notebooks/generative-ai/large-language-modelling/layer_and_rms_normalization.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "12c05039-1d88-4e0b-b091-722423a8ca0a",
   "metadata": {},
   "source": [
    "### 1. Why Layer Normalization?\n",
    "- **Purpose**: Stabilizes the training of deep neural networks by regularizing neuron dynamics within one layer (across features) via mean and variance statistics.\n",
    "- **Application**: Normalizes activations **per sample/token**, not across the batch.\n",
    "- **Use Case**: Works well for sequential data like transformers.\n",
    "\n",
    "### 2. Math: Layer Normalization\n",
    "Given input **X** ($n \\times d$), where:\n",
    "- $n$ = context length (number of tokens)\n",
    "- $d$ = embedding dimension\n",
    "1. **Mean** per token:\n",
    " $$\n",
    "\\mu_i = \\frac{1}{d} \\sum_{j=1}^{d} X_{ij} \\quad (\\mu \\in \\mathbb{R}^{n \\times 1})\n",
    "$$\n",
    "2. **Variance** per token:\n",
    " $$\n",
    "\\sigma^2_i = \\frac{1}{d} \\sum_{j=1}^{d} (X_{ij} - \\mu_i)^2 \\quad (\\sigma^2 \\in \\mathbb{R}^{n \\times 1})\n",
    "$$\n",
    "3. **Normalize**:\n",
    " $$\n",
    "\\hat{X}_{ij} = \\frac{X_{ij} - \\mu_i}{\\sqrt{\\sigma_i^2 + \\epsilon}} \\quad (\\hat{X} \\in \\mathbb{R}^{n \\times d})\n",
    "$$\n",
    "4. **Scale and Shift**:\n",
    " $$\n",
    "Y_{ij} = \\gamma_j \\hat{X}_{ij} + \\beta_j \\quad (Y \\in \\mathbb{R}^{n \\times d})\n",
    "$$\n",
    "- $\\gamma, \\beta \\in \\mathbb{R}^{d \\times 1}$\n",
    "---\n",
    "\n",
    "### 3. Can We Avoid Calculating the Mean? Why RMS Normalization?\n",
    "- **RMS Normalization**: Avoids the mean computation, uses RMS (because variance calculation needs mean) to simplify computations. Mean normalization has little impact on the success of LayerNorm.\n",
    "- **Use Case**: 7% to 64% reduced running term against LayerNorm.\n",
    "\n",
    "### 4. Math: RMS Normalization\n",
    "Given input **X** ($n \\times d$):\n",
    "1. **RMS** per token:\n",
    " $$\n",
    "\\text{RMS}_i = \\sqrt{\\frac{1}{d} \\sum_{j=1}^{d} (X_{ij})^2} \\quad (\\text{RMS} \\in \\mathbb{R}^{n \\times 1})\n",
    "$$\n",
    "2. **Normalize**:\n",
    " $$\n",
    "\\hat{X}_{ij} = \\frac{X_{ij}}{\\text{RMS}_i} \\quad (\\hat{X} \\in \\mathbb{R}^{n \\times d})\n",
    "$$\n",
    "3. **Scale**:\n",
    " $$\n",
    "Y_{ij} = \\gamma_j \\hat{X}_{ij} \\quad (Y \\in \\mathbb{R}^{n \\times d})\n",
    "$$\n",
    "- $\\gamma \\in \\mathbb{R}^{d \\times 1}$\n",
    "Reference: Zhang, B., & Sennrich, R. (2019). Root mean square layer normalization. Advances in Neural Information Processing Systems, 32."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0038e78c-8654-41be-b55c-7d9389168ac6",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "plt.style.use('dark_background')\n",
    "np.random.seed(47)\n",
    "torch.manual_seed(47)\n",
    "\n",
    "batch_size, context_length, embedding_size = 2, 4, 8\n",
    "batch_input = torch.randn(batch_size, context_length, embedding_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "fc9522c9-ad6c-4b63-9ecb-a27cfe002a62",
   "metadata": {},
   "outputs": [],
   "source": [
    "class LayerNorm(nn.Module):\n",
    "    def __init__(self, features, eps=1e-6):\n",
    "        super().__init__()\n",
    "        self.shift_parameters = nn.Parameter(\n",
    "            torch.zeros(features), requires_grad=True\n",
    "        )\n",
    "        self.scale_parameters = nn.Parameter(\n",
    "            torch.ones(features), requires_grad=True\n",
    "        )\n",
    "        self.eps = eps\n",
    "\n",
    "    def forward(self, input_):\n",
    "        mean_vector = input_.mean(axis=-1, keepdim=True)\n",
    "        var_vector = input_.var(axis=-1, keepdim=True)\n",
    "\n",
    "        mean_shifted_scaled_input = (\n",
    "            (input_ - mean_vector) /\n",
    "            torch.sqrt(var_vector + self.eps)\n",
    "        )\n",
    "        \n",
    "        parameterized_mean_shifted_scaled_input = (\n",
    "            mean_shifted_scaled_input * \n",
    "            self.scale_parameters + \n",
    "            self.shift_parameters\n",
    "        )\n",
    "        return parameterized_mean_shifted_scaled_input"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c7413e63-b30e-426f-bbd1-3928362efb2e",
   "metadata": {},
   "outputs": [],
   "source": [
    "class RMSNorm(nn.Module):\n",
    "    def __init__(self, features, eps=1e-5):\n",
    "        super().__init__()\n",
    "        self.scale_parameters = nn.Parameter(\n",
    "            torch.ones(features), \n",
    "            requires_grad=True\n",
    "        )\n",
    "        self.eps = eps\n",
    "\n",
    "    def forward(self, input_):\n",
    "        rms_vector = (\n",
    "            (input_ ** 2).mean(axis=-1, keepdim=True) + self.eps\n",
    "        ).sqrt()\n",
    "        \n",
    "        normalized_input = input_ / rms_vector\n",
    "        scaled_input = (\n",
    "            normalized_input * self.scale_parameters\n",
    "        )\n",
    "\n",
    "        return scaled_input"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2f8c6860-59b4-408a-8a50-30456c0b2636",
   "metadata": {},
   "outputs": [],
   "source": [
    "layer_norm = LayerNorm(features=embedding_size)\n",
    "rms_norm = RMSNorm(features=embedding_size)\n",
    "\n",
    "batch_input_post_layer_norm = layer_norm(batch_input)\n",
    "batch_input_post_rms_norm = rms_norm(batch_input)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "63b34260-a6ad-4754-a304-7118dffc9d8f",
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 3000x1800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "first_token_layer_norm = batch_input_post_layer_norm[0, 0].detach().numpy()\n",
    "first_token_rms_norm = batch_input_post_rms_norm[0, 0].detach().numpy()\n",
    "\n",
    "layer_norm_mean = np.mean(first_token_layer_norm)\n",
    "layer_norm_std = batch_input_post_layer_norm[0][0].std().detach().numpy()\n",
    "rms_norm_mean = np.mean(first_token_rms_norm)\n",
    "rms_norm_std = batch_input_post_rms_norm[0][0].std().detach().numpy()\n",
    "\n",
    "x = np.arange(1, len(first_token_layer_norm) + 1)\n",
    "\n",
    "plt.figure(figsize=(10, 6), dpi=300)\n",
    "\n",
    "plt.plot(x, first_token_layer_norm, 's', label=\"LayerNorm\", markersize=8, color='magenta')\n",
    "plt.plot(x, first_token_rms_norm, 'd', label=\"RMSNorm\", markersize=8, color='teal')\n",
    "\n",
    "# Add horizontal lines for mean and standard deviation\n",
    "plt.axhline(layer_norm_mean, color='magenta', linestyle='--', linewidth=2, alpha=1.0, label=\"LayerNorm Mean\")\n",
    "plt.axhline(layer_norm_mean + layer_norm_std, color='magenta', linestyle=':', linewidth=2, alpha=1.0, label=\"LayerNorm ± Std\")\n",
    "plt.axhline(layer_norm_mean - layer_norm_std, color='magenta', linestyle=':', linewidth=2, alpha=1.0)\n",
    "\n",
    "plt.axhline(rms_norm_mean, color='teal', linestyle='--', linewidth=2, alpha=1.0, label=\"RMSNorm Mean\")\n",
    "plt.axhline(rms_norm_mean + rms_norm_std, color='teal', linestyle=':', linewidth=2, alpha=1.0, label=\"RMSNorm ± Std\")\n",
    "plt.axhline(rms_norm_mean - rms_norm_std, color='teal', linestyle=':', linewidth=2, alpha=1.0)\n",
    "\n",
    "# Add labels and legend\n",
    "plt.title(\"First Token's Embeddings After Layer and RMS Normalization\", fontsize=12)\n",
    "plt.xlabel(\"Embedding Dimension\")\n",
    "plt.ylabel(\"Value\")\n",
    "plt.xticks(x)\n",
    "plt.legend(loc='lower center', bbox_to_anchor=(1.13, 0), title=\"Legend\", borderaxespad=0.)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "07b3ad12-f03e-4b3b-97be-a10c88fe3b7b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 3600x2400 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create a 2x2 subplot grid\n",
    "fig, axes = plt.subplots(2, 2, figsize=(12, 8), dpi=300)\n",
    "\n",
    "# Loop through each token (i.e., token 0, token 1, token 2, etc.)\n",
    "for token_index in range(context_length):\n",
    "    # Extract the token embeddings after LayerNorm and RMSNorm for each token\n",
    "    token_layer_norm = batch_input_post_layer_norm[0, token_index].detach().numpy()\n",
    "    token_rms_norm = batch_input_post_rms_norm[0, token_index].detach().numpy()\n",
    "\n",
    "    # Calculate the mean and standard deviation for each token's embeddings\n",
    "    layer_norm_mean = np.mean(token_layer_norm)\n",
    "    layer_norm_std = batch_input_post_layer_norm[0, token_index].std().detach().numpy()\n",
    "    rms_norm_mean = np.mean(token_rms_norm)\n",
    "    rms_norm_std = batch_input_post_rms_norm[0, token_index].std().detach().numpy()\n",
    "\n",
    "    # Create the x-axis values (embedding dimension)\n",
    "    x = np.arange(1, len(token_layer_norm) + 1)\n",
    "\n",
    "    # Select the appropriate subplot (2x2 grid)\n",
    "    ax = axes[token_index // 2, token_index % 2]\n",
    "\n",
    "    # Define distinct colors for LayerNorm and RMSNorm\n",
    "    layer_norm_color = 'magenta'\n",
    "    rms_norm_color = 'teal'\n",
    "\n",
    "    # Plot the embeddings for LayerNorm and RMSNorm for each token\n",
    "    ax.plot(x, token_layer_norm, 's', label=\"LayerNorm\", markersize=8, color=layer_norm_color)\n",
    "    ax.plot(x, token_rms_norm, 'd', label=\"RMSNorm\", markersize=8, color=rms_norm_color)\n",
    "\n",
    "    # Add horizontal lines for mean and standard deviation\n",
    "    ax.axhline(layer_norm_mean, color=layer_norm_color, linestyle='--', linewidth=2, alpha=0.7, label=\"LayerNorm Mean\")\n",
    "    ax.axhline(layer_norm_mean + layer_norm_std, color=layer_norm_color, linestyle=':', linewidth=2, alpha=0.7, label=\"LayerNorm ± Std\")\n",
    "    ax.axhline(layer_norm_mean - layer_norm_std, color=layer_norm_color, linestyle=':', linewidth=2, alpha=0.7)\n",
    "\n",
    "    ax.axhline(rms_norm_mean, color=rms_norm_color, linestyle='--', linewidth=2, alpha=0.7, label=\"RMSNorm Mean\")\n",
    "    ax.axhline(rms_norm_mean + rms_norm_std, color=rms_norm_color, linestyle=':', linewidth=2, alpha=0.7, label=\"RMSNorm ± Std\")\n",
    "    ax.axhline(rms_norm_mean - rms_norm_std, color=rms_norm_color, linestyle=':', linewidth=2, alpha=0.7)\n",
    "\n",
    "    # Set labels for the axes\n",
    "    ax.set_title(f\"Token {token_index+1} Embeddings After LayerNorm and RMSNorm\", fontsize=12)\n",
    "    ax.set_xlabel(\"Embedding Dimension\")\n",
    "    ax.set_ylabel(\"Value\")\n",
    "\n",
    "    if token_index == context_length - 1:\n",
    "        ax.legend(loc='lower center', bbox_to_anchor=(1.22, -0.0197), fontsize=10)\n",
    "\n",
    "# Adjust layout for better spacing\n",
    "plt.tight_layout()\n",
    "plt.savefig('layer_rms_normalization.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "45e6479e-6dc0-426f-8abf-91fa728203cc",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "genai1",
   "language": "python",
   "name": "genai1"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.16"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}