{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
\n", " \n", " Transformer Pre-processing

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1. Overview
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" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "## 1.1. Transformer Preprocessing\n", "\n", "This notebook focuses on the preprocessing techniques applied to raw text before it is input into the encoder and decoder blocks of the Transformer architecture. The objective is to explore the key preprocessing steps, particularly the role of positional encodings, and to understand their impact on the overall model performance.\n", "\n", "\n", "\n", "### 1.1.1. Objectives\n", "\n", "Upon completing this study, we will be able to:\n", "\n", "- Visualize positional encodings to develop a deeper understanding of their significance in Transformer models.\n", "- Investigate how positional encodings interact with word embeddings and their effect on the model's representation of text.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "

\n", "
2. Imports
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" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%load_ext autoreload\n", "%autoreload 2" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "import tensorflow as tf\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import os\n", "\n", "from tensorflow.keras.layers import Embedding\n", "from tensorflow.keras.preprocessing.text import Tokenizer\n", "from tensorflow.keras.preprocessing.sequence import pad_sequences\n", "\n", "from sklearn.decomposition import PCA" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "

\n", "
3. Positional Encoding
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" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The positional encodings are derived using the following formulas:\n", "\n", "$$\n", "PE_{(pos, 2i)} = \\sin\\left(\\frac{pos}{10000^{\\frac{2i}{d}}}\\right)\n", "$$\n", "\n", "$$\n", "PE_{(pos, 2i+1)} = \\cos\\left(\\frac{pos}{10000^{\\frac{2i}{d}}}\\right)\n", "$$\n", "\n", "In natural language processing (NLP), it is a standard practice to convert sentences into tokens before inputting them into a language model. Each token is then transformed into a numerical vector of fixed length, referred to as an embedding, which encapsulates the semantic meaning of the word. In the Transformer architecture, a positional encoding vector is added to the embedding to incorporate positional information, allowing the model to account for the order of words in the sequence.\n", "\n", "While these positional encoding vectors are challenging to interpret directly through their numerical representations, visualizations can provide valuable insights into their behavior. For instance, when embeddings are reduced to two dimensions and plotted, semantically similar words are typically located closer together, while dissimilar words are plotted farther apart. Similarly, when visualizing positional encoding vectors, words that are closer together in a sentence should appear closer on a Cartesian plane, whereas words that are farther apart should be more distanced.\n", "\n", "In this notebook, we will generate a series of visualizations of both word embeddings and positional encoding vectors. These visualizations will help us develop a deeper intuition regarding the effect of positional encodings on word embeddings and their role in maintaining sequential information throughout the Transformer model.\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "## 3.1. Visualizing Positional Encodings\n", "\n", "The `positional_encoding` function, is implemented below. Building upon this, we will create visualizations to further explore the behavior of positional encodings." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def positional_encoding(positions, d):\n", " \"\"\"\n", " Precomputes a matrix with all the positional encodings.\n", "\n", " Arguments:\n", " positions (int) -- Maximum number of positions to be encoded.\n", " d (int) -- Encoding size (dimensionality of the positional encoding).\n", "\n", " Returns:\n", " pos_encoding -- (1, positions, d) A matrix containing the positional encodings.\n", " \"\"\"\n", "\n", " # Initialize a matrix of angles\n", " angle_rads = np.arange(positions)[:, np.newaxis] / np.power(10000, (2 * (np.arange(d)[np.newaxis, :] // 2)) / np.float32(d))\n", " angle_rads[:, 0::2] = np.sin(angle_rads[:, 0::2])\n", " angle_rads[:, 1::2] = np.cos(angle_rads[:, 1::2])\n", " \n", " pos_encoding = angle_rads[np.newaxis, ...]\n", " \n", " return tf.cast(pos_encoding, dtype=tf.float32)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we define the embedding dimension as 100, which matches the dimensionality of the word embedding. According to the [\"Attention is All You Need\"](https://arxiv.org/abs/1706.03762) paper, embedding sizes typically range from 100 to 1024, depending on the specific task. Additionally, the paper utilizes a maximum sequence length ranging from 40 to 512, which we will set to 100 for this exercise. The maximum number of words is set to 64." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "2024-11-25 11:52:19.846115: E external/local_xla/xla/stream_executor/cuda/cuda_driver.cc:152] failed call to cuInit: INTERNAL: CUDA error: Failed call to cuInit: UNKNOWN ERROR (303)\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "EMBEDDING_DIM = 100\n", "MAX_SEQUENCE_LENGTH = 100\n", "MAX_NB_WORDS = 64\n", "pos_encoding = positional_encoding(MAX_SEQUENCE_LENGTH, EMBEDDING_DIM)\n", "\n", "# Visualizing the positional encoding matrix\n", "plt.pcolormesh(pos_encoding[0], cmap='RdBu')\n", "plt.xlabel('d')\n", "plt.xlim((0, EMBEDDING_DIM))\n", "plt.ylabel('Position')\n", "plt.colorbar()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "### 3.1.1. Observing Properties of Positional Encodings\n", "\n", "Having implemented the visualization, we now explore some interesting properties of the positional encoding matrix:\n", "\n", "1. **Constant Vector Norms**: The norm of each positional encoding vector remains constant, regardless of the position (`pos`). For example, when evaluating the norm of a positional encoding at `pos = 34`, we observe that the norm is always approximately 7.071068, regardless of the position." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pos = 34\n", "tf.norm(pos_encoding[0,pos,:])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- This consistency implies that the dot product between two positional encoding vectors is unaffected by the scale of the vectors. This characteristic has significant implications for correlation calculations, ensuring that the model's attention mechanism is not influenced by the magnitude of the vectors but rather by their relative positions.\n", "\n", "2. **Constant Difference Norms**: Another intriguing property is that the norm of the difference between two vectors separated by `k` positions also remains constant. If we fix `k` and change `pos`, the difference between the positional encoding vectors stays nearly the same. This property underscores the importance of relative position information, as the difference between encodings is independent of the specific positions of the words but is determined by their relative separation. Being able to express positional encodings as linear functions of one another can help the model to learn by focusing on the relative positions of words." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This reflection of the difference in the positions of words with vector encodings is difficult to achieve, especially given that the values of the vector encodings must remain small enough so that they do not distort the word embeddings. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "tf.Tensor(3.2668781, shape=(), dtype=float32)\n" ] } ], "source": [ "pos = 70\n", "k = 2\n", "print(tf.norm(pos_encoding[0,pos,:] - pos_encoding[0,pos + k,:]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Through these observations, we gain a deeper understanding of the properties of positional encoding vectors and their implications for the Transformer architecture. The constancy of the vector norms and the stability of the difference norms are essential for the model to maintain consistent and meaningful representations of word order, facilitating the model's ability to learn from sequential data without introducing distortion into the word embeddings.\n", "\n", "In the following sections, we will continue to explore how these properties affect the relationships between word embeddings and positional encodings, enhancing our intuition of how the Transformer model processes text sequences." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "## 3.2. Comparing Positional Encodings\n", "\n", "\n", "\n", "### 3.2.1. Correlation\n", "\n", "The positional encoding matrix allows us to visualize the unique vector representation for each position in a sequence. However, it is essential to understand how these vectors capture the relative positions of words within a sentence. To explore this, we calculate the correlation between pairs of positional encoding vectors at every position.\n", "\n", "A well-constructed positional encoding should produce a perfectly symmetric correlation matrix where the values are maximized along the main diagonal. This indicates that vectors at similar positions in the sequence have the highest correlation. As we move away from the diagonal, the correlation values should decrease, reflecting the decreasing similarity between vectors corresponding to positions farther apart in the sentence.\n", "\n", "The following code calculates the correlation between the positional encoding vectors at every position:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Compute the correlation matrix for positional encodings\n", "corr = tf.matmul(pos_encoding, pos_encoding, transpose_b=True).numpy()[0]\n", "\n", "# Visualizing the correlation matrix\n", "plt.pcolormesh(corr, cmap='RdBu')\n", "plt.xlabel('Position')\n", "plt.xlim((0, MAX_SEQUENCE_LENGTH))\n", "plt.ylabel('Position')\n", "plt.colorbar()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The resulting plot illustrates the correlation between positional encodings. The main diagonal should exhibit maximum values, indicating that vectors corresponding to positions that are closer in the sequence are highly correlated. As we move away from the diagonal, the correlation should decrease, reflecting the relative positions of the words in the sentence." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "### 3.2.2. Euclidean Distance\n", "\n", "In addition to correlation, we can also compare positional encoding vectors using the Euclidean distance. Unlike the correlation matrix, the Euclidean distance matrix will have zero values along the main diagonal, and the values off the diagonal will increase as the positional encodings represent words further apart in the sentence.\n", "\n", "The following code computes the Euclidean distance between positional encoding vectors at every position:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Compute the Euclidean distance matrix for positional encodings\n", "eu = np.zeros((MAX_SEQUENCE_LENGTH, MAX_SEQUENCE_LENGTH))\n", "\n", "# Calculate distances between all pairs of positional encodings\n", "for a in range(MAX_SEQUENCE_LENGTH):\n", " for b in range(a + 1, MAX_SEQUENCE_LENGTH):\n", " eu[a, b] = tf.norm(tf.math.subtract(pos_encoding[0, a], pos_encoding[0, b]))\n", " eu[b, a] = eu[a, b]\n", "\n", "# Visualizing the Euclidean distance matrix\n", "plt.pcolormesh(eu, cmap='RdBu')\n", "plt.xlabel('Position')\n", "plt.xlim((0, MAX_SEQUENCE_LENGTH))\n", "plt.ylabel('Position')\n", "plt.colorbar()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the resulting visualization, the diagonal values are all zero, reflecting the fact that the distance between a positional encoding and itself is zero. As the distance between positions increases, so does the Euclidean distance, with off-diagonal values growing as the separation between words in the sequence becomes larger." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "### 3.2.3. Discussion\n", "\n", "These visualizations—both the correlation matrix and the Euclidean distance matrix—serve as diagnostic tools for assessing the behavior of positional encodings. By ensuring that the main diagonal exhibits the highest correlation (or the lowest distance) and that the correlation (or distance) decreases as the positions in the sequence move farther apart, we can confirm that the positional encodings are effectively capturing the relative position of words in the sequence. These properties are crucial for the Transformer model to accurately process sequential data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "

\n", "
4. Semantic Embedding
\n", "

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Understanding the relationship between positional encodings and word embeddings is critical for analyzing how sequential information is captured in a Transformer model. In this section, we explore how positional encodings affect word embeddings by visualizing the sum of these vectors." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "## 4.1 - Load Pretrained Embedding\n", "\n", "To combine pretrained word embeddings with the positional encodings, we utilize a 100-dimensional embedding from the [GloVe](https://nlp.stanford.edu/projects/glove/) project. This embedding contains representations for 400,000 words, each represented as a 100-dimensional vector.\n", "\n", "The following code loads the pretrained GloVe embeddings:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Found 400000 word vectors.\n", "d_model: (100,)\n" ] } ], "source": [ "# Load GloVe embeddings\n", "embeddings_index = {}\n", "GLOVE_DIR = \"glove\"\n", "# mkdir glove\n", "# cd glove\n", "# pip install gdown\n", "# gdown https://drive.google.com/uc?id=1RdFBU9Zvm6onI3laothPLVrEJeoRd3zU\n", "# https://drive.google.com/file/d/1RdFBU9Zvm6onI3laothPLVrEJeoRd3zU/view?usp=sharing\n", "f = open(os.path.join(GLOVE_DIR, 'glove.6B.100d.txt')) \n", "for line in f:\n", " values = line.split()\n", " word = values[0]\n", " coefs = np.asarray(values[1:], dtype='float32')\n", " embeddings_index[word] = coefs\n", "f.close()\n", "\n", "# Display statistics\n", "print('Found %s word vectors.' % len(embeddings_index))\n", "print('d_model:', embeddings_index['hi'].shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Note:** This embedding is composed of 400,000 words and each word embedding has 100 features." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "### 4.1.1. Analyzing the Text Data\n", "\n", "We define two sentences for analysis. These sentences are designed to illustrate semantic similarities among groups of words. The first sentence contains consecutive groups of semantically similar words, while the second sentence randomizes the order of these words:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "texts = ['king queen man woman dog wolf football basketball red green yellow',\n", " 'man queen yellow basketball green dog woman football king red wolf']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To prepare the data for embedding, we apply tokenization, which converts each sentence into sequences of numerical indices. These indices correspond to the positions of the words in a dictionary created from the text. The sequences are padded to a uniform length defined by `MAX_SEQUENCE_LENGTH`.\n", "\n", "A quick summary of tokenization is as follows:\n", "\n", "* If we feed an array of plain text of different sentence lengths, and it will produce a matrix with one row for each sentence, each of them represented by an array of size `MAX_SEQUENCE_LENGTH`.\n", "* Each value in this array represents each word of the sentence using its corresponding index in a dictionary(`word_index`). \n", "* The sequences shorter than the `MAX_SEQUENCE_LENGTH` are padded with zeros to create uniform length. " ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Found 11 unique tokens.\n", "(2, 100)\n", "[[ 1 2 3 4 5 6 7 8 9 10 11 0 0 0 0 0 0 0 0 0 0 0 0 0\n", " 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n", " 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n", " 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n", " 0 0 0 0]\n", " [ 3 2 11 8 10 5 4 7 1 9 6 0 0 0 0 0 0 0 0 0 0 0 0 0\n", " 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n", " 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n", " 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n", " 0 0 0 0]]\n" ] } ], "source": [ "# Tokenize and sequence the text\n", "tokenizer = Tokenizer(num_words=MAX_NB_WORDS) # MAX_NB_WORDS = 64\n", "tokenizer.fit_on_texts(texts)\n", "sequences = tokenizer.texts_to_sequences(texts)\n", "\n", "# Generate the word index and padded sequences\n", "word_index = tokenizer.word_index\n", "print('Found %s unique tokens.' % len(word_index))\n", "\n", "data = pad_sequences(sequences, padding='post', maxlen=MAX_SEQUENCE_LENGTH) # MAX_SEQUENCE_LENGTH = 100\n", "print(data.shape)\n", "print(data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "### 4.1.2. Embedding Matrix Construction\n", "\n", "To simplify the analysis, we focus only on the 11 unique words present in the sentences. Each word is represented by its corresponding GloVe embedding. Words not found in the GloVe index are represented by a zero vector." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(12, 100)\n" ] } ], "source": [ "# Create an embedding matrix for the words in the text\n", "embedding_matrix = np.zeros((len(word_index) + 1, EMBEDDING_DIM))\n", "for word, i in word_index.items():\n", " embedding_vector = embeddings_index.get(word)\n", " if embedding_vector is not None:\n", " # Use the GloVe embedding if available\n", " embedding_matrix[i] = embedding_vector\n", "print(embedding_matrix.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "### 4.1.3. Embedding Layer Creation\n", "\n", "Using the extracted embedding matrix, we construct an embedding layer initialized with the GloVe embeddings. This layer transforms the tokenized input data into word embeddings." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(2, 100, 100)\n" ] } ], "source": [ "# Create the embedding layer\n", "embedding_layer = Embedding(len(word_index) + 1,\n", " EMBEDDING_DIM,\n", " embeddings_initializer=tf.keras.initializers.Constant(embedding_matrix),\n", " trainable=False)\n" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(2, 100, 100)\n" ] } ], "source": [ "\n", "# Transform tokenized data into embeddings\n", "embedding = embedding_layer(data)\n", "print(embedding.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "## 4.2. Visualization on a Cartesian plane\n", "\n", "To gain insights into how embeddings capture semantic information, we will visualize word embeddings on a Cartesian plane. Using Principal Component Analysis (PCA), we reduce the 100-dimensional GloVe embeddings to two dimensions for visualization purposes.\n", "\n", "\n", "\n", "### 4.2.1. PCA-Based Visualization\n", "\n", "The following function plots the embeddings of words in a given sentence. PCA is applied to reduce the high-dimensional embeddings to 2D coordinates, enabling clear visualization. Each word is annotated on the plot to reveal its position in the reduced space." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "def plot_words(embedding, sequences, sentence):\n", " \"\"\"\n", " Visualizes word embeddings on a Cartesian plane using PCA.\n", " \n", " Arguments:\n", " embedding -- Tensor containing word embeddings for the input sentences.\n", " sequences -- List of tokenized and padded sentences.\n", " sentence -- Index of the sentence to visualize.\n", "\n", " Returns:\n", " A scatter plot of words in the reduced 2D space.\n", " \"\"\"\n", " # Apply PCA to reduce embeddings to 2 dimensions\n", " pca = PCA(n_components=2)\n", " X_pca_train = pca.fit_transform(embedding[sentence, 0:len(sequences[sentence]), :])\n", "\n", " # Generate scatter plot with word annotations\n", " fig, ax = plt.subplots(figsize=(12, 6)) \n", " plt.rcParams['font.size'] = '12'\n", " ax.scatter(X_pca_train[:, 0], X_pca_train[:, 1])\n", " words = list(word_index.keys())\n", " for i, index in enumerate(sequences[sentence]):\n", " ax.annotate(words[index - 1], (X_pca_train[i, 0], X_pca_train[i, 1]))" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [3, 2, 11, 8, 10, 5, 4, 7, 1, 9, 6]]" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sequences" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualizing Sentences\n", "\n", "#### Sentence 1:\n", "The first sentence `king queen man woman dog wolf football basketball red green yellow` contains semantically grouped words in sequential order. Plotting its embeddings allows us to observe the spatial arrangement of words in the 2D space:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_words(embedding, sequences, 0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Sentence 2:\n", "The second sentence `man queen yellow basketball green dog woman football king red wolf` contains the same words as the first but in a different order. By plotting its embeddings, we verify that the word order does not influence the underlying vector representations:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_words(embedding, sequences, 1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "### 4.2.2. Observations\n", "\n", "1. **Semantic Clustering**: Words with similar meanings appear closer together, reflecting the embeddings' ability to capture semantic relationships.\n", "2. **Order Invariance**: The embeddings remain unchanged despite the shuffled order of words in the second sentence, confirming that the GloVe representations are independent of word sequence.\n", "\n", "\n", "\n", "### 4.2.3. Summary\n", "\n", "This visualization illustrates how pretrained word embeddings effectively encode semantic information. The PCA-reduced embeddings provide a clear and interpretable representation of word relationships in two dimensions. These plots offer valuable insights into the structure and properties of the embedding space, further demonstrating the robustness of GloVe embeddings in capturing semantic similarity." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "

\n", "
5. Semantic and positional embedding
\n", "

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this section, we'll combine semantic embeddings (from GloVe) with positional encodings to see how positional information affects the representation of words in a sentence. The results demonstrate how varying the relative importance (weights) of semantic and positional embeddings can dramatically alter word representations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "## 5.1. Combining Semantic and Positional Embeddings\n", "\n", "To combine the embeddings, use the following equation with adjustable weights:\n", "\n", "$$\n", "\\text{embedding2} = W_1 \\cdot \\text{semantic\\_embedding} + W_2 \\cdot \\text{positional\\_encoding}\n", "$$\n", "\n", "\n", "\n", "### 5.1.1. Equal Weights: $W_1 = W_2 = 1$\n", "\n", "The combined embeddings give equal importance to both semantic and positional features. Let's visualize the results:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "embedding2 = embedding * 1.0 + pos_encoding[:, :, :] * 1.0\n", "\n", "# Visualizing the embeddings\n", "plot_words(embedding2, sequences, 0) # First sentence\n", "plot_words(embedding2, sequences, 1) # Second sentence" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Observations:\n", "- The new plots differ significantly from the original ones.\n", "- Words that were semantically distant, such as `red` and `wolf` in the second sentence, now appear closer together due to the influence of positional encoding." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "### 5.1.2. Adjusted Weights\n", "\n", "By experimenting with the weights, we can observe how they influence the balance between semantic and positional representations:\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Case 1: Positional Encoding Dominates ($W_1 = 1, W_2 = 10$)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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PP6158+Zp6NChWr58uUqWLFnwFwAAAADA6VxdbGoZVF73NK6ilkHlb4lp8JeyGfktk1cMpKWlyW63KzU1Vd7e3kVdzj8SExOj2NhYBQcHq1atWurYsaMMw9CpU6f00ksvKSoqSm3bttXx48f13nvvydPTU5s3b1bZsmUlXZwqPnjwYLVq1Ur33Xef9u/fr1mzZsnHx0cBAQFOWXRu/e8ndf+MDdfsd+lKjwAAAABwMynoHMqU+JtIo0aNNHfuXEnSwYMHFRQUpHHjxmns2LFmn3vvvVe33367pk6dqrFjx+r8+fMaO3asGjdurLi4OJUqVUqSFBwcrKFDhyogIMAptbPSIwAAAADcGKbE30SGDRtm/vurr75STk6OoqKidOLECfPLz89PtWrVUlxcnCTpl19+UXJysoYNG2aGdUkaMGCA7Ha702pnpUcAAAAAuDGMsFtQdo7hsLBCzv9/aqF69epmn71798owDNWqVSvfY+Q+x33w4EFJytOvZMmSqlGjRmGUf0W5Kz1e/h52P7u7orsF3zIrPQIAAADA9SCwW8zS7Ul5Au2FTQckSR4eHmZbTk6ObDablixZIldX1zzH8fT0LPxi/4YbWekRAAAAAG5lBHYLWbo9SY/NTsjzjHdG1gVJ0qqdf6pvWAVJUlBQkAzDUPXq1VW7du0rHrNatWqSLo7I33XXXWb7+fPndeDAAYcV2Z0ld6VHAAAAAMCV8Qy7RWTnGIpdtCPfBdlyTVi2R9k5F3vce++9cnV1VWxsrC5f6N8wDJ08eVKS1KRJE/n6+uq///2vzp07Z/aZNWuWTp8+XdCXAQAAAAAoIIywW8TGAykO0+DzcywtUxsPpKhlUHlzhfgxY8YoMTFRPXr0kJeXlw4cOKCFCxdq6NChGjVqlEqWLKlx48bp0Ucf1V133aW+ffvqwIEDmjlzptOfYQcAAAAAXD8Cu0Ukp189rOfX7/nnn1ft2rU1efJkxcbGSpICAgLUoUMHde/e3ew3dOhQZWdna8KECfrXv/6lBg0a6Ntvv9VLL71UsBcBAAAAACgwNuPy+dTFREG/sL6wrf/9pO6fseGa/T4b0oLnvwEAAADAggo6h/IMu0U0q+4jf7t7nneU57JJ8rdfXFEdAAAAAFD8EdgtwtXFpuhuwZKUJ7Tnfo7uFszrzwAAAADgFkFgt5DIEH+93+8O+dndHdr97O56v98digzxL6LKAAAAAADOxqJzFhMZ4q+7g/208UCKktMzVdHr4jR4RtYBAAAA4NZCYLcgVxcbC8sBAAAAwC2OKfEAAAAAAFgQgR0AAAAAAAsisAMAAAAAYEEEdgAAAAAALIjADgAAAACABRHYAQAAAACwIAI7AAAAAAAWRGAHAAAAAMCCCOwAAAAAAFgQgR0AAAAAAAsisAMAAAAAYEEEdgAAAAAALIjADgAAAACABRHYAQAAAACwIAI7AAAAAAAWRGAHAAAAAMCCCOwAAAAAAFgQgR0AAAAAAAsisAMAAAAAYEEEdgAAAAAALIjADgAAAACABRHYAQAAAACwIAI7AAAAAAAWRGAHAAAAAMCCCOwAAAAAAFgQgR0AAAAAAAsisAMAAAAAYEEEdgAAAAAALIjADgAAAACABRHYAQAAAACwIAI7AAAAAAAWRGAHAAAAAMCCCOwAAAAAAFgQgR0AAAAAAAsisAMAAAAAYEEEdgAAAAAALIjADgAAAACABRHYAQAAAACwIKcF9oyMDEVHRysyMlI+Pj6y2WyaNWtWvn137typyMhIeXp6ysfHRw899JCOHz/urFIBAAAAAChyJZx1ohMnTuiVV15R1apV1ahRI61evTrffocPH1abNm1kt9v12muvKSMjQxMnTtS2bdu0ceNGlSpVylklAwAAAABQZJwW2P39/ZWUlCQ/Pz/98ssvatq0ab79XnvtNZ05c0b/+9//VLVqVUlSs2bNdPfdd2vWrFkaOnSos0oGAAAAAKDIOG1KvJubm/z8/K7Z78svv1TXrl3NsC5J7du3V+3atTVv3rzCLBEAAAAAAMtw2gj79Thy5IiSk5PVpEmTPNuaNWumxYsXX3HfrKwsZWVlmZ/T0tIKpUYAAAAAAJzBUqvEJyUlSbo4ff5y/v7+SklJcQjllxo/frzsdrv5FRAQUKi1AgAAAABQmCwV2M+ePSvp4vT5y7m7uzv0udyYMWOUmppqfh06dKjwCgUAAAAAoJBZakq8h4eHJOU7ip6ZmenQ53Jubm75Bn0AAAAAAG5Glhphz50Knzs1/lJJSUny8fEhlAMAAAAAbgmWCuxVqlSRr6+vfvnllzzbNm7cqMaNGzu/KAAAAAAAioClArsk9erVS999953DM+irVq3Snj171KdPnyKsDAAAAAAA53HqM+xTpkzR6dOndfToUUnSokWLdPjwYUnSE088IbvdrrFjx2r+/PmKiIjQU089pYyMDE2YMEENGjTQI4884sxyAQAAAAAoMjbDMAxnnSwwMFAHDx7Md9uBAwcUGBgoSfrtt9/0zDPPaO3atSpVqpS6dOmiSZMmqVKlStd9rrS0NNntdqWmpsrb27sgygcAAAAA4IoKOoc6NbA7E4EdAAAAAOBMBZ1DLfcMOwAAAAAAILBbRkxMjGw2m06cOHHFPgMGDDAfGwAAAAAAFG8EdgAAAAAALMipq8Tjn5kxY4ZycnKKugwAAAAAgBMQ2G8iJUuWLOoSAAAAAABOwpR4Czt48KBq1qypkJAQHTt2LM8z7ImJibLZbJo4caKmT5+uoKAgubm5qWnTptq0aVOe482fP1/BwcFyd3dXSEiIFi5cyHPxAAAAAGBRjLBb1O+//6677rpLPj4+WrFihSpUqHDFvnPnzlV6eroeffRR2Ww2vfnmm7r33nu1f/9+c1T++++/V9++fdWgQQONHz9ep06d0qBBg1SlShVnXRIAAAAA4AYQ2C1o165dateunapUqaJly5apXLlyV+3/xx9/aO/evWa/OnXq6J577tGyZcvUtWtXSdKYMWNUpUoV/fTTT/L09JQktWvXTuHh4apWrVrhXhAAAAAA4IYxJd5itm/frrZt2yowMFArV668ZliXpL59+zr0CwsLkyTt379fknT06FFt27ZN/fv3N8O6JLVt21YNGjQo4CsAAAAAABQEAnsRys4xtP73k/pmyxEdSvlLktStWzd5eXlp2bJl8vb2vq7jVK1a1eFzbng/deqUpIvPwktSzZo18+ybXxsAAAAAoOgxJb6ILN2epNhFO5SUmilJOp1wWJLU4q7OWvntPM2ZM0ePPvrodR3L1dU133bDMAqmWAAAAACA0xHYi8DS7Ul6bHaC8ovTu6vdo473umr48OHy8vLSAw888I/Pl/uM+r59+/Jsy68NAAAAAFD0mBLvZNk5hmIX7cg3rOc6fccj6tWrtx5++GF9++23//iclStXVkhIiD755BNlZGSY7T/++KO2bdv2j48PAAAAACh4jLA72cYDKeY0+PwYkv5MP6cJr7yjM2cyFBUVpcWLF+uuu+76R+d97bXXdM8996h169Z65JFHdOrUKU2ZMkUhISEOIR4AAAAAYA2MsDtZcvqVw/qlUjKztWDBArVo0UL33HOPfv7553903m7duumzzz7TuXPn9Pzzz+urr77SrFmzVKdOHbm7u/+jYwMAAAAACp7NKKYrk6Wlpclutys1NfW6V1t3hvW/n9T9MzZcs99nQ1qoZVD5Qq+ncePG8vX11YoVKwr9XAAAAABQGFavXq2IiAjFxcUpPDxckjRgwACtXr1aiYmJTqujoHMoI+xO1qy6j/zt7rJdYbtNkr/dXc2q+xToec+fP68LFy44tK1evVpbt241b2gAAAAAgHXwDLuTubrYFN0tWI/NTpBNclh8LjfER3cLlqvLlSL933PkyBG1b99e/fr1U+XKlbVr1y7997//lZ+fn4YNG1ag5wIAAAAA/HME9iIQGeKv9/vd4fAedknys7sruluwIkP8C/yc5cqV05133qkPPvhAx48fV5kyZdSlSxe9/vrrKl++8KfeAwAAAABuDFPii0hkiL/Wjr5Lnw1poXfua6zPhrTQ2tF3FUpYlyS73a4vvvhChw8fVlZWllJSUjR//nwFBQUVyvkAAAAA4Eri4uJks9m0cOHCPNvmzp0rm82m9evXS5J27dql3r17y8fHR+7u7mrSpMnffv31mTNn9OyzzyogIEBubm6qU6eOJk6cqEuXdrv33nt1xx13OOzXrVs32Ww2h/P+/PPPstlsWrJkyd+q5XoQ2IuQq4tNLYPK657GVdQyqHyBT4MHAAAAACsKDw9XQECA5syZk2fbnDlzFBQUpJYtW+q3335TixYttHPnTj3//POaNGmSypQpox49euQb9q/GMAx1795dkydPVmRkpN566y3VqVNH//rXv/TMM8+Y/cLCwrR161alpaWZ+/30009ycXFRfHy82S8+Pl4uLi5q3br13/wuXBuBHQAAAADgVDabTf369dN3332n1NRUs/348eNavny5+vXrJ0l66qmnVLVqVSUkJOi5557T448/rtWrV6tly5YaPXr0DZ3z22+/1Q8//KB///vfmjFjhh5//HF9++236t27t9555x39/vvvki4G9pycHP3000+SpO3bt+vUqVPq1atXnsDeqFGjQn0rGYEdAAAAAOB0/fv3V1ZWlhYsWGC2ffHFF7pw4YL69eunlJQU/fDDD4qKilJ6erpOnDihEydO6OTJk+rYsaP27t2rI0eOXPf5Fi9eLFdXVz355JMO7c8++6wMwzCntt9+++3y9PTUmjVrJF0M5rfddpv69++vhIQE/fXXXzIMQ2vXrlVYWFgBfCeujMAOAAAAAHCK7BxD638/qW+2HNGpkr5q0rSpw7T4OXPmqEWLFqpZs6b27dsnwzD00ksvydfX1+ErOjpakpScnHzd5z548KAqV64sLy8vh/Z69eqZ2yXJ1dVVLVu2NEfT4+PjFRYWptDQUGVnZ2vDhg3asWOHUlJSCj2ws0o8AAAAAKDQLd2elOdNWTa/5kr4fqq5OPaGDRs0ZcoUSVJOTo4kadSoUerYsWO+x6xZs2ah1BoaGqpXX31VmZmZio+P1wsvvKCyZcsqJCRE8fHxqlSpkiQR2AEAAAAAN7el25P02OwEGZe1Zwe2VI7+q5jJ01TVXlIlS5ZU3759JUk1atSQJJUsWVLt27f/xzVUq1ZNK1euVHp6usMo+65du8ztucLCwnTu3Dl99tlnOnLkiBnM27RpYwb22rVrm8G9sDAlHgAAAABQaLJzDMUu2pEnrEuSS2m7PGrcqc/mztWcOXMUGRmpChUqSJIqVqyo8PBwTZs2TUlJSXn2PX78+A3V0blzZ2VnZ5sj+LkmT54sm82mTp06mW3NmzdXyZIl9cYbb8jHx0f169eXdDHIb9iwQT/++GOhj65LjLADAAAAAArRxgMpDtPgL1cm5C6d+Hq89vwp/fvf/3bY9p///EehoaFq0KCBhgwZoho1aujYsWNav369Dh8+rK1bt153Hd26dVNERIReeOEFJSYmqlGjRlq+fLm++eYbjRw5UkFBQWbf0qVL684779SGDRvMd7BLF0fYz5w5ozNnzjglsDPCDgAAAAAoNMnpVw7rklS6ZjO5uHuqtKe3unfv7rAtODhYv/zyi7p06aJZs2bp8ccf13//+1+5uLjo5ZdfvqE6XFxc9O2332rkyJH67rvvNHLkSO3YsUMTJkzQW2+9lad/biAPDQ012/z8/Mzn5p0R2G2GYeQ3M+Gml5aWJrvdrtTU1EJ9Lx4AAAAA4MrW/35S98/YcMXtRk62Dv+nvzp37qpF82c7sbKCV9A5lBF2AAAAAEChaVbdR/52d9musP3snvXK+StVTw8f7NS6bgYEdgAAAABAoXF1sSm6W7AkOYT2rKO7lbFlqVJ++FBB9UJ0V0R4UZRnaQR2AAAAAEChigzx1/v97pCf3d1sS9+8WCdXTFWNAH99Pe+zIqzOuniGHQAAAADgFNk5hjYeSFFyeqYqermrWXUfubpcabL8zaegcyivdQMAAAAAOIWri00tg8oXdRk3DabEAwAAAABgQQR2AAAAAAAsiMAOAAAAAIAFEdgBAAAAALAgAjsAAAAAABZEYAcAAAAAwIII7AAAAAAAWBCBHQAAAAAACyKwAwAAAABgQQR2AAAAAAAsiMAOAAAAAIAFEdgBAAAAALAgAjsAAAAAABZEYAcAAAAAwIII7AAAAAAAWBCBHQAAAAAACyKwAwAAAABgQQR2AAAAAAAsiMAOAAAAAIAFEdgBAAAAALAgAjsAAAAAABZEYAcAAAAAwIII7AAAAAAAWBCBHQAAAAAACyKwAwAAAABgQQR2AAAAAAAsiMAOAAAAAIAFEdgBAAAAALAgAjsAAAAAABZEYAcAAAAAwIII7AAAAAAAWBCBHQAAAAAACyKwAwAAAABgQQR2AAAAAAAsiMAOAAAAAIAFEdgBAAAAALAgAjsAAAAAABZEYAcAAAAAwIII7AAAAAAAWBCBHQAAAAAACyKwAwAAAABgQQR2AAAAAAAsiMAOAAAAAIAFEdgBAAAAALAgAjsAAAAAABZEYAcAAAAAwIII7AAAAAAAWBCBHQAAAAAAC7JkYM/KytLo0aNVuXJleXh4qHnz5lqxYkVRlwUAAAAAgNNYMrAPGDBAb731lh588EG98847cnV1VefOnbV27dqiLg0AAAAAAKewGYZhFHURl9q4caOaN2+uCRMmaNSoUZKkzMxMhYSEqGLFilq3bt11HSctLU12u12pqany9vYuzJIBAAAAACjwHGq5EfYFCxbI1dVVQ4cONdvc3d01aNAgrV+/XocOHSrC6gAAAAAAcI4SRV3A5TZv3qzatWvn+WtEs2bNJElbtmxRQEBAnv2ysrKUlZVlfk5LSyvcQgEAAAAAKESWG2FPSkqSv79/nvbctqNHj+a73/jx42W3282v/EI9AAAAAAA3C8sF9rNnz8rNzS1Pu7u7u7k9P2PGjFFqaqr5xdR5AAAAAMDNzHJT4j08PBymtufKzMw0t+fHzc0t36APAAAAAMDNyHIj7P7+/kpKSsrTnttWuXJlZ5cEAAAAAIDTWS6wN27cWHv27MmzaNzPP/9sbgcAAAAAoLizXGDv3bu3srOzNX36dLMtKytLM2fOVPPmzVlMDgAAAABwS7DcM+zNmzdXnz59NGbMGCUnJ6tmzZr6+OOPlZiYqA8//LCoywMAAAAAwCksF9gl6ZNPPtFLL72kTz/9VKdOnVLDhg313XffqU2bNkVdGgAAAAAATmEzDMMo6iIKQ1pamux2u1JTU+Xt7V3U5QAAAAAAirmCzqGWe4YdAAAAAAAQ2AEAAAAAsCQCOwAAAAAAFkRgBwAAAADAggjsAAAAAABYEIEdAAAAAAALIrADAAAAAGBBBHYAAAAAACyIwA4AAAAAgAUR2AEAAAAAsCACOwAAAAAAFkRgBwAAAADAggjsAAAAAABYEIEdAAAAAAALIrADAAAAAGBBBHYAAAAAACyIwA4AAAAAgAUR2AEAAAAAsCACOwAAAAAAFkRgBwAAAADAggjsAAAAAABYEIEdAAAAAAALIrADAAAAAGBBBHYAAAAAACyIwA4AAAAAgAUR2AEAAAAAsCACOwAAAAAAFkRgBwAAAADAggjsAAAAAABYEIEdAAAAAAALIrADAAAAAGBBBHYAAAAAACyIwA4AAAAAgAUR2AEAAAAAsCACOwAAAAAAFkRgBwAAAADAggjsAAAAAABYEIEdAAAAAAALIrADAAAAAGBBBHYAAAAAACyIwA4AAAAAgAUR2AEAAAAAsCACOwAAAAAAFkRgBwAAAADAggjswGU2bdqkVq1aqUyZMrLZbNqyZYvTzh0YGKiuXbsW2PESExNls9k0a9Yssy0mJkY2m63AzgEAAACgcJQo6gIAKzl//rz69Okjd3d3TZ48WaVLl1a1atUK9Bw7duzQvHnzNGDAAAUGBhbosQEAAAAUHwR24BK///67Dh48qBkzZmjw4MGFco4dO3YoNjZW4eHhBHYAAAAAV8SUeOASycnJkqSyZcsWbSEAAAAAbnkEduD/GzBggNq2bStJ6tOnj2w2m8LDwyVJP/zwg8LCwlSmTBmVLVtW99xzj3bu3JnnGJs3b1anTp3k7e0tT09PtWvXThs2bDC3z5o1S3369JEkRUREyGazyWazafXq1Q7HWb58uRo3bix3d3cFBwfrq6++ctiekpKiUaNGqUGDBvL09JS3t7c6deqkrVu3FuB3BAAAAEBRYko88P89+uijqlKlil577TU9+eSTatq0qSpVqqSVK1eqU6dOqlGjhmJiYnT27Fm99957at26tRISEsxp7b/99pvCwsLk7e2t5557TiVLltS0adMUHh6uH3/8Uc2bN1ebNm305JNP6t1339XYsWNVr149STL/V5L27t2rvn37atiwYXr44Yc1c+ZM9enTR0uXLtXdd98tSdq/f7++/vpr9enTR9WrV9exY8c0bdo0tW3bVjt27FDlypWd/v0DAAAAULAI7MD/17JlS2VlZem1115TWFiYevfuLUm6/fbb5ePjo/Xr18vHx0eS1KNHD91+++2Kjo7Wxx9/LEl68cUXdf78ea1du1Y1atSQJPXv31916tTRc889px9//FE1atRQWFiY3n33Xd19993mCP6l9uzZoy+//FL33nuvJGnQoEGqW7euRo8ebQb2Bg0aaM+ePXJx+b9JMg899JDq1q2rDz/8UC+99FKhfZ8AAAAAOAdT4oGrSEpK0pYtWzRgwAAzrEtSw4YNdffdd2vx4sWSpOzsbC1fvlw9evQww7ok+fv764EHHtDatWuVlpZ2XeesXLmyevbsaX729vZW//79tXnzZv3555+SJDc3NzOsZ2dn6+TJk/L09FSdOnWUkJDwj68bAAAAV5b7mtwTJ0445Xy5r+qdOHFioZ5n9erVstlsWrBgQYEdM79XCgcGBmrAgAEFdo7ijMAOXMXBgwclSXXq1MmzrV69ejpx4oTOnDmj48eP66+//rpiv5ycHB06dOi6zlmzZs08P9Rq164t6eIPa0nKycnR5MmTVatWLbm5ualChQry9fXVr7/+qtTU1Bu5RAAAANxi5s6dq7fffruoy8B1ILDjlpedY2j97yf1zZYj+u3IzRF2X3vtNT3zzDNq06aNZs+erWXLlmnFihWqX7++cnJyiro8AAAAWBiB/ebBM+y4pS3dnqTYRTuUlJopScr8Y4ckafMfp9RbUrVq1SRJu3fvzrPvrl27VKFCBZUpU0bu7u4qXbr0Ffu5uLgoICBAkvKMnl9u3759MgzDod+ePXskyVzgbsGCBYqIiNCHH37osO/p06dVoUKF67hyAAAAAFbHCDtuWUu3J+mx2QlmWL/UjDX7tXR7kvz9/dW4cWN9/PHHOn36tLl9+/btWr58uTp37ixJcnV1VYcOHfTNN9+Y09Yl6dixY5o7d65CQ0Pl7e0tSSpTpowkORzvUkePHtXChQvNz2lpafrkk0/UuHFj+fn5meczDMNhv/nz5+vIkSM3/H0AAADA33PixAlFRUXJ29tb5cuX11NPPaXMzP/73XLmzJm66667VLFiRbm5uSk4OFjvv/9+nuP88ssv6tixoypUqCAPDw9Vr15dAwcOvOq5DcPQ0KFDVapUKYdXAM+ePVt33nmnPDw85OPjo/vuu8/h0czw8HB9//33OnjwoPmK4dxBoVzZ2dkaO3as/Pz8VKZMGXXv3j3P453x8fHq06ePqlatKjc3NwUEBOjpp5/W2bNnb+RbiGtghB23pOwcQ7GLdsi4Sp/YRTt0d7CfJkyYoE6dOqlly5YaNGiQ+Vo3u92umJgYs/+4ceO0YsUKhYaGavjw4SpRooSmTZumrKwsvfnmm2a/xo0by9XVVW+88YZSU1Pl5uZm/iCXLj6vPmjQIG3atEmVKlXSRx99pGPHjmnmzJnmMbp27apXXnlFjzzyiFq1aqVt27Zpzpw5DgveAQAAoHBFRUUpMDBQ48eP14YNG/Tuu+/q1KlT+uSTTyRJ77//vurXr6/u3burRIkSWrRokYYPH66cnBw9/vjjkqTk5GR16NBBvr6+ev7551W2bFklJiY6hPDLZWdna+DAgfriiy+0cOFCdenSRZL06quv6qWXXlJUVJQGDx6s48eP67333lObNm20efNmlS1bVi+88IJSU1N1+PBhTZ48WZLk6enpcPxXX31VNptNo0ePVnJyst5++221b99eW7ZskYeHh6SLg0V//fWXHnvsMZUvX14bN27Ue++9p8OHD2v+/PkF/r2+ZRnFVGpqqiHJSE1NLepSYEHr9p0wqo3+Ls9XpftfMyQZFe553qg2+jtj3b4ThmEYxsqVK43WrVsbHh4ehre3t9GtWzdjx44deY6bkJBgdOzY0fD09DRKly5tREREGOvWrcvTb8aMGUaNGjUMV1dXQ5IRFxdnGIZhVKtWzejSpYuxbNkyo2HDhoabm5tRt25dY/78+Q77Z2ZmGs8++6zh7+9veHh4GK1btzbWr19vtG3b1mjbtq3Z78CBA4YkY+bMmWZbdHS0UYz/0wcAACh0ub9Pde/e3aF9+PDhhiRj69athmEYxl9//ZVn344dOxo1atQwPy9cuNCQZGzatOmK58v9nW7ChAnG+fPnjb59+xoeHh7GsmXLzD6JiYmGq6ur8eqrrzrsu23bNqNEiRIO7V26dDGqVauW5zxxcXGGJKNKlSpGWlqa2T5v3jxDkvHOO++Ybfld2/jx4w2bzWYcPHjQbMvvd89q1aoZDz/88BWv92ZW0DmUEXbckpLT806DlyT3qg1VbfR3efq1a9dO7dq1u+Zxb7/9di1duvSa/QYPHqzBgwfnab90On2HDh2uuL+bm5smTpyY59Ueq1evdvgcGBiYZ+p8TEyMw8wAAAAA/D25o+S5nnjiCU2dOlWLFy9Ww4YNzdFoSUpNTdX58+fVtm1bLVu2TKmpqbLb7Spbtqwk6bvvvlOjRo1UsmTJK57v3Llz6tOnj1asWKHFixcrPDzc3PbVV18pJydHUVFRDq+b8/PzU61atRQXF6exY8de13X1799fXl5e5ufevXvL399fixcv1pNPPilJDtd25swZnT17Vq1atZJhGNq8ebOqVq16XefC1RHYcUuq6OVeoP0AAABw66lVq5bD56CgILm4uJiDMD/99JOio6O1fv16/fXXXw59cwN727Zt1atXL8XGxmry5MkKDw9Xjx499MADD8jNzc1hn/HjxysjI0NLlixxCOuStHfvXhmGkaemXFf7Q8C1rstms6lmzZoOg0t//PGHXn75ZX377bc6depUnmtDwSCw45bUrLqP/O3u+jM1M9/n2G2S/Ozualbdx9mlAQAAwIKycwxtPJCi5PRMHUr5K98+l77l5/fff1e7du1Ut25dvfXWWwoICFCpUqW0ePFiTZ482XwVr81m04IFC7RhwwYtWrRIy5Yt08CBAzVp0iRt2LDB4fnyjh07aunSpXrzzTcVHh4ud/f/G1zKycmRzWbTkiVL5Orqmqe2y59T/yeys7N19913KyUlRaNHj1bdunVVpkwZHTlyRAMGDOA1wwWIwI5bkquLTdHdgvXY7ATZJIfQnvtjNrpbsFxdrv4KNgAAABR/l78K+HTCYUnS3BUb9MLQ6ma/ffv2KScnR4GBgVq0aJGysrL07bffOkwPj4uLy/ccLVq0UIsWLfTqq69q7ty5evDBB/X55587PEbZokULDRs2TF27dlWfPn20cOFClShxMdIFBQXJMAxVr15dtWvXvur1XOs1w3v37nX4bBiG9u3bp4YNG0qStm3bpj179ujjjz9W//79zX4rVqy46nFx43itG25ZkSH+er/fHfKzO05797O76/1+dygyxL+IKgMAAIBVXO1VwK9OeEdLtyeZn9977z1JUqdOncxR7kvXE0pNTXV4848knTp1Ks+aQ40bN5YkZWVl5Tln+/bt9fnnn2vp0qV66KGHzNHse++9V66uroqNjc1zPMMwdPLkSfNzmTJlrjpt/ZNPPlF6err5ecGCBUpKSlKnTp0kKd9rMwxD77zzzhWPib+HEXbc0iJD/HV3sJ85vami18Vp8IysAwAA4FqvAr6QekwP9OmlV0Y8qJ83bNDs2bP1wAMPqFGjRnJ3d1epUqXUrVs3Pfroo8rIyNCMGTNUsWJFJSX9X8j/+OOPNXXqVPXs2VNBQUFKT0/XjBkz5O3trc6dO+d73h49emjmzJnq37+/vL29NW3aNAUFBWncuHEaM2aMEhMT1aNHD3l5eenAgQNauHChhg4dqlGjRkmS7rzzTn3xxRd65pln1LRpU3l6eqpbt27m8X18fBQaGqpHHnlEx44d09tvv62aNWtqyJAhkqS6desqKChIo0aN0pEjR+Tt7a0vv/wyz7Ps+OcI7LjlubrY1DKofFGXAQAAAIvZeCAl35H1XL7dR+v02tkaPfp5uZUqqREjRmjChAmSpDp16mjBggV68cUXNWrUKPn5+emxxx6Tr6+vBg4caB6jbdu22rhxoz7//HMdO3ZMdrtdzZo105w5c1S9evUrnVr9+vVTenq6hg8fLm9vb02YMEHPP/+8ateurcmTJys2NlaSFBAQoA4dOqh79+7mvsOHD9eWLVs0c+ZMTZ48WdWqVXMI7GPHjtWvv/6q8ePHKz09Xe3atdPUqVNVunRpSRcXsFu0aJGefPJJjR8/Xu7u7urZs6dGjBihRo0a/b1vNvJlMy6fL1FMpKWlyW63KzU1Vd7e3kVdDgAAAICbzDdbjuipz7dcs9879zXWPY2rFH5BsLyCzqE8ww4AAAAA+eBVwChqBHYAAAAAyEfuq4CvtLqRTZI/rwJGISKwAwAAAEA+cl8FLClPaOdVwHAGAjsAAAAAXAGvAkZRYpV4AAAAALgKXgWMokJgBwAAAIBr4FXAKApMiQcAAAAAwIII7AAAAAAAWBCBHQAAAAAACyKwAwAAAABgQQR2AAAAAAAsiMAOAAAAAIAFEdgBAAAAALAgAjsAAAAAABZEYAcAAAAAwIII7AAAAAAAWBCBHQAAAAAACyKwAwAAAABgQU4J7ElJSXr++ecVEREhLy8v2Ww2rV69+or9161bp9DQUJUuXVp+fn568sknlZGR4YxSAQAAAACwBKcE9t27d+uNN97QkSNH1KBBg6v23bJli9q1a6e//vpLb731lgYPHqzp06erT58+zigVAAAAAABLKOGMk9x55506efKkfHx8tGDBgquG77Fjx6pcuXJavXq1vL29JUmBgYEaMmSIli9frg4dOjijZAAAAAAAipRTRti9vLzk4+NzzX5paWlasWKF+vXrZ4Z1Serfv788PT01b968wiwTAAAAAADLcMoI+/Xatm2bLly4oCZNmji0lypVSo0bN9bmzZuvuG9WVpaysrLMz2lpaYVWJwAAAAAAhc1Sq8QnJSVJkvz9/fNs8/f319GjR6+47/jx42W3282vgICAQqsTAAAAAIDCdsOBPScnR5mZmdf1ZRjGDR377NmzkiQ3N7c829zd3c3t+RkzZoxSU1PNr0OHDt3YhQEAAAAAYCE3PCV+zZo1ioiIuK6+O3fuVN26da/72B4eHpLkMLU9V2Zmprk9P25ubvkGfQAAAAAAbkY3HNjr1q2rmTNnXlff/Ka2X0//3Knxl0pKSlLlypVv6HgAAAAAANysbjiw+/n5acCAAYVQihQSEqISJUrol19+UVRUlNl+7tw5bdmyxaENAAAAAIDizFKLztntdrVv316zZ89Wenq62f7pp58qIyPjqu9vBwAAAACgOHHaa93GjRsnSfrtt98kXQzha9eulSS9+OKLZr9XX31VrVq1Utu2bTV06FAdPnxYkyZNUocOHRQZGemscgEAAAAAKFI240aXcv+7J7LZrrjt8hLWrl2r0aNHKyEhQV5eXoqKitL48ePl5eV13edLS0uT3W5XamqqvL29/3bdAAAAAABcj4LOoU4L7M5GYAcAAAAAOFNB51BLPcMOAAAAAAAuIrADAAAAAGBBBHYAAAAAACyIwA4AAAAAgAUR2AEAAAAAsCACOwAAAAAAFkRgBwAAAADAggjsAAAAAABYEIEdAAAAAAALIrADAAAAAGBBBHYAAAAAACyIwA4AAAAAgAUR2AEAAAAAsCACOwAAAAAAFkRgBwAAAADAggjsAAAAAABYEIEdAAAAAAALIrADAAAAAGBBBHYAAAAAACyIwA4AAAAAgAUR2AEAAAAAsCACOwAAAAAAFkRgBwAAAADAggjsAAAAAABYEIEdAAAAAAALIrADAAAAAGBBBHYAAAAAACyIwA4AAAAAgAUR2AEAAAAAsCACOwAAAAAAFkRgBwAAAADAggjsAAAAAABYEIEdAAAAAAALIrADAAAAAGBBBHYAAAAAACyIwA4AAAAAgAUR2AEAAAAAsCACOwAAAAAAFkRgBwAAAADAggjsAAAAAABYEIEdAAAAAAALIrADAAAAAGBBBHYAAAAAACyIwA4AAAAAgAUR2AEAAAAAsCACOwAAAAAAFkRgBwAAAADAggjsAAAAAABYEIEdAAAAAAALIrADAAAAAGBBBHYAAAAAACyIwA4AAAAAgAUR2AEAAAAAsCACOwAAAAAAFkRgBwAAAADAggjsAAAAAABYEIEdAAAAAAALIrADAAAAAGBBBHYAAAAAACyIwA4AAAAAgAUR2AEAAAAAsCACOwAAAAAAFkRgBwAAAADAggjsAAAAAABYEIEdAAAAAAALIrADAAAAAGBBBHYAKAK//vqrbDabvv32W7Ptf//7n2w2m+644w6Hvp06dVLz5s3Nz1OnTlX9+vXl5uamypUr6/HHH9fp06cd9gkPD1dISIh+/fVXtW3bVqVLl1bNmjW1YMECSdKPP/6o5s2by8PDQ3Xq1NHKlSsd9j948KCGDx+uOnXqyMPDQ+XLl1efPn2UmJjo0G/WrFmy2Wz66aef9Mwzz8jX11dlypRRz549dfz48QL4TgEAANy6COwAUARCQkJUtmxZrVmzxmyLj4+Xi4uLtm7dqrS0NElSTk6O1q1bpzZt2kiSYmJi9Pjjj6ty5cqaNGmSevXqpWnTpqlDhw46f/68wzlOnTqlrl27qnnz5nrzzTfl5uam++67T1988YXuu+8+de7cWa+//rrOnDmj3r17Kz093dx306ZNWrdune677z69++67GjZsmFatWqXw8HD99ddfea7niSee0NatWxUdHa3HHntMixYt0ogRIwrjWwcAAHDLKFHUBQDArcjFxUWtW7dWfHy82RYfH68ePXrom2++0bp16xQZGWmG97CwMB0/flzjx49Xhw4dtGTJErm4XPyba926dTVixAjNnj1bjzzyiHm8o0ePau7cubr//vslSXfffbfq1q2rBx54QOvWrTNH7evVq6eOHTvqyy+/1IABAyRJXbp0Ue/evR1q7tatm1q2bKkvv/xSDz30kMO28uXLa/ny5bLZbJIu/qHh3XffVWpqqux2e8F+8wAAAG4RjLADQBEJCwtTQkKCzpw5I0lau3atOnfurMaNG5tBPj4+XjabTaGhoVq5cqXOnTunkSNHmmFdkoYMGSJvb299//33Dsf39PTUfffdZ36uU6eOypYtq3r16jlMsc/99/79+802Dw8P89/nz5/XyZMnVbNmTZUtW1YJCQl5rmXo0KFmWM+9tuzsbB08ePBvfW8AAADACDsAOE12jqGNB1KUnJ6pil7uatU6VBcuXND69esVEBCg5ORkhYWF6bfffnMI7MHBwfLx8THDb506dRyOW6pUKdWoUSNPOL7tttscQrQk2e12BQQE5GmTLk6hz3X27FmNHz9eM2fO1JEjR2QYhrktNTU1z7VVrVrV4XO5cuXyHBMAAAA3hsAOAE6wdHuSYhftUFJqptlWqYyrSrm5a82aNapataoqVqyo2rVrKywsTFOnTlVWVpbi4+PVs2fPv3VOV1fXG2q/NJQ/8cQTmjlzpkaOHKmWLVvKbrfLZrPpvvvuU05Ozt86JgAAAG4MgR0ACtnS7Ul6bHaCLo+uyWeyZatYU98sXaXG9WoqLCxM0sXp5FlZWZozZ46OHTtmLjhXrVo1SdLu3btVo0YN8zjnzp3TgQMH1L59+wKrecGCBXr44Yc1adIksy0zMzPPavQAAAAoPDzDDgCFKDvHUOyiHXnCuiQZktxvq6/tW/6nuLg4M7BXqFBB9erV0xtvvCFJZnv79u1VqlQpvfvuuw4j1x9++KFSU1PVpUuXAqvb1dU1z+j4e++9p+zs7AI7BwAAAK6OEXYAKEQbD6Q4TIO/nNttwUpd/4UOHTpkBnNJatOmjaZNm6bAwEDddtttkiRfX1+NGTNGsbGxioyMVPfu3bV7925NnTpVTZs2Vb9+/Qqs7q5du+rTTz+V3W5XcHCw1q9fr5UrV6p8+fIFdg4AAABcHYEdAApRcvqVw7okuVWpJ9lc5FG6tBo1amS2h4WFadq0aQ4hXrr4HnZfX19NmTJFTz/9tHx8fDR06FC99tprKlmyZIHV/c4778jV1VVz5sxRZmamWrdurZUrV6pjx44Fdg4AAABcnc0opisCpaWlyW63KzU1Vd7e3kVdDoBb1PrfT+r+GRuu2e+zIS3UMojRawAAgJtZQedQnmEHgELUrLqP/O3usl1hu02Sv91dzar7OLMsAAAA3AQI7ABQiFxdbIruFixJeUJ77ufobsFydblSpAcAAMCtisAOAIUsMsRf7/e7Q352d4d2P7u73u93hyJD/IuoMgAAAFgZi84BgBNEhvjr7mA/bTyQouT0TFX0ujgNnpF1AAAAXAmBHQCcxNXFxsJyAAAAuG5MiQcAAAAAwIKcEthXrVqlgQMHqnbt2ipdurRq1KihwYMHKykpKd/+69atU2hoqEqXLi0/Pz89+eSTysjIcEapAAAAAABYglPew96kSROlpKSoT58+qlWrlvbv368pU6aodOnS2rJli/z8/My+W7ZsUcuWLVWvXj0NHTpUhw8f1sSJExUREaElS5Zc9zl5DzsAAAAAwJkKOoc65Rn2t956S6GhoXJx+b8B/cjISLVt21ZTpkzRuHHjzPaxY8eqXLlyWr16tXmBgYGBGjJkiJYvX64OHTo4o2QAAAAAAIqUU6bEt2nTxiGs57b5+Pho586dZltaWppWrFihfv36Ofw1on///vL09NS8efOcUS4AAAAAAEWuyFaJz8jIUEZGhipUqGC2bdu2TRcuXFCTJk0c+pYqVUqNGzfW5s2br3i8rKwsZWVlmZ/T0tIKvmgAAADgEjk5OTp37pzc3d2LuhQAxVCRrRL/9ttv69y5c+rbt6/ZlrsInb+/f57+/v7+Onr06BWPN378eNntdvMrICCg4IsGAABAsbV69Wo1adJE7u7uCgoK0rRp0xQTEyObzWb2sdlsGjFihObMmaP69evLzc1NS5culSQdOXJEAwcOVKVKleTm5qb69evro48+ynOerKwsRUdHq2bNmnJzc1NAQICee+45h8GnS8/19ddfKyQkxDxm7vkAFH83PMKe+1fE6+Hm5ubwAy7XmjVrFBsbq6ioKN11111m+9mzZ839Lufu7m5uz8+YMWP0zDPPmJ/T0tII7QAAALgumzdvVmRkpPz9/RUbG6vs7Gy98sor8vX1zdP3hx9+0Lx58zRixAhVqFBBgYGBOnbsmFq0aGGGbF9fXy1ZskSDBg1SWlqaRo4cKeni79Ldu3fX2rVrNXToUNWrV0/btm3T5MmTtWfPHn399dcO51q7dq2++uorDR8+XF5eXnr33XfVq1cv/fHHHypfvrwTvjMAitINB/Y1a9YoIiLiuvru3LlTdevWdWjbtWuXevbsqZCQEH3wwQcO2zw8PCQpz18XJSkzM9Pcnh83N7d8gz4AAABwLdHR0XJ1ddVPP/2kypUrS5KioqJUr169PH13796tbdu2KTg42GwbPHiwsrOztW3bNjNIDxs2TPfff79iYmL06KOPysPDQ3PnztXKlSv1448/KjQ01Nw/JCREw4YN07p169SqVSuzfefOndqxY4eCgoIkSREREWrUqJE+++wzjRgxolC+FwCs44YDe926dTVz5szr6nv51PZDhw6pQ4cOstvtWrx4sby8vPLtn9/72ZOSkswfngAAAEBByc7O1sqVK9WzZ0+H3zdr1qypTp06adGiRQ7927Zt6xDWDcPQl19+qaioKBmGoRMnTpjbOnbsqM8//1wJCQlq3bq15s+fr3r16qlu3boO/XJnncbFxTkE9vbt25thXZIaNmwob29v7d+/v+C+AQAs64YDu5+fnwYMGHDDJzp58qQ6dOigrKwsrVq1Kt/n1ENCQlSiRAn98ssvioqKMtvPnTunLVu2OLQBAAAA/0R2jqGNB1K0a/9BnT17VjUuCca5atasmaetevXqDp+PHz+u06dPa/r06Zo+fXq+50pOTpYk7d27Vzt37sx3qv2l/XJVrVo1T59y5crp1KlT+V8UgGLFKavEnzlzRp07d9aRI0cUFxenWrVq5dvPbrerffv2mj17tl566SVzBP7TTz9VRkaG+vTp44xyAQAAUMwt3Z6k2EU7lJSaqQsZKZKkmT8lqvX2JEWG5B1YutTlj2nm5ORIkvr166eHH344330aNmxo9m3QoIHeeuutfPtdvgaTq6trvv0Mw7hqjQCKB6cE9gcffFAbN27UwIEDtXPnTod3r3t6eqpHjx7m51dffVWtWrVS27ZtNXToUB0+fFiTJk1Shw4dFBkZ6YxyAQAAUIwt3Z6kx2YnKDfyupa2y1ailE7/+Ycem52g9/vdYYb2ffv2XfN4vr6+8vLyUnZ2ttq3b3/VvkFBQdq6davatWuX7+LMAHApp7zWbcuWLZKkjz76SA899JDDV+6KmbnuuOMOrVy5Uh4eHnr66ac1ffp0DRo0SAsWLHBGqQAAACjGsnMMxS7aoUvHp20urnKv1kh/7d2gC+knFbtoh7JzDO3bt09Lliy55jFdXV3Vq1cvffnll9q+fXue7cePHzf/HRUVpSNHjmjGjBl5+p09e1Znzpz5W9cFoHhyygh7YmLiDfUPDQ3VTz/9VDjFAAAA4Ja18UCKklIz87TbQx/U2dmblTTnOWXc3kkjTq7Wt599pJCQEHPw6Wpef/11xcXFqXnz5hoyZIiCg4OVkpKihIQErVy5UikpF6fdP/TQQ5o3b56GDRumuLg4tW7dWtnZ2dq1a5fmzZunZcuWqUmTJgV92QBuUk4J7AAAAIAVJKfnDeuS5OZXUxX7xOp03Ec6HT9bX/9eReNeeUU7d+7Url27rnncSpUqaePGjXrllVf01VdfaerUqSpfvrzq16+vN954w+zn4uKir7/+WpMnT9Ynn3yihQsXqnTp0qpRo4aeeuop1a5du8CuFcDNz2YU0xUr0tLSZLfblZqaKm9v76IuBwAAABaw/veTun/Ghmv2+2xIC7UMKq8ePXrot99+0969e51QHYCbXUHnUKc8ww4AAABYQbPqPvK3uyu/5d5yzmfJJsnf7q5m1X20d+9eLV68WOHh4U6uEgAuIrADAADgluHqYlN0t2BJyhPaj04brFM/zlKzrM2KfvkltWjRQqVKldJzzz3n/EIBQAR2AAAA3GIiQ/z1fr875Gd3d2j3qdNMbn9s0LTXX9R7772npk2bas2aNapVq1YRVQrgVscz7AAAALglZecY2nggRcnpmarodXEavKsL70YH8PcVdA5llXgAAADcklxdbGoZVL6oywCAK2JKPAAAAAAAFkRgBwAAAADAggjsAAAAAABYEIEdAAAAAAALIrADAAAAAGBBBHYAAAAAACyIwA4AAAAAgAUR2AEAAAAAsCACOwAAAAAAFkRgBwAAAADAggjsAAAAAABYEIEdAAAAAAALIrADAAAAAGBBBHYAAAAAACyIwA4AAAAAgAUR2AEAAAAAsCACOwAAAAAAFkRgBwAAAADAggjsAAAAAABYEIEdAAAAAAALIrADAAAAAGBBBHYAAAAAACyIwA4AAAAAgAUR2AEAAAAAsCACOwAAKDAxMTGy2WxFXQYAAMUCgR0AAAAAAAsisAMAAAAAYEEEdgAAAAAALIjADgAA/pa1a9eqadOmcnd3V1BQkKZNm5anz4ULF/Tvf/9bQUFBcnNzU2BgoMaOHausrCyHfjk5OYqJiVHlypVVunRpRUREaMeOHQoMDNSAAQOcdEUAAFhLiaIuAAAA3Hy2bdumDh06yNfXVzExMbpw4YKio6NVqVIlh36DBw/Wxx9/rN69e+vZZ5/Vzz//rPHjx2vnzp1auHCh2W/MmDF688031a1bN3Xs2FFbt25Vx44dlZmZ6exLAwDAMgjsAADghr388ssyDEPx8fGqWrWqJKlXr15q0KCB2Wfr1q36+OOPNXjwYM2YMUOSNHz4cFWsWFETJ05UXFycIiIidOzYMb311lvq0aOHQ4iPjY1VTEyMU68LAAArYUo8AAC4IdnZ2Vq2bJl69OhhhnVJqlevnjp27Gh+Xrx4sSTpmWeecdj/2WeflSR9//33kqRVq1bpwoULGj58uEO/J554olDqBwDgZsEIOwAAuKbsHEMbD6QoOT1TrpmpOnv2rGrVqpWnX506dcygfvDgQbm4uKhmzZoOffz8/FS2bFkdPHjQ7CcpTz8fHx+VK1euMC4HAICbAoEdAABc1dLtSYpdtENJqRefJ8/OOCVJ2pecfl3722y2QqsNAIDijCnxAADgipZuT9JjsxPMsC5JLqW9ZSvhpm/XJGjp9iSH/rt37zb/Xa1aNeXk5Gjv3r0OfY4dO6bTp0+rWrVqZj9J2rdvn0O/kydP6tSpUwV6PQAA3EwI7AAAIF/ZOYZiF+2QcVm7zcVV7tVv1197N2jsp3HKzrnYY+fOnVq2bJnZr3PnzpKkt99+22H/t956S5LUpUsXSVK7du1UokQJvf/++w79pkyZUoBXAwDAzYcp8QAAIF8bD6Q4jKxfqmzog/rzQIJ+/e9IPWHsVhV7Kb333nuqX7++fv31V0lSo0aN9PDDD2v69Ok6ffq02rZtq40bN+rjjz9Wjx49FBERIUmqVKmSnnrqKU2aNEndu3dXZGSktm7dqiVLlqhChQpMqQcA3LII7AAAIF/J6Vd+B3qpitVVMeoVnfrhA814+3VVDbhNsbGxSkpKMgO7JH3wwQeqUaOGZs2apYULF8rPz09jxoxRdHS0w/HeeOMNlS5dWjNmzNDKlSvVsmVLLV++XKGhoXJ3dy+0awQAwMpshmFcPtOtWEhLS5Pdbldqaqq8vb2LuhwAAG46638/qftnbLhmv8+GtFDLoPIFfv7Tp0+rXLlyGjdunF544YUCPz4AAAWtoHMoz7ADAIB8NavuI3+7u640Id0myd/urmbVff7xuc6ePZunLffZ9/Dw8H98fAAAbkZMiQcAAPlydbEpuluwHpudIJvksPhcboiP7hYsV5d//oz5F198oVmzZqlz587y9PTU2rVr9dlnn6lDhw5q3br1Pz4+AAA3IwI7AAC4osgQf73f7w6H97BLkp/dXdHdghUZ4l8g52nYsKFKlCihN998U2lpaeZCdOPGjSuQ4wMAcDPiGXYAAHBN2TmGNh5IUXJ6pip6XZwGXxAj6wAAFCcFnUMZYQcAANfk6mIrlIXlAADAlbHoHAAAAAAAFkRgBwAAAADAggjsAAAAAABYEIEdAAAAAAALIrADAAAAAGBBBHYAAAAAACyIwA4AAAAAgAUR2AEAAAAAsCACOwAAAAAAFkRgBwAAAADAggjsAAAAAABYEIEdAAAAAAALIrADAAAAAGBBJYq6gMJiGIYkKS0trYgrAQAAAADcCnLzZ24e/aeKbWBPT0+XJAUEBBRxJQAAAACAW0l6errsdvs/Po7NKKjobzE5OTk6evSovLy8ZLPZiroc3CTS0tIUEBCgQ4cOydvbu6jLwS2MexFWwv0IK+F+hJVwP+JyhmEoPT1dlStXlovLP38CvdiOsLu4uOi2224r6jJwk/L29uaHLiyBexFWwv0IK+F+hJVwP+JSBTGynotF5wAAAAAAsCACOwAAAAAAFkRgBy7h5uam6Ohoubm5FXUpuMVxL8JKuB9hJdyPsBLuRxS2YrvoHAAAAAAANzNG2AEAAAAAsCACOwAAAAAAFkRgBwAAAADAggjsAAAAAABYEIEdAAAAAAALIrADklatWqWBAweqdu3aKl26tGrUqKHBgwcrKSkp3/7r1q1TaGioSpcuLT8/Pz355JPKyMhwctUorpKSkvT8888rIiJCXl5estlsWr169RX7cz+isGRlZWn06NGqXLmyPDw81Lx5c61YsaKoy0Ixl5GRoejoaEVGRsrHx0c2m02zZs3Kt+/OnTsVGRkpT09P+fj46KGHHtLx48edWzCKrU2bNmnEiBGqX7++ypQpo6pVqyoqKkp79uzJ05d7EYWF17oBkpo0aaKUlBT16dNHtWrV0v79+zVlyhSVLl1aW7ZskZ+fn9l3y5YtatmyperVq6ehQ4fq8OHDmjhxoiIiIrRkyZIivAoUF6tXr1ZERIRq1aqlChUqaP369YqLi1N4eHievtyPKEz333+/FixYoJEjR6pWrVqaNWuWNm3apLi4OIWGhhZ1eSimEhMTVb16dVWtWlU1atTQ6tWrNXPmTA0YMMCh3+HDh3X77bfLbrebf6icOHGiqlatqo0bN6pUqVJFcwEoNnr37q2ffvpJffr0UcOGDfXnn39qypQpysjI0IYNGxQSEiKJexGFzABg/Pjjj0Z2dnaeNknGCy+84NDeqVMnw9/f30hNTTXbZsyYYUgyli1b5pR6UbylpaUZJ0+eNAzDMObPn29IMuLi4vLty/2IwvLzzz8bkowJEyaYbWfPnjWCgoKMli1bFmFlKO4yMzONpKQkwzAMY9OmTYYkY+bMmXn6PfbYY4aHh4dx8OBBs23FihWGJGPatGnOKhfF2E8//WRkZWU5tO3Zs8dwc3MzHnzwQbONexGFiSnxgKQ2bdrIxcUlT5uPj4927txptqWlpWnFihXq16+fvL29zfb+/fvL09NT8+bNc1rNKL68vLzk4+NzzX7cjyhMCxYskKurq4YOHWq2ubu7a9CgQVq/fr0OHTpUhNWhOHNzc3OY2XYlX375pbp27aqqVauabe3bt1ft2rX5+YcC0apVqzyj47Vq1VL9+vUdfj/kXkRhIrADV5CRkaGMjAxVqFDBbNu2bZsuXLigJk2aOPQtVaqUGjdurM2bNzu7TNzCuB9RmDZv3qzatWs7/DFIkpo1aybp4uMYQFE5cuSIkpOT8/z8ky7eo/z8Q2ExDEPHjh0zfz/kXkRhI7ADV/D222/r3Llz6tu3r9mWuwidv79/nv7+/v46evSo0+oDuB9RmJKSkq54b0ni/kKRutbPv5SUFGVlZTm7LNwC5syZoyNHjpi/H3IvorCVKOoCgIKWk5Ojc+fOXVdfNzc32Wy2PO1r1qxRbGysoqKidNddd5ntZ8+eNfe7nLu7u7kdyFUQ9+OVcD+iMJ09e/aK91budqCoXOvnX26f/LYDf9euXbv0+OOPq2XLlnr44YclcS+i8DHCjmJnzZo18vDwuK6v3bt359l/165d6tmzp0JCQvTBBx84bPPw8JCkfP9SmpmZaW4Hcv3T+/FquB9RmDw8PK54b+VuB4rKtX7+XdoHKAh//vmnunTpIrvdbq7xIXEvovAxwo5ip27dupo5c+Z19b18+tKhQ4fUoUMH2e12LV68WF5eXvn2z+/97ElJSapcufLfrBrF1T+5H6+3P/cjCoO/v7+OHDmSpz33fuP+QlG61s8/Hx8fRjRRYFJTU9WpUyedPn1a8fHxDj//uBdR2AjsKHb8/PzyvKv1epw8eVIdOnRQVlaWVq1alW94CgkJUYkSJfTLL78oKirKbD937py2bNni0AZIf/9+vB7cjyhMjRs3VlxcnNLS0hwWnvv555/N7UBRqVKlinx9ffXLL7/k2bZx40buTxSYzMxMdevWTXv27NHKlSsVHBzssJ17EYWNKfGApDNnzqhz5846cuSIFi9erFq1auXbz263q3379po9e7bS09PN9k8//VQZGRnq06ePs0oGuB9RqHr37q3s7GxNnz7dbMvKytLMmTPVvHlzBQQEFGF1gNSrVy999913Dq8YXLVqlfbs2cPPPxSI7Oxs9e3bV+vXr9f8+fPVsmXLfPtxL6Iw2QzDMIq6CKCo9ejRQ998840GDhyoiIgIh22enp7q0aOH+TkhIUGtWrVScHCwhg4dqsOHD2vSpElq06aNli1b5uTKUVyNGzdOkvTbb7/p888/18CBA1W9enVJ0osvvmj2435EYYqKitLChQv19NNPq2bNmvr444+1ceNGrVq1Sm3atCnq8lCMTZkyRadPn9bRo0f1/vvv695779Xtt98uSXriiSdkt9t16NAh3X777SpbtqyeeuopZWRkaMKECbrtttu0adMmpiHjHxs5cqTeeecddevWLd9Za/369ZMk7kUUKgI7ICkwMFAHDx7Md1u1atWUmJjo0LZ27VqNHj1aCQkJ8vLyUlRUlMaPH5/nmXfg77raavGX/9jmfkRhyczM1EsvvaTZs2fr1KlTatiwof7973+rY8eORV0airmr/f/ygQMHFBgYKOniHzWfeeYZrV27VqVKlVKXLl00adIkVapUyYnVorgKDw/Xjz/+eMXtl/7/MfciCguBHQAAAAAAC+IZdgAAAAAALIjADgAAAACABRHYAQAAAACwIAI7AAAAAAAWRGAHAAAAAMCCCOwAAAAAAFgQgR0AAAAAAAsisAMAAAAAYEEEdgAAAAAALIjADgAAAACABRHYAQAAAACwIAI7AAAAAAAW9P8A2Ms2mRKnYIoAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "W1 = 1\n", "W2 = 10\n", "embedding2 = embedding * W1 + pos_encoding[:, :, :] * W2\n", "\n", "# Visualizing the embeddings\n", "plot_words(embedding2, sequences, 0)\n", "plot_words(embedding2, sequences, 1)\n", "\n", "# For reference\n", "#['king queen man woman dog wolf football basketball red green yellow',\n", "# 'man queen yellow basketball green dog woman football king red wolf']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Effect:**\n", "- The embeddings now emphasize positional information, resulting in a circular or spiral-like arrangement of words.\n", "- This effect arises because the positional encoding vectors dominate, overshadowing semantic similarities." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Case 2: Semantic Embedding Dominates ($W_1 = 10, W_2 = 1$)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "W1 = 10\n", "W2 = 1\n", "embedding2 = embedding * W1 + pos_encoding[:, :, :] * W2\n", "\n", "# Visualizing the embeddings\n", "plot_words(embedding2, sequences, 0)\n", "plot_words(embedding2, sequences, 1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Effect:**\n", "- The visualization closely resembles the original semantic embeddings.\n", "- Positional information has a minor influence, with only subtle shifts in the word positions." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Case 3: Balanced Weights ($W_1 = \\sqrt{\\text{EMBEDDING\\_DIM}}, W_2 = 1$)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "W1 = np.sqrt(EMBEDDING_DIM)\n", "W2 = 1\n", "embedding2 = embedding * W1 + pos_encoding[:, :, :] * W2\n", "\n", "# Visualizing the embeddings\n", "plot_words(embedding2, sequences, 0)\n", "plot_words(embedding2, sequences, 1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Effect:**\n", "- This setting mirrors the weighting approach used in the Transformer architecture $semantic\\_embedding * \\sqrt{d}$\n", "- The plot shows a balance between semantic clustering and positional shifts, maintaining meaningful word relationships while encoding positional context.\n", "\n", "\n", "\n", "### 5.1.3. Summary\n", "\n", "1. **Equal Weights ($W_1 = W_2$):** Positional encoding introduces noticeable changes, particularly in reordered sentences.\n", "2. **Dominant Positional Encoding ($W_2 \\gg W_1$):** Results in a layout that heavily reflects positional relationships, often at the cost of semantic similarity.\n", "3. **Dominant Semantic Embedding ($W_1 \\gg W_2$):** Closely resembles the original semantic embedding with minimal positional effects.\n", "4. **Balanced Weights ($W_1 = \\sqrt{d}, W_2 = 1$):** Achieves a balance, aligning with Transformer design principles.\n", "\n", "These experiments illustrate how relative weighting of semantic and positional embeddings affects word representation, showcasing the power of positional encoding in capturing sequential information within the Transformer architecture." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "

\n", "
6. Conclusion
\n", "

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "🎉 Congratulations! 🎉\n", "\n", "We've successfully completed this notebook, delving into the inputs of the Transformer network and exploring how positional encodings interact with word embeddings.\n", "\n", "## **Conclusion**\n", "\n", "This notebook has provided a comprehensive exploration of positional encodings and their role in Transformer architectures. By visualizing and analyzing their properties, we've observed how they encode relational information and influence word embeddings. This understanding is critical for appreciating how Transformers achieve state-of-the-art performance in natural language processing tasks.\n", "\n", "Positional encodings serve as a cornerstone for enabling sequential information flow through models, ensuring that context is preserved alongside semantic meaning. With the ability to control their weight, they offer flexibility in designing Transformer-based solutions for diverse applications.\n", "\n", "## **Key Takeaways:**\n", "\n", "1. **Positional Encodings:**\n", " - Capture relative positions of words in a sequence.\n", " - Exhibit unique relational properties:\n", " - The norm of each vector remains constant.\n", " - Differences between vectors depend on relative positions, not absolute ones.\n", "\n", "2. **Visualizations:**\n", " - Correlation and Euclidean distance matrices reveal how positional encodings maintain relational properties.\n", " - Cartesian plots highlight the interplay between word embeddings and positional encodings.\n", "\n", "3. **Semantic and Positional Embeddings:**\n", " - Combining GloVe embeddings with positional encodings demonstrates their influence on semantic clustering.\n", " - Adjusting weights between embeddings and positional encodings shows the flexibility of maintaining semantic meaning or emphasizing positional context." ] } ], "metadata": { "accelerator": "GPU", "colab": { "collapsed_sections": [], "name": "Transformer Assignment - Subclass.ipynb", "provenance": [] }, "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": "3.11.10" } }, "nbformat": 4, "nbformat_minor": 1 }