IntroductiontoLLM_Activity_1_Word2vec_unipd.ipynb

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        "# Introduction to Word2Vec\n",
        "by Eugenio Tufino, University of Padova, 9 December 2024\n",
        "\n",
        "[Link to Google Colab](https://colab.research.google.com/drive/1nxx5nuNEq4xFuBqHiyVrRdkSd2ROOZc5#scrollTo=pDKqQJFeSW0f&line=3&uniqifier=1)\n",
        "\n",
        "Word2Vec is a powerful algorithm introduced by Mikolov et al. (2013) for learning word embeddings—numerical vector representations of words. These embeddings capture  semantic relationships between words by analyzing their co-occurrences within a large corpus of text. Words that appear in similar contexts are mapped to vectors that are close to each other in a high-dimensional space, enabling the discovery of relationships such as analogies (e.g., \"king\" - \"man\" + \"woman\" ≈ \"queen\").\n",
        "\n",
        "By representing words as vectors, Word2Vec opens the door to exploring complex linguistic and conceptual relationships in an intuitive, mathematical form.\n",
        "\n",
        "\n",
        "This notebook allows students to explore the Word2Vec model interactively.\n",
        "\n",
        "\n",
        "**Further reading:**   \n",
        "\n",
        "- https://en.wikipedia.org/wiki/Word2vec\n",
        "\n",
        "- Mikolov, T., Chen, K., Corrado, G., & Dean, J. (2013). Efficient Estimation of Word Representations in Vector Space. arXiv preprint arXiv:1301.3781. [Link](https://arxiv.org/pdf/1301.3781)\n",
        "\n"
      ],
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        "Image by Grant Sanderson (3Blue1Brown Youtube 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      ],
      "metadata": {
        "id": "zFAulgI5Wv3E"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Import the libraries for using Word2Vec\n",
        "library gensim: https://github.com/piskvorky/gensim/blob/develop/gensim/models/word2vec.py"
      ],
      "metadata": {
        "id": "ji9zO4BzNLAN"
      }
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "VLUFnb0xEqzu"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 161,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qWFpRNz12cvF",
        "outputId": "93d86d0a-d822-4bb5-b9fb-318d68baea25"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: gensim in /usr/local/lib/python3.10/dist-packages (4.3.3)\n",
            "Requirement already satisfied: scikit-learn in /usr/local/lib/python3.10/dist-packages (1.5.2)\n",
            "Requirement already satisfied: numpy<2.0,>=1.18.5 in /usr/local/lib/python3.10/dist-packages (from gensim) (1.26.4)\n",
            "Requirement already satisfied: scipy<1.14.0,>=1.7.0 in /usr/local/lib/python3.10/dist-packages (from gensim) (1.13.1)\n",
            "Requirement already satisfied: smart-open>=1.8.1 in /usr/local/lib/python3.10/dist-packages (from gensim) (7.0.5)\n",
            "Requirement already satisfied: joblib>=1.2.0 in /usr/local/lib/python3.10/dist-packages (from scikit-learn) (1.4.2)\n",
            "Requirement already satisfied: threadpoolctl>=3.1.0 in /usr/local/lib/python3.10/dist-packages (from scikit-learn) (3.5.0)\n",
            "Requirement already satisfied: wrapt in /usr/local/lib/python3.10/dist-packages (from smart-open>=1.8.1->gensim) (1.17.0)\n"
          ]
        }
      ],
      "source": [
        "!pip install gensim scikit-learn\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import gensim.downloader as api\n",
        "from sklearn.decomposition import PCA\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## In this lesson and with the computational and time resources available, the choice is limited to the following two models:\n",
        "- glove-twitter-25\n",
        "- Glove-Wikipedia-Gigaword-100\n",
        "\n",
        "Different Word2Vec models have varying capabilities.\n",
        "Each Word2Vec model is trained on a specific corpus (data)\n",
        "and with different parameters, which affects its performance for particular tasks.\n",
        "\n",
        "With a little experience you can even customize your own Word2Vec model."
      ],
      "metadata": {
        "id": "Qt4J77PwQwZN"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### 1° Model"
      ],
      "metadata": {
        "id": "4nBOC7K45IYZ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "# Load the model (this might take a few minutes the first time)\n",
        "#model_twitter = api.load('glove-twitter-25')  #Uncomment this line if you want to load this model\n",
        "# it is a model used to understand twitter language, not very good for physics language\n"
      ],
      "metadata": {
        "id": "5SbiL5Sx2yQm"
      },
      "execution_count": 162,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### 2° Model\n",
        "\n",
        "Given that we want to talk about physics we will use this."
      ],
      "metadata": {
        "id": "t0Sbvtx_Riaz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Load the GloVe Wikipedia + Gigaword model\n",
        "print(\"Loading GloVe-Wikipedia-Gigaword-100...\")\n",
        "glove_model = api.load('glove-wiki-gigaword-100')\n",
        "print(\"GloVe-Wikipedia-Gigaword-100 loaded successfully!\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "F79St2NZRZtI",
        "outputId": "855d174e-caff-46db-d61f-c811af6f74fd"
      },
      "execution_count": 163,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Loading GloVe-Wikipedia-Gigaword-100...\n",
            "GloVe-Wikipedia-Gigaword-100 loaded successfully!\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### 3° Model, it is bigger infact the file is about 1.5 GB, try at home!\n",
        "- Word2Vec-Google-News-300"
      ],
      "metadata": {
        "id": "SuzZjkjYRIq_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Load the second model: Word2Vec-Google-News-300\n",
        "#UNCOMMENT the load command\n",
        "print(\"Loading the Word2Vec-Google-News-300 model...\")\n",
        "#UNCOMMENT the load command\n",
        "#google_news_model = api.load('word2vec-google-news-300')\n",
        "print(\"Word2Vec-Google-News-300 model loaded successfully!\")\n",
        "# This model is trained on Google News, providing a more formal and general language understanding.\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "U6RYLCU2Qu76",
        "outputId": "2821cf9a-7129-4465-fb14-dcdb856c3487"
      },
      "execution_count": 164,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Loading the Word2Vec-Google-News-300 model...\n",
            "Word2Vec-Google-News-300 model loaded successfully!\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "###  Check the size of the vocabulary of a model"
      ],
      "metadata": {
        "id": "hZLd9VctNDfc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Check the size of the vocabulary of the chosen model\n",
        "model=glove_model\n",
        "vocabulary_size = len(model.key_to_index)\n",
        "print(f\"Vocabulary size: {vocabulary_size}\")\n",
        "# Check the vector size (number of dimensions)\n",
        "vector_size = model.vector_size\n",
        "print(f\"Vector size (number of dimensions): {vector_size}\")\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "w7fbfpFgT3a5",
        "outputId": "e0631d30-fb5b-4dd9-ed28-9bb3f35c1fd4"
      },
      "execution_count": 165,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Vocabulary size: 400000\n",
            "Vector size (number of dimensions): 100\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Therefore the glove wikipedia model has 400000 words and represents each word as a vector with 100 dimensions."
      ],
      "metadata": {
        "id": "dNy9AFeoNfuN"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Functions"
      ],
      "metadata": {
        "id": "jtWwiPqe-7bq"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### We can check the list of all available functions and attributes of the model:"
      ],
      "metadata": {
        "id": "sob0vge-NKIO"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "public_methods = [method for method in dir(model) if not method.startswith(\"_\")]\n",
        "print(public_methods)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MJEZY0dbUuyJ",
        "outputId": "662eb971-aa3b-4315-da2b-697a0f95e25e"
      },
      "execution_count": 166,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "['add_lifecycle_event', 'add_vector', 'add_vectors', 'allocate_vecattrs', 'closer_than', 'cosine_similarities', 'distance', 'distances', 'doesnt_match', 'evaluate_word_analogies', 'evaluate_word_pairs', 'expandos', 'fill_norms', 'get_index', 'get_mean_vector', 'get_normed_vectors', 'get_vecattr', 'get_vector', 'has_index_for', 'index2entity', 'index2word', 'index_to_key', 'init_sims', 'intersect_word2vec_format', 'key_to_index', 'lifecycle_events', 'load', 'load_word2vec_format', 'log_accuracy', 'log_evaluate_word_pairs', 'mapfile_path', 'most_similar', 'most_similar_cosmul', 'most_similar_to_given', 'n_similarity', 'next_index', 'norms', 'rank', 'rank_by_centrality', 'relative_cosine_similarity', 'resize_vectors', 'save', 'save_word2vec_format', 'set_vecattr', 'similar_by_key', 'similar_by_vector', 'similar_by_word', 'similarity', 'similarity_unseen_docs', 'sort_by_descending_frequency', 'unit_normalize_all', 'vector_size', 'vectors', 'vectors_for_all', 'vectors_norm', 'vocab', 'wmdistance', 'word_vec', 'words_closer_than']\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "###  Most useful functions for Word2Vec models:"
      ],
      "metadata": {
        "id": "3rdJozd5OEiz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "# 1. model.most_similar(word, topn=5): Finds the top-N words most similar to the given word.\n",
        "#    Example: model.most_similar(\"physics\", topn=5)\n",
        "# 2. model.similarity(word1, word2): Computes the similarity score between two words.\n",
        "#    Example: model.similarity(\"physics\", \"science\")\n",
        "# 3. model.doesnt_match(list_of_words): Finds the word that doesn't fit with the others.\n",
        "#    Example: model.doesnt_match([\"physics\", \"chemistry\", \"dog\"])\n",
        "# 4. model.key_to_index: Retrieves the vocabulary of the model.\n",
        "#    Example: list(model.key_to_index.keys())[:10]  # First 10 words\n",
        "# 5. model.get_vector(word): Retrieves the vector representation of a word.\n",
        "#    Example: vector = model.get_vector(\"physics\")\n",
        "# 6. model.save(filepath) and model.load(filepath): Save and load models.\n",
        "#    Example: model.save(\"my_model.model\") and gensim.models.Word2Vec.load(\"my_model.model\")"
      ],
      "metadata": {
        "id": "Dg9JcV3mVtLJ"
      },
      "execution_count": 167,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "For convenience, in the following we define some functions/methods with parameters already set, that we can use:\n"
      ],
      "metadata": {
        "id": "WkLlV2StVJTm"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def find_similar_words(word, topn=5):\n",
        "  \"\"\"\n",
        "    Finds the top-N most similar words to the given word.\n",
        "\n",
        "    Parameters:\n",
        "        word (str): The word to find similar words for.\n",
        "        topn (int): Number of similar words to return (default: 5).\n",
        "\n",
        "    Returns:\n",
        "        list: A list of tuples (word, similarity score).\n",
        "  \"\"\"\n",
        "  return model.most_similar(word, topn=topn)\n",
        "\n",
        "def analogy(word1, word2, word3, topn=1):\n",
        "\n",
        "  \"\"\"\n",
        "  Solves an analogy of the form: word1 is to word2 as word3 is to ?.\n",
        "\n",
        "    Parameters:\n",
        "        word1 (str): The first word in the analogy (the \"base\" word to subtract).\n",
        "        word2 (str): The second word in the analogy (the \"target\" word to add).\n",
        "        word3 (str): The third word in the analogy (the \"comparison\" word to add).\n",
        "        topn (int): Number of results to return (default: 1).\n",
        "  \"\"\"\n",
        "\n",
        "  return model.most_similar(positive=[word2, word3], negative=[word1], topn=topn)\n",
        "\n",
        "def visualize_words(words):\n",
        "\n",
        "    \"\"\"\n",
        "    2D visualisation of word embeddings\n",
        "    This function takes a list of words, retrieves their corresponding word\n",
        "    embeddings from the loaded Word2Vec model, and reduces the dimensionality\n",
        "    of the embeddings to 2D using Principal Component Analysis (PCA).\n",
        "    The resulting 2D vectors are plotted as points in a scatter plot\n",
        "\n",
        "    \"\"\"\n",
        "    word_vectors = [model[word] for word in words]\n",
        "    pca = PCA(n_components=2)\n",
        "    word_vectors_2d = pca.fit_transform(word_vectors)\n",
        "\n",
        "    plt.figure(figsize=(10, 8))\n",
        "    plt.scatter(word_vectors_2d[:, 0], word_vectors_2d[:, 1])\n",
        "    for i, word in enumerate(words):\n",
        "        plt.annotate(word, xy=(word_vectors_2d[i, 0], word_vectors_2d[i, 1]))\n",
        "\n",
        "    plt.title(\"2D Visualization of Word Embeddings\", fontsize=18)\n",
        "    plt.grid(True)\n",
        "    plt.show()\n",
        "\n"
      ],
      "metadata": {
        "id": "HVdAxYWC9mhG"
      },
      "execution_count": 168,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "MKvXpz13PraH"
      },
      "execution_count": 168,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Similar words\n",
        "The function applies only to words included originally in the model vocabulary"
      ],
      "metadata": {
        "id": "Bm7wnM7VPr7F"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Example 1\n",
        "find_similar_words(\"physics\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "O3bWEWB5bRUA",
        "outputId": "36c4434b-e2d5-4eda-a8d8-8224184226ab"
      },
      "execution_count": 169,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[('chemistry', 0.8497999906539917),\n",
              " ('mathematics', 0.834094762802124),\n",
              " ('science', 0.7914698719978333),\n",
              " ('biology', 0.7894973158836365),\n",
              " ('theoretical', 0.7342938780784607)]"
            ]
          },
          "metadata": {},
          "execution_count": 169
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Example 2\n",
        "concept = \"wave\"\n",
        "print(f\"Words similar to '{concept}':\")\n",
        "print(find_similar_words(concept))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ssUH6V_M9rmQ",
        "outputId": "e404bf13-89ed-4a1b-ebff-c93206c8b0f1"
      },
      "execution_count": 170,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Words similar to 'wave':\n",
            "[('waves', 0.7943201065063477), ('massive', 0.6597336530685425), ('triggered', 0.6411253213882446), ('tide', 0.6409763097763062), ('violent', 0.6315351724624634)]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### To calculate the similary between two words, word2vec apply the cosine similarity concept (see Annex A)"
      ],
      "metadata": {
        "id": "TniIWPcqdkG0"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Exercise 1\n",
        "# Try it by yourself\n",
        "#Try changing the value of concept to other physics terms like \"force\", \"mass\", etc"
      ],
      "metadata": {
        "id": "YsrFiJru9lv1"
      },
      "execution_count": 171,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Analogies"
      ],
      "metadata": {
        "id": "EZZiwTC2_mez"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Analogies\n",
        "\n",
        "word1, word2, word3 = \"electron\", \"proton\", \"negative\"\n",
        "print(f\"\\nAnalogy: {word1} : {word2} :: {word3} : ?\")\n",
        "print(analogy(word1, word2, word3))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "P3WNmc5W5aIu",
        "outputId": "7981efad-e4fb-4954-9787-b316dec2d0f9"
      },
      "execution_count": 172,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Analogy: electron : proton :: negative : ?\n",
            "[('positive', 0.6567757725715637)]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"\\nAnalogy: man : woman :: king : ?\")\n",
        "print(analogy('man', 'woman', 'king'))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6x-in5DwQgRP",
        "outputId": "e3c12818-282b-4be0-8f58-da4150140906"
      },
      "execution_count": 173,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Analogy: man : woman :: king : ?\n",
            "[('queen', 0.7698540687561035)]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Something about food preferences\n"
      ],
      "metadata": {
        "id": "qpiVQDWBeGWA"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"\\nAnalogy: japanise : sushi :: italian : ?\")\n",
        "print(analogy('japanese', 'sushi', 'italian'))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cVrogLwGaLrv",
        "outputId": "cb8b3010-690e-4f05-d5f2-6f12f6568f4d"
      },
      "execution_count": 174,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Analogy: japanise : sushi :: italian : ?\n",
            "[('pasta', 0.6288173794746399)]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "So it is 'pasta'. We can set `topn=10` to read the other choices"
      ],
      "metadata": {
        "id": "LuqaryxCeLqW"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"\\nAnalogy: japanise : sushi :: italian : ?\")\n",
        "print(analogy('japanese', 'sushi', 'italian',topn=10))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KfuCPv8VdlP4",
        "outputId": "70a9a190-6d6c-49fc-b2ca-83e7863790b3"
      },
      "execution_count": 175,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Analogy: japanise : sushi :: italian : ?\n",
            "[('pasta', 0.6288173794746399), ('tapas', 0.6202685236930847), ('chef', 0.6200571656227112), ('dessert', 0.6084833145141602), ('chefs', 0.5927475690841675), ('cuisine', 0.5911109447479248), ('bistro', 0.5910441875457764), ('gourmet', 0.5872135758399963), ('ducasse', 0.5794909596443176), ('pastry', 0.5783949494361877)]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Surprisingly, there is no pizza listed!"
      ],
      "metadata": {
        "id": "D5NLOZ2CeVod"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Exercise 2\n",
        "#Try creating your own analogies by changing the values of word1, word2, and word3. Use physics concepts you're familiar with.\n",
        "#Experiment with different combinations and observe the results.\n"
      ],
      "metadata": {
        "id": "JE57SIWk5RDP"
      },
      "execution_count": 176,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### If you try:"
      ],
      "metadata": {
        "id": "2hw1rpJchEvj"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"\\nAnalogy: woman : nurse :: man : ?\")\n",
        "print(analogy('woman', 'nurse', 'man'))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2_Oxcpm9RCMu",
        "outputId": "73b1a034-d04b-4119-f15b-85c17ed3add0"
      },
      "execution_count": 177,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Analogy: woman : nurse :: man : ?\n",
            "[('doctor', 0.7208850979804993)]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "AS you can see the model reflects the biases present in the corpus (e.g., texts historically dominated by **gender stereotypes**)."
      ],
      "metadata": {
        "id": "ulIP-96cRWUj"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#We ask for the 5 words nearest:\n",
        "\n",
        "print(analogy('woman', 'nurse', 'man', topn=5))\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xvwImIO9hDRz",
        "outputId": "fdcc27dd-8a98-41e6-f1eb-7b51faa9cf5a"
      },
      "execution_count": 178,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[('doctor', 0.7208850979804993), ('physician', 0.6038255095481873), ('officer', 0.598569929599762), ('hospital', 0.597952127456665), ('surgeon', 0.5937884449958801)]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "For other examples see the Table 8 of the paper https://arxiv.org/pdf/1301.3781"
      ],
      "metadata": {
        "id": "Kz932ktQRyLU"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Possibile explanations of mistakes in the analogies:\n",
        "\n",
        "Model Quality: If the model was trained on a corpus (dataset) that does not sufficiently emphasize semantic relationships between terms like \"king,\" \"queen,\" \"man,\" and \"woman,\" the results may be different or less accurate.\n",
        "\n",
        "Corpus Ambiguity: If the corpus includes multiple meanings for a word (e.g., \"king\" used metaphorically), the model may capture less specific relationships.\n",
        "\n",
        "Static Model Limitations: Models like Word2Vec or GloVe assign a **single vector** to each word, ignoring specific context. This can lead to errors, especially with polysemous words."
      ],
      "metadata": {
        "id": "nYjYNhUshp5Z"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Visualize Word Embedding in two dimensions\n",
        "\n",
        "The visualization of a vector of size 100 (with the model loaded) in 2D is obtained with PCA (Principal Component Analysis). PCA reduces the high-dimensional 100-dimensional vector space to 2D. PCA may may lose important relationships between words in the reduced dimensions. It’s best suited for visualization, not precise analysis."
      ],
      "metadata": {
        "id": "s8__BKhuiQyR"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Visualyze some words in 2d space\n",
        "visualize_words(['physics', 'energy', 'matter', 'space', 'time'])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 704
        },
        "id": "0Tei59bJ82pb",
        "outputId": "ec550e09-0869-4a8a-d79f-df71a526d64e"
      },
      "execution_count": 179,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x800 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### It is possible to retrieve all the components of  a given word vector"
      ],
      "metadata": {
        "id": "H5N18UfNWygk"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# # Define the word to retrieve the vector for\n",
        "word = \"physics\"\n",
        "\n",
        "# Try to retrieve the vector for the given word\n",
        "try:\n",
        "    vector = model[word]  # Retrieve the vector\n",
        "    print(f\"Vector for '{word}':\\n{vector} \\n It has {len(vector)} components\")\n",
        "\n",
        "except KeyError:\n",
        "    print(f\"The word '{word}' is not in the model vocabulary.\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "czyMB9FnktVr",
        "outputId": "3c41f99c-d3cd-4002-93ed-2e9e56d16587"
      },
      "execution_count": 182,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Vector for 'physics':\n",
            "[ 0.38438    0.6775     0.19917    0.85868    0.64199   -0.86999\n",
            "  0.97737   -0.3251    -0.79189    0.84747    0.16542   -1.0649\n",
            " -0.22364    1.0078    -0.21329   -0.053761  -0.12243    0.98599\n",
            "  0.17041   -0.37046   -0.65436   -0.019153   0.49521   -0.27765\n",
            "  0.30316   -0.4635    -0.11864   -0.20677    0.38216    0.17818\n",
            " -1.2728     0.24467   -1.3661     0.24187   -0.82715    0.16062\n",
            " -0.26667    0.66961   -0.40382   -0.42986   -0.71138   -0.097292\n",
            " -1.3057    -0.83636   -0.60994    0.30468    0.71529    0.8308\n",
            " -0.58492    0.58139    1.0738    -0.50557    0.43983    0.40325\n",
            "  0.2703    -0.62618    0.50101    0.4127     0.97117   -0.0023844\n",
            " -0.12813    0.60037   -0.56398    0.1131     1.0617     0.50948\n",
            "  0.31724    0.66798    0.38002    0.61937   -0.18941    0.57344\n",
            "  0.93109    0.296     -1.1131     0.28911    0.73269   -0.90771\n",
            " -0.59169   -0.09907    0.12467    0.33638   -0.72382   -0.95562\n",
            " -1.0909     1.2556     0.49731   -0.92081   -0.18294   -0.94388\n",
            "  0.29059   -0.16549    0.16734    1.1485     0.25645    0.48812\n",
            " -0.45504   -0.65206    0.34716   -0.098853 ] \n",
            " It has 100 components\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The other model 'Glove-Twitter' ha vector of 25 components.\n",
        "\n",
        "As said the reduction of a 100 components vector to 2 components vector has been managed by the PCA techinque."
      ],
      "metadata": {
        "id": "DLI430EaoI-g"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Another example\n",
        "parole_da_visualizzare = ['force', 'mass', 'acceleration', 'velocity', 'momentum']  # Gli studenti possono cambiare queste\n",
        "visualize_words(parole_da_visualizzare)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 704
        },
        "id": "_cko_JsY38v5",
        "outputId": "acb5da45-6f4d-4b40-b430-3c71236f6fcc"
      },
      "execution_count": 183,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x800 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Exercise:\n",
        "#Add the following word to the previous list. 'cat', 'dog'"
      ],
      "metadata": {
        "id": "kc_g-WfTqWd2"
      },
      "execution_count": 156,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Reflect on these questions\n",
        "1. Do the spatial relationships between words match your understanding of how these concepts are related in physics?\n",
        "2. Are there any surprising placements or groupings?\n",
        "3. How might this kind of visualization be useful (or misleading) in understanding physics concepts?"
      ],
      "metadata": {
        "id": "4uAbCY6-ALi_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "def analyze_word_relations(word, model, topn=10):\n",
        "    \"\"\"\n",
        "  It dentifies and prints the top-N words that are most similar to a given word based\n",
        "  on their vector embeddings in the provided Word2Vec model.\n",
        "    \"\"\"\n",
        "    similar_words = model.most_similar(word, topn=topn)\n",
        "    print(f\"Words most similar to '{word}':\")\n",
        "    for similar_word, similarity in similar_words:\n",
        "        print(f\"  {similar_word}: {similarity:.4f}\")"
      ],
      "metadata": {
        "id": "NRpBi-eSCdH_"
      },
      "execution_count": 186,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Example\n",
        "analyze_word_relations(\"nature\", model, topn=10)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jfgTmxUMX5zj",
        "outputId": "52e2b9ac-0475-43ec-8c93-7cc6e66e2c5a"
      },
      "execution_count": 187,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Words most similar to 'nature':\n",
            "  natural: 0.7198\n",
            "  true: 0.7150\n",
            "  aspects: 0.7124\n",
            "  life: 0.7035\n",
            "  view: 0.6961\n",
            "  knowledge: 0.6918\n",
            "  particular: 0.6814\n",
            "  fact: 0.6810\n",
            "  existence: 0.6780\n",
            "  mind: 0.6775\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Analyze some physics words\n",
        "for word in ['acceleration', 'entropy', 'force', 'energy']:    # for loop\n",
        "    analyze_word_relations(word, model)\n",
        "    print()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "j99rlxrkXUmp",
        "outputId": "a3ee9d16-f0c9-4e1f-cc8a-e349ba46b9bd"
      },
      "execution_count": 188,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Words most similar to 'acceleration':\n",
            "  deceleration: 0.7234\n",
            "  braking: 0.6989\n",
            "  speed: 0.6343\n",
            "  velocity: 0.6001\n",
            "  speeds: 0.5813\n",
            "  displacement: 0.5788\n",
            "  torque: 0.5612\n",
            "  vibration: 0.5600\n",
            "  accelerating: 0.5540\n",
            "  coupled: 0.5512\n",
            "\n",
            "Words most similar to 'entropy':\n",
            "  thermodynamic: 0.6863\n",
            "  equilibrium: 0.6304\n",
            "  enthalpy: 0.6246\n",
            "  equation: 0.6054\n",
            "  thermodynamics: 0.5856\n",
            "  formula_4: 0.5829\n",
            "  variance: 0.5807\n",
            "  permeability: 0.5805\n",
            "  formula_10: 0.5802\n",
            "  formula_9: 0.5797\n",
            "\n",
            "Words most similar to 'force':\n",
            "  forces: 0.8348\n",
            "  military: 0.8106\n",
            "  army: 0.7940\n",
            "  troops: 0.7541\n",
            "  air: 0.7521\n",
            "  command: 0.7431\n",
            "  personnel: 0.7120\n",
            "  combat: 0.7104\n",
            "  deployed: 0.7018\n",
            "  civilian: 0.6977\n",
            "\n",
            "Words most similar to 'energy':\n",
            "  resources: 0.7294\n",
            "  gas: 0.7245\n",
            "  renewable: 0.7101\n",
            "  natural: 0.7034\n",
            "  petroleum: 0.6990\n",
            "  electricity: 0.6933\n",
            "  oil: 0.6860\n",
            "  power: 0.6644\n",
            "  development: 0.6643\n",
            "  fuel: 0.6633\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Questions after the activities:\n",
        "\n",
        "1. What interesting relationships did you discover?\n",
        "2. Were there any surprising or unexpected outcomes?\n",
        "3. What limitations do you notice in this approach to word representation?"
      ],
      "metadata": {
        "id": "k_MScPUVZM4a"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Finally a well-known example: king - man + woman ≈ queen\n",
        "\n",
        "We want to keep the same code without introducing new functions.\n",
        "We construct the vector: king - man + woman and temporarily add it to the vocabulary.\n",
        "Then we plot it and observe that it is close to the word queen."
      ],
      "metadata": {
        "id": "cOVhJM6p0F_l"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Words to visualize\n",
        "words_to_visualize = ['king', 'man', 'woman', 'queen']\n",
        "\n",
        "# Define and Compute the result vector\n",
        "result_vector = model['king'] - model['man'] + model['woman']\n",
        "\n",
        "# Add the result vector to the model\n",
        "model['Result'] = result_vector\n",
        "\n",
        "# Visualize 'queen' and the result\n",
        "visualize_words(['king', 'man', 'woman','queen', 'Result'])\n",
        "\n",
        "# Clean up: Remove the temporary vector from the model\n",
        "del model.key_to_index['Result']"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 704
        },
        "id": "r0j8q1UU4puC",
        "outputId": "d8acb143-dc35-4ebe-bc2d-d9d5512d5731"
      },
      "execution_count": 190,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x800 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "You can see that the word  vector '**Result**' and '**queen**' are near in the 2D space.\n",
        "You can calculate as exercise the cosine similarity  between 'Result' and 'queen' (see Annex A)\n",
        "\n"
      ],
      "metadata": {
        "id": "rGi6kXXqAsfl"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### The exercises with this notebook end here. Good job! :-)"
      ],
      "metadata": {
        "id": "XgpO6XfaXrxp"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Optional Section: Explore on your own\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "YKfqUOA_r_AZ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Run the following code."
      ],
      "metadata": {
        "id": "E3C2DqPaOqL8"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# We introduce a function  to visualize word groups\n",
        "\n",
        "def visualize_words(word_groups):\n",
        "    words = [word for group in word_groups for word in group if word in model.key_to_index]\n",
        "    word_vectors = [model[word] for word in words]\n",
        "\n",
        "    pca = PCA(n_components=2)\n",
        "    word_vectors_2d = pca.fit_transform(word_vectors)\n",
        "\n",
        "    plt.figure(figsize=(12, 10))\n",
        "    colors = ['r', 'g', 'b', 'c', 'm']\n",
        "\n",
        "    for i, group in enumerate(word_groups):\n",
        "        group_words = [word for word in group if word in model.key_to_index]\n",
        "        group_vectors = [word_vectors_2d[words.index(word)] for word in group_words]\n",
        "        x, y = zip(*group_vectors) if group_vectors else ([], [])\n",
        "        plt.scatter(x, y, c=colors[i], label=f'Group {i+1}')\n",
        "\n",
        "        for word, (x, y) in zip(group_words, group_vectors):\n",
        "            plt.annotate(word, xy=(x, y), xytext=(5, 2), textcoords='offset points')\n",
        "\n",
        "    plt.title(\"2D Visualization of Physics Concepts (GloVe Model)\")\n",
        "    plt.legend()\n",
        "    plt.grid(True)\n",
        "    plt.show()"
      ],
      "metadata": {
        "id": "VDqAQWFwDcrC"
      },
      "execution_count": 191,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Example\n",
        "# Definy the following group of words\n",
        "mechanics = ['force', 'mass', 'acceleration', 'velocity', 'momentum']\n",
        "thermodynamics = ['heat', 'temperature', 'entropy', 'energy', 'pressure']\n",
        "electromagnetism = ['charge', 'current', 'voltage', 'magnetic', 'electric']\n",
        "quantum = ['quantum', 'wave', 'particle', 'uncertainty', 'atom']\n",
        "\n",
        "# Visualize the group words\n",
        "visualize_words([mechanics, thermodynamics, electromagnetism, quantum])\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 853
        },
        "id": "XgX72ufANzje",
        "outputId": "37b55bf5-cb52-4bb0-93ab-0df635c32bf7"
      },
      "execution_count": 192,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x1000 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Annex A. Cosine Similarity"
      ],
      "metadata": {
        "id": "JABob8os9gSk"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "image from Wikipedia![cosinesimilarity.png](data:image/png;base64,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)"
      ],
      "metadata": {
        "id": "UCEs3p4T6JX4"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Cosine Similarity\n",
        "# Define the vectors\n",
        "A = np.array([1, 2, 3])\n",
        "B = np.array([4, 5, 6])\n",
        "\n",
        "# Calculate the cosine similarity\n",
        "# np.dot(A, B) returns the dot product of A and B.\n",
        "cosine_similarity = np.dot(A, B) / (np.linalg.norm(A) * np.linalg.norm(B))\n",
        "print(f\"Cosine Similarity: {cosine_similarity:.4f}\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fgbgdXTZd1oU",
        "outputId": "4e688f45-25ed-45c6-aba5-15d01a3b4acd"
      },
      "execution_count": 197,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Cosine Similarity: 0.9746\n"
          ]
        }
      ]
    }
  ]
}