Notebooks and Code Used in the blog post

20260121-reverse-preprocessing.ipynb

20260122-reverse-preprocessing.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6acf63e6-176b-409a-8570-e865892c92a2",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import numpy as np\n",
    "from PIL import Image\n",
    "from transformers.utils.import_utils import is_flash_attn_2_available\n",
    "\n",
    "from colpali_engine.models import ColQwen2, ColQwen2Processor\n",
    "from colpali_engine.interpretability import get_similarity_maps_from_embeddings\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "from plot_utils import plot_similarity_map"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "79730c3b-f038-480d-a892-539eb7122e27",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "The image processor of type `Qwen2VLImageProcessor` is now loaded as a fast processor by default, even if the model checkpoint was saved with a slow processor. This is a breaking change and may produce slightly different outputs. To continue using the slow processor, instantiate this class with `use_fast=False`. Note that this behavior will be extended to all models in a future release.\n"
     ]
    }
   ],
   "source": [
    "model_name = \"vidore/colqwen2-v1.0\"\n",
    "\n",
    "processor = ColQwen2Processor.from_pretrained(model_name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5e9914ff-1264-4536-aada-3de1cc941ca3",
   "metadata": {},
   "outputs": [],
   "source": [
    "images = [\n",
    "    Image.open(\"../data/attention-is-all-you-need/page-0.png\"),\n",
    "    Image.open(\"../data/attention-is-all-you-need/page-1.png\"),\n",
    "    Image.open(\"../data/attention-is-all-you-need/page-2.png\"),\n",
    "    Image.open(\"../data/attention-is-all-you-need/page-3.png\"),\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7f18d60e-f26d-4edd-b2ee-030b3c59048b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([4, 2976, 1176])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "batch_images = processor.process_images(images)\n",
    "batch_images[\"pixel_values\"].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f0fe7c1a-153b-43fe-b68d-a871ddfb88b2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[ 1, 62, 48],\n",
       "        [ 1, 62, 48],\n",
       "        [ 1, 62, 48],\n",
       "        [ 1, 62, 48]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "batch_images[\"image_grid_thw\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "1ccae831-9879-4cfc-8d3e-f51610b4a092",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(672, 868)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The shape of the resized image\n",
    "48 * 14, 62 * 14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2e085490-c428-46f1-b1e6-c130e04cd263",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`torch_dtype` is deprecated! Use `dtype` instead!\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b745a5d6ed8e4cc2af0ddf5c636c4e64",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Fetching 2 files:   0%|          | 0/2 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "45799375af544003b2f8faf08958a997",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Loading checkpoint shards:   0%|          | 0/2 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = ColQwen2.from_pretrained(\n",
    "    model_name,\n",
    "    torch_dtype=torch.bfloat16,\n",
    "    device_map=\"cuda:0\",\n",
    "    attn_implementation=\"flash_attention_2\" if is_flash_attn_2_available() else None,\n",
    ").eval()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3d8343f8-186d-478d-a39f-1f2a54609737",
   "metadata": {},
   "outputs": [],
   "source": [
    "queries = [\n",
    "    \"What are the key innovations of the Transformer architecture?\",\n",
    "    \"How do the Encoder and Decoder stacks work together in Transformers?\",\n",
    "]\n",
    "batch_queries = processor.process_queries(queries).to(model.device)\n",
    "batch_images = batch_images.to(model.device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1fefd2dc-e6ef-4525-a85a-e94ceef24c2a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([4, 755, 128]), torch.Size([2, 22, 128]))"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Forward pass\n",
    "with torch.no_grad():\n",
    "    image_embeddings = model(**batch_images)\n",
    "    query_embeddings = model(**batch_queries)\n",
    "image_embeddings.shape, query_embeddings.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "8c972025-aa52-4861-b1eb-7706e32662be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[13.5625, 13.7500, 15.0000,  7.8750],\n",
       "        [13.5000, 13.8750, 17.0000,  8.9375]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scores = processor.score_multi_vector(query_embeddings, image_embeddings)\n",
    "scores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "e279323d-82ed-4747-af0a-1bc4b2e23a8e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(24, 31)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get the number of image patches\n",
    "n_patches = processor.get_n_patches(image_size=images[0].size, spatial_merge_size=2)\n",
    "n_patches"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "23c8e5df-6382-48d4-a6e3-8c5fad12639f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([4, 755]), 744)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get the tensor mask to filter out the embeddings that are not related to the image\n",
    "image_mask = processor.get_image_mask(batch_images)\n",
    "image_mask.shape, image_mask[0].sum().item()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "e0522f5e-c521-45ce-a60f-283daafb7d97",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([22, 24, 31])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Generate the similarity maps\n",
    "query_idx = 1\n",
    "image_idx = 2\n",
    "batched_similarity_maps = get_similarity_maps_from_embeddings(\n",
    "    image_embeddings=image_embeddings[image_idx].unsqueeze(0),\n",
    "    query_embeddings=query_embeddings[query_idx].unsqueeze(0),\n",
    "    n_patches=n_patches,\n",
    "    image_mask=image_mask[image_idx].unsqueeze(0),\n",
    ")\n",
    "batched_similarity_maps[0].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "95c95f31-4a99-472f-896b-872c94cfc9b1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(['How',\n",
       "  'Ġdo',\n",
       "  'Ġthe',\n",
       "  'ĠEncoder',\n",
       "  'Ġand',\n",
       "  'ĠDecoder',\n",
       "  'Ġstacks',\n",
       "  'Ġwork',\n",
       "  'Ġtogether',\n",
       "  'Ġin',\n",
       "  'ĠTransformers',\n",
       "  '?'],\n",
       " 12)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Tokenize the query\n",
    "query_content = processor.decode(batch_queries.input_ids[query_idx]).replace(processor.tokenizer.pad_token, \"\")\n",
    "query_content = query_content.replace(processor.query_augmentation_token, \"\").strip()\n",
    "\n",
    "query_tokens = processor.tokenizer.tokenize(query_content)\n",
    "query_tokens, len(query_tokens)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "e5b261f6-f69f-40c7-8d4b-ee8bafc98739",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Token: `ĠDecoder` Max_Value: 0.84\n"
     ]
    },
    {
     "data": {
      "image/png": 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

plot_utils.py