.png\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"images/ssl/ce_4.png\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"images/ssl/ce_5.png\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Rotation classifier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "Learn many features to understand position\n",
    "<img src=\"images/ssl/rc_1.png\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    "<img src=\"images/ssl/rc_2.png\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"images/ssl/rc_3.png\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
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   "source": [
    "<img src=\"images/ssl/rc_4.png\" height=\"800\" width=\"800\">"
   ]
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   "source": [
    "Spyros Gidaris, Praveer Singh, Nikos Komodakis\n",
    "\n",
    "UNSUPERVISED REPRESENTATION LEARNING BY PREDICTING IMAGE ROTATIONS"
   ]
  },
  {
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   "source": [
    "We can consider that $(X, \\mathcal{R}_X)$ where $X = \\mathbb{R}^{3 \\times h \\times w}$ for RGB images and we have relations $((x, y) \\in 90 )$"
   ]
  },
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   "source": [
    "#### Instance discrimination"
   ]
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     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"images/add1/id_1.png\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
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   },
   "source": [
    "<img src=\"images/add1/id_2.png\" height=\"800\" width=\"800\">"
   ]
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   "source": [
    "Image complexity\n",
    "- Blur\n",
    "- Contoures\n",
    "- $$z = \\alpha x + (1 - \\alpha) y$$\n",
    "- $(x, z) \\in \\alpha$ and $(y, z) \\in (1 = \\alpha)$\n",
    "- $R_X = (90, \\alpha, g, c_1, c_2, u_1, u_2)$ $R_Z$"
   ]
  },
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   "metadata": {
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   },
   "source": [
    "## Questions\n",
    "\n",
    "<img src=\"images/od/questions_2.jpg\" height=\"800\" width=\"800\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "## Thank you"
   ]
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   "source": []
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