vsm_03_retrofitting.ipynb

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   "source": [
    "# Vector-space models: retrofitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "__author__ = \"Christopher Potts\"\n",
    "__version__ = \"CS224u, Stanford, Spring 2021\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "## Contents\n",
    "\n",
    "1. [Overview](#Overview)\n",
    "1. [Set-up](#Set-up)\n",
    "1. [The retrofitting model](#The-retrofitting-model)\n",
    "1. [Examples](#Examples)\n",
    "  1. [Only node 0 has outgoing edges](#Only-node-0-has-outgoing-edges)\n",
    "  1. [All nodes connected to all others](#All-nodes-connected-to-all-others)\n",
    "  1. [As before, but now 2 has no outgoing edges](#As-before,-but-now-2-has-no-outgoing-edges)\n",
    "  1. [All nodes connected to all others, but $\\alpha = 0$](#All-nodes-connected-to-all-others,-but-$\\alpha-=-0$)\n",
    "1. [WordNet](#WordNet)\n",
    "  1. [Background on WordNet](#Background-on-WordNet)\n",
    "  1. [WordNet and VSMs](#WordNet-and-VSMs)\n",
    "  1. [Reproducing the WordNet synonym graph experiment](#Reproducing-the-WordNet-synonym-graph-experiment)\n",
    "1. [Other retrofitting models and ideas](#Other-retrofitting-models-and-ideas)"
   ]
  },
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   "cell_type": "markdown",
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    "## Overview\n",
    "\n",
    "Thus far, all of the information in our word vectors has come solely from co-occurrences patterns in text. This information is often very easy to obtain – though one does need a __lot__ of text – and it is striking how rich the resulting representations can be.\n",
    "\n",
    "Nonetheless, it seems clear that there is important information that we will miss this way – relationships that just aren't encoded at all in co-occurrences or that get distorted by such patterns. \n",
    "\n",
    "For example, it is probably straightforward to learn representations that will support the inference that all puppies are dogs (_puppy_ entails _dog_), but it might be difficult to learn that _dog_ entails _mammal_ because of the unusual way that very broad taxonomic terms like _mammal_ are used in text.\n",
    "\n",
    "The question then arises: how can we bring structured information – labels – into our representations? If we can do that, then we might get the best of both worlds: the ease of using co-occurrence data and the refinement that comes from using labeled data.\n",
    "\n",
    "In this notebook, we look at one powerful method for doing this: the __retrofitting__ model of [Faruqui et al. 2016](http:https://www.aclweb.org/anthology/N15-1184). In this model, one learns (or just downloads) distributed representations for nodes in a knowledge graph and then updates those representations to bring connected nodes closer to each other.\n",
    "\n",
    "This is an incredibly fertile idea; the final section of the notebook reviews some recent extensions, and new ones are likely appearing all the time."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Set-up"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import defaultdict\n",
    "from nltk.corpus import wordnet as wn\n",
    "import numpy as np\n",
    "import os\n",
    "import pandas as pd\n",
    "import retrofitting\n",
    "from retrofitting import Retrofitter\n",
    "import utils"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_home = 'data'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Note__: To make full use of this notebook, you will need the NLTK data distribution – or, at the very least, its WordNet files. Anaconda comes with NLTK but not with its data distribution. To install that, open a Python interpreter and run \n",
    "\n",
    "```import nltk; nltk.download()```\n",
    "\n",
    "If you decide to download the data to a different directory than the default, then you'll have to set `NLTK_DATA` in your shell profile. (If that doesn't make sense to you, then we recommend choosing the default download directory!)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
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   },
   "source": [
    "## The retrofitting model\n",
    "\n",
    "For an __an existing VSM__ $\\widehat{Q}$ of dimension $m \\times n$, and a set of __edges__  $E$ (pairs of indices into rows in  $\\widehat{Q}$), the retrofitting objective is to obtain a new VSM $Q$ (also dimension $m \\times n$)  according to the following objective:\n",
    "\n",
    "$$\\sum_{i=1}^{m} \\left[ \n",
    "\\alpha_{i}\\|q_{i} - \\widehat{q}_{i}\\|_{2}^{2}\n",
    "+\n",
    "\\sum_{j : (i,j) \\in E}\\beta_{ij}\\|q_{i} - q_{j}\\|_{2}^{2}\n",
    "\\right]$$\n",
    "\n",
    "The left term encodes a pressure to stay like the original vector. The right term encodes a pressure to be more like one's neighbors. In minimizing this objective, we should be able to strike a balance between old and new, VSM and graph.\n",
    "\n",
    "Definitions:\n",
    "\n",
    "1. $\\|u - v\\|_{2}^{2}$ gives the __squared euclidean distance__ from $u$ to $v$.\n",
    "\n",
    "1. $\\alpha$ and $\\beta$ are weights we set by hand, controlling the relative strength of the two pressures. In the paper, they use $\\alpha=1$ and $\\beta = \\frac{1}{\\{j : (i, j) \\in E\\}}$."
   ]
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   "source": [
    "## Examples\n",
    "\n",
    "To get a feel for what's happening, it's helpful to visualize the changes that occur in small, easily understood VSMs and graphs. The function `retrofitting.plot_retro_path` helps with this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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    "### Only node 0 has outgoing edges"
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\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "edges_0 = {0: {1, 2}, 1: set(), 2: set()}\n",
    "\n",
    "_ = retrofitting.plot_retro_path(Q_hat, edges_0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### All nodes connected to all others"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "edges_all = {0: {1, 2}, 1: {0, 2}, 2: {0, 1}}\n",
    "\n",
    "_ = retrofitting.plot_retro_path(Q_hat, edges_all)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### As before, but now 2 has no outgoing edges"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "edges_isolated = {0: {1, 2}, 1: {0, 2}, 2: set()}\n",
    "\n",
    "_ = retrofitting.plot_retro_path(Q_hat, edges_isolated)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### All nodes connected to all others, but $\\alpha = 0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = retrofitting.plot_retro_path(\n",
    "    Q_hat, edges_all,\n",
    "    retrofitter=Retrofitter(alpha=lambda x: 0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## WordNet\n",
    "\n",
    "Faruqui et al. conduct experiments on three knowledge graphs: [WordNet](https://wordnet.princeton.edu), [FrameNet](https://framenet.icsi.berkeley.edu/fndrupal/), and the [Penn Paraphrase Database (PPDB)](http:https://paraphrase.org/). [The repository for their paper](https://github.com/mfaruqui/retrofitting) includes the graphs that they derived for their experiments.\n",
    "\n",
    "Here, we'll reproduce just one of the two WordNet experiments they report, in which the graph is formed based on synonymy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Background on WordNet\n",
    "\n",
    "WordNet is an incredible, hand-built lexical resource capturing a wealth of information about English words and their inter-relationships. ([Here is a collection of WordNets in other languages.](http:https://globalwordnet.org)) For a detailed overview using NLTK, see [this tutorial](http:https://compprag.christopherpotts.net/wordnet.html).\n",
    "\n",
    "The core concepts:\n",
    "\n",
    "* A __lemma__ is something like our usual notion of __word__. Lemmas are highly sense-disambiguated. For instance, there are six lemmas that are consistent with the string `crane`: the bird, the machine, the poets, ...\n",
    "\n",
    "* A __synset__ is a collection of lemmas that are synonymous in the WordNet sense (which is WordNet-specific; words with intuitively different meanings might still be grouped together into synsets.).\n",
    "\n",
    "WordNet is a graph of relations between lemmas and between synsets, capturing things like hypernymy, antonymy, and many others. For the most part, the relations are defined between nouns; the graph is sparser for other areas of the lexicon."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "======================================================================\n",
      "Lemma name: Crane\n",
      "Lemma Synset: Synset('crane.n.01')\n",
      "Synset definition: United States writer (1871-1900)\n",
      "======================================================================\n",
      "Lemma name: Crane\n",
      "Lemma Synset: Synset('crane.n.02')\n",
      "Synset definition: United States poet (1899-1932)\n",
      "======================================================================\n",
      "Lemma name: Crane\n",
      "Lemma Synset: Synset('grus.n.01')\n",
      "Synset definition: a small constellation in the southern hemisphere near Phoenix\n",
      "======================================================================\n",
      "Lemma name: crane\n",
      "Lemma Synset: Synset('crane.n.04')\n",
      "Synset definition: lifts and moves heavy objects; lifting tackle is suspended from a pivoted boom that rotates around a vertical axis\n",
      "======================================================================\n",
      "Lemma name: crane\n",
      "Lemma Synset: Synset('crane.n.05')\n",
      "Synset definition: large long-necked wading bird of marshes and plains in many parts of the world\n",
      "======================================================================\n",
      "Lemma name: crane\n",
      "Lemma Synset: Synset('crane.v.01')\n",
      "Synset definition: stretch (the neck) so as to see better\n"
     ]
    }
   ],
   "source": [
    "lems = wn.lemmas('crane', pos=None)\n",
    "\n",
    "for lem in lems:\n",
    "    ss = lem.synset()\n",
    "    print(\"=\"*70)\n",
    "    print(\"Lemma name: {}\".format(lem.name()))\n",
    "    print(\"Lemma Synset: {}\".format(ss))\n",
    "    print(\"Synset definition: {}\".format(ss.definition()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### WordNet and VSMs\n",
    "\n",
    "A central challenge of working with WordNet is that one doesn't usually encounter lemmas or synsets in the wild. One probably gets just strings, or maybe strings with part-of-speech tags. Mapping these objects to lemmas is incredibly difficult.\n",
    "\n",
    "For our experiments with VSMs, we simply collapse together all the senses that a given string can have. This is expedient, of course. It might also be a good choice linguistically: senses are flexible and thus hard to individuate, and we might hope that our vectors can model multiple senses at the same time. \n",
    "\n",
    "(That said, there is excellent work on creating sense-vectors; see [Reisinger and Mooney 2010](http:https://www.aclweb.org/anthology/N10-1013); [Huang et al 2012](http:https://www.aclweb.org/anthology/P12-1092).)\n",
    "\n",
    "The following code uses the NLTK WordNet API to create the edge dictionary we need for using the `Retrofitter` class:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_wordnet_edges():\n",
    "    edges = defaultdict(set)\n",
    "    for ss in wn.all_synsets():\n",
    "        lem_names = {lem.name() for lem in ss.lemmas()}\n",
    "        for lem in lem_names:\n",
    "            edges[lem] |= lem_names\n",
    "    return edges"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "wn_edges = get_wordnet_edges()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Reproducing the WordNet synonym graph experiment"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "For our VSM, let's use the 300d file included in this distribution from the GloVe team, as it is close to or identical to the one used in the paper:\n",
    "\n",
    "http:https://nlp.stanford.edu/data/glove.6B.zip\n",
    "\n",
    "If you download this archive, place it in `vsmdata`, and unpack it, then the following will load the file into a dictionary for you:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "glove_dict = utils.glove2dict(\n",
    "    os.path.join(data_home, 'glove.6B', 'glove.6B.300d.txt'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the initial embedding space $\\widehat{Q}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_glove = pd.DataFrame(glove_dict).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(300, 400000)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_glove.T.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Now we just need to replace all of the strings in `edges` with indices into `X_glove`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def convert_edges_to_indices(edges, Q):\n",
    "    lookup = dict(zip(Q.index, range(Q.shape[0])))\n",
    "    index_edges = defaultdict(set)\n",
    "    for start, finish_nodes in edges.items():\n",
    "        s = lookup.get(start)\n",
    "        if s:\n",
    "            f = {lookup[n] for n in finish_nodes if n in lookup}\n",
    "            if f:\n",
    "                index_edges[s] = f\n",
    "    return index_edges"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "wn_index_edges = convert_edges_to_indices(wn_edges, X_glove)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "And now we can retrofit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "wn_retro = Retrofitter(verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Converged at iteration 10; change was 0.0043 "
     ]
    }
   ],
   "source": [
    "X_retro = wn_retro.fit(X_glove, wn_index_edges)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "You can now evaluate `X_retro` using the homework/bake-off notebook [hw_wordrelatedness.ipynb](hw_wordrelatedness.ipynb)!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Optionally write `X_retro` to disk for use elsewhere:\n",
    "#\n",
    "# X_retro.to_csv(\n",
    "#     os.path.join(data_home, 'glove6B300d-retrofit-wn.csv.gz'),\n",
    "#     compression='gzip')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Other retrofitting models and ideas\n",
    "\n",
    "* The retrofitting idea is very close to __graph embedding__, in which one learns distributed representations of nodes based on their position in the graph. See [Hamilton et al. 2017](https://arxiv.org/pdf/1709.05584.pdf) for an overview of these methods. There are numerous parallels with the material we've reviewed here.\n",
    "\n",
    "* If you think of the input VSM as a \"warm start\" for graph embedding algorithms, then you're essentially retrofitting. This connection opens up a number of new opportunities to go beyond the similarity-based semantics that underlies Faruqui et al.'s model. See [Lengerich et al. 2017](https://arxiv.org/pdf/1708.00112.pdf), section 3.2, for more on these connections.\n",
    "\n",
    "* [Mrkšić  et al. 2016](https://www.aclweb.org/anthology/N16-1018) address the limitation of Faruqui et al's model that it assumes connected nodes in the graph are similar. In a graph with complex, varied edge semantics, this is likely to be false. They address the case of antonymy in particular.\n",
    "\n",
    "* [Lengerich et al. 2017](https://arxiv.org/pdf/1708.00112.pdf) present a __functional retrofitting__ framework in which the edge meanings are explicitly modeled, and they evaluate instantiations of the framework with linear and neural edge penalty functions. (The Faruqui et al. model emerges as a specific instantiation of this framework.)"
   ]
  }
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