paper_note/lynx/end_to_end_fsdp.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.rcParams[\"font.family\"] = \"Times New Roman\"\n",
    "plt.rcParams[\"font.size\"] = 16\n",
    "\n",
    "g_label_fontsize = 16\n",
    "\n",
    "colors = [\n",
    "    \"#455D7A\",\n",
    "    \"#233142\",\n",
    "    \"#F95959\",\n",
    "]\n",
    "\n",
    "edgecolors = [\n",
    "    \"#FFFFFF\",\n",
    "    \"#FFFFFF\",\n",
    "    \"#FFFFFF\",\n",
    "]\n",
    "\n",
    "hatches = [\"\", \"\", \"\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 2100x2333.33 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(\n",
    "    figsize=(7, 14 / 1.8), ncols=1, nrows=3, constrained_layout=True, dpi=300\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [],
   "source": [
    "labels_name = [\n",
    "    \"ModelA\\n8GPUs\",\n",
    "    \"ModelA\\n16GPUs\",\n",
    "    \"ModelB\\n8GPUs\",\n",
    "    \"ModelB\\n16GPUs\",\n",
    "    \"ModelC\\n8GPUs\",\n",
    "    \"ModelC\\n16GPUs\",\n",
    "    \"ModelD\\n8GPUs\",\n",
    "    \"ModelD\\n16GPUs\",\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [],
   "source": [
    "# MFU\n",
    "data_a = {\n",
    "    labels_name[0]: [53, 53, 65],  # 22.64\n",
    "    labels_name[1]: [53, 53, 65],  # 22.64\n",
    "    labels_name[2]: [35, 35, 48],  # 37\n",
    "    labels_name[3]: [35, 35, 48],  # 37\n",
    "    labels_name[4]: [53, 53, 65],  # 22.64\n",
    "    labels_name[5]: [53, 53, 65],  # 22.64\n",
    "    labels_name[6]: [53, 53, 65],  # 22.64\n",
    "    labels_name[7]: [53, 53, 65],  # 22.64\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [],
   "source": [
    "# overlapping rate\n",
    "data_b = {\n",
    "    labels_name[0]: [54, 62, 12],\n",
    "    labels_name[1]: [54, 62, 12],\n",
    "    labels_name[2]: [52, 62, 12],\n",
    "    labels_name[3]: [52, 62, 12],\n",
    "    labels_name[4]: [52, 62, 12],\n",
    "    labels_name[5]: [52, 62, 12],\n",
    "    labels_name[6]: [53, 62, 12],\n",
    "    labels_name[7]: [52, 62, 12],\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [],
   "source": [
    "# communication baseline\n",
    "data_c = {\n",
    "    labels_name[0]: 70,\n",
    "    labels_name[1]: 70,\n",
    "    labels_name[2]: 70,\n",
    "    labels_name[3]: 70,\n",
    "    labels_name[4]: 70,\n",
    "    labels_name[5]: 70,\n",
    "    labels_name[6]: 70,\n",
    "    labels_name[7]: 70,\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_d = {\n",
    "    labels_name[0]: [124, 124, 128],  # 22.64\n",
    "    labels_name[1]: [124, 124, 128],  # 22.64\n",
    "    labels_name[2]: [124, 124, 128],  # 37\n",
    "    labels_name[3]: [124, 124, 128],  # 37\n",
    "    labels_name[4]: [124, 124, 128],  # 22.64\n",
    "    labels_name[5]: [124, 124, 128],  # 22.64\n",
    "    labels_name[6]: [124, 124, 128],  # 22.64\n",
    "    labels_name[7]: [124, 124, 128],  # 22.64\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [],
   "source": [
    "legend_labels = [\"FSDP\", \"XLA\", \"DLRover-Lynx\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [],
   "source": [
    "bar_width = 0.2\n",
    "group_spaing = 0.15\n",
    "\n",
    "group_positions = {}\n",
    "current_pos = 0\n",
    "\n",
    "for x_label, y_data in data_a.items():\n",
    "    group_positions[x_label] = []\n",
    "    for i in range(len(y_data)):\n",
    "        group_positions[x_label].append(current_pos)\n",
    "        current_pos += bar_width\n",
    "    current_pos += group_spaing\n",
    "\n",
    "group_centers = {}\n",
    "for x_label, positions in group_positions.items():\n",
    "    group_centers[x_label] = sum(positions) / len(positions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '(a)')"
      ]
     },
     "execution_count": 160,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "label_set = set()\n",
    "for x_label, y_data in data_a.items():\n",
    "    positions = group_positions[x_label]\n",
    "    for i, (pos, value, color, edgecolor, hatch, label) in enumerate(\n",
    "        zip(\n",
    "            positions,\n",
    "            y_data,\n",
    "            colors,\n",
    "            edgecolors,\n",
    "            hatches,\n",
    "            legend_labels,\n",
    "        )\n",
    "    ):\n",
    "        if label in label_set:\n",
    "            local_label = None\n",
    "        else:\n",
    "            local_label = label\n",
    "            label_set.add(local_label)\n",
    "        ax[0].bar(\n",
    "            pos,\n",
    "            value,\n",
    "            width=bar_width,\n",
    "            color=color,\n",
    "            label=local_label,\n",
    "            hatch=hatch,\n",
    "            edgecolor=edgecolor,\n",
    "        )\n",
    "\n",
    "ax[0].set_xticks(list(group_centers.values()))\n",
    "ax[0].set_xticklabels(list(data_a.keys()))\n",
    "\n",
    "ax[0].set_ylim(0, 100)\n",
    "ax[0].set_yticks([0, 50, 100])\n",
    "ax[0].set_yticklabels([\"0\", \"50\", \"100\"], rotation=90, ha=\"center\", va=\"center\")\n",
    "\n",
    "ax[0].tick_params(axis=\"x\", bottom=False, labelsize=11, pad=1)\n",
    "ax[0].tick_params(axis=\"y\", left=True, labelsize=g_label_fontsize, pad=5)\n",
    "\n",
    "ax[0].set_ylabel(\"MFU (%)\", fontsize=g_label_fontsize)\n",
    "ax[0].set_title(\"(a)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '(b)')"
      ]
     },
     "execution_count": 161,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "label_set = set()\n",
    "total_label = \"Total Communication Ratio\"\n",
    "\n",
    "for x_label, y_data in data_b.items():\n",
    "    positions = group_positions[x_label]\n",
    "    for i, (pos, value, diff_value, color, edgecolor, label, hatch) in enumerate(\n",
    "        zip(\n",
    "            positions,\n",
    "            y_data,\n",
    "            list(data_c.values()),\n",
    "            colors,\n",
    "            edgecolors,\n",
    "            legend_labels,\n",
    "            hatches,\n",
    "        )\n",
    "    ):\n",
    "        if label in label_set:\n",
    "            local_label = None\n",
    "        else:\n",
    "            local_label = label\n",
    "            label_set.add(local_label)\n",
    "\n",
    "        ax[1].bar(\n",
    "            pos,\n",
    "            value,\n",
    "            width=bar_width,\n",
    "            color=color,\n",
    "            edgecolor=edgecolor,\n",
    "            hatch=hatch,\n",
    "            #label=local_label,\n",
    "        )\n",
    "\n",
    "        ax[1].bar(\n",
    "            pos,\n",
    "            diff_value - value,\n",
    "            bottom=value,\n",
    "            color=\"#E3E3E3\",\n",
    "            edgecolor=edgecolor,\n",
    "            width=bar_width,\n",
    "            label=total_label,\n",
    "        )\n",
    "        if total_label is not None:\n",
    "            total_label = None\n",
    "\n",
    "ax[1].set_xticks(list(group_centers.values()))\n",
    "ax[1].set_xticklabels(list(data_a.keys()))\n",
    "\n",
    "ax[1].set_ylim(0, 100)\n",
    "ax[1].set_yticks([0, 50, 100])\n",
    "ax[1].set_yticklabels([\"0\", \"50\", \"100\"], rotation=90, ha=\"center\", va=\"center\")\n",
    "\n",
    "ax[1].tick_params(axis=\"x\", bottom=False, labelsize=11, pad=1)\n",
    "ax[1].tick_params(axis=\"y\", left=True, labelsize=g_label_fontsize, pad=5)\n",
    "\n",
    "ax[1].set_ylabel(\"Overlapping Ratio (%)\", fontsize=g_label_fontsize)\n",
    "ax[1].set_title(\"(b)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '(c)')"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for x_label, y_data in data_d.items():\n",
    "    positions = group_positions[x_label]\n",
    "    for i, (pos, value, color, edgecolor, hatch) in enumerate(\n",
    "        zip(\n",
    "            positions,\n",
    "            y_data,\n",
    "            colors,\n",
    "            edgecolors,\n",
    "            hatches,\n",
    "        )\n",
    "    ):\n",
    "        ax[2].bar(\n",
    "            pos,\n",
    "            value,\n",
    "            width=bar_width,\n",
    "            color=color,\n",
    "            edgecolor=edgecolor,\n",
    "            hatch=hatch,\n",
    "            label=local_label,\n",
    "        )\n",
    "\n",
    "\n",
    "ax[2].set_xticks(list(group_centers.values()))\n",
    "ax[2].set_xticklabels(list(data_a.keys()))\n",
    "\n",
    "ax[2].set_ylim(0, 150)\n",
    "ax[2].set_yticks([0, 50, 100])\n",
    "ax[2].set_yticklabels([\"0\", \"50\", \"100\"], rotation=90, ha=\"center\", va=\"center\")\n",
    "\n",
    "ax[2].tick_params(axis=\"x\", bottom=False, labelsize=11, pad=1)\n",
    "ax[2].tick_params(axis=\"y\", left=True, labelsize=g_label_fontsize, pad=5)\n",
    "\n",
    "ax[2].set_ylabel(\"Throughput (tokens/s)\", fontsize=g_label_fontsize)\n",
    "ax[2].set_title(\"(c)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f5a4eb7b410>"
      ]
     },
     "execution_count": 163,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ax[0].legend(\n",
    "    ncol=3,\n",
    "    loc=\"upper center\",\n",
    "    frameon=False,\n",
    "    shadow=False,\n",
    "    fontsize=g_label_fontsize,\n",
    ")\n",
    "\n",
    "ax[1].legend(\n",
    "    ncol=1,\n",
    "    loc=\"upper center\",\n",
    "    frameon=False,\n",
    "    shadow=False,\n",
    "    fontsize=g_label_fontsize,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 2100x2333.33 with 3 Axes>"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig.savefig(\"end_to_end_fsdp.pdf\", bbox_inches=\"tight\", dpi=1000)\n",
    "fig"
   ]
  }
 ],
 "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": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}