diff --git a/notebooks/how-to-finetune-paligemma2-on-latex-ocr-dataset.ipynb b/notebooks/how-to-finetune-paligemma2-on-latex-ocr-dataset.ipynb
index 411ca28..f52af00 100644
--- a/notebooks/how-to-finetune-paligemma2-on-latex-ocr-dataset.ipynb
+++ b/notebooks/how-to-finetune-paligemma2-on-latex-ocr-dataset.ipynb
@@ -14,6 +14,7 @@
         "\n",
         "[![GitHub](https://badges.aleen42.com/src/github.svg)](https://github.com/google-research/big_vision/blob/main/big_vision/configs/proj/paligemma/README.md)\n",
         "[![arXiv](https://img.shields.io/badge/arXiv-2412.03555-b31b1b.svg)](https://arxiv.org/abs/2412.03555)\n",
+        "[![Roboflow](https://raw.githubusercontent.com/roboflow-ai/notebooks/main/assets/badges/roboflow-blogpost.svg)](https://blog.roboflow.com/fine-tune-paligemma-2/)\n",
         "\n",
         "PaliGemma 2 is built by combining the SigLIP-So400m vision encoder with the more recent and capable language models from the Gemma 2 family.\n",
         "\n",
@@ -67,20 +68,20 @@
     },
     {
       "cell_type": "code",
-      "execution_count": null,
+      "execution_count": 1,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/"
         },
         "id": "O_8BLW6R_x-z",
-        "outputId": "373534e4-564f-443f-a0c3-f81bd0acb7e8"
+        "outputId": "785d09a8-5ab1-4a59-ed6b-7fdba1f52420"
       },
       "outputs": [
         {
           "output_type": "stream",
           "name": "stdout",
           "text": [
-            "Sun Dec  8 07:15:10 2024       \n",
+            "Wed Dec 11 13:02:13 2024       \n",
             "+---------------------------------------------------------------------------------------+\n",
             "| NVIDIA-SMI 535.104.05             Driver Version: 535.104.05   CUDA Version: 12.2     |\n",
             "|-----------------------------------------+----------------------+----------------------+\n",
@@ -89,7 +90,7 @@
             "|                                         |                      |               MIG M. |\n",
             "|=========================================+======================+======================|\n",
             "|   0  NVIDIA A100-SXM4-40GB          Off | 00000000:00:04.0 Off |                    0 |\n",
-            "| N/A   32C    P0              41W / 400W |      2MiB / 40960MiB |      0%      Default |\n",
+            "| N/A   31C    P0              43W / 400W |      2MiB / 40960MiB |      0%      Default |\n",
             "|                                         |                      |             Disabled |\n",
             "+-----------------------------------------+----------------------+----------------------+\n",
             "                                                                                         \n",
@@ -120,43 +121,92 @@
     },
     {
       "cell_type": "code",
-      "execution_count": null,
+      "source": [
+        "!pip install -q roboflow supervision peft bitsandbytes"
+      ],
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/"
         },
-        "id": "Wtvz4QZ9YuG8",
-        "outputId": "e54cb46b-3a39-42f0-bd0d-7019da14ef7b"
+        "id": "2A-B4zT3_T3Q",
+        "outputId": "f9e9b00f-e34e-429f-bfbf-a64839300874"
       },
+      "execution_count": 2,
       "outputs": [
         {
           "output_type": "stream",
           "name": "stdout",
           "text": [
-            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m43.5/43.5 kB\u001b[0m \u001b[31m3.8 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
-            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m10.1/10.1 MB\u001b[0m \u001b[31m106.0 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
-            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m80.9/80.9 kB\u001b[0m \u001b[31m2.4 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
-            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m66.8/66.8 kB\u001b[0m \u001b[31m3.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
-            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m181.5/181.5 kB\u001b[0m \u001b[31m13.3 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
-            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m69.1/69.1 MB\u001b[0m \u001b[31m25.9 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
-            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m3.0/3.0 MB\u001b[0m \u001b[31m83.4 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[?25l   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m0.0/80.9 kB\u001b[0m \u001b[31m?\u001b[0m eta \u001b[36m-:--:--\u001b[0m\r\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m80.9/80.9 kB\u001b[0m \u001b[31m7.6 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[?25h\u001b[?25l   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m0.0/66.8 kB\u001b[0m \u001b[31m?\u001b[0m eta \u001b[36m-:--:--\u001b[0m\r\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m66.8/66.8 kB\u001b[0m \u001b[31m6.1 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m181.5/181.5 kB\u001b[0m \u001b[31m17.2 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m69.1/69.1 MB\u001b[0m \u001b[31m32.3 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
             "\u001b[?25h"
           ]
         }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "!pip uninstall -y transformers"
       ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "cZEiR39L_XvZ",
+        "outputId": "c6b664bf-77e8-400c-b750-4a794a0282f6"
+      },
+      "execution_count": 3,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "Found existing installation: transformers 4.46.3\n",
+            "Uninstalling transformers-4.46.3:\n",
+            "  Successfully uninstalled transformers-4.46.3\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
       "source": [
-        "!pip install -q roboflow supervision peft bitsandbytes transformers==4.47.0"
+        "!pip install -q git+https://github.com/probicheaux/transformers.git@main"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "Ku_9wFMd_b9Q",
+        "outputId": "ba9433e1-6bb9-410a-9a3a-fd563f64e35d"
+      },
+      "execution_count": 4,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "  Installing build dependencies ... \u001b[?25l\u001b[?25hdone\n",
+            "  Getting requirements to build wheel ... \u001b[?25l\u001b[?25hdone\n",
+            "  Preparing metadata (pyproject.toml) ... \u001b[?25l\u001b[?25hdone\n",
+            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m3.0/3.0 MB\u001b[0m \u001b[31m77.4 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[?25h  Building wheel for transformers (pyproject.toml) ... \u001b[?25l\u001b[?25hdone\n"
+          ]
+        }
       ]
     },
     {
       "cell_type": "code",
-      "execution_count": null,
+      "execution_count": 5,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/"
         },
         "id": "TGDFTYVnY4zn",
-        "outputId": "0dc33426-3a4e-44fe-eb82-efc0c9fbcd56"
+        "outputId": "d11fc59c-091c-4a22-ea92-4cb7cf7f7a8d"
       },
       "outputs": [
         {
@@ -171,7 +221,7 @@
           "output_type": "stream",
           "name": "stderr",
           "text": [
-            "Downloading Dataset Version Zip in unsloth-latex-ocr-1 to jsonl:: 100%|██████████| 44290/44290 [00:03<00:00, 11852.87it/s]"
+            "Downloading Dataset Version Zip in unsloth-latex-ocr-2 to jsonl:: 100%|██████████| 75703/75703 [00:05<00:00, 13110.13it/s]"
           ]
         },
         {
@@ -186,7 +236,7 @@
           "name": "stderr",
           "text": [
             "\n",
-            "Extracting Dataset Version Zip to unsloth-latex-ocr-1 in jsonl:: 100%|██████████| 13981/13981 [00:01<00:00, 9656.00it/s] \n"
+            "Extracting Dataset Version Zip to unsloth-latex-ocr-2 in jsonl:: 100%|██████████| 23947/23947 [00:02<00:00, 10276.47it/s]\n"
           ]
         }
       ],
@@ -198,39 +248,39 @@
         "rf = Roboflow(api_key=ROBOFLOW_API_KEY)\n",
         "\n",
         "project = rf.workspace(\"roboflow-jvuqo\").project(\"unsloth-latex-ocr\")\n",
-        "version = project.version(1)\n",
+        "version = project.version(2)\n",
         "dataset = version.download(\"jsonl\")"
       ]
     },
     {
       "cell_type": "markdown",
-      "source": [
-        "**NOTE:** Let's read the first few lines of the annotation file and examine the dataset format."
-      ],
       "metadata": {
         "id": "CU-Ol8tE61fI"
-      }
+      },
+      "source": [
+        "**NOTE:** Let's read the first few lines of the annotation file and examine the dataset format."
+      ]
     },
     {
       "cell_type": "code",
-      "execution_count": null,
+      "execution_count": 6,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/"
         },
         "id": "WLhSenP5AtQe",
-        "outputId": "33e71721-51e0-4c48-b212-61f1300a2b01"
+        "outputId": "65f47ea2-9534-4997-f873-380f6e6f02bf"
       },
       "outputs": [
         {
           "output_type": "stream",
           "name": "stdout",
           "text": [
-            "{\"image\":\"602d220b909f4973426fefbf6999e4cc_png.rf.acd4eada696860173db01f9716dacb7f.jpg\",\"prefix\":\"read in latex\",\"suffix\":\"\\\\left( \\\\alpha ( P ^ { 2 } + m ^ { 2 } ) + \\\\varepsilon m ( P J - \\\\varepsilon \\\\alpha m ) \\\\right) \\\\Psi = 0 ,\"}\n",
-            "{\"image\":\"880b59a23ee60a1a87fa42d15fd74c22_png.rf.acf3b6961a42e92d466a5b0eecefffcc.jpg\",\"prefix\":\"read in latex\",\"suffix\":\"\\\\vec { d } _ { e } \\\\cdot \\\\vec { d } _ { e } = \\\\vec { d } _ { m } \\\\cdot \\\\vec { d } _ { m } = 8 \\\\frac { 1 + b \\\\chi + \\\\chi ^ { 2 } } { 4 - b ^ { 2 } }\"}\n",
-            "{\"image\":\"c7b26159b532e5a3d3bd60e1dccd975c_png.rf.acdf8492321cdda95f97fa49fdd915c5.jpg\",\"prefix\":\"read in latex\",\"suffix\":\"( g f ) ( x ) \\\\doteq f ( g ^ { - 1 } x ) ,\"}\n",
-            "{\"image\":\"af3f191888dc917814619c1638e01f4a_png.rf.acd914b506089c2658490414f0611b39.jpg\",\"prefix\":\"read in latex\",\"suffix\":\"\\\\mu _ { 0 } = \\\\frac { \\\\pi m _ { V } ^ { 2 } } { 2 e ^ { 2 } } \\\\int _ { 0 } ^ { \\\\infty } d u \\\\frac { e ^ { - u } } { u + \\\\frac { m _ { V } ^ { 2 } } { 2 \\\\Lambda ^ { 2 } } } ,\"}\n",
-            "{\"image\":\"8f3f715794a25ce47756fdbfc99d27a7_png.rf.ad2669ad62643aff48eb6d1e3c30ac91.jpg\",\"prefix\":\"read in latex\",\"suffix\":\"[ L _ { n } , L _ { m } ] = ( n - m ) L _ { n + m } + \\\\frac { d - 2 6 + 2 2 } { 1 2 } ( m ^ { 3 } - m ) \\\\delta _ { n + m , 0 } .\"}\n"
+            "{\"image\":\"0eb741ce399e127abe1d390aa7612979_png.rf.3399c69af6a1019db9095a1ac1327be8.jpg\",\"prefix\":\"read in latex\",\"suffix\":\"L = T _ { 1 0 } \\\\int d ^ { 1 0 } x [ 1 - ( - \\\\mathrm { D e t } ( \\\\eta _ { M N } + F _ { M N } ) ) ^ { { \\\\frac { 1 } { 2 } } } ]\"}\n",
+            "{\"image\":\"2f3e2971f7cae6b0fc28b6ae6a58f3e2_png.rf.339a0574dace8f7a9bfad4083e558997.jpg\",\"prefix\":\"read in latex\",\"suffix\":\"\\\\Gamma ^ { a } : = \\\\gamma ^ { a } - i k ^ { a } \\\\gamma ^ { 3 } , \\\\qquad \\\\Gamma ^ { 3 } : = \\\\gamma ^ { 3 } + i k ^ { a } \\\\gamma _ { a } .\"}\n",
+            "{\"image\":\"193bab6f414f17dbfce0cb14f891edc7_png.rf.33adb0be7b2bea8e03d7fd03420400ec.jpg\",\"prefix\":\"read in latex\",\"suffix\":\"\\\\Gamma [ h ] = \\\\frac { 1 } { 1 2 \\\\pi } t r \\\\int _ { B } d ^ { 3 } y \\\\epsilon _ { i j k } h ^ { - 1 } \\\\partial ^ { i } h h ^ { - 1 } \\\\partial ^ { j } h h ^ { - 1 } \\\\partial ^ { k } h ,\"}\n",
+            "{\"image\":\"317dc5ccc58419fbeea610a84fd3d956_png.rf.33a4d3d873412bdeb07a8c4f6b453765.jpg\",\"prefix\":\"read in latex\",\"suffix\":\"\\\\delta W = { \\\\frac { m } { 2 } } \\\\mathrm { T r } \\\\Phi _ { 3 } ^ { 2 } .\"}\n",
+            "{\"image\":\"e2732e11e0a3e3ae53459a29bb7cdbd2_png.rf.3393a9604c0747703957faa7292e3473.jpg\",\"prefix\":\"read in latex\",\"suffix\":\"N _ { 2 2 } ( x , y , a , b ) = \\\\frac { 1 } { 4 a b } \\\\sum _ { n = 1 } ^ { \\\\infty } \\\\cos ( \\\\frac { 2 n \\\\pi x } { a } ) \\\\int _ { \\\\frac { n \\\\pi } { a } b } ^ { \\\\infty } d q \\\\left( \\\\coth q - 1 \\\\right) \\\\cosh ( \\\\frac { 2 q y } { b } ) .\"}\n"
           ]
         }
       ],
@@ -240,42 +290,60 @@
     },
     {
       "cell_type": "code",
-      "source": [
-        "!wc -l < {dataset.location}/train/annotations.jsonl\n",
-        "!wc -l < {dataset.location}/valid/annotations.jsonl\n",
-        "!wc -l < {dataset.location}/test/annotations.jsonl"
-      ],
+      "execution_count": 7,
       "metadata": {
-        "id": "PLehZP3xWCV8",
-        "outputId": "64aa3aee-8caf-4d3e-9db3-b6845ac985bb",
         "colab": {
           "base_uri": "https://localhost:8080/"
-        }
+        },
+        "id": "PLehZP3xWCV8",
+        "outputId": "531fe319-45b7-446f-e8ee-f022c3fba689"
       },
-      "execution_count": null,
       "outputs": [
         {
           "output_type": "stream",
           "name": "stdout",
           "text": [
-            "9992\n",
+            "19964\n",
             "1992\n",
             "1999\n"
           ]
         }
+      ],
+      "source": [
+        "!wc -l < {dataset.location}/train/annotations.jsonl\n",
+        "!wc -l < {dataset.location}/valid/annotations.jsonl\n",
+        "!wc -l < {dataset.location}/test/annotations.jsonl"
       ]
     },
     {
-      "cell_type": "markdown",
+      "cell_type": "code",
       "source": [
-        "### Set up and test data loaders"
+        "# !head -n 10000 {dataset.location}/train/annotations.jsonl > {dataset.location}/train/annotations.sample.jsonl\n",
+        "# !head -n 1000 {dataset.location}/valid/annotations.jsonl > {dataset.location}/valid/annotations.sample.jsonl\n",
+        "# !head -n 1000 {dataset.location}/test/annotations.jsonl > {dataset.location}/test/annotations.sample.jsonl"
       ],
+      "metadata": {
+        "id": "2Q8_r99-BT7L"
+      },
+      "execution_count": 8,
+      "outputs": []
+    },
+    {
+      "cell_type": "markdown",
       "metadata": {
         "id": "-8I_k2o77WI7"
-      }
+      },
+      "source": [
+        "### Set up and test data loaders"
+      ]
     },
     {
       "cell_type": "code",
+      "execution_count": 9,
+      "metadata": {
+        "id": "R8ceYFDy7W3U"
+      },
+      "outputs": [],
       "source": [
         "import os\n",
         "import json\n",
@@ -309,15 +377,15 @@
         "        image_path = os.path.join(self.image_directory_path, entry['image'])\n",
         "        image = Image.open(image_path)\n",
         "        return image, entry"
-      ],
-      "metadata": {
-        "id": "R8ceYFDy7W3U"
-      },
-      "execution_count": null,
-      "outputs": []
+      ]
     },
     {
       "cell_type": "code",
+      "execution_count": 10,
+      "metadata": {
+        "id": "lR4rf1Uu7bvc"
+      },
+      "outputs": [],
       "source": [
         "train_dataset = JSONLDataset(\n",
         "    jsonl_file_path=f\"{dataset.location}/train/annotations.jsonl\",\n",
@@ -331,112 +399,225 @@
         "    jsonl_file_path=f\"{dataset.location}/test/annotations.jsonl\",\n",
         "    image_directory_path=f\"{dataset.location}/test\",\n",
         ")"
-      ],
-      "metadata": {
-        "id": "lR4rf1Uu7bvc"
-      },
-      "execution_count": null,
-      "outputs": []
+      ]
     },
     {
       "cell_type": "code",
-      "source": [
-        "from tqdm import tqdm\n",
-        "import supervision as sv\n",
-        "\n",
-        "\n",
-        "images = []\n",
-        "for i in range(25):\n",
-        "    image, label = train_dataset[i]\n",
-        "    images.append(image)\n",
-        "\n",
-        "sv.plot_images_grid(images, (5, 5))"
-      ],
+      "execution_count": 11,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
-          "height": 715
+          "height": 675
         },
         "id": "NCznuPbs87H6",
-        "outputId": "bdbca914-d1a1-4136-a32b-dd3d353d398d"
+        "outputId": "9d34f13b-5bed-41a0-9920-0e717750b8e5"
       },
-      "execution_count": null,
       "outputs": [
         {
           "output_type": "display_data",
           "data": {
             "text/plain": [
-              "<Figure size 1200x1200 with 25 Axes>"
+              "<IPython.core.display.HTML object>"
             ],
-            "image/png": 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+              "            <td>Prefix: read in latex<br>Suffix: L = T _ { 1 0 } \\int d ^ { 1 0 } x [ 1 - ( - \\mathrm { D e t } ( \\eta _ { M N } + F _ { M N } ) ) ^ { { \\frac { 1 } { 2 } } } ]</td>\n",
+              "        </tr>\n",
+              "        \n",
+              "        <tr>\n",
+              "            <td><img src=\"data:image/jpeg;base64,/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAAoARgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD2/UNY03SmhXUNQtrQzttiE8oQyH0XPU8jgVQuPF+gW9u0/wDatvMFl8krbt5z+ZgnbtTJyACTxwASeBXOfFNlU+DcsF/4qazPJx/eroNX8JabrVwbp2nt7hshprdgrMpRo2GSD1VsZHPAwRQBr6ffQanp1tf2snmW1zEs0T4I3IwyDg8jgirdZukaXHo2kW+nwSSyRWyBFeZtzED16D8AAB2rlG8QahFYWJtvEFpqG+Is15Z6BcXcUx3sMhoZCq4xgjJOQTxnFAHe0VzPhnVL3UJp0u7rz9igr/xJrmxxz6ysQ30HSs3XbzxXo051Rbm1uLaW5FpDpkcYAAkOyKQyHDFt5UsAMBScZ25IBvHxPpC6/Hov2stfSOYwixsy7whkKFwNobYN2Cc4x6itquUTwVZJq9vqrXl6J4rhroxxuqxtK6BXbGM/NtBxn2HBIOtq17qVmYf7O0r7fuzv/wBJWLZjGPvdc8/lQBq1Ukv7SKd4JLmJZo4vOeMuNyx5xuI67cgjPtVHS9Q1a7nkTUNENhGFysn2pJdxz0wvIrhH8V31qfG11dT2rXdjB5Vp5MQDiQZ+QNgMyBpYgCer78ccUAd9L4g0qHRxqzX8T2DY2TRHeJCTtATbksSeABkk9Km0nVbPW9PS+sJTLbszoHKMhyrFWGGAIwykfhXnPguwOr6bb6Ne6l5B0tI0jsIIEElncW8hRpPM+ZX3EdxyckAY46ePwvqej6Tb6R4d1Y2dv5kkst1dKLiZSTlVRSAuCSck88dyxYAF3xTr9x4dsUvUslntgWM8zzbFhAUlcgAs25sKMDjOTwK09IvjqmjWOoND5JuoI5jFvD7Nyg43Dg4z1Fclptpf+NNMjvNTubrTZ7aaSCFrGRRuKqYpW5DKVZt+3I4ABBya6fTjpmlLa+HbS4iSW1tE8q1aUGUQrhA2M5I4xn1oA1aKKKACqGo6tp2kRxyahf21okjbEaeUIGb0BPU+1X68/wDi8wHhOzyQP+JradTj/lpQBs6l4utYrR5tLks9Q8iZUvClyP8AREYN87hQW6gAADJz7GtHw5q39veHNP1YweQbyBZvL8wPt3DONw61X1Xw5a6tcR3iXNzZ3iMjJc2rqG+TftyGBVh+8fggjmp9O0u28P8AhyLTbGXyILSApHJMd23AJ3MTjPOSen4UAa9FcPda9fwWun/Zdat7oPbK73VtoNzdxznJG5Whfao4+7k/qK0vDOqXuoTTpd3Xn7FBX/iTXNjjn1lYhvoOlAHTVyR8W3MfjSDw9caYsX2iSQRSG4BZolj3CXbjGC2V253DGcYqnrt34s0ac6mtza3FtLci0h0yNAABIdkUhkOGLbypYAYCk4+7k6Vt4Qtodci1WW/vp5Y5nuVgeQeUs7x+WzgY3D5cgLu2jJwM0AdPRXF+PdR1e28N63FaaQ0lt/Z8xN4t4sZT5DkhevHt1rd0e91O7WX+0NJ+wbAvl/6Sk2/rn7o4xx+dAFqXUrKCS4WS8hQ2yLJOrSAGJDnDMOwODyfQ1Wudf0y00u31KS7Q2tyUW3eMFzMX+4ECgls54wOnPSvOH1/UZ/DfjPzZbaXVHlXTbf7PGEcu7GAAEAEqsrSKhbJwhPetLwhbjxHpsMU+rMg08RNaWlvCkb6cyedbuu/5g4IVwD1wNw25GADvdK1Wz1vTINR0+bzrS4TfFJtK7h9CAavVxEnh/XNC0eGx8OarHbWNhbl0N2omkuHBJEbk4VI9oAyvPOeMHdLY+ObCHSbK91uYWk2oKLmG2EbO0MDuqRl9oOMlkGTgbmwOlAHZUVTh1CzuLy5s4buCW5ttvnwpIC8W4ZXco5XI5GetXKACiiigAooooAq3FjaXmz7Vawz7fu+bGGx9MjirCqFUKoAUDAA7U6igAqGC3htYVhgiSKNeiRqFA79BU1FABWfqGmw6jLYvOXxZ3AuUAIwzhWUbvYbs9uQK0KKACiiigArPfR9Nd53bT7Um4dJJiYVzIyEFWbjkggEE9MVoUUAVILCztbm4uLe1hinuWDTyRxhWlIGAWI5OB61aIyCKWigDP0jTYNG0m2063LGK3jCBnOWb1Y47k5J9zTTpMJ1xNWd3M8du1ui4UKFZgxPTJPyjqcDnAGTnSooAKKKKACq1zZWt6qrdW0M6qcgSxhgD+NWaKAI40SGNY41VEUAKqjAA9AKcyq6lWAKkYIIyDTqKAIooooIlihjSONRhURQAB7AVLRRQBn6hpsOoy2Lzl8WdwLlACMM4VlG72G7PbkCtCiigCpf2UGpafcWN1H5lvcRtFKmSNysMEZHI4NWgAAAOgpaKAKC6Rpiu7rp1qGecXLEQrkyjpIePve/WpLaxs7KSd7W2hgaeQyzGKMKZHPBZsdTx1NW6KAKWo2K6lpt1YvJJGlzC8TvGQGUMCCRkEZ5rD1fwRpuqN/x8Xlovkwwstq6ruWF98XVSflYnp1zznAx1NFAFaK2ggdniiRZHADuB8z4GBuPU4HrVmiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAP/9k=\" alt=\"Image\" style=\"max-width:300px; max-height:300px; object-fit:cover;\"></td>\n",
+              "            <td>Prefix: read in latex<br>Suffix: \\Gamma ^ { a } : = \\gamma ^ { a } - i k ^ { a } \\gamma ^ { 3 } , \\qquad \\Gamma ^ { 3 } : = \\gamma ^ { 3 } + i k ^ { a } \\gamma _ { a } .</td>\n",
+              "        </tr>\n",
+              "        \n",
+              "        <tr>\n",
+              "            <td><img src=\"data:image/jpeg;base64,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\" alt=\"Image\" style=\"max-width:300px; max-height:300px; object-fit:cover;\"></td>\n",
+              "            <td>Prefix: read in latex<br>Suffix: \\Gamma [ h ] = \\frac { 1 } { 1 2 \\pi } t r \\int _ { B } d ^ { 3 } y \\epsilon _ { i j k } h ^ { - 1 } \\partial ^ { i } h h ^ { - 1 } \\partial ^ { j } h h ^ { - 1 } \\partial ^ { k } h ,</td>\n",
+              "        </tr>\n",
+              "        \n",
+              "        <tr>\n",
+              "            <td><img src=\"data:image/jpeg;base64,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\" alt=\"Image\" style=\"max-width:300px; max-height:300px; object-fit:cover;\"></td>\n",
+              "            <td>Prefix: read in latex<br>Suffix: \\delta W = { \\frac { m } { 2 } } \\mathrm { T r } \\Phi _ { 3 } ^ { 2 } .</td>\n",
+              "        </tr>\n",
+              "        \n",
+              "        <tr>\n",
+              "            <td><img src=\"data:image/jpeg;base64,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\" alt=\"Image\" style=\"max-width:300px; max-height:300px; object-fit:cover;\"></td>\n",
+              "            <td>Prefix: read in latex<br>Suffix: N _ { 2 2 } ( x , y , a , b ) = \\frac { 1 } { 4 a b } \\sum _ { n = 1 } ^ { \\infty } \\cos ( \\frac { 2 n \\pi x } { a } ) \\int _ { \\frac { n \\pi } { a } b } ^ { \\infty } d q \\left( \\coth q - 1 \\right) \\cosh ( \\frac { 2 q y } { b } ) .</td>\n",
+              "        </tr>\n",
+              "        \n",
+              "        <tr>\n",
+              "            <td><img src=\"data:image/jpeg;base64,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\" alt=\"Image\" style=\"max-width:300px; max-height:300px; object-fit:cover;\"></td>\n",
+              "            <td>Prefix: read in latex<br>Suffix: \\Phi = l \\ln g _ { s } , \\quad l = \\left( \\frac { 8 } { D - 2 } \\right) ^ { 1 / 2 } ,</td>\n",
+              "        </tr>\n",
+              "        \n",
+              "        <tr>\n",
+              "            <td><img src=\"data:image/jpeg;base64,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\" alt=\"Image\" style=\"max-width:300px; max-height:300px; object-fit:cover;\"></td>\n",
+              "            <td>Prefix: read in latex<br>Suffix: d s ^ { 2 } = d r ^ { 2 } + \\rho _ { 0 } ^ { 2 } \\sinh ^ { 2 } \\left( r / \\rho _ { 0 } \\right) \\left[ - H ^ { 2 } d t ^ { 2 } + \\cosh ^ { 2 } \\left( H t \\right) d \\Omega _ { 4 } ^ { 2 } \\right] .</td>\n",
+              "        </tr>\n",
+              "        \n",
+              "        <tr>\n",
+              "            <td><img src=\"data:image/jpeg;base64,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\" alt=\"Image\" style=\"max-width:300px; max-height:300px; object-fit:cover;\"></td>\n",
+              "            <td>Prefix: read in latex<br>Suffix: \\Sigma _ { \\mu \\nu } ( p , M ) = - \\epsilon _ { \\mu \\nu \\lambda } p _ { \\lambda }</td>\n",
+              "        </tr>\n",
+              "        \n",
+              "        <tr>\n",
+              "            <td><img src=\"data:image/jpeg;base64,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\" alt=\"Image\" style=\"max-width:300px; max-height:300px; object-fit:cover;\"></td>\n",
+              "            <td>Prefix: read in latex<br>Suffix: R _ { \\mu \\nu } = R _ { \\mu \\lambda \\nu } ^ { \\lambda } = \\partial _ { \\rho } \\gamma _ { \\mu \\nu } ^ { \\rho } - \\partial _ { \\nu } \\gamma _ { \\mu \\rho } ^ { \\rho } - \\gamma _ { \\mu \\lambda } ^ { \\rho } \\gamma _ { \\nu \\rho } ^ { \\lambda } + \\gamma _ { \\lambda \\rho } ^ { \\rho } \\gamma _ { \\mu \\nu } ^ { \\lambda } .</td>\n",
+              "        </tr>\n",
+              "        \n",
+              "        <tr>\n",
+              "            <td><img src=\"data:image/jpeg;base64,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\" alt=\"Image\" style=\"max-width:300px; max-height:300px; object-fit:cover;\"></td>\n",
+              "            <td>Prefix: read in latex<br>Suffix: \\Big [ { \\bf b } _ { i } ( \\vec { K } ) , { \\bf b } _ { i } ^ { \\dagger } ( { \\vec { K } } ^ { \\prime } ) \\Big ] = 2 ( 2 \\pi ) ^ { 3 } w _ { i } ( \\vec { K } ) \\delta ^ { 3 } ( \\vec { K } - { \\vec { K } } ^ { \\prime } ) ,</td>\n",
+              "        </tr>\n",
+              "        \n",
+              "        </table>\n",
+              "    </body>\n",
+              "    </html>\n",
+              "    "
+            ]
           },
           "metadata": {}
         }
+      ],
+      "source": [
+        "from IPython.core.display import display, HTML\n",
+        "from PIL import Image\n",
+        "import io\n",
+        "import base64\n",
+        "\n",
+        "def pil_image_to_base64(img):\n",
+        "    \"\"\"Convert a PIL image to a base64 string.\"\"\"\n",
+        "    buffered = io.BytesIO()\n",
+        "    img.save(buffered, format=\"JPEG\")\n",
+        "    img_str = base64.b64encode(buffered.getvalue()).decode(\"utf-8\")\n",
+        "    return f\"data:image/jpeg;base64,{img_str}\"\n",
+        "\n",
+        "def display_images_and_text(dataset, num_entries=10):\n",
+        "    \"\"\"\n",
+        "    Display images and their corresponding text side by side in an HTML table.\n",
+        "\n",
+        "    :param dataset: PyTorch dataset to extract images and texts from.\n",
+        "    :param num_entries: Number of entries to display.\n",
+        "    \"\"\"\n",
+        "    images = []\n",
+        "    texts = []\n",
+        "\n",
+        "    for i in range(min(num_entries, len(dataset))):\n",
+        "        img, data = dataset[i]\n",
+        "        images.append(pil_image_to_base64(img))\n",
+        "        text = f\"Prefix: {data['prefix']}<br>Suffix: {data['suffix']}\"\n",
+        "        texts.append(text)\n",
+        "\n",
+        "    rows = []\n",
+        "    for img, text in zip(images, texts):\n",
+        "        row_html = f\"\"\"\n",
+        "        <tr>\n",
+        "            <td><img src=\"{img}\" alt=\"Image\" style=\"max-width:300px; max-height:300px; object-fit:cover;\"></td>\n",
+        "            <td>{text}</td>\n",
+        "        </tr>\n",
+        "        \"\"\"\n",
+        "        rows.append(row_html)\n",
+        "\n",
+        "    html_content = f\"\"\"\n",
+        "    <html>\n",
+        "    <head>\n",
+        "        <style>\n",
+        "            body {{ font-family: Arial, sans-serif; margin: 0; padding: 0; }}\n",
+        "            table {{ width: 100%; border-collapse: collapse; margin: 20px 0; }}\n",
+        "            th, td {{ border: 1px solid #ddd; padding: 8px; text-align: left; }}\n",
+        "            img {{ display: block; margin: auto; }}\n",
+        "        </style>\n",
+        "    </head>\n",
+        "    <body>\n",
+        "        <table>\n",
+        "            <tr>\n",
+        "                <th>Image</th>\n",
+        "                <th>Text</th>\n",
+        "            </tr>\n",
+        "            {''.join(rows)}\n",
+        "        </table>\n",
+        "    </body>\n",
+        "    </html>\n",
+        "    \"\"\"\n",
+        "\n",
+        "    display(HTML(html_content))\n",
+        "\n",
+        "display_images_and_text(train_dataset, num_entries=10)"
       ]
     },
     {
       "cell_type": "markdown",
+      "metadata": {
+        "id": "_ZvYNxYbBtE3"
+      },
       "source": [
         "### Load PaliGemma2 model\n",
         "\n",
-        "**NOTE:** PaliGemma2 offers 9 pre-trained models with sizes of `3B`, `10B`, and `28B` parameters, and resolutions of `224`, `448`, and `896` pixels. In this tutorial, I'll be using the [`google/paligemma2-3b-pt-448`](https://huggingface.co/google/paligemma2-3b-pt-448) checkpoint. Resolution has a key impact on the accuracy of the trained model, and it seems that `448` offers the most optimal balance between performance and compute resources required to train the model."
-      ],
-      "metadata": {
-        "id": "_ZvYNxYbBtE3"
-      }
+        "**NOTE:** PaliGemma2 offers 9 pre-trained models with sizes of `3B`, `10B`, and `28B` parameters, and resolutions of `224`, `448`, and `896` pixels. In this tutorial, I'll be using the [`google/paligemma2-10b-pt-448`](https://huggingface.co/google/paligemma2-10b-pt-224) checkpoint."
+      ]
     },
     {
       "cell_type": "code",
+      "execution_count": 12,
+      "metadata": {
+        "id": "l0DpE_ibx9aB"
+      },
+      "outputs": [],
       "source": [
         "import torch\n",
         "from transformers import PaliGemmaProcessor, PaliGemmaForConditionalGeneration\n",
         "\n",
-        "MODEL_ID =\"google/paligemma2-3b-pt-448\"\n",
+        "MODEL_ID =\"google/paligemma2-10b-pt-224\"\n",
         "DEVICE = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")"
-      ],
-      "metadata": {
-        "id": "l0DpE_ibx9aB"
-      },
-      "execution_count": null,
-      "outputs": []
+      ]
     },
     {
       "cell_type": "code",
-      "source": [
-        "from huggingface_hub import notebook_login\n",
-        "notebook_login()"
-      ],
+      "execution_count": 13,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
-          "height": 17,
+          "height": 303,
           "referenced_widgets": [
-            "d14f91af605b4ddaa6a04a936afb6726",
-            "c85a9d2063204a92a64f11b066b14098",
-            "230f750695f848b580fae9e7e5fc6cd2",
-            "6e4a11669c8e40299882ed8c94d68d2b",
-            "e4c01ad80f65417a83d89a6fe456a53e",
-            "ba55831dc72a471e893dbd76c5b8c77c",
-            "315af73ed83744b099320c20dc59508f",
-            "2341d14200204994888759f7a1be98ed",
-            "e67c7eaf6aac481e82b568671c4e08cc",
-            "24e433a74d6b4bd194848f97999c333c",
-            "ac0b9d70d3ba41b49cd75488bf0aea8d",
-            "93228f56864747c482827fe18a6a3653",
-            "dbefa99013a1487eafe4b42261f8a3bc",
-            "ae50c0206be34c1399d2f6c4c065a4bb",
-            "1f77b30eeb9a4e56bd0ec0a306cb7219",
-            "d20cae74f2964ec7a643bb0089bb2d43",
-            "9a45a471f91744b68b022188177dc09c",
-            "6a9b48da04904bf297cc70649e60f875",
-            "cb35fbbef21b4ed9a62f96fcccb88f15",
-            "839ec515bcad402cbb8802dbf12d757a"
+            "f84389f96f5b4f0083393a909405d361",
+            "0a2efe8e7cc0441bb245a16143fccacd",
+            "8efc673032d94642803c17bca21be187",
+            "94d4353a335d4b27b0279db0ee02949a",
+            "2ee0184baa3e4dc9affce75c4b14e586",
+            "b17882b8b6424f29a9b5839478bc2e01",
+            "b9915f38865247269dce618c67db0d9f",
+            "39348d6db7dc4047bf142604b63596b2",
+            "af937e8993534b949629dbffeaea4826",
+            "918b7742e2044bbcae74a9fde46a23f1",
+            "3e218b0a4a34445080a5a2ed3eef511b",
+            "60e707662cdd4337a611ec62a7c0903d",
+            "f6372b23105b49ab8ade7802c5c8064a",
+            "508746f3b1174f9c97c8234230ba75bc",
+            "40941a70fc354c63aaeb084d523e0e76",
+            "654e31910dbb47cfb9a544dc6c5f000c",
+            "ae5f08a1ac7f421f91ca2e64a44a6b2b"
           ]
         },
         "id": "_DgILBz3LHw1",
-        "outputId": "a03d44bc-5c3c-4d9d-f230-1fcb13b1c65c"
+        "outputId": "4733164c-e9b2-4027-e033-3db22b9bf1f3"
       },
-      "execution_count": null,
       "outputs": [
         {
           "output_type": "display_data",
@@ -447,84 +628,85 @@
             "application/vnd.jupyter.widget-view+json": {
               "version_major": 2,
               "version_minor": 0,
-              "model_id": "d14f91af605b4ddaa6a04a936afb6726"
+              "model_id": "f84389f96f5b4f0083393a909405d361"
             }
           },
           "metadata": {}
         }
+      ],
+      "source": [
+        "from huggingface_hub import notebook_login\n",
+        "notebook_login()"
       ]
     },
     {
       "cell_type": "code",
-      "source": [
-        "processor = PaliGemmaProcessor.from_pretrained(MODEL_ID)"
-      ],
+      "execution_count": 14,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
           "height": 145,
           "referenced_widgets": [
-            "8f08e58d8dbc4d9c8d711e268c91779e",
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-            "1b6e5d8d811844b68dd38853bb2d6c23",
-            "72c7880d09f3463d8cd7ef84ab53c733",
-            "06d03215531740dab05b0c3acf0a15f0",
-            "b8937875231c4a1098fc521192a960ce",
-            "2539c990ce034d7fa802a0c7692ce92f",
-            "99c535c834af4f4aaf99a43f67173196",
-            "879fc03f3f594503bd191b38daf3bf12",
-            "01264b2a14994c679364a1ae687188e2",
-            "559594a7d2e54357b2e769c026bb47dc",
-            "5e0421e735a84a588ad08efbbec072b5",
-            "203c2abfa4f44aeaa48a14746847ceee",
-            "c8f3bd5ddf544d6db5aaec8e251becc4",
-            "8f2e90355fa94a0b9c7a2dd24ecb248d",
-            "d28bb2a775884189bd0dba5182796249",
-            "470a169789334df791dcb43ab6715856",
-            "122a6e6fb5ab4d39948aa1afbe1ba327",
-            "26e78b1b7a784679af973b9e427aa3db",
-            "8c2be6acc9d54d139335a71c9d4d95f3",
-            "f9b29007c3b84575b22336fe147878de",
-            "762e3605672d450188f87ebd91a62e13",
-            "1fc6379bdb6946e49f437343dabc2f3b",
-            "f330df7f8dbb4d0f805f2a5a2a499dba",
-            "c9eb05cddd7246dc93fe0394dbd9a938",
-            "ae52d4d9402d4ecdb15eb1112c6da328",
-            "3d5539eeb3744bb1ab2f8792f2fba682",
-            "38141d7ff86f4f17a4d977d84fe58c2f",
-            "f0ac6ae241014fb3882fe2b1ea1aca82",
-            "699b70579f9f4c2d94a96c961cafdffd",
-            "98afcff4beaa47a59b6c0c94ac1b38c0",
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-            "9a2c312f321140c8abe7eeed8c24aa16",
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-            "94b60faf70b64c3f86336b6cd8787f43",
-            "edff2d85b0d445f89d5ce119aa4f6426",
-            "358d64313bb740dd934ed1f2de757772",
-            "45bcbfea26a34fe59ee984af88024d4b"
+            "5d3b1476587a4643b6d89525f79f84d3",
+            "bef02e81428d4cf692f1cd6e0ba814ac",
+            "c604aed144224913a0c6ae5002cb688c",
+            "1496a1539b86488e91481ae971d18b3e",
+            "8e3d181d47d741b0949678e0f02eba53",
+            "3aa1fae13f9a478cac2ad96fb56844a7",
+            "cde77f0c227b4afda2c2175aea49e339",
+            "24b0220fa4a747df95df46f453a28108",
+            "6b972e333b9742ef8d2c8c0fc4e74e23",
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+            "84fa2487fed04ef6b990e4b1bdd583c0",
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+            "fade30557a1f43ca94949afee28b2456",
+            "9563585b2832451cb12c1028ddc0b776",
+            "ab62ae70883f4616adeee165359c20dd",
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+            "1a403cfd7ba44c87abf5c453f9fc1ccc",
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+            "53608ccb553e48eb9c4e78132c44d2f4",
+            "7f8047914bb44223b79158b95cdbcb1f",
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           ]
         },
         "id": "ntXj4A3SyEAa",
-        "outputId": "7fd8424b-bcb1-4479-da7b-5e364c40c97e"
+        "outputId": "f924b914-b394-4e74-c786-5178895f582d"
       },
-      "execution_count": null,
       "outputs": [
         {
           "output_type": "display_data",
           "data": {
             "text/plain": [
-              "preprocessor_config.json:   0%|          | 0.00/425 [00:00<?, ?B/s]"
+              "preprocessor_config.json:   0%|          | 0.00/424 [00:00<?, ?B/s]"
             ],
             "application/vnd.jupyter.widget-view+json": {
               "version_major": 2,
               "version_minor": 0,
-              "model_id": "8f08e58d8dbc4d9c8d711e268c91779e"
+              "model_id": "5d3b1476587a4643b6d89525f79f84d3"
             }
           },
           "metadata": {}
@@ -538,7 +720,7 @@
             "application/vnd.jupyter.widget-view+json": {
               "version_major": 2,
               "version_minor": 0,
-              "model_id": "879fc03f3f594503bd191b38daf3bf12"
+              "model_id": "2fca4c5efaa34b3e871f8ad1aad192a8"
             }
           },
           "metadata": {}
@@ -552,7 +734,7 @@
             "application/vnd.jupyter.widget-view+json": {
               "version_major": 2,
               "version_minor": 0,
-              "model_id": "8c2be6acc9d54d139335a71c9d4d95f3"
+              "model_id": "8dd05fa0632c491e9e8a384d45794a40"
             }
           },
           "metadata": {}
@@ -566,170 +748,187 @@
             "application/vnd.jupyter.widget-view+json": {
               "version_major": 2,
               "version_minor": 0,
-              "model_id": "98afcff4beaa47a59b6c0c94ac1b38c0"
+              "model_id": "8491ed88a8034410b0def84abf09f250"
             }
           },
           "metadata": {}
         }
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "source": [
-        "**NOTE:** Depending on the multimodal task you are trying to solve, we have prepared two training versions that optimize VRAM consumption.\n",
-        "\n",
-        "- Freeze the image encoder and fine-tune only the text decoder.\n",
-        "- Fine-tune the entire model with LoRA and QLoRA."
       ],
-      "metadata": {
-        "id": "DwLQf92pCDw6"
-      }
+      "source": [
+        "processor = PaliGemmaProcessor.from_pretrained(MODEL_ID)"
+      ]
     },
     {
       "cell_type": "code",
-      "execution_count": null,
+      "execution_count": 15,
       "metadata": {
-        "id": "IRanM-7XMxSl"
+        "id": "_qsRTZZAM03R"
       },
       "outputs": [],
       "source": [
-        "# @title Freeze the image encoder\n",
-        "\n",
-        "# TORCH_DTYPE = torch.bfloat16\n",
-        "\n",
-        "# model = PaliGemmaForConditionalGeneration.from_pretrained(MODEL_ID, torch_dtype=TORCH_DTYPE).to(DEVICE)\n",
-        "\n",
-        "# for param in model.vision_tower.parameters():\n",
-        "#     param.requires_grad = False\n",
-        "\n",
-        "# for param in model.multi_modal_projector.parameters():\n",
-        "#     param.requires_grad = False"
+        "USE_LORA = False\n",
+        "USE_QLORA = True\n",
+        "FREEZE_VISION = False"
       ]
     },
     {
       "cell_type": "code",
-      "source": [
-        "# @title Fine-tune the entire model with LoRA and QLoRA\n",
-        "\n",
-        "from transformers import BitsAndBytesConfig\n",
-        "from peft import get_peft_model, LoraConfig\n",
-        "\n",
-        "bnb_config = BitsAndBytesConfig(\n",
-        "    load_in_4bit=True,\n",
-        "    bnb_4bit_compute_dtype=torch.bfloat16\n",
-        ")\n",
-        "\n",
-        "lora_config = LoraConfig(\n",
-        "    r=8,\n",
-        "    target_modules=[\"q_proj\", \"o_proj\", \"k_proj\", \"v_proj\", \"gate_proj\", \"up_proj\", \"down_proj\"],\n",
-        "    task_type=\"CAUSAL_LM\",\n",
-        ")\n",
-        "\n",
-        "model = PaliGemmaForConditionalGeneration.from_pretrained(MODEL_ID, device_map=\"auto\")\n",
-        "model = get_peft_model(model, lora_config)\n",
-        "model.print_trainable_parameters()\n",
-        "\n",
-        "TORCH_DTYPE = model.dtype"
-      ],
+      "execution_count": 16,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
-          "height": 258,
+          "height": 340,
           "referenced_widgets": [
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+            "ae25eda4f50642bca76e6926f82eb1a1"
           ]
         },
-        "id": "F3T6XCGvygcQ",
-        "outputId": "f1b76717-d4ec-4607-b9ee-2c36eca519cc"
+        "id": "rEpM9zgOM5lr",
+        "outputId": "34ef8b04-5cdd-4f84-86d5-f0167233d7a9"
       },
-      "execution_count": null,
       "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stderr",
+          "text": [
+            "Unused kwargs: ['bnb_4bit_compute_type']. These kwargs are not used in <class 'transformers.utils.quantization_config.BitsAndBytesConfig'>.\n"
+          ]
+        },
+        {
+          "output_type": "display_data",
+          "data": {
+            "text/plain": [
+              "config.json:   0%|          | 0.00/1.33k [00:00<?, ?B/s]"
+            ],
+            "application/vnd.jupyter.widget-view+json": {
+              "version_major": 2,
+              "version_minor": 0,
+              "model_id": "afecda55d65f45c6a17cb660fc210cf6"
+            }
+          },
+          "metadata": {}
+        },
+        {
+          "output_type": "display_data",
+          "data": {
+            "text/plain": [
+              "model.safetensors.index.json:   0%|          | 0.00/92.6k [00:00<?, ?B/s]"
+            ],
+            "application/vnd.jupyter.widget-view+json": {
+              "version_major": 2,
+              "version_minor": 0,
+              "model_id": "51a938146e374ac8888b702039e138bc"
+            }
+          },
+          "metadata": {}
+        },
         {
           "output_type": "display_data",
           "data": {
             "text/plain": [
-              "config.json:   0%|          | 0.00/1.36k [00:00<?, ?B/s]"
+              "Downloading shards:   0%|          | 0/4 [00:00<?, ?it/s]"
             ],
             "application/vnd.jupyter.widget-view+json": {
               "version_major": 2,
               "version_minor": 0,
-              "model_id": "b843791871f04a588d53cfdd96ee49fd"
+              "model_id": "18266e7b3bde40cfb94ea9e43e8ef46a"
             }
           },
           "metadata": {}
@@ -738,12 +937,12 @@
           "output_type": "display_data",
           "data": {
             "text/plain": [
-              "model.safetensors.index.json:   0%|          | 0.00/75.1k [00:00<?, ?B/s]"
+              "model-00001-of-00004.safetensors:   0%|          | 0.00/4.95G [00:00<?, ?B/s]"
             ],
             "application/vnd.jupyter.widget-view+json": {
               "version_major": 2,
               "version_minor": 0,
-              "model_id": "ad86fa575f044255b2e52af6d65e8f3a"
+              "model_id": "bebfe14b72d54f65990269ce0a4c57f7"
             }
           },
           "metadata": {}
@@ -752,12 +951,12 @@
           "output_type": "display_data",
           "data": {
             "text/plain": [
-              "Downloading shards:   0%|          | 0/2 [00:00<?, ?it/s]"
+              "model-00002-of-00004.safetensors:   0%|          | 0.00/4.95G [00:00<?, ?B/s]"
             ],
             "application/vnd.jupyter.widget-view+json": {
               "version_major": 2,
               "version_minor": 0,
-              "model_id": "1fc96bb08c4049d69e059bb49ce1c473"
+              "model_id": "000f5b367bd94ea68ba25fbf439bccee"
             }
           },
           "metadata": {}
@@ -766,12 +965,12 @@
           "output_type": "display_data",
           "data": {
             "text/plain": [
-              "model-00001-of-00002.safetensors:   0%|          | 0.00/5.00G [00:00<?, ?B/s]"
+              "model-00003-of-00004.safetensors:   0%|          | 0.00/4.96G [00:00<?, ?B/s]"
             ],
             "application/vnd.jupyter.widget-view+json": {
               "version_major": 2,
               "version_minor": 0,
-              "model_id": "1a258f0aa77a44ffafe3a14a1c36c118"
+              "model_id": "852c25d25cab43b68c4a2177961a4442"
             }
           },
           "metadata": {}
@@ -780,12 +979,12 @@
           "output_type": "display_data",
           "data": {
             "text/plain": [
-              "model-00002-of-00002.safetensors:   0%|          | 0.00/1.07G [00:00<?, ?B/s]"
+              "model-00004-of-00004.safetensors:   0%|          | 0.00/4.46G [00:00<?, ?B/s]"
             ],
             "application/vnd.jupyter.widget-view+json": {
               "version_major": 2,
               "version_minor": 0,
-              "model_id": "bba1b49f14d842bc936333389d429e44"
+              "model_id": "981ae87618124ac281ede48cdc512c6c"
             }
           },
           "metadata": {}
@@ -794,12 +993,12 @@
           "output_type": "display_data",
           "data": {
             "text/plain": [
-              "Loading checkpoint shards:   0%|          | 0/2 [00:00<?, ?it/s]"
+              "Loading checkpoint shards:   0%|          | 0/4 [00:00<?, ?it/s]"
             ],
             "application/vnd.jupyter.widget-view+json": {
               "version_major": 2,
               "version_minor": 0,
-              "model_id": "c712f856fbc64d87bcaff95db5169f6e"
+              "model_id": "9350592ec8b748d2a3f5d500c7dc025d"
             }
           },
           "metadata": {}
@@ -813,7 +1012,7 @@
             "application/vnd.jupyter.widget-view+json": {
               "version_major": 2,
               "version_minor": 0,
-              "model_id": "6060579e6e084133be39e517a0be0feb"
+              "model_id": "45228c76493b411ead5b13f5302ca4ef"
             }
           },
           "metadata": {}
@@ -822,22 +1021,64 @@
           "output_type": "stream",
           "name": "stdout",
           "text": [
-            "trainable params: 11,876,352 || all params: 3,045,003,504 || trainable%: 0.3900\n"
+            "trainable params: 28,502,016 || all params: 9,691,140,848 || trainable%: 0.2941\n"
           ]
         }
+      ],
+      "source": [
+        "from peft import get_peft_model, LoraConfig\n",
+        "from transformers import BitsAndBytesConfig\n",
+        "\n",
+        "if USE_LORA or USE_QLORA:\n",
+        "    lora_config = LoraConfig(\n",
+        "    r=8,\n",
+        "    target_modules=[\"q_proj\", \"o_proj\", \"k_proj\", \"v_proj\", \"gate_proj\", \"up_proj\", \"down_proj\"],\n",
+        "    task_type=\"CAUSAL_LM\",\n",
+        "    )\n",
+        "    if USE_QLORA:\n",
+        "        bnb_config = BitsAndBytesConfig(\n",
+        "        load_in_4bit=True,\n",
+        "        bnb_4bit_quant_type=\"nf4\",\n",
+        "        bnb_4bit_compute_type=torch.bfloat16\n",
+        "            )\n",
+        "    model = PaliGemmaForConditionalGeneration.from_pretrained(\n",
+        "        MODEL_ID,\n",
+        "        device_map=\"auto\",\n",
+        "        quantization_config=bnb_config if USE_QLORA else None,\n",
+        "        torch_dtype=torch.bfloat16)\n",
+        "    model = get_peft_model(model, lora_config)\n",
+        "    model = model.to(DEVICE)\n",
+        "    model.print_trainable_parameters()\n",
+        "else:\n",
+        "    model = PaliGemmaForConditionalGeneration.from_pretrained(MODEL_ID, device_map=\"auto\").to(DEVICE)\n",
+        "    model = model.to(DEVICE)\n",
+        "\n",
+        "    if FREEZE_VISION:\n",
+        "        for param in model.vision_tower.parameters():\n",
+        "            param.requires_grad = False\n",
+        "\n",
+        "        for param in model.multi_modal_projector.parameters():\n",
+        "            param.requires_grad = False\n",
+        "\n",
+        "TORCH_DTYPE = model.dtype"
       ]
     },
     {
       "cell_type": "markdown",
-      "source": [
-        "### Fine-tune PaliGemma2 on LaTeX OCR dataset"
-      ],
       "metadata": {
         "id": "8W1JY6x98WTq"
-      }
+      },
+      "source": [
+        "### Fine-tune PaliGemma2 on LaTeX OCR dataset"
+      ]
     },
     {
       "cell_type": "code",
+      "execution_count": 17,
+      "metadata": {
+        "id": "ErMInlMt8gHU"
+      },
+      "outputs": [],
       "source": [
         "from transformers import Trainer, TrainingArguments\n",
         "\n",
@@ -860,20 +1101,20 @@
         "    return inputs\n",
         "\n",
         "args = TrainingArguments(\n",
-        "    num_train_epochs=4,\n",
+        "    num_train_epochs=3,\n",
         "    remove_unused_columns=False,\n",
-        "    per_device_train_batch_size=1,\n",
-        "    gradient_accumulation_steps=16,\n",
+        "    per_device_train_batch_size=3,\n",
+        "    gradient_accumulation_steps=12,\n",
         "    warmup_steps=2,\n",
         "    learning_rate=2e-5,\n",
         "    weight_decay=1e-6,\n",
         "    adam_beta2=0.999,\n",
-        "    logging_steps=200,\n",
-        "    optim=\"adamw_hf\",\n",
+        "    logging_steps=100,\n",
+        "    optim=\"paged_adamw_8bit\" if USE_QLORA else \"adamw_hf\",\n",
         "    save_strategy=\"steps\",\n",
         "    save_steps=1000,\n",
         "    save_total_limit=1,\n",
-        "    output_dir=\"paligemma2_latex_ocr\",\n",
+        "    output_dir=\"paligemma2_latex_ocr_v5\",\n",
         "    bf16=True,\n",
         "    report_to=[\"tensorboard\"],\n",
         "    dataloader_pin_memory=False\n",
@@ -886,35 +1127,142 @@
         "    data_collator=collate_fn,\n",
         "    args=args\n",
         ")"
-      ],
-      "metadata": {
-        "id": "ErMInlMt8gHU"
-      },
-      "execution_count": null,
-      "outputs": []
+      ]
     },
     {
       "cell_type": "code",
-      "source": [
-        "trainer.train()"
-      ],
+      "execution_count": 18,
       "metadata": {
-        "id": "6T8G03yQ9LJF"
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 594
+        },
+        "id": "6T8G03yQ9LJF",
+        "outputId": "6b7b32b1-3132-46cf-d737-f77673b57126"
       },
-      "execution_count": null,
-      "outputs": []
+      "outputs": [
+        {
+          "output_type": "display_data",
+          "data": {
+            "text/plain": [
+              "<IPython.core.display.HTML object>"
+            ],
+            "text/html": [
+              "\n",
+              "    <div>\n",
+              "      \n",
+              "      <progress value='1662' max='1662' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
+              "      [1662/1662 4:15:51, Epoch 2/3]\n",
+              "    </div>\n",
+              "    <table border=\"1\" class=\"dataframe\">\n",
+              "  <thead>\n",
+              " <tr style=\"text-align: left;\">\n",
+              "      <th>Step</th>\n",
+              "      <th>Training Loss</th>\n",
+              "    </tr>\n",
+              "  </thead>\n",
+              "  <tbody>\n",
+              "    <tr>\n",
+              "      <td>100</td>\n",
+              "      <td>9.844200</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <td>200</td>\n",
+              "      <td>5.440100</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <td>300</td>\n",
+              "      <td>4.329200</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <td>400</td>\n",
+              "      <td>3.641700</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <td>500</td>\n",
+              "      <td>3.248500</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <td>600</td>\n",
+              "      <td>2.916000</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <td>700</td>\n",
+              "      <td>2.652100</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <td>800</td>\n",
+              "      <td>2.485000</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <td>900</td>\n",
+              "      <td>2.333900</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <td>1000</td>\n",
+              "      <td>2.345000</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <td>1100</td>\n",
+              "      <td>2.157600</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <td>1200</td>\n",
+              "      <td>2.009000</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <td>1300</td>\n",
+              "      <td>1.928500</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <td>1400</td>\n",
+              "      <td>1.859700</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <td>1500</td>\n",
+              "      <td>1.915800</td>\n",
+              "    </tr>\n",
+              "    <tr>\n",
+              "      <td>1600</td>\n",
+              "      <td>1.883600</td>\n",
+              "    </tr>\n",
+              "  </tbody>\n",
+              "</table><p>"
+            ]
+          },
+          "metadata": {}
+        },
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "TrainOutput(global_step=1662, training_loss=3.1394706432282855, metrics={'train_runtime': 15363.293, 'train_samples_per_second': 3.899, 'train_steps_per_second': 0.108, 'total_flos': 1.1381261608321336e+18, 'train_loss': 3.1394706432282855, 'epoch': 2.99534184823441})"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 18
+        }
+      ],
+      "source": [
+        "trainer.train()"
+      ]
     },
     {
       "cell_type": "markdown",
-      "source": [
-        "### Run inference with fine-tuned PaliGemma2 model"
-      ],
       "metadata": {
         "id": "1c4FK0XXCxPU"
-      }
+      },
+      "source": [
+        "### Run inference with fine-tuned PaliGemma2 model"
+      ]
     },
     {
       "cell_type": "code",
+      "execution_count": 19,
+      "metadata": {
+        "id": "3a8sis7pHGtM"
+      },
+      "outputs": [],
       "source": [
         "# @title Function to render text diffs\n",
         "\n",
@@ -995,58 +1343,35 @@
         "    </html>\n",
         "    \"\"\"\n",
         "    return html"
-      ],
-      "metadata": {
-        "id": "3a8sis7pHGtM"
-      },
-      "execution_count": 30,
-      "outputs": []
+      ]
     },
     {
       "cell_type": "code",
-      "source": [
-        "# @title Suffix vs. generated text\n",
-        "\n",
-        "for i in range (10):\n",
-        "    image, label = test_dataset[i]\n",
-        "    prefix = \"<image>\" + label[\"prefix\"]\n",
-        "    suffix = label[\"suffix\"]\n",
-        "\n",
-        "    inputs = processor(\n",
-        "        text=prefix,\n",
-        "        images=image,\n",
-        "        return_tensors=\"pt\"\n",
-        "    ).to(TORCH_DTYPE).to(DEVICE)\n",
-        "\n",
-        "    prefix_length = inputs[\"input_ids\"].shape[-1]\n",
-        "\n",
-        "    with torch.inference_mode():\n",
-        "        generation = model.generate(**inputs, max_new_tokens=256, do_sample=False, num_beams=3)\n",
-        "        generation = generation[0][prefix_length:]\n",
-        "        generated_text = processor.decode(generation, skip_special_tokens=True)\n",
-        "\n",
-        "    html_diff = side_by_side_diff_divs(suffix, generated_text)\n",
-        "    display(image)\n",
-        "    display(HTML(html_diff))"
-      ],
+      "execution_count": 20,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
           "height": 1000
         },
         "id": "dRR4I4QANy5K",
-        "outputId": "8f6aa4e8-97d7-42a2-92ed-f41ad663d62e"
+        "outputId": "b594b0e1-0c5a-4f18-9fb9-1701cac8c047"
       },
-      "execution_count": 28,
       "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stderr",
+          "text": [
+            "The 'batch_size' attribute of HybridCache is deprecated and will be removed in v4.49. Use the more precisely named 'self.max_batch_size' attribute instead.\n"
+          ]
+        },
         {
           "output_type": "display_data",
           "data": {
             "text/plain": [
-              "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=400x50>"
+              "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=280x40>"
             ],
-            "image/png": 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DgOaA+ewALJAcIXWcom94wxsKDG/iSHWXEYoat3o1r9wIKNWshUmA2mxzkdNXilwXDG2J41wn3re//e14Un4okLM4DjL3SUQ/Ntl7770ZYubz0Simrjbs86PkPrv6khuymw6LGIeSxV73kVLwZCc7mfX8VKc6laO42o2VXlllZmY1PlS6+93v3uzCXPJZKvmwucSN5pXKbkaN0EpZowTVrsp2nW/b7VMYjSlEjYc85CFkIYtPY/GHWZdmJouvn/MxFsNyC/9eYYYslrpjuu9978sVJoYu2WaWAvhQSQJoqoxNTbsVpUG8IB0x2AJA72DlwHiKU5zCvaGLDIWMkzlKNLkUHgeUudRSarXPahhDcEhJDlH9NVoZy41OPVKXJoqUo1kbK9YpEBhKDDqkOa0sXZBiSgEKK5SWCqaJtTNd0lUrQeEilIJOokMiJQHf+MY3wPAcxUWYW2bkz6Me9SiUKQwJKEt7etWryBrLdsZKEqraV1YXyKWGfDC2IVe+8pVtjgiSUZ6kqFYyJJPR86f66+ubLYUCerOb3UyWVtrQa9nCdrrRVtRSr7wCQ3qO+WvuGDXIwCjps2rTC58HwGPe0UFJqh6VQp41ZJTpm4xoko4D5KptkTQ87mlwLgAbzwW4G1yXoyzPonFL55qTxro87QK+8pWvqMcmGzEi1zogRToGG67la71pHE2w8BuYy/BHPFV3dDVEb4sbetwsngID2cDWgWDIYTnpguRiz5qjDLVISghIfOxZVIeSXpAcMTjEq83/7W53O3zcwRNkLHvpbP4gM9akkgdcjEZjiPymMAUyjaOsUXE2bYjODzD2bmc4wxk43D19kxkHCmtLzBZ/lWrN9EMVSd9Ohw70ZL5AJAUlVmRxBc4J0gWmA21j1RNnePYiSAr6IQ4+D/OnOTmcHBP8EcQne73i5juDomCI0qwXMYb42PV05vVqsrGUuzC5wQ1uYOdON6u3Kz+3PGwxioHyB0wur8rygkhVJSm5WWQfZNdJOmK51y0YDpxg40YQPs95znOs55Dc1eYUbAEWWTFSC8SXYpyvNGAubZQJW3U7C8PhYZxTbIcZS1BTl1ZOG1lKHJ59Oig67GIRl1ZofNA0iV7zmtfg1kTgLi0vZdGIFxqG8xvbOcoRmHqlEA9IqrxtFM3pLwMpBok/G9kL300ZJl6dsOyqjOU0lPJQFHJpoj2b41RKEG5avUyjALghEXgNCcA5W0oGi1brk4FxaCAyY20UzB1+k8ByYHBD6RWNp+XBZjkR5SF4AIMt5KJg4c53yUDkRGC8bNDlIsOFlG2qlaqrBO5zF6NLM0oGABSs4rSEXhimeNtw8j6MVzrVlZ1gQGOTW28uQ4+zhoY9XjMSEzDKjJRVjki+dMDoihs4moZj7nVIx9/67FMdsiFXwllR7Rl5H0/Huk2bNoHNxg0bNrhrtye3AFoBZNUIKg6j0dOZyFUa5yBzoONitlszm/lEmHjyXmpKSgdt84fyltYznelM3/3ud7HKgWjMChsrIZCX9lMomWbaPOMZz5BkbEfsCVkgh0o4p1JpBDaK7Uu+PKg2wRsyAsEPmtf4WJkcZOIft+E94sDIuDRiAyFNVDUu4pwPaV/wghe8ABKG2s5izPEFzV9jOCbbStjLWHIRFDgKGEXV+Hj1qVs1P+MZz2gyqIAwem2HTU40FLAvq1iImitnUkRKCFSfEo/rIOnMISa2rTFKpwHf+9LfbkXpxB+ZckZDUjA3C3i7k2n6iM7znvc8Wz8p8dznPjedVaIuv/F3KBHrzLeEM9/GR3zFUQUpuDShPFj5MMSmjMn4GyUxhu0xoYnclgCY8DCdDVQWHdBSSQFlKRu5yFwby8yDHvQgi1y/2xBH3NQLU5gsCiTFWCYr/bEqYcyy9IHMP+nWKz6jgjQfYSip3fjGN7aPi1UJD4aPW8TmXUVNzuiti3oAsqx5Fg9AmgAiyxXoA+i/ByWckmyJCcC63SOpN7nJTRhpg0AVSeB4KN42mUa6iyHGxK5JGgAByUOmwBtu248tJBHYcpAMyHeyRyDhBRUrZFLtqle9qjlMBzHAED17PJ0utQCqA1hFZ5w9bVVMVOVAkGBo7iaSYXFArBFhwyLenEJ/GiKQuPgD5L07SzXCXIK0FHCfxdN2wECqOkiqv5IGK8MJYqyxumhLeaPsw89znvM4AEoFBExQASHLD4bLYNYtqXMYK57GA+YPhqohzWX8Fa94RQXLrQEFFDtNdlKMUYY7QuJgqpDIOsNxU+yExr6A1cgEkWI5UBIzIYk9yeI66hmOktrMZ4VeCogabp4+icIg9sStIWE4HMBqEfEUDrKYLJR8wsnYwuBpbn/+85+PWAk2sW0kDbcnoq1iZAtgUvEwQ4yiFX2ooWEOtpVglMmAoVfNHpkflFQcXK4rXsbSUPRt/F2Bdy+Gp0CjcbC158KZZ1gqQOit87bMMpld9rB04G0prbhzOEOETCwMZxFW/OAUCaO6uZRkMrx8xtCOzBGVjeqpeocYpV7J7OaOwmyhHkrDESuODpjqlAlFJU9pYL9PW5byfE4e3nCT6HCtEslwPsHkS1/6kl0/MoVPMvjmIBl42yWG6wh4jV2UpIwA6aLG1a52NTnPDxGYCJQBW6c9KakLsfCNZGD1gIkurJEJR6zgDeE3Tmajcm/jwgNJKYjM5xCsOJYOFEPJUr3IADhACo08T+GGwwMQEwfOOYA95BDlmE0JZR5sC0eAvbSEc+/o4y4LWUWeCz+BlB/xQgZvbOI9BTLYlMCZrp5swJbqvAyDj14DZQY96IQbL8MD+DfmIgrAkD0oEZCLWFNidFnoxB4feMyxsq7KZlZQiZ7Mg8eQzTC6MAGjZKynXnw00wCslziXGi5TnQhULnsxTjTE5QtBTKMMzlg1UFeRMBNQssucgbSEumiwlZBVTJZkduxCSw36I8aKgRmiSMlFZ3ATzH2cL1bOSuYGSgWdRGyJ4wRpzRx2ZRqMVGY10fa/JgAyVqAXMuFTSjg/PwsEoaxGgHNhMpa20lGq6XI9jKGaKLJEM9lqRFsYNF7JFUqviixNzAp8OA19gSMaAbxlXzk2BF6RMrUwN2P9IKtA+/kIbdEj9szPaUUWQaaxhsYrQ2giKDZluqhq/XC1TDQCEvHUkFE7TQTCYqaX+Wo6M+3C+N86arsHVgj0ijIXKVVM8MpLwgS41KUuxQSC+N8rp9FtxB1Pp3Weue51ryvfBFrhq5dvKRBsLOXB5pQbBttwB09a+aGT8koZqUsxHiBiuALeKxGss4cCl8Y2fZDXuta1sJVX8AgQa6oVB/IDWFJJOQBbSEfGjQERMMQhQK8VGp4/FywO/HeKRQ0rOntKYzaSxfl2xDKWVzHURWeO4m0wf0pgbCHRcJp0Mi8gMRcXQ2AQ6PKsxYf5PMaHuiiDGENIvaymlRRiryEwCyVldm5tF41I5BxKIU0k3/iNB2vSVGAMo6hXynlygTLEI+PXN5D8ZTm17Vf4x3B47u6VEpokgNQwSTpWlIbRZSNtlRZ7nsXK3bZJIreUc4FHY0PLANbGU4F3vOIXSaCJtIQTPMXIJlGvIYRaYC3aJIJhQtoZ7bXXXizCypMyvuurhnpbcjmU+V57LrRfukRbjJ80hgsYlZQee8l6zCKTBJ9eiQYg8+RtEo0CSz4JBDCcXeYz2EaAw7vUkD1opA68VuAAcabPEvqgR57MObAGurbnE0lmacUqR3ER3/bhwqYdngLGslQNdRdpvyBNhQClmmgUej/OZBe25JqK2ggEo+AdXqZHb3XQkZlvmY+5+OaBkXW5JYZgDZmEGXa5MndWLTrILADlj9AgzpPwkA3hlhLVVyMTwF0bPIZoCFVujMoEWVdYddVExFgcGHUgbmFpUmIiQ0SkXovT8HMYauTGXk1pCz/YSmnUBS5wAZMLAR0i6EmNmHulgwYYOthgyiuYkrkhngU6Ymq0EjgW6JIkPAZIFnGljQku0PD5EJArBIVjnQxEXIVyGlUKJYyZxUvI+EQi4QnfAVwymKQaYpTyBAeUNfrkB1tgp0IKFJR6ixSvOsmp1yVDhiAYuuXb/LCHKshgfjRA7F1a6bCS4+LVvl39gvFU5NRallQLJQEaSKzVRQYQgA/V2SO54Y2CMeU0evgpoFpDLRrI+yzxxMRwSis3TMJWYbaPdUikFQ4wzqeQfvJng2M+WwdUSZrgbDg/WiTlBCkaJSUETRBQg4Ht9nHATQU0xEDJAYAkxZcjFuHjibNNAQIOFVcAibjJJ+5iXa80py3bBdtChBW8korez3M8o+dM+UFWDJHlGa/U04xiFO8ZJWNs1zG5yEUu4grDOu/qRBIgZoI1FjewRmdPe14hK/DZTiUmgI1y2FFieJsIEbEr4WSvhFKYSjIME3cujioAtlDDWFaz1/2dMykkWRSjOfMNlxgWD55EjJIf8NfYRbpXSCKs0gJHClki4hoUBw0HBMRpXO2VLHivRGNS4GAAkGY4cU64XoXSEClk4SHC2ExY8Fo6QdAWDSaJ4Mx99tmHJzds2OBcL6zF15UF+pwp65ZGL8JNf/lAUNsTRumiFQw8WEoLN9gWiSyzF5OuC+ApwyeIdeWcnlZNTrA9dK7kFgeXElsuISaFIRRDkya9GuuVn73SzebUbFdxZAK8KcCrFEaQhmgAcklvmlMDf3g0cQ5vVMwRwAtZrqCDMJl3yDRyeVI2in5e4lVNWLtTw5Yr3HejsSrzvFdxIZFpfMhdVIKEwVBMy1sSdcEjgyHdWATh8ScXfvChJIKFOFPUfyiEL/utY/rsk/FSYl3dG4x1qvgFAzIKGQIwFnGasY0XeAeGonIaTwPLKjTwxJf3ypMlt7gKkmlgrC5aMolojqOM0FKaIMMpYwYikK/M4z5reBtjIvICV7JZKTRJ2gvg4FWADcRWeOQ6WwSewqwwlhpESyn1BQEO9JR8FKaMLh4Aa/R0t5Usr4LEQIA0NQqrBdFhDqNWBtRLNHE40wpDzEWFaEhkej3LVJoAnF8YYpmyotqi0gRglCy3tNrJ0h8Sh6TggCEX0cdwynBLNipDeHImSjScjEYv70HiWQSVA85B4zhsScAKT9qi4XOBMMqFETeynfPRoGdvowDsItEofoAkKM4AycDnaACUISW3oCfCK/caTj3DERQUulHDpIKkHjJskWlxEBeA3PDkDcTYagZGYKCfbl772tfGUE23B7RYUkNDUCw8Bd2rWNDHWBy8hqFYBnpmHSXZxcPICqg0K0XpAG+g2FEy72HoFbL47rfffhKSV/nf9wd4nFOYLArDaJxGEKB8BuiKj7GVeNmLyZI/FucsfkDjNScjpmFTbMFxaeoRxEu6VDRXY5A2EJ5U5aJ6hU98Odzy1sQxL4o4SomtXAKobS5IAzRyg1H0pwZK6tEhTVBim6u5i5JVQHgEulhaOMTdK7a9Zgsya4wNY1EueRa+KC3wclNDD46wsRJjknCB15BFSUWfe6WgV1F0F2CxIsmFsUOQwOOumW+puxh2YMNNlzecw+FcpsobmHqR1fAfonm/gdG0s5UHllD4TKjLq+HNOgAOZZt0ceth1gkGtd2qoNQoI4q+rYCN4vqEDtHcqkumLqgP3IHHn716I6h3jEqZROuCz2oArUrQiOE1P+RTx92J8Bu7/KmdnPbNUY7a3vOSdQzsmSBPfKaivUKiDFjSa3GdNOgDiKZb6kUfng68Kr7OHfX2xC2GBuKZRUVNkjhb0UrOOMJLjFghk0ipiknEuoQpw8GDZ0M8dQ3lp0gwhoOenvXmvWHg4Jw4skwkk4czTUhe7ZdW8HEYWo2BgHgmK5VKiSRG2cASEjxCjMZAqkbcq6ckkTyf/OQn6eADNIcA7LaiHGqghNFiOOxSCnVNySKgKuLIyGUXms2bN/uds3x2QHEWVpsQ69Uw0QzxpBId7DfBeSO8V/Qt0mDDPccrWOMENOVG0t0kWA90UQDnJaqD8tC8863T2ilP3DvL6mFLQmmOgxg1xYbhigwljXIxgmcmLNa3XlBzjWar2d0TvjhG4AmmpRmlQnnV61XR9QnM+ZZtDuoxlfcbN260TUNg1Fa1rF35zJie/EUBT3dPbfqIgMlZI6ExgYyV6Nr0OVzwjgC4n6IwbRH4mauVgZswHHFdqcCOw5T6wuPOyBGP//2+xnag6yqKjSRQ1im8auPqVdvWqm1L4rBjVEsCgMd4ZhkfOhAnB1xW0pyGfsdcqnGvrxYWXlmBbDpw2eu0a31hcaSeoEsG+kubnCNPDuUQ5zpCRdO1F+ew1G+zaVXFmRq+PboZKxwsFTipbjMuw70yeYjg/15ppRY4xOkSNWPbMZRgkNLPt1RL+5577mkdKgNHGmRFSEJ96HSQjFWyRqDHvKOSxNaoZwgCLWXMShPQL37FiIikRLDyudhh1QxG6mmYMIMBw4Nxh7H8OiMk0kDidR3IY/FfmLaaYL5YKXJtzJTVFM62ihHpNNHr53mW0MhyHwd5zfsE0X+ox6IRP4phmHUOm5a7eA57p6J3KFx4iKBA+9bEZUJwxkazJe/RfNUWh0P+tAWwe+cfzSheGg6cMoHUNZSPplcxcqnvV7LoqcSuNfhMea4vnKMoQM9a/gm/vrIOIbdxWc63EpW7qDQdmxunmIOFcZiO8ipb+JwIT4ZPOQxKMbJz6XdYqk/4iMEKq7/+sWtRVX34Utqo2qU7bs3B2DZQ/e0HuiUq5FQrY807yBSbqhQSKyL2XvpKUNZ56lq1LT78o9Yc65xgnS09HcsBGmS9no6Xmt8Tu4vtTwfItt+GVCyoiMY0Y79kdX0gJJyyNGgrHkPcMoAyMJ1jaUi0V7/ucZPlS5arJZWLaEd3fqFVw7M52Fhb5SyiGIbi4WexPnPY0MJrFI24Z66cYtYdZguefMWBzv9gPvTMhLyKhiHgjjZ6V7b0X/lcSbk2xmW/8PlhmiSTarxUfJe5oogShxs35jdBkWo2iS4+uFQXnWluLErc1ha9vr1DQyZoFAizvlIOlpts5AG1A2V3qRwr/WRjWk055MYp5mBhvtUGGTNlizwhwpOICKIZ/L2aNf1QDgwvdt29gh3BXJioUIb7UZ5LTz8ocepnhYDiX2EiNOt8GvJbHK/o02TlvMM2xQYNubjB23uOselJ+fisfC4SDtFoScKoAI8B+Abb6vs8aaOoRiTblgoSrPS6ufA5T0VzciQVt8Fh+wE+ZTM+dCOO+xRWhdnx0zwx573qHULprDFtYPTCIGYgGBPLiB9ku4MELzM5nyDboS192EV5U5puo9q2CA/prKDSwqTV2iDbToAmrt79CsxvKfKbsIovtqRPmXOXxpOWAXhlKxOo7TcEfdmE59ih73T4DoLprK2M3dAhIAKUO0iNwZY/eck6qk5BmuEjh+EH2TYDmLBoDGcXo0pvyIUvltog8AZWy1QZX9jaasHQyncVw2Wgn9G6CHPG79uCykV562hF1lOrBBsFoIDJjiZNhoeTNURjTjENANlTeviTEsMddFIszjFZ+fy3aoVF5nmClzXIhDFJl+1Mr6bZoBywwEjcgV8XIHFDNwoMtqnkNaFD9DAn5VsZkNkSKn+ArhXjPLgFNHYZcke8inRs5cTQcKUgCg/3ruxdLwxX5Bm3mcONmG/JG9EMtQHjyNAhffgWhzivl6qr8knPnkSPtox4ECzD74hXOmBbigbvCCl4Mgp/ThYFT81rlg6JykHw/vvvr0Bs3ry5V+tNQFELFkpbJzVxIMekIwJnZIDgMQchE9qTDgimyJiPp/sv27fhGRpOE2+QBSxqfFYBalW1A98O+m94c0Y5pLdVt0VDuXWjhs7kB+cpxATgfND47YY4Ds8KMGbWc68AKwCVAO6ArAkAz7w5rdCGK+fUQ9BuGeA+bsoTZrQt+WEQrBfQDoXCAEsWDW1aB3N48fZKee4d+GUAK1Zty8gO9pU4goTSPSiG0Qv3lrxBJSnBtyilLP3FpZoFbngJVkocrALbSbAs4l5XZRh+S72rDtlmZGf8UpSL8OGxbea2xkDmlOQ8H+AJqRklmk2KOPhdmxD7LS68ALm4pCcCVysI7K89FbV9993Xr/PF1Ks1zMQBGEJEM7EoE5GBiViSecAjTYwayDRBqakhpPimiSy3UKZZbMgqTTc6DRetqgyI3XgudS4ei3J64E8TSsRRm/XCMGOssdOiOzhsD1A1HByoR5xXOmjBXlVoXYNsCgwaBLT1hULvloinA3cQzEWMohVlpiJyMsw0OlOCZTATVm3LyA7hK1ZRCuXKII7eaHLpWBWldfjIWOe1XWRwvYfmc5nCh6ZosqaRLdD/KT+kDG+UXe52/NrAR2o5NvLN5iP/+EcQ1Avf0Ht1wxUwAm3IGFUXPltyNSfo0gDMb6ynj3ik9BvD9nFjhsZz2VNdW/yudyyGqmBVbRmd1/AoiQSrtcaip0RdSgaMV/VYllulK7r1bueTkTgQZ/0H8JonZK+MtERQySpBPRV6GIIsN3myoiUCkoa0dT1sTk6JdR2ajYsoljPFmzJJ5+dCIDoaJGO1LenGhFXblujXxmNVlIWS9OCGlAnpBkNhygtHgZDu1u2ig4ZpWCGLA4evLXf7e0mspeHQc/s5bxsHczKrzUaKlX58BabbtvFcOWoYO7pgDnDEvwuijC7Jj9JP//y5ewtMAZKB/fzVD2v8Ssvtku9a/rLNT/n9QE/6GVtAMS9FAVgVcalSb2rowtbTqDB6KcB8Y2t+R+kLnj+k80WizR0XpV5Dlj0XB7dlqPl19sDsgV3VAypL2wj7CT+s9VeNNr/+GLuqClY1nAH9s8gKh3KjKUN+bed7Wt9eYFqctspFSmHF2qhR9SxvdPAXdf6x1kRX3dbgf8Atw1bJnolnD8we+C/1gMNHtUOlsPvzj0zYQ23evHnjxo3KhGoF6bn30h9XAFQreB8Qx06qM0EF7pA7oX1Td2F25dg6DPnFqdurPihXpNSyNaoVcXPBOuQ+nylnD/zXe6BDmcOdE5mLFDss/3iJv3a22YFhnoLl3/byd/jRKC5tiKojeretYOEcf0fjdmr++Xl/JOsf3nHY1DsK1touno+Ea/tn7p09sEt5QMWxu2m7ZJdUMfK7dr/+c8tu/2VXxWAHNBsxx8DqiEulNkcNn57vDqF37Kdwi9hlN1n+vQ3/3zb/gJX6RQ0q0UeVpN4aPOeCtYZz5q7ZA7uaB0atURoUCI2F6pFftLuc8meDXt3E+3pYBenOq7qWLxDbZE0v1w+hj/w4RkHU0PtXLvwPMlQrrDAfdapt3RoM54K1hnPmrtkDu6AH2iUpE05n6oUCZO8D6VQIcHCzx6lwODN2U648KWdKmC77o345uA2uIcXezXdkf47js2DlUg3FtgpYZaxWrsp/LlirumVGzh7YZT3Q97ipef1O2OlvVIrxMRHZOAYiqMRsw/YKn8E80Sogzirm2FWNfdwaHyJ3+O9ipn6Z4dkDswf+4x5wS2XrpEz04yknNV8Mq0Q99aoj6lqqVp5stRQspcTr6DrkthiIOaGqUj82xK3zIAAf+yy9U4mrMp93WKu6ZUbOHpg9sDN6YN5h7YxRmXWaPTB7YFUPzAVrVbfMyNkDswd2Rg/MBWtnjMqs0+yB2QOremAuWKu6ZUbOHpg9sDN6YC5YO2NUZp1mD8weWNUDc8Fa1S0zcvbA7IGd0QNzwdoZozLrNHtg9sCqHpgL1qpumZGzB2YP7IwemAvWzhiVWafZA7MHVvXA/wEx/3YNvtROgAAAAABJRU5ErkJggg==\n",
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\n",
+            "image/jpeg": "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\n"
           },
           "metadata": {}
         },
@@ -1087,10 +1412,10 @@
               "    <body>\n",
               "        <div class=\"container\">\n",
               "            <div class=\"column\" style=\"border-right: 1px solid #ccc;\">\n",
-              "                <br>F ( 1 ) = - ( - 1 ) ^ { ( d - 1 ) / 2 } d <span class='diff-remove'>! !</span> = - ( - 1 ) ^ { ( d - 1 ) / 2 } 2 ^ { ( d + 1 ) / 2 } \\pi ^ { - 1 / 2 } \\Gamma \\left( { \\frac { d } { 2 } } + 1 \\right) .<br><br>\n",
+              "                <br>H = <span class='diff-remove'>\\dot {</span> x <span class='diff-remove'>}</span> _ { i } \\Pi _ { x <span class='diff-remove'>^ { i }</span> } + \\Pi _ { x <span class='diff-remove'>^ { i</span> } <span class='diff-remove'>} \\dot {</span> x <span class='diff-remove'>}</span> _ { i } ^ { <span class='diff-remove'>*</span> } + <span class='diff-remove'>\\dot {</span> \\psi <span class='diff-remove'>} _ { i }</span> \\Pi _ { \\psi <span class='diff-remove'>_ { i }</span> } - \\Pi _ { \\psi <span class='diff-remove'>_ { i</span> } ^ { <span class='diff-remove'>* } } \\dot { \\psi } _ { i } ^ { *</span> } +<br><br>\n",
               "            </div>\n",
               "            <div class=\"column\">\n",
-              "                <br>F ( 1 ) = - ( - 1 ) ^ { ( d - 1 ) / 2 } d <span class='diff-add'>_ { 1 }</span> = - ( - 1 ) ^ { ( d - 1 ) / 2 } 2 <span class='diff-add'>_ { 5 }</span> ^ { ( d + 1 ) / 2 } \\pi ^ { - 1 / 2 } \\Gamma \\left( { \\frac { d } { 2 } } + 1 \\right) . <span class='diff-add'>\\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\nonumber . \\</span><br><br>\n",
+              "                <br>H = x _ { i } \\Pi _ { x } + \\Pi _ { x } x _ { i } ^ { <span class='diff-add'>\\ast</span> } + <span class='diff-add'>i</span> \\psi \\Pi _ { \\psi } - \\Pi _ { \\psi } <span class='diff-add'>\\psi</span> ^ { <span class='diff-add'>\\ast</span> } +<br><br>\n",
               "            </div>\n",
               "        </div>\n",
               "    </body>\n",
@@ -1104,10 +1429,10 @@
           "output_type": "display_data",
           "data": {
             "text/plain": [
-              "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=280x40>"
+              "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=360x40>"
             ],
-            "image/png": 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\n",
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\n",
+            "image/jpeg": 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           },
           "metadata": {}
         },
@@ -1148,10 +1473,10 @@
               "    <body>\n",
               "        <div class=\"container\">\n",
               "            <div class=\"column\" style=\"border-right: 1px solid #ccc;\">\n",
-              "                <br>H = \\dot { x } _ { i } \\Pi _ { x ^ { i } } + \\Pi _ { x ^ { i } } \\dot { x } _ { i } ^ { * } + \\dot { \\psi } _ { i } \\Pi _ { \\psi _ { i } } - \\Pi _ { \\psi _ { i } <span class='diff-remove'>^ { * }</span> } \\dot { \\psi } _ { i } ^ { * } +<br><br>\n",
+              "                <br>\\psi _ { j } ( C _ { r } <span class='diff-remove'>^ { \\vee }</span> , t ) = \\frac { 4 \\sinh 2 j <span class='diff-remove'>t</span> ( \\cosh ( 2 <span class='diff-remove'>w</span> _ { 1 } t ) \\cosh ( 2 <span class='diff-remove'>w</span> _ { 2 } t ) - \\cos ^ { 2 } ( x t ) ) } { \\sinh 2 t \\cosh <span class='diff-remove'>h</span> t } .<br><br>\n",
               "            </div>\n",
               "            <div class=\"column\">\n",
-              "                <br>H = \\dot { x } _ { i } \\Pi _ { x ^ { i } } + \\Pi _ { x ^ { i } } \\dot { x } _ { i } ^ { * } + \\dot { \\psi } _ { i } \\Pi _ { \\psi _ { i } } - \\Pi _ { \\psi _ { i } } \\dot { \\psi } _ { i } ^ { * } + <span class='diff-add'>\\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad</span><br><br>\n",
+              "                <br>\\psi _ { j } ( C _ { r } , t ) = \\frac { 4 \\sinh 2 j ( \\cosh ( 2 <span class='diff-add'>u</span> _ { 1 } t ) \\cosh ( 2 <span class='diff-add'>u</span> _ { 2 } t ) - \\cos ^ { 2 } ( x t ) ) } { \\sinh 2 t \\cosh <span class='diff-add'>k</span> t } .<br><br>\n",
               "            </div>\n",
               "        </div>\n",
               "    </body>\n",
@@ -1165,10 +1490,10 @@
           "output_type": "display_data",
           "data": {
             "text/plain": [
-              "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=360x40>"
+              "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=500x100>"
             ],
-            "image/png": 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\n",
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\n",
+            "image/jpeg": 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           },
           "metadata": {}
         },
@@ -1209,10 +1534,10 @@
               "    <body>\n",
               "        <div class=\"container\">\n",
               "            <div class=\"column\" style=\"border-right: 1px solid #ccc;\">\n",
-              "                <br>\\psi _ { j } ( C _ { r } <span class='diff-remove'>^ { \\vee }</span> , t ) = \\frac { 4 \\sinh 2 j t ( \\cosh ( 2 w <span class='diff-remove'>_ { 1 }</span> t ) \\cosh ( 2 w _ { 2 } t ) - <span class='diff-remove'>\\cos</span> ^ { 2 } ( x t ) ) } { \\sinh 2 t \\cosh h t } .<br><br>\n",
+              "                <br><span class='diff-remove'>-</span> \\frac { <span class='diff-remove'>h</span> ^ { 2 } } { 2 <span class='diff-remove'>\\lambda</span> } \\int d <span class='diff-remove'>t d</span> ^ { <span class='diff-remove'>2</span> } x <span class='diff-remove'>d</span> ^ { <span class='diff-remove'>2</span> } x ^ { <span class='diff-remove'>\\prime</span> } ( <span class='diff-remove'>{ \\tilde {</span> J <span class='diff-remove'>} }</span> _ { k } - \\frac { <span class='diff-remove'>J</span> _ { <span class='diff-remove'>k</span> } ^ { <span class='diff-remove'>0</span> } } { \\rho _ { 0 } } <span class='diff-remove'>{ \\tilde</span> { J <span class='diff-remove'>}</span> } _ { 0 } ) ( <span class='diff-remove'>t , x )</span> \\Delta ^ { - 1 } ( x - x ^ { \\prime } ) <span class='diff-remove'>( { \\tilde { J } } _ { k } - \\frac {</span> J _ { k } ^ { <span class='diff-remove'>0</span> } } { \\rho _ { 0 } } <span class='diff-remove'>{ \\tilde</span> { J <span class='diff-remove'>}</span> } _ { 0 } ) ( <span class='diff-remove'>t</span> , x ^ { \\prime } ) <span class='diff-remove'>.</span><br><br>\n",
               "            </div>\n",
               "            <div class=\"column\">\n",
-              "                <br>\\psi _ { j } ( C _ { r } , t ) = \\frac { 4 \\sinh 2 j t ( \\cosh ( 2 w <span class='diff-add'>\\cdot</span> t ) \\cosh ( 2 w _ { 2 } t ) - <span class='diff-add'>\\cosh</span> ^ { 2 } ( x t ) ) } { \\sinh 2 t \\cosh h t } . <span class='diff-add'>\\, . \\, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</span><br><br>\n",
+              "                <br>\\frac { <span class='diff-add'>k</span> ^ { 2 } } { 2 <span class='diff-add'>k</span> } \\int d <span class='diff-add'>x</span> ^ { <span class='diff-add'>0</span> } <span class='diff-add'>d</span> x ^ { <span class='diff-add'>1</span> } x ^ { <span class='diff-add'>0</span> } ( J _ { k } - \\frac { <span class='diff-add'>\\mu</span> _ { <span class='diff-add'>0</span> } ^ { <span class='diff-add'>2</span> } } { \\rho _ { 0 } } <span class='diff-add'>\\bar</span> { J } _ { 0 } ) ( <span class='diff-add'>1 -</span> \\Delta ^ { - 1 } ( x - x ^ { \\prime } ) <span class='diff-add'>)</span> J _ { k } <span class='diff-add'>( - \\frac { \\mu _ { 0 }</span> ^ { <span class='diff-add'>2</span> } } { \\rho _ { 0 } } <span class='diff-add'>\\bar</span> { J } _ { 0 } ) ( <span class='diff-add'>k</span> , x ^ { \\prime } )<br><br>\n",
               "            </div>\n",
               "        </div>\n",
               "    </body>\n",
@@ -1226,10 +1551,10 @@
           "output_type": "display_data",
           "data": {
             "text/plain": [
-              "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=240x40>"
+              "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=160x40>"
             ],
-            "image/png": 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\n",
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+            "image/png": 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\n",
+            "image/jpeg": "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\n"
           },
           "metadata": {}
         },
@@ -1270,10 +1595,10 @@
               "    <body>\n",
               "        <div class=\"container\">\n",
               "            <div class=\"column\" style=\"border-right: 1px solid #ccc;\">\n",
-              "                <br>H = H _ { 0 } + \\int d ^ { 3 } x A _ { 0 } ( \\nabla \\cdot <span class='diff-remove'>\\mathrm { \\boldmath</span> \\pi <span class='diff-remove'>}</span> + e \\psi ^ { \\dagger } \\psi ) ,<br><br>\n",
+              "                <br>\\bar { \\Phi } _ { 0 } = \\frac { ( \\tilde { Q } _ { 0 } \\tilde { Q } _ { 1 } \\tilde { Q } _ { 2 } ) ^ { 1 / 2 } } { l ^ { 3 } }<br><br>\n",
               "            </div>\n",
               "            <div class=\"column\">\n",
-              "                <br>H = H _ { 0 } + \\int d ^ { 3 } x A _ { 0 } ( \\nabla \\cdot \\pi + e \\psi ^ { \\dagger } \\psi ) , <span class='diff-add'>\\nonumber \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad</span><br><br>\n",
+              "                <br>\\bar { \\Phi } _ { 0 } = \\frac { ( \\tilde { Q } _ { 0 } \\tilde { Q } _ { 1 } \\tilde { Q } _ { 2 } ) ^ { 1 / 2 } } { l ^ { 3 } }<br><br>\n",
               "            </div>\n",
               "        </div>\n",
               "    </body>\n",
@@ -1287,10 +1612,10 @@
           "output_type": "display_data",
           "data": {
             "text/plain": [
-              "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=500x100>"
+              "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=200x50>"
             ],
-            "image/png": 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\n",
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\n",
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           },
           "metadata": {}
         },
@@ -1331,10 +1656,10 @@
               "    <body>\n",
               "        <div class=\"container\">\n",
               "            <div class=\"column\" style=\"border-right: 1px solid #ccc;\">\n",
-              "                <br><span class='diff-remove'>-</span> \\frac { h ^ { 2 } } { 2 \\lambda } \\int d t d ^ { 2 } <span class='diff-remove'>x</span> d ^ { 2 } x ^ { \\prime } ( <span class='diff-remove'>{ \\tilde { J } }</span> _ { k } - <span class='diff-remove'>\\frac { J _ { k } ^ { 0 } } { \\rho _ { 0 } } { \\tilde { J } }</span> _ { 0 } ) ( t , x ) \\Delta ^ { - 1 } ( x - x ^ { \\prime } ) ( <span class='diff-remove'>{ \\tilde { J } }</span> _ { k } - <span class='diff-remove'>\\frac { J _ { k } ^ { 0 } } { \\rho _ { 0 } } { \\tilde { J } }</span> _ { 0 } ) ( t , x ^ { \\prime } ) .<br><br>\n",
+              "                <br>f ( \\sigma ) = f _ { 0 } \\frac { 1 } { \\sqrt { \\pi } } + \\sum _ { <span class='diff-remove'>r</span> = 1 } ^ { \\infty } f _ { n }<br><br>\n",
               "            </div>\n",
               "            <div class=\"column\">\n",
-              "                <br><span class='diff-add'>{</span> \\frac { h ^ { 2 } } { 2 \\lambda <span class='diff-add'>}</span> } \\int d t d ^ { 2 } <span class='diff-add'>z</span> d ^ { 2 } x ^ { \\prime } ( <span class='diff-add'>J</span> _ { k } - <span class='diff-add'>{ \\frac { J _ { 0 } ^ { 0 } } { \\rho _ { 0 } } } J</span> _ { 0 } ) ( t , x ) \\Delta ^ { - 1 } ( x - x ^ { \\prime } ) ( <span class='diff-add'>J</span> _ { k } - <span class='diff-add'>{ \\frac { J _ { 0 } } { \\rho _ { 0 } } } J</span> _ { 0 } ) ( t , x ^ { \\prime } ) . <span class='diff-add'>} . { \\frac { J _ { 0 } ^ { 0 } } { \\rho _ { 0 } } } . { \\frac { J _ { 0 } ^ { 0 } } { \\rho _ { 0 } } } . } . { \\frac { J _ { 0 } ^ { 0 } } { \\rho _ { 0 } } } . { \\frac { J _ { 0 } ^ { 0 } } { \\rho _ {</span><br><br>\n",
+              "                <br>f ( \\sigma ) = f _ { 0 } \\frac { 1 } { \\sqrt { \\pi } } + \\sum _ { <span class='diff-add'>n</span> = 1 } ^ { \\infty } f _ { n }<br><br>\n",
               "            </div>\n",
               "        </div>\n",
               "    </body>\n",
@@ -1348,10 +1673,10 @@
           "output_type": "display_data",
           "data": {
             "text/plain": [
-              "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=200x50>"
+              "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=200x40>"
             ],
-            "image/png": 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\n",
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\n",
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           },
           "metadata": {}
         },
@@ -1392,10 +1717,10 @@
               "    <body>\n",
               "        <div class=\"container\">\n",
               "            <div class=\"column\" style=\"border-right: 1px solid #ccc;\">\n",
-              "                <br>f ( t , z , \\bar { z } ) = F _ { <span class='diff-remove'>\\star</span> } \\left( t , \\frac { z } { \\sqrt { 2 \\theta } } , \\frac { \\bar { z } } { \\sqrt { 2 \\theta } } \\right) ,<br><br>\n",
+              "                <br>C _ { \\mathrm { b u l k } } ^ { ( 3 ) } = \\frac { 2 \\sqrt { 2 } } { 3 } \\beta \\sinh ( \\sqrt { 2 } \\beta \\phi _ { 0 } ) ,<br><br>\n",
               "            </div>\n",
               "            <div class=\"column\">\n",
-              "                <br>f ( t , z , \\bar { z } ) = F _ { <span class='diff-add'>*</span> } \\left( t , <span class='diff-add'>{</span> \\frac { z } { \\sqrt { 2 \\theta } } <span class='diff-add'>}</span> , <span class='diff-add'>{</span> \\frac { \\bar { z } } { \\sqrt { 2 \\theta } } <span class='diff-add'>}</span> \\right) , <span class='diff-add'>\\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\nonumber , \\</span><br><br>\n",
+              "                <br>C _ { \\mathrm { b u l k } } ^ { ( 3 ) } = \\frac { 2 \\sqrt { 2 } } { 3 } \\beta \\sinh ( \\sqrt { 2 } \\beta \\phi _ { 0 } ) ,<br><br>\n",
               "            </div>\n",
               "        </div>\n",
               "    </body>\n",
@@ -1409,10 +1734,10 @@
           "output_type": "display_data",
           "data": {
             "text/plain": [
-              "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=240x50>"
+              "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=200x50>"
             ],
-            "image/png": 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\n",
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+            "image/png": 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\n",
+            "image/jpeg": "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\n"
           },
           "metadata": {}
         },
@@ -1453,10 +1778,10 @@
               "    <body>\n",
               "        <div class=\"container\">\n",
               "            <div class=\"column\" style=\"border-right: 1px solid #ccc;\">\n",
-              "                <br><span class='diff-remove'>{</span> \\frac { ( <span class='diff-remove'>\\det</span> ( e ) ) ^ { \\prime \\prime } } { <span class='diff-remove'>\\det</span> ( e ) <span class='diff-remove'>}</span> } = f ( r ) = \\mathrm { r e g u l a r f u n c t i o n o f } <span class='diff-remove'>r</span><br><br>\n",
+              "                <br>\\pi ^ { \\mu } ( x ) = \\frac { \\partial { \\cal <span class='diff-remove'>{</span> L <span class='diff-remove'>}</span> } } { \\partial \\dot { A _ { \\mu <span class='diff-remove'>}</span> } } = - F ^ { 0 \\mu } ( x ) .<br><br>\n",
               "            </div>\n",
               "            <div class=\"column\">\n",
-              "                <br>\\frac { ( <span class='diff-add'>\\mathrm { d e t }</span> ( e ) ) ^ { \\prime \\prime } } { <span class='diff-add'>\\mathrm { d e t }</span> ( e ) } = f ( r ) = \\mathrm { r e g u l a r f u n c t i o n o f <span class='diff-add'>r</span> } <span class='diff-add'>\\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\quad . \\</span><br><br>\n",
+              "                <br>\\pi ^ { \\mu } ( x ) = \\frac { \\partial { \\cal L } } { \\partial \\dot { A <span class='diff-add'>}</span> _ { \\mu } } = - F ^ { 0 \\mu } ( x ) .<br><br>\n",
               "            </div>\n",
               "        </div>\n",
               "    </body>\n",
@@ -1470,10 +1795,10 @@
           "output_type": "display_data",
           "data": {
             "text/plain": [
-              "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=200x50>"
+              "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=320x40>"
             ],
-            "image/png": 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\n",
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\n",
+            "image/jpeg": "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\n"
           },
           "metadata": {}
         },
@@ -1514,10 +1839,10 @@
               "    <body>\n",
               "        <div class=\"container\">\n",
               "            <div class=\"column\" style=\"border-right: 1px solid #ccc;\">\n",
-              "                <br>\\pi ^ { \\mu } ( x ) = \\frac { \\partial { \\cal <span class='diff-remove'>{</span> L } } <span class='diff-remove'>}</span> { \\partial <span class='diff-remove'>\\dot {</span> A _ { \\mu <span class='diff-remove'>}</span> } } = - F ^ { 0 \\mu } ( x ) .<br><br>\n",
+              "                <br><span class='diff-remove'>{ \\cal</span> P <span class='diff-remove'>}</span> Q ^ { ( <span class='diff-remove'>a</span> ) } | E _ { n } \\rangle = <span class='diff-remove'>{ \\cal</span> P <span class='diff-remove'>}</span> ( - i ) D ^ { ( <span class='diff-remove'>a</span> ) } ( X _ { n } ) | 0 \\rangle = - P <span class='diff-remove'>_ { n }</span> Q ^ { ( <span class='diff-remove'>a</span> ) } | E _ { n } \\rangle ,<br><br>\n",
               "            </div>\n",
               "            <div class=\"column\">\n",
-              "                <br>\\pi ^ { \\mu } ( x ) = \\frac { \\partial { \\cal L } } { \\partial A _ { \\mu } } = - F ^ { 0 \\mu } ( x ) . <span class='diff-add'>\\qquad \\mathrm { c . c . } . \\qquad \\mathrm { c . c . } . \\qquad \\mathrm { c . c . } . \\qquad \\mathrm { c . c . } . \\qquad \\mathrm { c . c . } . \\qquad \\mathrm { c . c . } . \\qquad \\mathrm { c . c . } . \\qquad \\mathrm { c . c . } . \\qquad \\mathrm { c . c . } . \\qquad \\mathrm { c . c . } . \\qquad \\mathrm { c . c . } . \\qquad \\mathrm { c . c . } . \\qquad \\mathrm { c . c . } . \\qquad \\mathrm { c . c . } . \\qquad \\mathrm { c . c . } . \\qquad \\mathrm { c . c . } . \\qquad \\mathrm { c . c . } . \\qquad \\mathrm { c . c . } . \\qquad \\mathrm { c . c . } . \\</span><br><br>\n",
+              "                <br>P Q ^ { ( <span class='diff-add'>s</span> ) } | E _ { n } \\rangle = P ( - i ) D ^ { ( <span class='diff-add'>s</span> ) } ( X _ { n } ) | 0 \\rangle = - P <span class='diff-add'>\\</span> Q ^ { ( <span class='diff-add'>s</span> ) } | E _ { n } \\rangle ,<br><br>\n",
               "            </div>\n",
               "        </div>\n",
               "    </body>\n",
@@ -1531,10 +1856,10 @@
           "output_type": "display_data",
           "data": {
             "text/plain": [
-              "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=200x40>"
+              "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=200x50>"
             ],
-            "image/png": 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\n",
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\n",
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           },
           "metadata": {}
         },
@@ -1575,10 +1900,10 @@
               "    <body>\n",
               "        <div class=\"container\">\n",
               "            <div class=\"column\" style=\"border-right: 1px solid #ccc;\">\n",
-              "                <br>C _ <span class='diff-remove'>{ \\mathrm</span> { b u l k <span class='diff-remove'>}</span> } ^ { ( 3 ) } = \\frac { 2 \\sqrt { 2 } } { 3 } \\beta \\sinh ( \\sqrt { 2 } \\beta \\phi _ { 0 } ) ,<br><br>\n",
+              "                <br>s = <span class='diff-remove'>\\Big (</span> { \\frac { 4 \\pi } { n } } <span class='diff-remove'>\\Big )</span> \\sqrt { \\gamma ( \\rho - { \\frac { \\Phi \\tilde { \\rho } } { 2 } } - { \\frac { k \\gamma } { a ^ { 2 } } } <span class='diff-remove'>)</span> } .<br><br>\n",
               "            </div>\n",
               "            <div class=\"column\">\n",
-              "                <br>C _ { b u l k } ^ { ( 3 ) } = \\frac { 2 \\sqrt { 2 } } { 3 } \\beta \\sinh ( \\sqrt { 2 } \\beta \\phi _ { 0 } ) , <span class='diff-add'>\\, }</span><br><br>\n",
+              "                <br>s = <span class='diff-add'>\\left(</span> { \\frac { 4 \\pi } { n } } <span class='diff-add'>\\right)</span> \\sqrt { \\gamma ( \\rho - { \\frac { \\Phi \\tilde { \\rho } } { 2 } } - { \\frac { k \\gamma } { a ^ { 2 } } } } <span class='diff-add'>\\right)</span> .<br><br>\n",
               "            </div>\n",
               "        </div>\n",
               "    </body>\n",
@@ -1594,8 +1919,8 @@
             "text/plain": [
               "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=200x50>"
             ],
-            "image/png": 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tfiqJbRWGdE84MXM0NEjjkVmzTa+4W0dFqxoeDPjCXE+LgvXFCUuC8csSz+p75ZVXmtyCvcgiizhGRUKekRx85JkaOktOMrEJE+EBk2fYSI45zVhJk1SXnxwkj/SNzNCeoMB2qJLdbR/VRDgiAA0nOshA+CE1MwdwYVEC9jRQunjan/E/BVxHy1gWxNK8PByxff/ZyFjspDf77SJtZSSJzC1eCG7MQjy+8bWPFid0DONr/gotQvj9vxS/zuLPFMSpkBY55Y4KEpDF7xiIIgS/3ZV11uLrDK8LsRlF5HbeeWfqpTJd0IarJ4LMgMOVR35cUkmsp9J8uPNaikUNNYm91wiJqtVdvZIwIyQYO6TMQH0DUx1T4DXyEeaqoysTTGDSHESmm246MNKEWV+VllT5Hs17tgGuhdGF7FJVZd8vjT+VES3pDQH8zl9MTbTQSTCJuiOYO+LUlK95gffD6RYnKw4XB51DuCCckVbwwtNMexW5ZJHKeSo7Ckwgqy8dlCDj1ltvtbuX/HTE5vcZKXC//fYDNbRsISElohjYgodWSqzzDKE1DJ5ac7+ApoxThYNLo3kwcHWJ2qmMwjzp7Cw5PfbYY/GqmUNUdnjpS20EzUt+6RZzIjBsofv4sx/9GJkzbU5MYumoL1rZ9vKCNYhfqsjPOVHzQq5AgVJf0zEHqHDyQp1ijOKVTKubExkGMXDeCWeQUfJtLCjgNZog4MyulovpmdXNq2xBiFZyrNFurYLmHNzcYrsHP/bYY19++WWnWnGintEd/UiAOemwf//+tCKzjI0OKomKnmrwq/FUyScIGrpAfuqpp1xZ6c52OoCU1hhFoE8qHHfsCJ944ombbrrJuPadeDDn5Esy5LGCcIbkwBTDWepQacayBUNxsqL6RtW+++QsUecI4GBhJorKvHpqFRJP0eWIJKqaT0CpySsJuofWKx0zZXkto2hV0hRaffrmlYRw8mwk65umPCtNRrJBFZzuFAQbT4Q7W7gscJOOzU+c2267LWL77bcXZpfdkVlGpQs5pWSNgjPMnhhitZRs+bMTFVQgA6yKrqgXHINvTUGGW9BoGCWlrhiYQQmvVBeiVsDoSUk8cUJLPBsZq/zSigS423Vdeumltl9HH310kpwjpBnvXl56EHtR9B/eHWxdlLhwtz4Kv9QigQm2zVzXhkNA0JPk7dUFGNxAvwI3EpVKAkOogQb3dp5ocHQx5ltT1/rGMmiGgxXqdT10C7e2BPy7UBKwHMudE11SS0g4XVu7ZYCeZFA18s0GG2yQ/7zqBs7vQiqbE0DS0tBGAZokSFBAY/OKqAxXHZNdvFbqTRP51ZQEqb5ZgZLQNsRQ/5dOq8wVuzp/OuHEE0+0QvmPyNR2MvXnX2zCkj/EWFAvuOACB3ixtD76GEGmyXqHHz5q/epodVJRUovkRyaBEpj8RIhWMuUkUFMvjXmVBZONbJLsR8nUq1ZGDBmlUlfHQdugpuWBlSxi5y547oSgxAcX/n6Q7Y4mUYQGnw77MUDSwmPPLrdZKLMLxtN1FBN+T5JxQhgaKMEItiCMzGytjEWalGO9A2XMjggqzznnHDdYNRD+jJik1fXoLdzaNrnXH0oQcj8PuC5ilGzhKfwx0NkQMoRZmkn480xrVrrQHZ+EZNtuRSMkDCFIqy25+gAOkYXPcuwL2IEDB8KH1JUR6RAJpVte2+zZ8pt3MRMwOy1RX3DBBf3afd9999lyqRddC1AWKdtnNWIpgSEARe6xAqbGitZ8uMPQXGAoayVRNuOevuFxzwnBLlx8pucrRYcGEoBD9nKgk7QATh6Fder5C0eyplsbr0aUtHAaorJX83DtQbf8qUTOsK7lXs2fDXL6gypZwUkwl2oWLGASTsd4OAMpsVfEL0mi6wCHP8yBlzszqy1s5eM+A/nO0SchzozA7dVSK3UBjf95Boi+P9YEUgo5IQxNyTYGVjtkLOGUfgSpbm6hQUSFUIBdOEGVNJObJ6FVkqKSgcQ4IU9Tp09Ji5BcKECJb1l9L+TLaeDAb2ifu/gFCaqM4ko9W3UfIaqhni+8XZPKWM2nBPXGba7pdOgWrWz5jMXv4h3vJ2+hk5AQdY3ZjCr1WfiAD901quBJwhN+2IUSBHy4VZeHdARK+PCx2mmnnSZ3pgbOcPoEw7WZJRitr1NqMFR4onZwSYf2K+0ArL81KllGs81KHrKf8+OMC09NkKHSbb4flWEXpORCGJIydbFGO6haKNEuRGwBXc9mGth4QSEJf6vy/6LwdlgK/wH3wYFRJB5IUvyAjfYdR7410jTEipY852lTHyT5dd/PhTCHGfg8uzguaG31MgxY3USwDozwZBWz9mWdDXTSWX3WNfgLjPRKPstrjYFBR5VZf7PJq9Z2IoYBq5towpMFrhlGOngNdOQtAMoRIYeAym3VBaeCU1bDDFJBVeS062o4bI/VDbCgCge4QECgIz95tX+ycwoskpbABQMAYdAFmOQ2OclziFVPRwwBZTfDt2zzsIz1P4TOtj2bpPSRzBBBXtV4hRugSVoCQbRnwCRpeQ2zlAaCWVhT007PYRmr+2jCRPbmyU/SEkjBTTOkwqMy+y1CsVVHrwUg9Ulp0lhVdq9Eq3EMy1itFrEW0bflv25oET//36n5X2nv2xjERLasAAAAAElFTkSuQmCC\n",
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\n",
+            "image/jpeg": "/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAAyAMgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD3+iiuatPHHh7UNLvdRstRW4tbKbyJXjjbmQkAKuR85JIA25ySMUAdLRVVLuFp1t/MRbgx+b5JYbwucZI9M8Z9atUAFFFUbnVtOspRFd39rbykbgksyoSPXBNAF6is+x1O11C4u7eFz59nL5U0bDDIcZU49CpBB7g/WtCgAoorH1HxJpWlX9tY3t2Irq6z5EWxmaTHXaADnHf0oA2KazBFLMQFAySe1UNK1iw1uGaWwuVnSGUxSYBBRwAcEEAg4IP41hfESeVvDS6TbyNHcazdRaajr1VZG/eH8Iw5oA09B1p/EEE19DbmLTmk22c7v81yo4Mm3HyoT93nLDngEVt1TJs9L09AWhtbSBFRdxCIijAUc8AdBVygAoorzfx7ayalrtlCNE1a4giTBvLRpAVcniOPaw2Fhw8pBAX5ep4APSKKht4Ut7eKGNAiRoFVB0UAYAqagAqtc3K2drJcSLKyRjJWGJpHP0VQST7AVZrA8XNOPDV2ltp9zqE8q+WlrBKYmlJ7FwRtX1OemQOSKAL2m6rBqyO9vHdoqEA/aLSWAn6CRRke4qxdPcR2sz20SzTqjGON32B2xwC2DgE98HFcv8PdNWw0SVhZ3ls0kn/L0rxkgDgJG5JjjUkqqkngZ712NAGToOtQa5p32mFZI5I5GhuIJPvwSqcOjY4yD6cEYI4Na1cWrnRvikYEG211yxaYqOn2iAhWb2zG6gn/AGB17dpQAUUUUAc744vf7O8D61eCZ4mhs5GRk4O7b8o6HGTgfjWDJps2k/8ACA6TId9pBdbJTI4O10tZPLUEYyAwOOvKiuh13wzbeIpbM3l1epBbvva2hm2xT/MrASLj5gCg9D19TVrXNIj1mwFuZXgnjkSe3nQAtDKhyrgHg4PUHggkd6AOK03U7KH4k+JtSvtQlAs4VtEVgMRwxJ50ruAuVQNKACeuOC2eNfxl4jtLbwjBfQatLbJfGP7PNa7N8qsMja8g2xjByZGGFGT1xXSz2SywXCq7QXE8XlvcwKqyDggEEg8jJIzkCltNPtrLT7exijBhghECB/mOwADBJ68AZ9aAMDw7rUEOj6aNV8QxaheajM6Q3AQJHO44KxADBUY4Pfr3rmfG97aXHjG209dYjtrgRKrK1tBIBk/dXepaSVt67UXAXG5sg4Pf3ukw3stizPIkdnL5yQx4COwUhdwxkhc5ABHIHpV028RYMYkLK28EqMhsYz9ccZoA5qMrF8TZ442w0mjxtMoP3tszBCR/wJwD9fSqHiDUtdh1maKzm1dIFC4FtpCTp0BOHLAn8q6XT9Iis9R1DUGkaa6vnUySN/CighI1HZQCT7lmPetXAoA53wpdahc2c/8AaMl88iyYVruxW2bGOwUkEe9cprMl5r/xGvYdE1C2iu9H0h4oWfDBbmducDcOQsa5POM8jpn03FMCIDuCqD64oA5ix8ReHLPxHLokF4japORJNl9zSSKBF83fdhF7AY5qp4zG/wAUeCopnZLQ6q7swHHmrBIYxn3ORjvzXQLoOmrrjayttjUWTyzcb23FMAbOv3eAcdM89eaw/iKpttCstZUFho2oQX7qBkmNTsk/JHY/hQBR+J0kbWGi6fc3klvbXmoxi4IwB5UQM7HJH3v3QAAIJJ4B6V1enazY39xPZ21xvu7RImuIXBEkXmLuXeMcEjnFXHjhuUQukcqhg6bgGAI5BHv3BqC301LfVLzUPNlkmuRGhDsNsaIDhVAHAyzNzk5Y84wAAZr3fisSuI9H0hkBO0tqkgJHbI8g4rJ1Xxdq+iSwx6lZ6FBJMrNGh1WZmYDGThbYnAyOfeugi8QafL4huNCWZhfwQidkZCoKE4ypPDYyM46ZFcpDa6vrDTeIbOeOBNRulh81pPLeLTIw+GjYqcM7HzOnRgMjAIAG/wDCx7j/AJ5aH/4HXX/yLXQad4stJdKtbvUbiztjd3QtIBFK7q8h+6oLohycHt+NcLZ+J9Zu9N03Sp7y8MOo6ndC31GNT50umQYO/KgEM+VUOADg7veun8HQTeIvAui3GpXV1IFuDcoS/M8aSuYd5OWI2iNuoJKjPcEA6LU59ailjGmWFlcoR85ubxoSD7ARvn9Kyr7WfEem2Ut3e6ZoVvbRLueWTVpAqj/wH/CtPWtfsNAS0fUJZI47m4S3RxGWVWY4BYjhRkgZPHIrH1xLjXfEtvpttsMGloL+befle55FujY7AgyH/dT1oAyv+Fkz/wDPPQ//AAOuv/kWtfwz4tl17UXtnTTlCxGT/RbmaRuCB0eFBjn1z7enKzeI9c8L6leS390+oJZ6KbvVYQ++KC6JAjVGCjbv5+TsvPudHwPdaqfE99Z3d7fXZj022lvhc7gI7yR5GYIrfcXZjAUYwB36gGl4nUD4geCJNo3/AGm7Td32m2ckfTIB/AV0tzq1haanZ6dPdRx3l7v+zRMfml2DLY+grmZ0/tX4s2e3Bh0TTZHdgucS3DBVXP8AuRk/iPWukutMju9RsryWaf8A0Mu8cQYBC7Lt3MMZJALAc4+Y8HjABo0UUUAFFFFABRRRQAUUUUAFFFFABRRRQAVBPbxXVvLbzxrJDKhR0YZDKRgg+xFT0UAYPhvTL7RLFtKnnjuLO1YJYzFj5vk9kkGMZT7oYH5gBnBzneoooA5Dxn4RuPEc2nXFje/YrmBngnlHV7WVdsyDj72ACp7EVoeIfDNv4i0H+xWu7uxtDtDiyKoWQDGw5Ujb0yMc4x0yK36KAOJm+HsUtvHH/beqtLiaKa5kaNpZYpVRXQHaAnEaAFQCAD6111rbQ2NpDa20SxQQosccaDCooGAAPQAVYooAyvEOi2/iLw/faPc5EV3C0ZYDlSejD3Bwfwqj4X0S+0nQmi1O9+0arcs015dxgfNKQBlcjoqhQMj+HpXR0UAcFb/DCxgtr23k1zWbqO6SQEXM0bhZHILS4CDc+VH3sjGRjFb2maG+hWF+9tL9t1S7Zp5Li6bb50u3CglR8qAAKAAdqjvW/RQBieHdEbRrSY3NwbrULuY3F5cEY8yQgDCjsigBVHYAVt0UUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQB//Z\n"
           },
           "metadata": {}
         },
@@ -1636,10 +1961,10 @@
               "    <body>\n",
               "        <div class=\"container\">\n",
               "            <div class=\"column\" style=\"border-right: 1px solid #ccc;\">\n",
-              "                <br>f ( \\sigma ) = f _ { 0 } \\frac { 1 } { \\sqrt { \\pi } } + \\sum _ { r = 1 } ^ { \\infty } f _ { n }<br><br>\n",
+              "                <br>f ( t , z , \\bar { z } ) = F _ { <span class='diff-remove'>\\star</span> } \\left( t , \\frac { z } { \\sqrt { 2 \\theta } } , \\frac { \\bar { z } } { \\sqrt { 2 \\theta } } \\right) ,<br><br>\n",
               "            </div>\n",
               "            <div class=\"column\">\n",
-              "                <br>f ( \\sigma ) = f _ { 0 } \\frac { 1 } { \\sqrt { \\pi } } + \\sum _ { r = 1 } ^ { \\infty } f _ { n } <span class='diff-add'>, \\qquad f ( \\sigma ) = f _ { 0 } \\frac { 1 } { \\sqrt { \\pi } } + \\infty \\sum _ { r = 1 } ^ { \\infty } f _ { n } , \\qquad f ( \\sigma ) = f _ { 0 } \\frac { 1 } { \\sqrt { \\pi } } + \\infty \\sum _ { r = 1 } ^ { \\infty } f _ { n } , \\qquad f ( \\sigma ) = f _ { 0 } \\frac { 1 } { \\sqrt { \\pi } } + \\infty \\sum _ { r = 1 } ^ { \\infty } f _ { n } , \\qquad f ( \\sigma ) = f _ { 0 } \\frac { 1 } { \\sqrt { \\pi } } + \\infty \\sum _ { r = 1 } ^ { \\infty } f _ { n } , \\qquad f ( \\</span><br><br>\n",
+              "                <br>f ( t , z , \\bar { z } ) = F _ { <span class='diff-add'>*</span> } \\left( t , \\frac { z } { \\sqrt { 2 \\theta } } , \\frac { \\bar { z } } { \\sqrt { 2 \\theta } } \\right) ,<br><br>\n",
               "            </div>\n",
               "        </div>\n",
               "    </body>\n",
@@ -1649,19 +1974,49 @@
           },
           "metadata": {}
         }
+      ],
+      "source": [
+        "# @title Suffix vs. generated text\n",
+        "\n",
+        "for i in range (10):\n",
+        "    image, label = test_dataset[i]\n",
+        "    prefix = \"<image>\" + label[\"prefix\"]\n",
+        "    suffix = label[\"suffix\"]\n",
+        "\n",
+        "    inputs = processor(\n",
+        "        text=prefix,\n",
+        "        images=image,\n",
+        "        return_tensors=\"pt\"\n",
+        "    ).to(TORCH_DTYPE).to(DEVICE)\n",
+        "\n",
+        "    prefix_length = inputs[\"input_ids\"].shape[-1]\n",
+        "\n",
+        "    with torch.inference_mode():\n",
+        "        generation = model.generate(**inputs, max_new_tokens=256, do_sample=False, num_beams=3)\n",
+        "        generation = generation[0][prefix_length:]\n",
+        "        generated_text = processor.decode(generation, skip_special_tokens=True)\n",
+        "\n",
+        "    html_diff = side_by_side_diff_divs(suffix, generated_text)\n",
+        "    display(image)\n",
+        "    display(HTML(html_diff))"
       ]
     },
     {
       "cell_type": "markdown",
-      "source": [
-        "### Evaluate fine-tuned PaliGemma2 model"
-      ],
       "metadata": {
         "id": "5cU-C88_IfAQ"
-      }
+      },
+      "source": [
+        "### Evaluate fine-tuned PaliGemma2 model"
+      ]
     },
     {
       "cell_type": "code",
+      "execution_count": 21,
+      "metadata": {
+        "id": "6zUxJufnIVMK"
+      },
+      "outputs": [],
       "source": [
         "import numpy as np\n",
         "\n",
@@ -1688,109 +2043,94 @@
         "\n",
         "        targets.append(suffix)\n",
         "        predictions.append(generated_text)"
-      ],
-      "metadata": {
-        "id": "6zUxJufnIVMK"
-      },
-      "execution_count": 29,
-      "outputs": []
+      ]
     },
     {
       "cell_type": "markdown",
-      "source": [
-        "**NOTE:** BLEU (Bilingual Evaluation Understudy) is a metric used to measure the similarity between a VLM's generated text (like a caption for an image) and a human-written reference text. It works by calculating the overlap of words and phrases, giving a score between 0 and 1.  A higher BLEU score indicates better agreement between the generated text and the reference, meaning the VLM is doing a better job of producing expected output."
-      ],
       "metadata": {
         "id": "ulb7SNacJua5"
-      }
+      },
+      "source": [
+        "**NOTE:** BLEU (Bilingual Evaluation Understudy) is a metric used to measure the similarity between a VLM's generated text (like a caption for an image) and a human-written reference text. It works by calculating the overlap of words and phrases, giving a score between 0 and 1.  A higher BLEU score indicates better agreement between the generated text and the reference, meaning the VLM is doing a better job of producing expected output."
+      ]
     },
     {
       "cell_type": "code",
-      "source": [
-        "!pip install -q evaluate"
-      ],
+      "execution_count": 22,
       "metadata": {
-        "id": "3c2S5avCKiDM",
         "colab": {
           "base_uri": "https://localhost:8080/"
         },
-        "outputId": "b74e19e8-cd01-46b3-909c-3fe24a264aa6"
+        "id": "3c2S5avCKiDM",
+        "outputId": "d15c19b8-7d85-4c45-a1a2-bf491816caa2"
       },
-      "execution_count": 31,
       "outputs": [
         {
           "output_type": "stream",
           "name": "stdout",
           "text": [
-            "\u001b[?25l   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m0.0/84.0 kB\u001b[0m \u001b[31m?\u001b[0m eta \u001b[36m-:--:--\u001b[0m\r\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m84.0/84.0 kB\u001b[0m \u001b[31m7.8 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
-            "\u001b[?25h\u001b[?25l   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m0.0/480.6 kB\u001b[0m \u001b[31m?\u001b[0m eta \u001b[36m-:--:--\u001b[0m\r\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m480.6/480.6 kB\u001b[0m \u001b[31m31.9 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
-            "\u001b[?25h\u001b[?25l   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m0.0/116.3 kB\u001b[0m \u001b[31m?\u001b[0m eta \u001b[36m-:--:--\u001b[0m\r\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m116.3/116.3 kB\u001b[0m \u001b[31m11.9 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
-            "\u001b[?25h\u001b[?25l   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m0.0/179.3 kB\u001b[0m \u001b[31m?\u001b[0m eta \u001b[36m-:--:--\u001b[0m\r\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m179.3/179.3 kB\u001b[0m \u001b[31m17.1 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
-            "\u001b[?25h\u001b[?25l   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m0.0/134.8 kB\u001b[0m \u001b[31m?\u001b[0m eta \u001b[36m-:--:--\u001b[0m\r\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m134.8/134.8 kB\u001b[0m \u001b[31m13.7 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
-            "\u001b[?25h\u001b[?25l   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m0.0/194.1 kB\u001b[0m \u001b[31m?\u001b[0m eta \u001b[36m-:--:--\u001b[0m\r\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m194.1/194.1 kB\u001b[0m \u001b[31m18.8 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[?25l   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m0.0/84.0 kB\u001b[0m \u001b[31m?\u001b[0m eta \u001b[36m-:--:--\u001b[0m\r\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m84.0/84.0 kB\u001b[0m \u001b[31m7.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[?25h\u001b[?25l   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m0.0/480.6 kB\u001b[0m \u001b[31m?\u001b[0m eta \u001b[36m-:--:--\u001b[0m\r\u001b[2K   \u001b[91m━━━━━━━━━━━━━━━━\u001b[0m\u001b[90m╺\u001b[0m\u001b[90m━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m194.6/480.6 kB\u001b[0m \u001b[31m10.6 MB/s\u001b[0m eta \u001b[36m0:00:01\u001b[0m\r\u001b[2K   \u001b[91m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[91m╸\u001b[0m\u001b[90m━━━\u001b[0m \u001b[32m440.3/480.6 kB\u001b[0m \u001b[31m6.5 MB/s\u001b[0m eta \u001b[36m0:00:01\u001b[0m\r\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m480.6/480.6 kB\u001b[0m \u001b[31m5.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[?25h\u001b[?25l   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m0.0/116.3 kB\u001b[0m \u001b[31m?\u001b[0m eta \u001b[36m-:--:--\u001b[0m\r\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m116.3/116.3 kB\u001b[0m \u001b[31m9.9 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[?25h\u001b[?25l   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m0.0/179.3 kB\u001b[0m \u001b[31m?\u001b[0m eta \u001b[36m-:--:--\u001b[0m\r\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m179.3/179.3 kB\u001b[0m \u001b[31m15.8 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[?25h\u001b[?25l   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m0.0/134.8 kB\u001b[0m \u001b[31m?\u001b[0m eta \u001b[36m-:--:--\u001b[0m\r\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m134.8/134.8 kB\u001b[0m \u001b[31m12.9 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[?25h\u001b[?25l   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m0.0/194.1 kB\u001b[0m \u001b[31m?\u001b[0m eta \u001b[36m-:--:--\u001b[0m\r\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m194.1/194.1 kB\u001b[0m \u001b[31m17.0 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
             "\u001b[?25h\u001b[31mERROR: pip's dependency resolver does not currently take into account all the packages that are installed. This behaviour is the source of the following dependency conflicts.\n",
             "gcsfs 2024.10.0 requires fsspec==2024.10.0, but you have fsspec 2024.9.0 which is incompatible.\u001b[0m\u001b[31m\n",
             "\u001b[0m"
           ]
         }
+      ],
+      "source": [
+        "!pip install -q evaluate"
       ]
     },
     {
       "cell_type": "code",
-      "source": [
-        "# @title Calculate BLEU\n",
-        "\n",
-        "from evaluate import load\n",
-        "\n",
-        "bleu = load(\"bleu\")\n",
-        "\n",
-        "results = bleu.compute(predictions=predictions, references=targets)\n",
-        "print(results)"
-      ],
+      "execution_count": 23,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
-          "height": 151,
+          "height": 130,
           "referenced_widgets": [
-            "ca7aebc964004606bc4bb2ded7845dba",
-            "1f72cb4fabc34524afbc492d35941834",
-            "910afed62aef457eb2de11ef0ba2f846",
-            "c3fb5a3f8659432690e74b9839d1beba",
-            "fc4626bd7d154d1b9077bb8e3b1a1ca8",
-            "6891878df8e94fad94d1b0043e211477",
-            "0c624ee250244606a6333fb04448c611",
-            "6e6def764f3e4be2aa694e7e46ed9f79",
-            "e5ef21ef83804f1b9bbd1287a12c8c2b",
-            "cce52c92b61b49a790c43748ba3df469",
-            "48521394be8e46199701bf86bc9ce45b",
-            "c3e9a08a931547b68a9a4027e288443a",
-            "32cf287379c540dea0fa6bae096a606b",
-            "d333b0fb43184394b88178a93c0a8c9c",
-            "5900a96b6eec4efaa7334b7885385f4d",
-            "26e8841f88244287a77fa381dc9e68c5",
-            "988f41845d21476ba76ea017e109cd49",
-            "5de998d0e21e47a7a5fc1fed9c379b8f",
-            "b2eb2780ff6c49879141760d2ddec932",
-            "e12b6026469f4329b09eb8d9a4f94db3",
-            "65ee27bae1044d16acd443ad4db25614",
-            "d7fbd5c089ce48218df82079ae667e60",
-            "171e4e3012e346d08a4d11cdf571fc35",
-            "5e2ee6332e214d6b9c3be718d0b41665",
-            "a3ab6e6436ff47e8ad7284253e18f399",
-            "4cb23557c6214a16a3ad46810118108e",
-            "4be42740a20640a5b44dd14bfe782400",
-            "02b4e70706274c619d3c226bca79e090",
-            "b13129bbd7674bb783ca8cd1d47c5575",
-            "470a106c3bee4c658271c595fb842a61",
-            "5fa51694da274034b17fbfda7fc26027",
-            "0eca508f03c9424aa34b8216e02b4f0e",
-            "e73d62976231495384b1fba212969acf"
+            "65de82823814445c90eccec2b8202db1",
+            "94f0b6a012ab4178b53ea6332e2eb50c",
+            "9981cd15dec94796810e1e141576765f",
+            "a1b3684587c949aca3055369f790d5a7",
+            "e8048c541d5a42ba9aa7736fb9b6859c",
+            "7a357ce1b9c14872b6ccb9730faa961b",
+            "147584d42e8d4c63b1614a995d9408a9",
+            "8a30e2c843484cc186865e33020104ff",
+            "b031598a947f4b2c94156d81854a8813",
+            "8866699020a54ef89b459a39dc18e2df",
+            "d136ecf468a74980baf3ea71adcecde7",
+            "88810a621c9d41449d7dbd0234f22904",
+            "ef5e154e32334abc9103f98602a89c37",
+            "b6cb53fd090c41f0bc0f3d947b7f4102",
+            "1320a30ebc1d4ea8aad5263d67267995",
+            "2448c9f029c44ff6a8079ddf45d1b651",
+            "566b4d04baf542099388a850bec050e0",
+            "f3e8cc24eaf0468d8393b28a9e586a0e",
+            "c65b95f237ea4f79abc106cb8f1fd79d",
+            "21bce2ffb0c64643acf1705c1d9cf7f1",
+            "0c82d7e13a4245e7bdf47d1839e660ae",
+            "61d1d81f980941bba3c647eab8a67ae7",
+            "4760b69b8e204119ba1df519d810c3cd",
+            "288e9c53ae4f40b4b910c228c2d68dab",
+            "34eb2d74cf704ceb95abbf2ab8ad7e45",
+            "e26ab30e13594a62929c52aa903378d9",
+            "5f42f1c9e9ac4e2c96d12f06165d57d4",
+            "d8507df327cb459aa954ae500181cb47",
+            "77ca22841d7348788dd710f57ba2f7c5",
+            "7c248573664740d8aaba2c94ff0acae3",
+            "e79f982a893046ed8d73dff3cb696bc7",
+            "63797809b54248b28850c9dcb042db53",
+            "6b9efce422524b958ca542f24311624c"
           ]
         },
         "id": "ATtWcyjFH9EC",
-        "outputId": "d9b4d23b-ec9b-491a-fd4d-714d08695f43"
+        "outputId": "1fe5cc3d-46ef-4ac3-cf38-2da28a273575"
       },
-      "execution_count": 32,
       "outputs": [
         {
           "output_type": "display_data",
@@ -1801,7 +2141,7 @@
             "application/vnd.jupyter.widget-view+json": {
               "version_major": 2,
               "version_minor": 0,
-              "model_id": "ca7aebc964004606bc4bb2ded7845dba"
+              "model_id": "65de82823814445c90eccec2b8202db1"
             }
           },
           "metadata": {}
@@ -1815,7 +2155,7 @@
             "application/vnd.jupyter.widget-view+json": {
               "version_major": 2,
               "version_minor": 0,
-              "model_id": "c3e9a08a931547b68a9a4027e288443a"
+              "model_id": "88810a621c9d41449d7dbd0234f22904"
             }
           },
           "metadata": {}
@@ -1829,7 +2169,7 @@
             "application/vnd.jupyter.widget-view+json": {
               "version_major": 2,
               "version_minor": 0,
-              "model_id": "171e4e3012e346d08a4d11cdf571fc35"
+              "model_id": "4760b69b8e204119ba1df519d810c3cd"
             }
           },
           "metadata": {}
@@ -1838,78 +2178,79 @@
           "output_type": "stream",
           "name": "stdout",
           "text": [
-            "{'bleu': 0.2701860980264998, 'precisions': [0.3021834061135371, 0.2802631578947368, 0.25903083700440527, 0.24292035398230089], 'brevity_penalty': 1.0, 'length_ratio': 3.1586206896551725, 'translation_length': 2290, 'reference_length': 725}\n"
+            "{'bleu': 0.7391661684279524, 'precisions': [0.9650455927051672, 0.8796296296296297, 0.7915360501567398, 0.7181528662420382], 'brevity_penalty': 0.886866522219942, 'length_ratio': 0.89280868385346, 'translation_length': 658, 'reference_length': 737}\n"
           ]
         }
+      ],
+      "source": [
+        "# @title Calculate BLEU\n",
+        "\n",
+        "from evaluate import load\n",
+        "\n",
+        "bleu = load(\"bleu\")\n",
+        "\n",
+        "results = bleu.compute(predictions=predictions, references=targets)\n",
+        "print(results)"
       ]
     },
     {
       "cell_type": "code",
-      "source": [
-        "!pip install -q sacrebleu"
-      ],
+      "execution_count": 24,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/"
         },
         "id": "LdWWIf4kKWqs",
-        "outputId": "70da191d-1ad5-4cdc-fced-8e764682d6e3"
+        "outputId": "8140f93e-11c1-481b-8a2f-1875260137d6"
       },
-      "execution_count": 33,
       "outputs": [
         {
           "output_type": "stream",
           "name": "stdout",
           "text": [
-            "\u001b[?25l     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m0.0/51.8 kB\u001b[0m \u001b[31m?\u001b[0m eta \u001b[36m-:--:--\u001b[0m\r\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m51.8/51.8 kB\u001b[0m \u001b[31m4.7 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
-            "\u001b[?25h\u001b[?25l   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m0.0/104.0 kB\u001b[0m \u001b[31m?\u001b[0m eta \u001b[36m-:--:--\u001b[0m\r\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m104.0/104.0 kB\u001b[0m \u001b[31m10.3 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m51.8/51.8 kB\u001b[0m \u001b[31m4.7 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m104.0/104.0 kB\u001b[0m \u001b[31m9.1 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
             "\u001b[?25h"
           ]
         }
+      ],
+      "source": [
+        "!pip install -q sacrebleu"
       ]
     },
     {
       "cell_type": "markdown",
-      "source": [
-        "**NOTE:** Translation Error Rate (TER) is another metric used to evaluate machine translation, often applied to VLMs that generate text. Unlike BLEU, which focuses on overlap, TER calculates the number of edits (insertions, deletions, substitutions, shifts) needed to change the generated text into a human-written reference."
-      ],
       "metadata": {
         "id": "07DPD2UPKyBR"
-      }
+      },
+      "source": [
+        "**NOTE:** Translation Error Rate (TER) is another metric used to evaluate machine translation, often applied to VLMs that generate text. Unlike BLEU, which focuses on overlap, TER calculates the number of edits (insertions, deletions, substitutions, shifts) needed to change the generated text into a human-written reference."
+      ]
     },
     {
       "cell_type": "code",
-      "source": [
-        "# @title Calculate TER\n",
-        "\n",
-        "from evaluate import load\n",
-        "\n",
-        "ter = load(\"ter\")\n",
-        "results = ter.compute(predictions=predictions, references=targets, case_sensitive=True)\n",
-        "print(results)"
-      ],
+      "execution_count": 25,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
-          "height": 67,
+          "height": 66,
           "referenced_widgets": [
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+            "58040ae1bf5f4a5bb1d94cf2e67dbb59",
+            "2a4ed96361d14a8fbf4e32eba3280ada",
+            "18e9b7c41f83466fb76eb96222dfb01f",
+            "aee8117c5c5142de8ada83734f74a719",
+            "1e061226a8e845ec94420a185bab40a6"
           ]
         },
         "id": "ykKFf808JwfK",
-        "outputId": "f926d0c5-dc6a-47cf-a565-3899f0b882c0"
+        "outputId": "bec63ba6-6e3b-4c68-f25f-921091f93368"
       },
-      "execution_count": 34,
       "outputs": [
         {
           "output_type": "display_data",
@@ -1920,7 +2261,7 @@
             "application/vnd.jupyter.widget-view+json": {
               "version_major": 2,
               "version_minor": 0,
-              "model_id": "9a735f3919644616bcc4c585d06d645d"
+              "model_id": "a245eeb765664b5fb97e3156f67e4090"
             }
           },
           "metadata": {}
@@ -1929,9 +2270,18 @@
           "output_type": "stream",
           "name": "stdout",
           "text": [
-            "{'score': 204.27892234548338, 'num_edits': 1289, 'ref_length': 631.0}\n"
+            "{'score': 17.472698907956318, 'num_edits': 112, 'ref_length': 641.0}\n"
           ]
         }
+      ],
+      "source": [
+        "# @title Calculate TER\n",
+        "\n",
+        "from evaluate import load\n",
+        "\n",
+        "ter = load(\"ter\")\n",
+        "results = ter.compute(predictions=predictions, references=targets, case_sensitive=True)\n",
+        "print(results)"
       ]
     }
   ],
@@ -1951,7 +2301,7 @@
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             "box_style": "",
-            "children": [],
-            "layout": "IPY_MODEL_315af73ed83744b099320c20dc59508f"
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+            "placeholder": "​",
+            "style": "IPY_MODEL_af937e8993534b949629dbffeaea4826",
+            "value": "<center> <img\nsrc=https://huggingface.co/front/assets/huggingface_logo-noborder.svg\nalt='Hugging Face'> <br> Copy a token from <a\nhref=\"https://huggingface.co/settings/tokens\" target=\"_blank\">your Hugging Face\ntokens page</a> and paste it below. <br> Immediately click login after copying\nyour token or it might be stored in plain text in this notebook file. </center>"
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+            "disabled": false,
+            "indent": true,
+            "layout": "IPY_MODEL_60e707662cdd4337a611ec62a7c0903d",
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