notebooks/functorial-learning.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 0. Generate a language\n",
    "\n",
    "We first build the pregroup diagrams for a simple subject-verb-object language."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8*3*8 = 192 sentences:\n",
      "Alice loves Alice\n",
      "Alice loves Bob\n",
      "Alice loves Charlie\n",
      "...\n",
      "Isabel kills Fred\n",
      "Isabel kills George\n",
      "Isabel kills Isabel\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pregroup diagram for 'Alice loves Bob'\n"
     ]
    }
   ],
   "source": [
    "from discopy import Ty, Word, Cup, Id\n",
    "\n",
    "nouns = [\"Alice\", \"Bob\", \"Charlie\", \"Diane\", \"Eve\", \"Fred\", \"George\", \"Isabel\"]\n",
    "verbs = [\"loves\", \"hates\", \"kills\"]\n",
    "\n",
    "s, n = Ty('s'), Ty('n')\n",
    "tv = n.r @ s @ n.l\n",
    "\n",
    "vocab = [Word(noun, n) for noun in nouns] + [Word(verb, tv) for verb in verbs]\n",
    "\n",
    "grammar = Cup(n, n.r) @ Id(s) @ Cup(n.l, n)\n",
    "\n",
    "sentences = [\n",
    "    \"{} {} {}\".format(subj, verb, obj)\n",
    "    for subj in nouns for verb in verbs for obj in nouns]\n",
    "\n",
    "print(\"{}*{}*{} = {} sentences:\\n{}\\n\".format(\n",
    "    len(nouns), len(verbs), len(nouns), len(sentences), \"\\n\".join(sentences[:3] + [\"...\"] + sentences[-3:])))\n",
    "\n",
    "diagrams = {\n",
    "    sentence: Word(subj, n) @ Word(verb, tv) @ Word(obj, n) >> grammar\n",
    "    for sentence in sentences for subj, verb, obj in [sentence.split(' ')]}\n",
    "\n",
    "diagrams[sentences[1]].draw()\n",
    "print(\"Pregroup diagram for '{}'\".format(sentences[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Build a random dataset\n",
    "\n",
    "We then generate a toy dataset with scalars attached to each diagram.\n",
    "\n",
    "In order to do so, we apply a random functor from Pregroup to Tensor to each diagram in the corpus.\n",
    "\n",
    "A `TensorFunctor` is defined by two mappings `ob` from types to dimension (i.e. hyper-parameters) and `ar` from words to matrices (i.e. parameters)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import jax.numpy as np; import numpy; np.random = numpy.random; np.random.seed(42)\n",
    "from discopy import TensorFunctor\n",
    "\n",
    "# N.B. defining ob[tv] is not necessary, indeed F(tv) == F(n) * F(s) * F(n)\n",
    "ob = {n: 2, s: 1, tv: 4}\n",
    "ar0 = {word: np.random.randn(ob[word.cod]) for word in vocab}\n",
    "F0 = TensorFunctor(ob, ar0)\n",
    "\n",
    "def sigmoid(x):\n",
    "    return 1 / (1 + np.exp(-x))\n",
    "\n",
    "dataset = {sentence: sigmoid(F0(diagram).array) for sentence, diagram in diagrams.items()}\n",
    "y_true = [float(y) for y in dataset.values()]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's have a look at what this random dataset looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "plt.hist(y_true, bins=100)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "61 true sentences:\n",
      "George kills Diane\n",
      "Diane loves Eve\n",
      "Eve loves George\n",
      "...\n",
      "Eve kills Isabel\n",
      "Isabel loves Diane\n",
      "Eve hates Isabel\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from random import shuffle\n",
    "\n",
    "delta = 0.1\n",
    "\n",
    "true_sentences = [sentence for sentence in dataset if dataset[sentence] > 0.5 + delta]\n",
    "shuffle(true_sentences)\n",
    "print(\"{} true sentences:\\n{}\\n\".format(\n",
    "    len(true_sentences), \"\\n\".join(true_sentences[:3] + ['...'] + true_sentences[-3:])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Does Alice love Bob?\n",
      "No\n"
     ]
    }
   ],
   "source": [
    "print(\"Does Alice love Bob?\\n{}\".format(\n",
    "    \"Yes\" if dataset[\"Alice loves Bob\"] > 0.5 + delta else \"No\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Learn the functor from data\n",
    "\n",
    "We split the dataset into training and testing.\n",
    "We forget `F0` and initialise some new random functor.\n",
    "\n",
    "We define the mean squared loss on testing and training set and compile them just-in-time.\n",
    "\n",
    "We use automatic differentiation and vanilla gradient descent to learn the parameters for the functor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial training loss: 0.12394743412733078\n",
      "Initial testing loss: 0.10969964414834976\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "training, testing = train_test_split(sentences, test_size=0.25, random_state=42)\n",
    "\n",
    "def loss(ar, sample=training):\n",
    "    F = TensorFunctor(ob, ar)\n",
    "    y_pred = [sigmoid(F(diagrams[sentence]).array) for sentence in sample]\n",
    "    y_true = [dataset[sentence] for sentence in sample]\n",
    "    return np.mean((np.array(y_true) - np.array(y_pred)) ** 2)\n",
    "\n",
    "ar = {word: np.random.randn(ob[word.cod]) for word in vocab}\n",
    "\n",
    "print(\"Initial training loss: {}\\nInitial testing loss: {}\".format(loss(ar), loss(ar, testing)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "59 seconds to just-in-time compile the gradient:\n",
      "Alice: [-0.01686156 -0.01012888]\n",
      "Bob: [-0.0085393   0.00930784]\n",
      "Charlie: [-0.00412429 -0.01343251]\n",
      "Diane: [ 0.00908923 -0.00716087]\n",
      "Eve: [-0.00673484 -0.0107691 ]\n",
      "Fred: [-0.01174346 -0.00308988]\n",
      "George: [0.01267174 0.01413585]\n",
      "Isabel: [-0.00672528 -0.02229434]\n",
      "hates: [-0.00208589 -0.00725513  0.00607718 -0.00264032]\n",
      "kills: [-0.00403996  0.00772784  0.00631926  0.00695181]\n",
      "loves: [-0.00456121 -0.0044004  -0.00093371  0.01333533]\n"
     ]
    }
   ],
   "source": [
    "from time import time\n",
    "from jax import jit, grad\n",
    "\n",
    "training_loss = jit(loss)\n",
    "testing_loss = jit(lambda ar: loss(ar, testing))\n",
    "gradient = jit(grad(training_loss))\n",
    "start = time()\n",
    "\n",
    "print(\"{1:.0f} seconds to just-in-time compile the gradient:\\n{0}\".format(\"\\n\".join(\n",
    "    \"{}: {}\".format(word, dx) for word, dx in gradient(ar).items()), time() - start))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1 (18.116 seconds)\n",
      "Epoch 2 (0.713 seconds)\n",
      "Epoch 3 (0.821 seconds)\n",
      "Epoch 4 (0.831 seconds)\n",
      "Epoch 5 (0.733 seconds)\n",
      "Epoch 6 (0.730 seconds)\n",
      "Epoch 7 (0.701 seconds)\n",
      "Epoch 8 (0.706 seconds)\n",
      "Epoch 9 (0.705 seconds)\n",
      "Epoch 10 (0.773 seconds)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "learning_rate = 1\n",
    "epochs = 10\n",
    "iterations = 100\n",
    "\n",
    "training_losses = []\n",
    "testing_losses = []\n",
    "\n",
    "for i in range(epochs):\n",
    "    start = time()\n",
    "    for _ in range(iterations):\n",
    "        g = gradient(ar)\n",
    "        for word in vocab:\n",
    "            ar[word] = ar[word] - g[word] * learning_rate\n",
    "        training_losses.append(float(training_loss(ar)))\n",
    "        testing_losses.append(float(testing_loss(ar)))\n",
    "    print(\"Epoch {} ({:.3f} seconds)\".format(i + 1, time() - start))\n",
    "\n",
    "F = TensorFunctor(ob, ar)\n",
    "y_pred = [float(sigmoid(F(diagrams[sentence]).array)) for sentence in sentences]\n",
    "\n",
    "plt.plot(training_losses)\n",
    "plt.xlabel(\"n_iterations\")\n",
    "plt.ylabel(\"training_loss\")\n",
    "plt.show()\n",
    "\n",
    "plt.plot(testing_losses)\n",
    "plt.xlabel(\"n_iterations\")\n",
    "plt.ylabel(\"testing_loss\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Evaluate the learnt functor on some task\n",
    "\n",
    "Here we show the results for a binary classification task, i.e. yes-no question answering:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              precision    recall  f1-score   support\n",
      "\n",
      "       False       0.99      1.00      1.00       131\n",
      "        True       1.00      0.98      0.99        61\n",
      "\n",
      "    accuracy                           0.99       192\n",
      "   macro avg       1.00      0.99      0.99       192\n",
      "weighted avg       0.99      0.99      0.99       192\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import classification_report\n",
    "\n",
    "print(classification_report(np.array(y_true) > .5 + delta, np.array(y_pred) > .5 + delta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Does Alice love Bob?\n",
      "No\n"
     ]
    }
   ],
   "source": [
    "print(\"Does Alice love Bob?\\n{}\".format(\n",
    "    \"Yes\" if y_pred[sentences.index(\"Alice loves Bob\")] > 0.5 + delta else \"No\"))"
   ]
  }
 ],
 "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}