{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Positional Encoding\n",
    "\n",
    "Transformers, unlike RNNs, do not process tokens sequentially. \n",
    "They operate on the entire sequence simultaneously, so they lack inherent information \n",
    "about the order of tokens. Positional encoding injects this information into the input embeddings.\n",
    "\n",
    "\n",
    "## Absolute Positional Encoding\n",
    "\n",
    "The original transformer model introduces a sinusoidal positional encoding:\n",
    "\n",
    "* Alternates between sine and cosine functions for even and odd dimensions.\n",
    "* Encodes each position as a vector:\n",
    "\n",
    "$$\n",
    "   PE_{\\text{pos}, 2i} = \\sin\\left(\\frac{\\text{pos}}{10000^{\\frac{2i}{d}}}\\right), \\quad\n",
    "   PE_{\\text{pos}, 2i+1} = \\cos\\left(\\frac{\\text{pos}}{10000^{\\frac{2i}{d}}}\\right)\n",
    "$$ \n",
    "   \n",
    "     Where $pos$ is the position and $i$ is the dimension index.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import jax.numpy as jnp\n",
    "from flax import nnx\n",
    "import pytest\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_positional_encoding(d_model: int, max_seq_len: int = 512) -> jnp.ndarray:\n",
    "    \"\"\"\n",
    "    Computes the positional encoding for a given sequence length and embedding dimension.\n",
    "    \n",
    "    Args:\n",
    "        d_model (int): The dimension of the model (embedding size).\n",
    "        max_seq_len (int): The maximum sequence length for which positional encodings\n",
    "                           are computed.\n",
    "    \n",
    "    Returns:\n",
    "        jnp.ndarray: The computed positional encodings of shape (1, max_seq_len, d_model).\n",
    "    \"\"\"\n",
    "    # Initialize positional encoding array\n",
    "    pe = jnp.zeros((max_seq_len, d_model))\n",
    "    \n",
    "    # Create position indices for the sequence\n",
    "    position = jnp.arange(0, max_seq_len, dtype=jnp.float32)[:, jnp.newaxis]\n",
    "    \n",
    "    # Calculate the division term for the sine and cosine functions\n",
    "    div_term = jnp.exp(jnp.arange(0, d_model, 2) * (jnp.log(10000.0) / d_model))  # exp(log(x)) = x\n",
    "    \n",
    "    # Apply the sine and cosine functions to even and odd indices\n",
    "    pe = pe.at[:, 0::2].set(jnp.sin(position / div_term))\n",
    "    pe = pe.at[:, 1::2].set(jnp.cos(position / div_term))\n",
    "    \n",
    "    # Expand the positional encoding to have a batch dimension\n",
    "    pe = jnp.expand_dims(pe, axis=0)\n",
    "    \n",
    "    return pe\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First few values of the positional encoding: (Array(0., dtype=float32), Array(0.84147096, dtype=float32), Array(0.9092974, dtype=float32))\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 1500x1000 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1. Testing the function\n",
    "def test_positional_encoding():\n",
    "    # Test case 1: Check the shape of the returned positional encoding\n",
    "    d_model = 64\n",
    "    max_seq_len = 100\n",
    "    pe = compute_positional_encoding(d_model, max_seq_len)\n",
    "    assert pe.shape == (1, max_seq_len, d_model), f\"Expected shape (1, {max_seq_len}, {d_model}), but got {pe.shape}\"\n",
    "\n",
    "    # Test case 2: Check the first few values of the positional encoding\n",
    "    expected_values = pe[0, 0, 0], pe[0, 1, 0], pe[0, 2, 0]\n",
    "    print(f\"First few values of the positional encoding: {expected_values}\")\n",
    "\n",
    "test_positional_encoding()\n",
    "\n",
    "# 2. Plotting the Positional Encodings\n",
    "def plot_positional_encoding(pe: jnp.ndarray, max_seq_len: int, d_model: int):\n",
    "    # Convert JAX array to numpy array for plotting\n",
    "    pe = jnp.array(pe)\n",
    "\n",
    "    # Set the seaborn style for the plot\n",
    "    sns.set(style=\"whitegrid\", palette=\"muted\")\n",
    "\n",
    "    plt.figure(figsize=(15, 10))\n",
    "    \n",
    "    # Use seaborn's heatmap for a better-looking plot\n",
    "    ax = sns.heatmap(pe[0], cmap='coolwarm', cbar_kws={'label': 'Encoding Value'}, \n",
    "                     xticklabels=False, yticklabels=True, square=False, linewidths=0.5, linecolor='gray')\n",
    "    \n",
    "    # Set plot title and labels\n",
    "    ax.set_title('Positional Encoding Heatmap', fontsize=20)\n",
    "    ax.set_xlabel('Embedding Dimension', fontsize=14)\n",
    "    ax.set_ylabel('Sequence Position', fontsize=14)\n",
    "    \n",
    "    # Rotate y-axis labels and improve layout\n",
    "    plt.xticks(rotation=90)\n",
    "    plt.tight_layout()\n",
    "    \n",
    "    plt.show()\n",
    "\n",
    "# Compute positional encoding and plot it\n",
    "d_model = 64\n",
    "max_seq_len = 50\n",
    "pe = compute_positional_encoding(d_model, max_seq_len)\n",
    "plot_positional_encoding(pe, max_seq_len, d_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Relative Positional Encoding\n",
    "Relative positional encoding replaces absolute positions with the distance between tokens:\n",
    "\n",
    "* More expressive for certain tasks (e.g., dependency parsing).\n",
    "* Commonly used in models like T5, ALiBi, and DeBERTa."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_relative_positional_encoding(max_seq_len: int) -> jnp.ndarray:\n",
    "    \"\"\"\n",
    "    Computes the relative positional encoding for a sequence of given length.\n",
    "\n",
    "    Args:\n",
    "        max_seq_len (int): The maximum sequence length.\n",
    "\n",
    "    Returns:\n",
    "        jnp.ndarray: A 2D array of shape (max_seq_len, max_seq_len) representing\n",
    "                     the relative positional encoding.\n",
    "    \"\"\"\n",
    "    # Create the positional indices\n",
    "    pe = jnp.arange(max_seq_len)\n",
    "    \n",
    "    # Compute the relative positional encoding (RPE)\n",
    "    rpe = pe - pe[:, jnp.newaxis]  # Shape: (max_seq_len, max_seq_len)\n",
    "    \n",
    "    # Offset the RPE to ensure non-negative values\n",
    "    rpe += max_seq_len\n",
    "    \n",
    "    return rpe\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1200x1000 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Improved plotting function for relative positional encoding\n",
    "def plot_relative_positional_encoding(rpe: jnp.ndarray, max_seq_len: int):\n",
    "    rpe = jnp.array(rpe)\n",
    "\n",
    "    # Set the seaborn style for the plot\n",
    "    sns.set_theme(style=\"whitegrid\", palette=\"muted\")\n",
    "\n",
    "    plt.figure(figsize=(12, 10))\n",
    "    \n",
    "    # Use seaborn's heatmap for a better-looking plot\n",
    "    ax = sns.heatmap(rpe, cmap='coolwarm', cbar_kws={'label': 'Relative Distance'}, \n",
    "                     xticklabels=False, yticklabels=False, square=True, linewidths=0.5, linecolor='gray')\n",
    "    \n",
    "    # Set plot title and labels\n",
    "    ax.set_title('Relative Positional Encoding Heatmap', fontsize=20)\n",
    "    ax.set_xlabel('Position', fontsize=14)\n",
    "    ax.set_ylabel('Position', fontsize=14)\n",
    "    \n",
    "    # Improve layout\n",
    "    plt.xticks(rotation=90)\n",
    "    plt.tight_layout()\n",
    "    \n",
    "    plt.show()\n",
    "\n",
    "# Compute relative positional encoding and plot it\n",
    "max_seq_len = 50\n",
    "rpe = compute_relative_positional_encoding(max_seq_len)\n",
    "plot_relative_positional_encoding(rpe, max_seq_len)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "venv",
   "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": "3.10.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}