{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e3a8391d",
   "metadata": {
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     "duration": 0.004853,
     "end_time": "2026-05-31T09:45:55.530382+00:00",
     "exception": false,
     "start_time": "2026-05-31T09:45:55.525529+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "# Convolution Tutorial Series — Part 1: Kernel Size and Bias\n",
    "\n",
    "**Goal:** Understand how a 3x3 kernel functions as a 'stencil' to solve ARC tasks. This is the first episode in a series that we want to create, covering all the attributes of the ONNX Conv function, in this notebook we will cover the basics of the convolution. We will explain these as simply as possible, using some tasks as examples, similar to this [notebook](https://www.kaggle.com/code/massimilianoghiotto/best-public-6066-58-eda-111) that we made and EDA notebooks made by @cdeotte.\n",
    "\n",
    "**Task (ARC 015):** \n",
    "1. **Red (2) triggers Yellow (4):** Every Red pixel should have Yellow pixels at its 4 diagonals (corners).\n",
    "2. **Blue (1) triggers Orange (7):** Every Blue pixel should have Orange pixels at its Top, Bottom, Left, and Right (cross shape).\n",
    "3. **Persistence:** The original Red and Blue pixels must stay.\n",
    "\n",
    "**Score formula:** `Points = max(1.0, 25.0 - log(Mem_bytes + Params))`\n",
    "\n",
    "**Our result:** Mem=0, Params=900, **18.198 points**\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "da51b56d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-31T09:45:55.540674Z",
     "iopub.status.busy": "2026-05-31T09:45:55.540332Z",
     "iopub.status.idle": "2026-05-31T09:46:17.055712Z",
     "shell.execute_reply": "2026-05-31T09:46:17.054631Z"
    },
    "papermill": {
     "duration": 21.522421,
     "end_time": "2026-05-31T09:46:17.057796+00:00",
     "exception": false,
     "start_time": "2026-05-31T09:45:55.535375+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m16.6/16.6 MB\u001b[0m \u001b[31m51.8 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\r\n",
      "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m17.2/17.2 MB\u001b[0m \u001b[31m53.2 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\r\n",
      "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m56.2/56.2 kB\u001b[0m \u001b[31m797.1 kB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\r\n",
      "\u001b[?25h"
     ]
    }
   ],
   "source": [
    "!pip install -q numpy==2.4.4 2>/dev/null\n",
    "!pip install -q onnx==1.21.0 2>/dev/null\n",
    "!pip install -q onnxruntime==1.24.4 2>/dev/null\n",
    "!pip install -q onnx-tool==1.0.1 2>/dev/null"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b75e1555",
   "metadata": {
    "papermill": {
     "duration": 0.004086,
     "end_time": "2026-05-31T09:46:17.066711+00:00",
     "exception": false,
     "start_time": "2026-05-31T09:46:17.062625+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "# 1. Task 015"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "094b6afa",
   "metadata": {
    "_kg_hide-input": true,
    "execution": {
     "iopub.execute_input": "2026-05-31T09:46:17.078057Z",
     "iopub.status.busy": "2026-05-31T09:46:17.076748Z",
     "iopub.status.idle": "2026-05-31T09:46:17.519001Z",
     "shell.execute_reply": "2026-05-31T09:46:17.518050Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "papermill": {
     "duration": 0.449803,
     "end_time": "2026-05-31T09:46:17.520753+00:00",
     "exception": false,
     "start_time": "2026-05-31T09:46:17.070950+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
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\n",
      "text/plain": [
       "<Figure size 1440x240 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import json, math, warnings, sys\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.patches as patches\n",
    "import onnx\n",
    "from onnx import helper, TensorProto\n",
    "import onnxruntime as ort\n",
    "\n",
    "warnings.filterwarnings('ignore')\n",
    "plt.rcParams['figure.dpi'] = 120\n",
    "\n",
    "arc_colors = [\n",
    "    '#000000',  # 0: black\n",
    "    '#0074D9',  # 1: blue\n",
    "    '#FF4136',  # 2: red\n",
    "    '#2ECC40',  # 3: green\n",
    "    '#FFDC00',  # 4: yellow\n",
    "    '#AAAAAA',  # 5: gray\n",
    "    '#F012BE',  # 6: magenta\n",
    "    '#FF851B',  # 7: orange\n",
    "    '#7FDBCA',  # 8: teal\n",
    "    '#870C25',  # 9: maroon\n",
    "]\n",
    "color_names = ['black','blue','red','green','yellow','gray','magenta','orange','teal','maroon']\n",
    "\n",
    "def plot_arc_grid(grid, ax, title=''):\n",
    "    H, W = len(grid), len(grid[0])\n",
    "    img = np.zeros((H, W, 3), dtype=np.uint8)\n",
    "    for r in range(H):\n",
    "        for c in range(W):\n",
    "            hex_c = arc_colors[grid[r][c]].lstrip('#')\n",
    "            img[r,c] = [int(hex_c[i:i+2], 16) for i in (0, 2, 4)]\n",
    "    ax.imshow(img, interpolation='nearest')\n",
    "    ax.set_xticks([]); ax.set_yticks([])\n",
    "    if title: ax.set_title(title, fontsize=10, fontweight='bold')\n",
    "    for r in range(H+1): ax.axhline(r-0.5, color='gray', lw=0.5, alpha=0.3)\n",
    "    for c in range(W+1): ax.axvline(c-0.5, color='gray', lw=0.5, alpha=0.3)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(12, 2))\n",
    "for i, (c, nm) in enumerate(zip(arc_colors, color_names)):\n",
    "    ax.add_patch(patches.Rectangle((i*1.2, 0), 1, 1, facecolor=c, edgecolor='gray', lw=1))\n",
    "    ax.text(i*1.2+0.5, 0.5, str(i), ha='center', va='center', fontsize=16, fontweight='bold',\n",
    "            color='white' if i in [0,9] else 'black')\n",
    "    ax.text(i*1.2+0.5, -0.2, nm, ha='center', va='top', fontsize=8)\n",
    "ax.set_xlim(-0.5, 12.5)\n",
    "ax.set_ylim(-0.3, 1.5)\n",
    "ax.axis('off')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6dd1be1",
   "metadata": {
    "papermill": {
     "duration": 0.004299,
     "end_time": "2026-05-31T09:46:17.529946+00:00",
     "exception": false,
     "start_time": "2026-05-31T09:46:17.525647+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "The rules are:\n",
    "1. **Red (2) triggers Yellow (4):** Every Red pixel should have Yellow pixels at its 4 diagonals (corners).\n",
    "2. **Blue (1) triggers Orange (7):** Every Blue pixel should have Orange pixels at its Top, Bottom, Left, and Right (cross shape).\n",
    "3. **Persistence:** The original colored pixels must stay."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "947c7941",
   "metadata": {
    "_kg_hide-input": true,
    "execution": {
     "iopub.execute_input": "2026-05-31T09:46:17.540715Z",
     "iopub.status.busy": "2026-05-31T09:46:17.540268Z",
     "iopub.status.idle": "2026-05-31T09:46:17.642912Z",
     "shell.execute_reply": "2026-05-31T09:46:17.641856Z"
    },
    "papermill": {
     "duration": 0.109937,
     "end_time": "2026-05-31T09:46:17.644427+00:00",
     "exception": false,
     "start_time": "2026-05-31T09:46:17.534490+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with open('/kaggle/input/competitions/neurogolf-2026/task015.json') as f:\n",
    "    task = json.load(f)\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, figsize=(10, 5))\n",
    "plot_arc_grid(task['train'][0]['input'], axes[0], 'Input')\n",
    "plot_arc_grid(task['train'][0]['output'], axes[1], 'Target Output')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab748fb3",
   "metadata": {
    "papermill": {
     "duration": 0.004416,
     "end_time": "2026-05-31T09:46:17.653821+00:00",
     "exception": false,
     "start_time": "2026-05-31T09:46:17.649405+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "# 2. Convolution design\n",
    "\n",
    "In ONNX, the `Conv` operator weights W have the shape **[M, C, kH, kW]**:\n",
    "- `M` = number of **output** channels (10, one per color)\n",
    "- `C` = number of **input** channels (10, one per color)\n",
    "- `kH, kW` = kernel height and width (both 3 in this case)\n",
    "\n",
    "This means that every input color (0-9) can influence every output color (0-9) through a unique 3x3 pattern of weights. We have 100 unique 3x3 patterns (10 output colors x 10 input colors).\n",
    "\n",
    "### The 3×3 Stencil\n",
    "\n",
    "When the convolution produces pixel `(x,y)` in the output, it looks at a 3×3 window of the input centered at `(x,y)`. The window coordinates (offset from center) are:\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "(-1,-1) & ( 0,-1) & ( 1,-1) \\\\\n",
    "(-1, 0) & ( 0, 0) & ( 1, 0) \\\\\n",
    "(-1, 1) & ( 0, 1) & ( 1, 1)\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "The offset `(0,0)` is the **center** — the pixel directly below the output position. The other offsets are its neighbors.\n",
    "\n",
    "### The Formula\n",
    "The output for a color O at position (x,y) is:\n",
    "$$ Output_{O}(x,y) = \\sum_{i=0}^{9} \\sum_{r=-1}^{1} \\sum_{c=-1}^{1} Input_{i}(x+r, y+c) \\cdot W(O, i, r, c) $$\n",
    "\n",
    "## 2.1 The Identity Kernel — \"Pixel stays where it is\"\n",
    "\n",
    "### The Identity Kernel\n",
    "\n",
    "The simplest kernel is the **identity**: it copies an input pixel straight to the output without moving it. For every color `c`, we set:\n",
    "\n",
    "$$W[c,\\;c,\\;1,\\;1] = 1.0$$\n",
    "\n",
    "This says: \"for output channel `c`, look at input channel `c`, at offset `(0,0)` (the center), and multiply by 1.0.\" All other offsets are 0, so no neighboring pixels leak in.\n",
    "\n",
    "Visually, the identity kernel for any color `c` looks like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3e23e8fb",
   "metadata": {
    "_kg_hide-input": true,
    "execution": {
     "iopub.execute_input": "2026-05-31T09:46:17.664586Z",
     "iopub.status.busy": "2026-05-31T09:46:17.664265Z",
     "iopub.status.idle": "2026-05-31T09:46:17.749763Z",
     "shell.execute_reply": "2026-05-31T09:46:17.749075Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "papermill": {
     "duration": 0.092806,
     "end_time": "2026-05-31T09:46:17.751247+00:00",
     "exception": false,
     "start_time": "2026-05-31T09:46:17.658441+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 420x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Only the center (0,0) is 1.0 — the pixel passes through unchanged.\n",
      "All other offsets are 0.0 — no neighbor pixels bleed in.\n"
     ]
    }
   ],
   "source": [
    "def visualize_kernel(kernel, title, cmap='RdBu', highlight_center=True):\n",
    "    fig, ax = plt.subplots(figsize=(3.5, 3))\n",
    "    im = ax.imshow(kernel, cmap=cmap, vmin=-1.2, vmax=1.2)\n",
    "    for i in range(3):\n",
    "        for j in range(3):\n",
    "            val = kernel[i, j]\n",
    "            c = 'black' if abs(val) < 0.5 else 'white'\n",
    "            ax.text(j, i, f'{val:.1f}', ha='center', va='center',\n",
    "                    color=c, fontweight='bold', fontsize=13)\n",
    "    if highlight_center:\n",
    "        ax.add_patch(plt.Rectangle((0.5, 0.5), 1, 1, fill=False,\n",
    "                     edgecolor='lime', lw=3, linestyle='--'))\n",
    "    ax.set_xticks(range(3), ['-1','0','1'])\n",
    "    ax.set_yticks(range(3), ['-1','0','1'])\n",
    "    ax.set_xlabel('Column offset', fontsize=9)\n",
    "    ax.set_ylabel('Row offset', fontsize=9)\n",
    "    ax.set_title(title, fontsize=11, fontweight='bold')\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "\n",
    "k_identity = np.array([[0, 0, 0], [0, 1, 0], [0, 0, 0]])\n",
    "visualize_kernel(k_identity, 'Identity: W[c, c, :, :]')\n",
    "\n",
    "print(\"Only the center (0,0) is 1.0 — the pixel passes through unchanged.\")\n",
    "print(\"All other offsets are 0.0 — no neighbor pixels bleed in.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d58da69",
   "metadata": {
    "papermill": {
     "duration": 0.006139,
     "end_time": "2026-05-31T09:46:17.762616+00:00",
     "exception": false,
     "start_time": "2026-05-31T09:46:17.756477+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## 2.2 Red Triggers Yellow — Two Kernels for One Rule\n",
    "\n",
    "Now the real work begins. The task rule is:\n",
    "\n",
    "> **Every Red (2) pixel must have Yellow (4) pixels at its four diagonal corners.**\n",
    "\n",
    "But there's a subtlety: what if a corner position was **Black (0)** background? The Yellow pixel needs to *replace* the Black. So we need:\n",
    "\n",
    "1. **A \"write Yellow\" kernel** — when the center is Red, vote +1.0 for Yellow at the corners.\n",
    "2. **A \"suppress Black\" kernel** — when the center is Red, vote −1.0 for Black at those same corners.\n",
    "\n",
    "### The Two Corners Kernels\n",
    "\n",
    "Both kernels use the same 3×3 pattern — the four corners — but with opposite signs.\n",
    "\n",
    "| Kernel | Expression | Effect |\n",
    "|--------|-----------|--------|\n",
    "| `W[4, 2, :, :]` = corners pattern × **+1** | Each corner adds 1.0 to Yellow's score | **Creates** Yellow at the diagonals |\n",
    "| `W[0, 2, :, :]` = corners pattern × **−1** | Each corner subtracts 1.0 from Black's score | **Suppresses** Black at those same spots |\n",
    "\n",
    "The corners pattern is:\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "1 & 0 & 1 \\\\\n",
    "0 & 0 & 0 \\\\\n",
    "1 & 0 & 1\n",
    "\\end{bmatrix}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "050dbfc3",
   "metadata": {
    "_kg_hide-input": true,
    "execution": {
     "iopub.execute_input": "2026-05-31T09:46:17.773940Z",
     "iopub.status.busy": "2026-05-31T09:46:17.773691Z",
     "iopub.status.idle": "2026-05-31T09:46:17.914713Z",
     "shell.execute_reply": "2026-05-31T09:46:17.913461Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "papermill": {
     "duration": 0.149167,
     "end_time": "2026-05-31T09:46:17.916905+00:00",
     "exception": false,
     "start_time": "2026-05-31T09:46:17.767738+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The two kernels are identical in pattern (corners), opposite in sign.\n",
      "Together they ensure: when center is Red → corners become Yellow, not Black.\n"
     ]
    }
   ],
   "source": [
    "k_corners_pos = np.array([[ 1,  0,  1],\n",
    "                          [ 0,  0,  0],\n",
    "                          [ 1,  0,  1]])\n",
    "k_corners_neg = np.array([[-1,  0, -1],\n",
    "                          [ 0,  0,  0],\n",
    "                          [-1,  0, -1]])\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, figsize=(7.5, 3))\n",
    "for ax, kernel, title, cm in zip(axes,\n",
    "    [k_corners_pos, k_corners_neg],\n",
    "    [r'W[4, 2, :, :]  — Write Yellow (4)', r'W[0, 2, :, :]  — Suppress Black (0)'],\n",
    "    ['YlOrRd', 'Blues_r']):\n",
    "    im = ax.imshow(kernel, cmap=cm, vmin=-1.2, vmax=1.2)\n",
    "    for i in range(3):\n",
    "        for j in range(3):\n",
    "            val = kernel[i, j]\n",
    "            c = 'white' if abs(val) > 0.5 else 'black'\n",
    "            ax.text(j, i, f'{val:+.1f}', ha='center', va='center',\n",
    "                    color=c, fontweight='bold', fontsize=14)\n",
    "    ax.set_xticks(range(3), ['-1','0','1'])\n",
    "    ax.set_yticks(range(3), ['-1','0','1'])\n",
    "    ax.set_title(title, fontsize=10, fontweight='bold')\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(\"The two kernels are identical in pattern (corners), opposite in sign.\")\n",
    "print(\"Together they ensure: when center is Red → corners become Yellow, not Black.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5187813",
   "metadata": {
    "papermill": {
     "duration": 0.005325,
     "end_time": "2026-05-31T09:46:17.928085+00:00",
     "exception": false,
     "start_time": "2026-05-31T09:46:17.922760+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "### How the Convolution \"Walks\" Across the Grid\n",
    "Let's trace what the convolution computes at **three different output positions** on a 5×5 grid with a single Red at (2,2).\n",
    "\n",
    "We fix $W[4, 3, :, :]$ and for each position we show:\n",
    "1. **Where the kernel is centered** — first column — marked with an orange square on the input grid\n",
    "2. **What the 3×3 kernel \"sees\"** — second column — each cell shows the input pixel color AND the weight value for (input→output) at that offset\n",
    "3. **The score breakdown** — third column — how each channel's score is computed, and which wins"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a8e117ff",
   "metadata": {
    "_kg_hide-input": true,
    "execution": {
     "iopub.execute_input": "2026-05-31T09:46:17.941267Z",
     "iopub.status.busy": "2026-05-31T09:46:17.940314Z",
     "iopub.status.idle": "2026-05-31T09:46:18.411040Z",
     "shell.execute_reply": "2026-05-31T09:46:18.410270Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "papermill": {
     "duration": 0.479343,
     "end_time": "2026-05-31T09:46:18.412619+00:00",
     "exception": false,
     "start_time": "2026-05-31T09:46:17.933276+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
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G7dq1y9ZhlZmzlRGo2dnZVssWvO2+qONh3cHzF/Tbnn0W2zxdXNSjQT0bRXT14roEKgeTg4O8u3WTR8uWkiRzWpqyLlywKBM7e7b2deyobV5e2ururr3t2il27txCdZ37v//Tjpo1tc3TU4fuukuZp05ZPWfUwIHGNBFAeXMJDZVvz55K3rLF2JYZHa2jDz2kyOrVtaNGDZ14/nnl5PsCM+7HH7WrXj1t8/XVsSFDpKysIutPXLlS2/38jOdZ8fE6ct992u7np12NGilp9eoKaZckBT39tHy6d5fJza1Mx6fu3atdjRop7eDBMsdgcnRUwKBByklKUtqBA8b22DlztKdFC23389PeiAglrVtn7CtNHyVv3KjI6tWN5ydeeklbnJ2V/c/dSNGTJ+tQ796SpNOjR+tQvpG7W0wmnf/sM+1u1kzbfHx06M47jUR1Tnq6oh5/XNsDA7XN11e7mzVT8qZNZe4HoLRIAgMAUAYffPCBvvrqKy1ZskQXLlzQDTfcoFtvvdXqreqVQcF5W2HdgfMX9PHa9crKl7B0dHDQ0A4R8injP1MoGtclcG0x590h4eAgp4AAY/vpt97S0YceUvKGDcpJTpY5LU0pmzbp6AMP6OwHHxjlLnz1lU4OH67MU6eUk5Kii7/8osP33HOlm4Fr2PGnntJ2P78if5L++qtE9aRHRenib7/JrUEDSbnX9uE775RTtWpqfviwmuzcqZTISJ0ZO1aSlHbggI4++KBqTpyo62Ji5NGmjS4uXlziuE8895yy4uPVLCpKDZYvV8zMmaVv/BWQduiQDnbvrmqvvSa3+vXLXI85M1MXpk6VycVFLv8sDHtx0SKdHD5c4TNmqGVsrKqNGKFDvXsrKyZGUun6yKNNG+UkJyt1715JUuLy5XKtVUtJa9YYz71vuqnI4+PmzVOD5cvV/PhxZZw8qXMTJ0qSYr7+WqmRkWp26JCui49X3fnz5cwaBriCSAIDAFAGn3zyiYYPH67mzZvL3d1d77zzjjIyMvTTTz9ZLR8dHa3du3db/Bw6dOgKR100a/OmOv5zW25Jthd1iz7+FXn6jD5as05pmf+O7HEwmTSoXVs1Cg6yYWRXL65LoHIw5+QoceVKpe7YIUny7d1bDv8snpl+9KjOjB8vSar69NNqGRurlnFx8v9nIabTb72lrLg4mXNydGbMGEmSg4+PGq5fr5bnz8u9WTMbtOjqdvKll4xF4PJ+Tg0fbuw/NXx4of0nX3rJhhFfOWGffKLr4uOL/PHq1KnY43fWqqVtnp7aVbu2XMLDVeOfazJl82alHTyomv/9rxw8POQUEKDqI0cqdvZsSVLc3Lny7t5dfr17y+TkpKpPPFHiJKk5O1txc+cqZOxYOfn5yaVGDQW//PLldUQFOfHMM8o8c0Ynn3++0OKQeT8Xpk0r8vjzn36q7X5+2urmptOjRqn2nDlyDsr9Gyp6yhQFv/yyPFq3lsnBQf59+8qtUSNdXLSo1H1kcnKSV+fOSlyxQlmxsco8e1ZVn3xSiStW5L5frVpVbBI4+JVX5BwUJCc/P/n366eUf0aEm5ydlZ2YqLS9eyWzWW4NGsgllOnAcOWwMBwAAKV08eJFRUVFqV2+udCcnJzUqlUrbdu2TY888kihYz755BON+ecfgatRampqoW2u//wDXpLt1o7Hv9YdPaZvtmyzmAfYycFBQzpE6LqQGjaM7OrGdQnYvzNjxhjJW0nyue02hX/5pfE8YelS6Z9pYM5PmaLzU6ZYHG9OTVXyhg1yb9pUGcePS5L877lHXh06SMpdtCnxzz8LnTd8xgyFz5hR3s1BJdf82DE5+vrq4m+/6fiwYcqKjZWjj48yoqKUHR+vyHwLnprNZuPazjh92hjRmqfg86JkXbggc0aGRfmSHpvn7LvvGvMXm3NylJOUZDHdRNgnn6jKgw+Wqk5rQt57T8mbNqn6668roIiFJR28vYs8vuqTTyp00iRlxcbq6MMPK3ndOvn36SNJyoiK0umRI3Vm1CijvDkzU5mnTpWpj7y7dVPiihVyDg6W9403yrt7dx0bMkQp27ZJDg5yb9GiyGPzj+518PRUdmKiJCngkUeUeeaMjj/xhDJOnJDfnXeq5gcfyCkwsNhYgPJCEhgAgFJKSEiQJPnl++NYkvz9/Y19BT311FO69957LbYdOnRId18lq//GxsYW2ubl5VVom4ODQ6HFtpKTk62O2ESupfsP6sedu/+9zVmSm7OTnrq+gxoGVbVhZFc/rkug8slJSpI539zfWefPX/KYrNhYZZ45Yzx3CQkxHjvX4Iu2gtxbtJCjr6/Ftuz4eKXu3Jm7v3lzORb4G6e0ScVr1bEnnlDsrFlF7q/3++/y7ty52DpMJpP87rhDiffco5MvvKC6P/0k59BQOQUFqWW+6zQ/lxo1lLR+vcW2jOPH5fnPlxnFcQoMlMnZWRnHjsk5ONg4tjSqvfaaqr32mqTcqSwOdO2q5lFRpaqjJDxatlT9xYt18Lbb5Nu7d5mnhHCqUkW1pk3T7gYNVOXBB+XRqpVcQkMV9OyzqvrEE4XKm7OzS91H3t266dx778m5alV533ST3Fu2VMbx44r/6Sd5d+1apimnTE5Oqj5ypKqPHKnMc+d0tH9/nR4zRmGTJ0tShfQ5kB9JYAAASsnHx0eSFB8fb7E9Li5OIfn+8cwvKChIQUFX7y3/586dK7Qt0MqohICAADk4WM4mdfbs2QqL61o3f8cuLdlvufCJj5ubnuvUUaH+frYJ6hrCdQnYv+qjRqnaa6/p3P/9n06/8YaS/vpLxwYNUr2FCyXJYoRc3QUL5HfXXRbHm81mmUwmi4RORr7F4DJPn67gFlx7AgYMKLQtJTLSmBKiyoABxiJ9lU2tzz5Trc8+K5e6gl99Vbvq1FHy5s3yjIiQS2ioTr3xhqq9+qocvLyUcfy40vbskW/PnvK/7z6dGTtWF3/7TT633qoL06dbLHhWHJOjo/zvu0+n33pLtefMUU5Kis7997/l0gZrcjIypJwcKSdH5qws5aSlyeTkJJNTydJLnhERarp792XPhetSo4YCBg7U6TffVL1ff1XVp5/Wieefl0dEhDxat5Y5NVVJ69bJrVEjudSsWeo+8mjVSuasLMV8+60aP/+8TCaTvDp3VvTkyQqZMKFMMScsXy6nKlXk3qyZHDw9ZXJzK3G/AeWBOYEBACglX19fhYeHa1O+1XyzsrK0fft2tWrVyoaRlV1ycrKio6MttlWvXr3QaOdGjRoVOvbIkSMVGdo1KScnR99s3lYoARzk5aVXu91IAriEuC6BysHBzU3VX39dntdfL0m6+OuvSly1SpLk06OH9M+XPKfeeEMpO3YoJyND6VFRip4yRQd79JAkOdesKZewMElS3A8/KHnjRmVduKAzRSRrogYONOYgBSqCS40aChgwQKffeksmR0fV+/VXZZ46pd2NG2u7r68O3X670v9ZH8KtYUOFf/ONjj/3nLYHBCh540b53nZbic8VOnmyHLy8tLNWLR246SYFFJia7Mz48TrYs2e5tOvgLbdom7u7ktas0amXX9Y2d3djgbuSKq/F0Kq98ooS/vhDyX//Lb/evVXz3Xd1bMgQRfr7a2ft2or+3/9yE9a6dB8VZHJwkNeNN8rR29tY4M+ne3flJCTIp5j5gIuT9c/o3+1+ftpVu7YcfX1VPd/0FbubNlX8r7+WqW6gJPjKAQCAMnjqqaf0wQcf6KabblLdunU1duxYOTs7q88/85JdiyIjI9Xjn3+mpdzbGbt37659+/YpNTVVoaGhqlmzpsUxZ8+eLZSkgzRj01ZtPH7CYpuzo6O61aujo7FxOhobZ/W4RkFV5e1mfc7byorrEqg8aowZYyR1T48apYYrV8q1Th1Ve/VVnZ0wQWm7dmlvgRGqedMUmBwcVH3UKB0bNEg5CQna989t9I4BAVe2EZVE8saNFtMmFLy1/szo0TI5O0uSPNq3V8DDD1/R+K401/Bwtck37VOeWlOnGo+dg4IUPn16kXVUue8+VbnvvhKdz7trV12X7440J39/1f3hB4syQc89ZzyuPnJkieqVcttS3LQEDVeuLHFd5cnaHN4uYWFqnW8RWP9775V/genX8lyqj6yp9/PPFs+rPvmkqj75pMW2GqNHWzwveB0EP/+8gp9/XpJUpX9/VflnUUtrmu7eXWw8wOUiCQwAQBkMHz5ciYmJuvnmm5WQkKC2bdtq8eLFVucrvVZER0drz549atKkibHNzc1N1113ndXyaWlp2rBhwxWK7tpyKCam0LbM7GzN3b6j2ONe6tqZJHABXJdA5eFz883y6tRJSX/9paRVq5SwbJl8undXyPjxcmvaVOc/+USpO3bInJ0tl5AQeXboYJFQCXz8cWXHxenchx8qKy5O3t26qdorr+hA1662a5Sdyo6PV9q+fUXuTz982HjsHBp6JUICAFwCSWAAAMrAZDLp7bff1ttvv23rUMrVtm3blJ2drWbNmhW74MXFixe1atUqJScnX8HoUFlxXQL2JXDgQAUOHGh1X8M1a6xuD3joIQU89NAl6w5+6SUFv/SSxTZrIzTDZ8ywOrIQAAB7RRIY//K/Tuq+ovTHAADsyo4dOxQVFaV69eqpRo0acnd3l5OTk9LT0xUbG6vjx4/r6NGjMlv5pxqoKFyXAFBxPFq2VP2lS0tc3ufWW+Vz660VGBEAoLyRBMa/XPyk4K62jgIAcBVISEjQ1q1btXXrVluHck0a34t/jCsC1yVw9XDw8FDiypXaZWVhRkkKePTRKxwRAAAoDklgSIcPXrrMlagDAAAAwDXBs107NStmTlgAAHB1IQkMacpEW0cAAAAAACgHJqfcf/PNmZk2jqR4efGZnJ1tHAkAVA4Otg4AAAAAAACUD+eQEElSVkyMsi5csHE01mXFxSkrOlrSv/ECACoWSWAAAAAAAOyE35135j4wm3V+6lTlpKbaNqACctLSdGHqVCknR1K+eAEAFYrpIAAAAAA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      "text/plain": [
       "<Figure size 1680x1200 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Simplified weight patterns\n",
    "W_identity = np.array([[0,0,0],[0,1,0],[0,0,0]])       # W[c,c,:,:]\n",
    "W_corners_pos = np.array([[1,0,1],[0,0,0],[1,0,1]])    # W[4,2,:,:]: +1 at corners\n",
    "W_corners_neg = np.array([[-1,0,-1],[0,0,0],[-1,0,-1]]) # W[0,2,:,:]: -1 at corners\n",
    "\n",
    "grid = [[0]*5 for _ in range(5)]\n",
    "grid[2][2] = 2  # Red at center\n",
    "\n",
    "W_pos_colors = {1: ('#22AA22', 'white'), -1: ('#CC3333', 'white'), 0: ('none', 'none')}\n",
    "\n",
    "def compute_scores_at(out_y, out_x):\n",
    "    \"\"\"Simulate Conv at (out_y, out_x). Returns (scores_dict, input_tile).\"\"\"\n",
    "    score_black, score_red, score_yellow = 0.0, 0.0, 0.0\n",
    "    tile = [[None]*3 for _ in range(3)]\n",
    "    for dy in range(3):\n",
    "        for dx in range(3):\n",
    "            iy, ix = out_y - 1 + dy, out_x - 1 + dx  # with pads=[1,1,1,1]\n",
    "            ch = grid[iy][ix] if (0 <= iy < 5 and 0 <= ix < 5) else 0\n",
    "            tile[dy][dx] = ch\n",
    "\n",
    "            if ch == 2:\n",
    "                score_red += W_identity[dy, dx]\n",
    "                score_yellow += W_corners_pos[dy, dx]\n",
    "                score_black += W_corners_neg[dy, dx]\n",
    "            elif ch == 0:\n",
    "                score_black += W_identity[dy, dx]\n",
    "    return {'Black': score_black, 'Red': score_red, 'Yellow': score_yellow}, tile\n",
    "\n",
    "\n",
    "def draw_weight_cell(ax, dy, dx, ch, W_yellow_val, W_black_val):\n",
    "    \"\"\"Draw one cell of the 3x3 zoom: background = input color, text = weights.\"\"\"\n",
    "    # Background: input pixel color\n",
    "    hex_c = arc_colors[ch].lstrip('#')\n",
    "    bg = np.array([int(hex_c[i:i+2], 16) for i in (0, 2, 4)])\n",
    "    # Lighten it a bit\n",
    "    bg = (bg * 0.6 + np.array([255, 255, 255]) * 0.4).astype(np.uint8)\n",
    "    ax.fill_between([dx-0.5, dx+0.5], dy-0.5, dy+0.5, color=bg/255, ec='white', lw=1.5)\n",
    "\n",
    "    # Top line: +1 weights (W[4,2] create Yellow)\n",
    "    if W_yellow_val == 1:\n",
    "        ax.text(dx, dy-0.2, 'Y+1', ha='center', va='center', fontsize=8,\n",
    "                fontweight='bold', color='#115511',\n",
    "                bbox=dict(boxstyle='round,pad=0.1', facecolor='#88FF88', alpha=0.9, ec='none'))\n",
    "\n",
    "    # Bottom line: -1 weights (W[0,2] suppress Black)\n",
    "    if W_black_val == -1:\n",
    "        ax.text(dx, dy+0.2, 'B\\u22121', ha='center', va='center', fontsize=8,\n",
    "                fontweight='bold', color='#551111',\n",
    "                bbox=dict(boxstyle='round,pad=0.1', facecolor='#FF8888', alpha=0.9, ec='none'))\n",
    "\n",
    "    # Show input channel number in center\n",
    "    ch_color = 'white' if ch in (0, 9) else 'black'\n",
    "    ax.text(dx, dy, str(ch), ha='center', va='center', fontsize=16,\n",
    "            fontweight='bold', color=ch_color, alpha=0.6)\n",
    "\n",
    "\n",
    "cases = [\n",
    "    (2, 2, 'Kernel centered ON Red'),\n",
    "    (1, 1, 'Kernel centered at corner (1,1)'),\n",
    "    (4, 4, 'Kernel centered at (4,4), far from Red'),\n",
    "]\n",
    "\n",
    "fig, axes = plt.subplots(3, 3, figsize=(14, 10))\n",
    "fig.subplots_adjust(hspace=0.35, wspace=0.3)\n",
    "\n",
    "for case_idx, (oy, ox, case_title) in enumerate(cases):\n",
    "    scores, tile = compute_scores_at(oy, ox)\n",
    "\n",
    "    # --- Column 1: full input grid with marker ---\n",
    "    ax = axes[case_idx, 0]\n",
    "    plot_arc_grid(grid, ax)\n",
    "    rect = patches.Rectangle((ox-1.5, oy-1.5), 3, 3, linewidth=2.5,\n",
    "                              edgecolor='lime', facecolor='none')\n",
    "    ax.add_patch(rect)\n",
    "    ax.plot(ox, oy, marker='s', color='orange', markersize=9,\n",
    "            markeredgecolor='white', markeredgewidth=1.5)\n",
    "    ax.set_title(f'Output at ({oy},{ox})', fontsize=10, fontweight='bold', color='#CC6600')\n",
    "\n",
    "    # --- Column 2: zoomed 3x3 window with weights ---\n",
    "    ax = axes[case_idx, 1]\n",
    "    ax.set_xlim(-0.5, 2.5); ax.set_ylim(-0.5, 2.5)\n",
    "    ax.set_aspect('equal')\n",
    "    ax.set_xticks(range(3)); ax.set_yticks(range(3))\n",
    "    ax.set_xticklabels(['-1','0','+1']); ax.set_yticklabels(['-1','0','+1'])\n",
    "    ax.tick_params(labelsize=8)\n",
    "\n",
    "    for dy in range(3):\n",
    "        for dx in range(3):\n",
    "            # Note: matrix (dy,dx) vs plot (x=dx, y=dy) — matplotlib uses (x,y)\n",
    "            ch = tile[2-dy][dx] if tile[2-dy][dx] is not None else 0  # flip y for visual\n",
    "            # Actually, tile[dy][dx] is already row dy, so in plot coords it's y=dy, x=dx\n",
    "            # Just need to invert y for display since images have y=0 at top\n",
    "            draw_weight_cell(ax, 2-dx, dy, tile[dy][dx],\n",
    "                           W_corners_pos[dy, dx], W_corners_neg[dy, dx])\n",
    "\n",
    "    ax.set_title('3\\u00d73 kernel window', fontsize=10, fontweight='bold')\n",
    "\n",
    "    # --- Column 3: score breakdown ---\n",
    "    ax = axes[case_idx, 2]\n",
    "    ax.axis('off')\n",
    "\n",
    "    # Compute per-channel contributions\n",
    "    contrib_black = {'identity': 0.0, 'suppress_from_red': 0.0}\n",
    "    contrib_red = {'identity': 0.0}\n",
    "    contrib_yellow = {'create_from_red': 0.0}\n",
    "    for dy in range(3):\n",
    "        for dx in range(3):\n",
    "            ch = tile[dy][dx]\n",
    "            if ch == 2:\n",
    "                contrib_red['identity'] += W_identity[dy, dx]\n",
    "                contrib_yellow['create_from_red'] += W_corners_pos[dy, dx]\n",
    "                contrib_black['suppress_from_red'] += W_corners_neg[dy, dx]\n",
    "            elif ch == 0:\n",
    "                contrib_black['identity'] += W_identity[dy, dx]\n",
    "\n",
    "    ax.text(0.5, 0.92, 'Score computation:', ha='center', fontsize=10, fontweight='bold')\n",
    "\n",
    "    lines = [\n",
    "        ('Black',  scores['Black'],\n",
    "         f\"Black id. {contrib_black['identity']:+.0f}  +  Red\\u2192Black {contrib_black['suppress_from_red']:+.0f}\",\n",
    "         '#666666'),\n",
    "        ('Red',    scores['Red'],\n",
    "         f\"Red id. {contrib_red['identity']:+.0f}\",\n",
    "         '#CC0000'),\n",
    "        ('Yellow', scores['Yellow'],\n",
    "         f\"Red\\u2192Yellow {contrib_yellow['create_from_red']:+.0f}\",\n",
    "         '#BB8800'),\n",
    "    ]\n",
    "\n",
    "    winner_name = max(scores, key=scores.get)\n",
    "    for i, (name, total, formula, c) in enumerate(lines):\n",
    "        y_pos = 0.72 - i * 0.22\n",
    "        is_winner = (name == winner_name)\n",
    "        marker = '\\u2b50' if is_winner else '  '\n",
    "        total_str = f'{total:+.0f}' if total != 0 else ' 0 '\n",
    "        winner_label = f'  \\u2190 {name} wins!' if is_winner else ''\n",
    "\n",
    "        # Total score (bold)\n",
    "        ax.text(0.05, y_pos, f'{marker} {name}:', fontsize=9, color=c, fontweight='bold', va='center')\n",
    "        ax.text(0.35, y_pos, total_str, fontsize=13, color=c, fontweight='bold', va='center',\n",
    "                bbox=dict(boxstyle='round,pad=0.2', facecolor=c+'22' if not is_winner else c+'44',\n",
    "                         ec=c, lw=1.5 if is_winner else 0.5))\n",
    "        ax.text(0.55, y_pos, f'= {formula}{winner_label}', fontsize=7.5,\n",
    "                color='#444444' if not is_winner else c, va='center')\n",
    "\n",
    "fig.suptitle('Three output positions, one kernel, three different results',\n",
    "             fontsize=13, fontweight='bold', y=1.01)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a123ae8",
   "metadata": {
    "papermill": {
     "duration": 0.005954,
     "end_time": "2026-05-31T09:46:18.425178+00:00",
     "exception": false,
     "start_time": "2026-05-31T09:46:18.419224+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## 2.3 Blue Triggers Orange — Same Strategy, Different Pattern\n",
    "\n",
    "The second rule is:\n",
    "\n",
    "> **Every Blue (1) pixel must have Orange (7) pixels at its Top, Bottom, Left, and Right (a cross shape).**\n",
    "\n",
    "Same logic as Red → Yellow, but with a different 3×3 stencil: the **cross** instead of the corners.\n",
    "\n",
    "| Kernel | Expression | Effect |\n",
    "|--------|-----------|--------|\n",
    "| `W[7, 1, :, :]` = cross pattern × **+1** | Each cross arm adds 1.0 to Orange's score | **Creates** Orange in the cardinal directions |\n",
    "| `W[0, 1, :, :]` = cross pattern × **−1** | Each cross arm subtracts 1.0 from Black's score | **Suppresses** Black at those same spots |\n",
    "\n",
    "The cross pattern is:\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "0 & 1 & 0 \\\\\n",
    "1 & 0 & 1 \\\\\n",
    "0 & 1 & 0\n",
    "\\end{bmatrix}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "09544002",
   "metadata": {
    "_kg_hide-input": true,
    "execution": {
     "iopub.execute_input": "2026-05-31T09:46:18.439048Z",
     "iopub.status.busy": "2026-05-31T09:46:18.438783Z",
     "iopub.status.idle": "2026-05-31T09:46:18.670627Z",
     "shell.execute_reply": "2026-05-31T09:46:18.669445Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "papermill": {
     "duration": 0.241396,
     "end_time": "2026-05-31T09:46:18.672643+00:00",
     "exception": false,
     "start_time": "2026-05-31T09:46:18.431247+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 900x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Blue at center → Orange created at cross positions, Black suppressed there.\n"
     ]
    }
   ],
   "source": [
    "k_cross_pos = np.array([[ 0,  1,  0],\n",
    "                        [ 1,  0,  1],\n",
    "                        [ 0,  1,  0]])\n",
    "k_cross_neg = np.array([[ 0, -1,  0],\n",
    "                        [-1,  0, -1],\n",
    "                        [ 0, -1,  0]])\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, figsize=(7.5, 3))\n",
    "for ax, kernel, title, cm in zip(axes,\n",
    "    [k_cross_pos, k_cross_neg],\n",
    "    [r'W[7, 1, :, :]  — Write Orange (7)', r'W[0, 1, :, :]  — Suppress Black (0)'],\n",
    "    ['Oranges', 'Blues_r']):\n",
    "    im = ax.imshow(kernel, cmap=cm, vmin=-1.2, vmax=1.2)\n",
    "    for i in range(3):\n",
    "        for j in range(3):\n",
    "            val = kernel[i, j]\n",
    "            c = 'white' if abs(val) > 0.5 else 'black'\n",
    "            ax.text(j, i, f'{val:+.1f}', ha='center', va='center',\n",
    "                    color=c, fontweight='bold', fontsize=14)\n",
    "    ax.set_xticks(range(3), ['-1','0','1'])\n",
    "    ax.set_yticks(range(3), ['-1','0','1'])\n",
    "    ax.set_title(title, fontsize=10, fontweight='bold')\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(\"Blue at center → Orange created at cross positions, Black suppressed there.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a64bd615",
   "metadata": {
    "papermill": {
     "duration": 0.006752,
     "end_time": "2026-05-31T09:46:18.686341+00:00",
     "exception": false,
     "start_time": "2026-05-31T09:46:18.679589+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## 2.4 Putting It All Together — Constructing the Model\n",
    "\n",
    "We have now defined **five** distinct 3×3 kernels:\n",
    "\n",
    "| # | From | To | Pattern | Weight | Purpose |\n",
    "|---|------|----|---------|--------|---------|\n",
    "| 1 | Any color `c` | Same color `c` | Center (0,0) only | +1.0 | **Identity** — pixel stays |\n",
    "| 2 | Red (2) | Yellow (4) | Corners | +1.0 | Create Yellow at diagonals |\n",
    "| 3 | Red (2) | Black (0) | Corners | −1.0 | Suppress Black at diagonals |\n",
    "| 4 | Blue (1) | Orange (7) | Cross | +1.0 | Create Orange at cardinal dirs |\n",
    "| 5 | Blue (1) | Black (0) | Cross | −1.0 | Suppress Black at cardinal dirs |\n",
    "\n",
    "**All other (input, output) pairs are zero — no other color influences another.**\n",
    "\n",
    "When we run the convolution, each output channel accumulates votes from all input channels. The final output is processed in a way that all elements grather than zero becomes $1.0$ and all the others becomes $0.0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "5bc1aa3b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-31T09:46:18.701546Z",
     "iopub.status.busy": "2026-05-31T09:46:18.701188Z",
     "iopub.status.idle": "2026-05-31T09:46:18.710303Z",
     "shell.execute_reply": "2026-05-31T09:46:18.709392Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "papermill": {
     "duration": 0.018548,
     "end_time": "2026-05-31T09:46:18.711716+00:00",
     "exception": false,
     "start_time": "2026-05-31T09:46:18.693168+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "def create_task015_model():\n",
    "    W = np.zeros((10, 10, 3, 3), dtype=np.float32)\n",
    "    # 1. Identity for all colors\n",
    "    for c in range(10):\n",
    "        W[c, c, 1, 1] = 1.0\n",
    "    # 2. Red (2) -> Yellow (4) at corners\n",
    "    for r, c in [(0,0), (0,2), (2,0), (2,2)]:\n",
    "        W[4, 2, r, c] = 1.0\n",
    "        W[0, 2, r, c] = -1.0\n",
    "    # 3. Blue (1) -> Orange (7) at cross\n",
    "    for r, c in [(0,1), (2,1), (1,0), (1,2)]:\n",
    "        W[7, 1, r, c] = 1.0\n",
    "        W[0, 1, r, c] = -1.0\n",
    "    input_info = helper.make_tensor_value_info('input', TensorProto.FLOAT, [1, 10, 30, 30])\n",
    "    output_info = helper.make_tensor_value_info('output', TensorProto.FLOAT, [1, 10, 30, 30])\n",
    "    W_init = helper.make_tensor('W', TensorProto.FLOAT, [10, 10, 3, 3], W.flatten())\n",
    "    conv_node = helper.make_node('Conv', ['input', 'W'], ['output'], kernel_shape=[3, 3], pads=[1, 1, 1, 1])\n",
    "    graph = helper.make_graph([conv_node], 'task015', [input_info], [output_info], [W_init])\n",
    "    model = helper.make_model(graph, opset_imports=[helper.make_operatorsetid('', 11)])\n",
    "    return model\n",
    "\n",
    "model = create_task015_model()\n",
    "onnx.save(model, 'task015_demo.onnx')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "493c8830",
   "metadata": {
    "papermill": {
     "duration": 0.006222,
     "end_time": "2026-05-31T09:46:18.724487+00:00",
     "exception": false,
     "start_time": "2026-05-31T09:46:18.718265+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "# 3. Running the Model\n",
    "Let's run the model on a test case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "c920c2fb",
   "metadata": {
    "_kg_hide-input": true,
    "execution": {
     "iopub.execute_input": "2026-05-31T09:46:18.738628Z",
     "iopub.status.busy": "2026-05-31T09:46:18.738331Z",
     "iopub.status.idle": "2026-05-31T09:46:19.327363Z",
     "shell.execute_reply": "2026-05-31T09:46:19.326560Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "papermill": {
     "duration": 0.598313,
     "end_time": "2026-05-31T09:46:19.329088+00:00",
     "exception": false,
     "start_time": "2026-05-31T09:46:18.730775+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1560x1320 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1560x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results on ARC-AGI examples: 4 pass, 0 fail\n",
      "Results on ARC-GEN examples: 261 pass, 0 fail\n",
      "\n",
      "Your network IS READY for submission!\n",
      "\n",
      "Performance stats (memory values reported here are approximate):\n",
      "Name    Type    Forward_MACs    FPercent    Memory    MPercent      Params  PPercent    InShape     OutShape\n",
      "------  ------  --------------  ----------  --------  ----------  --------  ----------  ----------  ----------\n",
      "Conv_0  Conv    810,000         100.00%     39,600    100.00%          900  100.00%     1x10x30x30  1x10x30x30\n",
      "Total   _       810,000         100%        39,600    100%             900  100%        _           _\n",
      "\n",
      "It appears to require 0 bytes + 900 params, yielding 18.198 points.\n",
      "\n",
      "Next steps:\n",
      " * Click the link below to download task015.onnx onto your local machine.\n",
      " * Create a zip file containing that network along with all others.\n",
      " * Submit that zip file to the Kaggle competition so that it can be officially scored.\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<a href='task015.onnx' target='_blank'>task015.onnx</a><br>"
      ],
      "text/plain": [
       "/kaggle/working/task015.onnx"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import sys\n",
    "sys.path.append(\"/kaggle/input/competitions/neurogolf-2026/neurogolf_utils\")\n",
    "from neurogolf_utils import *\n",
    "\n",
    "def run_inference(grid, model_path):\n",
    "    oh = np.zeros((1, 10, 30, 30), dtype=np.float32)\n",
    "    for r in range(len(grid)):\n",
    "        for c in range(len(grid[0])):\n",
    "            oh[0, grid[r][c], r, c] = 1.0\n",
    "    sess = ort.InferenceSession(model_path)\n",
    "    out = sess.run(None, {'input': oh})[0]\n",
    "    return np.argmax(out[0], axis=0)\n",
    "\n",
    "# Test on all train examples\n",
    "fig, axes = plt.subplots(2, 3, figsize=(13, 11))\n",
    "for i in range(2):\n",
    "    inp = task['train'][i]['input']\n",
    "    target = task['train'][i]['output']\n",
    "    pred = run_inference(inp, 'task015_demo.onnx')\n",
    "    H, W = len(inp), len(inp[0])\n",
    "    plot_arc_grid(inp, axes[i, 0], f'Train {i+1} Input')\n",
    "    plot_arc_grid(target, axes[i, 1], f'Train {i+1} Target')\n",
    "    plot_arc_grid(pred[:H, :W], axes[i, 2], f'Train {i+1} Prediction')\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# Test on test example\n",
    "test_inp = task['test'][0]['input']\n",
    "test_tgt = task['test'][0]['output']\n",
    "test_pred = run_inference(test_inp, 'task015_demo.onnx')\n",
    "fig, axes = plt.subplots(1, 3, figsize=(13, 4))\n",
    "plot_arc_grid(test_inp, axes[0], 'Test Input')\n",
    "plot_arc_grid(test_tgt, axes[1], 'Test Target')\n",
    "plot_arc_grid(test_pred[:len(test_inp), :len(test_inp[0])], axes[2], 'Test Prediction')\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# Verify with official checker\n",
    "passed = verify_network(model, 15, task)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "858babc8",
   "metadata": {
    "papermill": {
     "duration": 0.007599,
     "end_time": "2026-05-31T09:46:19.344381+00:00",
     "exception": false,
     "start_time": "2026-05-31T09:46:19.336782+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "# 4. Beyond Hand-Design: Task 151 and the Bias Term\n",
    "\n",
    "Not all ARC tasks have rules as clean as task 015. Consider **task 151**: whenever a vertical line crosses a horizontal line, a 3×3 Yellow block appears around the intersection, but the center pixel keeps its original color.\n",
    "\n",
    "**Our result:** Mem=0, Params=910, **18.187 points**\n",
    "\n",
    "Let's look at some examples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "88674250",
   "metadata": {
    "_kg_hide-input": true,
    "execution": {
     "iopub.execute_input": "2026-05-31T09:46:19.361067Z",
     "iopub.status.busy": "2026-05-31T09:46:19.360737Z",
     "iopub.status.idle": "2026-05-31T09:46:19.588095Z",
     "shell.execute_reply": "2026-05-31T09:46:19.586987Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "papermill": {
     "duration": 0.23835,
     "end_time": "2026-05-31T09:46:19.590087+00:00",
     "exception": false,
     "start_time": "2026-05-31T09:46:19.351737+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 960x960 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with open('/kaggle/input/competitions/neurogolf-2026/task151.json') as f:\n",
    "    task151 = json.load(f)\n",
    "\n",
    "fig, axes = plt.subplots(3, 2, figsize=(8, 8))\n",
    "for i in range(3):\n",
    "    plot_arc_grid(task151['train'][i]['input'], axes[i, 0], f'Train {i+1} Input')\n",
    "    plot_arc_grid(task151['train'][i]['output'], axes[i, 1], f'Train {i+1} Target Output')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5293b29",
   "metadata": {
    "papermill": {
     "duration": 0.007512,
     "end_time": "2026-05-31T09:46:19.605236+00:00",
     "exception": false,
     "start_time": "2026-05-31T09:46:19.597724+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Notice the pattern: there is always a vertical line of one color and a horizontal line of another. Where they intersect, a 3×3 Yellow block appears, but the center pixel keeps its original line color.\n",
    "\n",
    "This is still solvable with a **single 3×3 Conv** — the same architecture as task 015! — but the weights are no longer simple $\\pm 1.0$ patterns. Instead, we train the convolution, and the resulting weights are floating-point values.\n",
    "\n",
    "### What is the Bias?\n",
    "\n",
    "In a standard Conv, each output channel also gets a **bias** term — a single scalar added to every pixel of that output channel:\n",
    "\n",
    "$$\\text{Output}_c(x, y) = \\sum_{i=0}^{9} \\sum_{r=-1}^{1} \\sum_{c=-1}^{1} \\text{Input}_i(x+r, y+c) \\cdot W_c[i, r, c] \\; + \\; \\text{Bias}[c]$$\n",
    "\n",
    "The bias shifts the *baseline activation* for a channel. In task 015 we had no bias (it defaults to 0), for task 151, we need to introduce them."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "effb073e",
   "metadata": {
    "papermill": {
     "duration": 0.007581,
     "end_time": "2026-05-31T09:46:19.620269+00:00",
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     "start_time": "2026-05-31T09:46:19.612688+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "### Building and Running the Task 151 Model\n",
    "\n",
    "The only difference from task 015 is that we pass `\"B\"` as the third input to the Conv node, and include the bias tensor in the initializers. The trained kernel weights replace our hand-crafted ±1.0 patterns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "10cc41c1",
   "metadata": {
    "_kg_hide-input": true,
    "execution": {
     "iopub.execute_input": "2026-05-31T09:46:19.638965Z",
     "iopub.status.busy": "2026-05-31T09:46:19.638644Z",
     "iopub.status.idle": "2026-05-31T09:46:19.675691Z",
     "shell.execute_reply": "2026-05-31T09:46:19.674809Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "papermill": {
     "duration": 0.048982,
     "end_time": "2026-05-31T09:46:19.677063+00:00",
     "exception": false,
     "start_time": "2026-05-31T09:46:19.628081+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bias vector (10 output channels):\n",
      "  [0] black   : -0.0100\n",
      "  [1] blue    : -0.0100\n",
      "  [2] red     : -0.0100\n",
      "  [3] green   : -0.0100\n",
      "  [4] yellow  : -0.0133\n",
      "  [5] gray    : -0.0100\n",
      "  [6] magenta : -0.0100\n",
      "  [7] orange  : -0.0100\n",
      "  [8] teal    : -0.0100\n",
      "  [9] maroon  : -0.0100\n",
      "\n",
      "Total params: 910 (900 weights + 10 biases)\n"
     ]
    }
   ],
   "source": [
    "# Build the task151 model using trained weights from src/task151.py\n",
    "import sys, os\n",
    "sys.path.insert(0, os.path.abspath('..'))\n",
    "\n",
    "# Copy the model-building code from src/task151.py\n",
    "W = np.zeros((10, 10, 3, 3), dtype=np.float32)\n",
    "W[0, 0, 1, 1] = 0.03999999911\n",
    "W[0, 1, 0, 1] = -0.01999999955\n",
    "W[0, 1, 1, 0] = -0.01999999955\n",
    "W[0, 1, 1, 2] = -0.01999999955\n",
    "W[0, 1, 2, 1] = -0.01999999955\n",
    "W[0, 2, 0, 1] = -0.01999999955\n",
    "W[0, 2, 1, 0] = -0.01999999955\n",
    "W[0, 2, 1, 2] = -0.01999999955\n",
    "W[0, 2, 2, 1] = -0.01999999955\n",
    "W[0, 3, 0, 1] = -0.01999999955\n",
    "W[0, 3, 1, 0] = -0.01999999955\n",
    "W[0, 3, 1, 2] = -0.01999999955\n",
    "W[0, 3, 2, 1] = -0.01999999955\n",
    "W[0, 5, 0, 1] = -0.01999999955\n",
    "W[0, 5, 1, 0] = -0.01999999955\n",
    "W[0, 5, 1, 2] = -0.01999999955\n",
    "W[0, 5, 2, 1] = -0.01999999955\n",
    "W[0, 6, 0, 1] = -0.01999999955\n",
    "W[0, 6, 1, 0] = -0.01999999955\n",
    "W[0, 6, 1, 2] = -0.01999999955\n",
    "W[0, 6, 2, 1] = -0.01999999955\n",
    "W[0, 7, 0, 1] = -0.01999999955\n",
    "W[0, 7, 1, 0] = -0.01999999955\n",
    "W[0, 7, 1, 2] = -0.01999999955\n",
    "W[0, 7, 2, 1] = -0.01999999955\n",
    "W[0, 8, 0, 1] = -0.01999999955\n",
    "W[0, 8, 1, 0] = -0.01999999955\n",
    "W[0, 8, 1, 2] = -0.01999999955\n",
    "W[0, 8, 2, 1] = -0.01999999955\n",
    "W[0, 9, 0, 1] = -0.01999999955\n",
    "W[0, 9, 1, 0] = -0.01999999955\n",
    "W[0, 9, 1, 2] = -0.01999999955\n",
    "W[0, 9, 2, 1] = -0.01999999955\n",
    "W[1, 1, 1, 1] = 0.01999999955\n",
    "W[1, 2, 0, 0] = -0.01999999955\n",
    "W[1, 2, 2, 2] = -0.01999999955\n",
    "W[1, 3, 0, 2] = -0.01999999955\n",
    "W[1, 3, 2, 0] = -0.01999999955\n",
    "W[1, 5, 0, 0] = -0.01999999955\n",
    "W[1, 5, 2, 2] = -0.01999999955\n",
    "W[1, 6, 0, 2] = -0.01999999955\n",
    "W[1, 6, 2, 0] = -0.01999999955\n",
    "W[1, 7, 0, 2] = -0.01999999955\n",
    "W[1, 7, 2, 0] = -0.01999999955\n",
    "W[1, 8, 0, 0] = -0.01999999955\n",
    "W[1, 8, 2, 2] = -0.01999999955\n",
    "W[1, 9, 0, 0] = -0.01999999955\n",
    "W[1, 9, 2, 2] = -0.01999999955\n",
    "W[2, 1, 0, 2] = -0.01999999955\n",
    "W[2, 1, 2, 0] = -0.01999999955\n",
    "W[2, 2, 1, 1] = 0.01999999955\n",
    "W[2, 3, 0, 0] = -0.01999999955\n",
    "W[2, 3, 2, 2] = -0.01999999955\n",
    "W[2, 5, 0, 2] = -0.01999999955\n",
    "W[2, 5, 2, 0] = -0.01999999955\n",
    "W[2, 6, 0, 2] = -0.01999999955\n",
    "W[2, 6, 2, 0] = -0.01999999955\n",
    "W[2, 7, 0, 0] = -0.01999999955\n",
    "W[2, 7, 2, 2] = -0.01999999955\n",
    "W[2, 8, 0, 2] = -0.01999999955\n",
    "W[2, 8, 2, 0] = -0.01999999955\n",
    "W[2, 9, 0, 2] = -0.01999999955\n",
    "W[2, 9, 2, 0] = -0.01999999955\n",
    "W[3, 1, 0, 2] = -0.01999999955\n",
    "W[3, 1, 2, 0] = -0.01999999955\n",
    "W[3, 2, 0, 2] = -0.01999999955\n",
    "W[3, 2, 2, 0] = -0.01999999955\n",
    "W[3, 3, 1, 1] = 0.01999999955\n",
    "W[3, 5, 0, 0] = -0.01999999955\n",
    "W[3, 5, 2, 2] = -0.01999999955\n",
    "W[3, 6, 0, 0] = -0.01999999955\n",
    "W[3, 6, 2, 2] = -0.01999999955\n",
    "W[3, 7, 0, 0] = -0.01999999955\n",
    "W[3, 7, 2, 2] = -0.01999999955\n",
    "W[3, 8, 0, 2] = -0.01999999955\n",
    "W[3, 8, 2, 0] = -0.01999999955\n",
    "W[3, 9, 0, 0] = -0.01999999955\n",
    "W[3, 9, 2, 2] = -0.01999999955\n",
    "W[4, 0, 0, 0] = -0.006666666828\n",
    "W[4, 0, 0, 1] = -0.02333333343\n",
    "W[4, 0, 0, 2] = -0.006666666828\n",
    "W[4, 0, 1, 0] = -0.02333333343\n",
    "W[4, 0, 1, 1] = -0.003333333414\n",
    "W[4, 0, 1, 2] = -0.02333333343\n",
    "W[4, 0, 2, 0] = -0.006666666828\n",
    "W[4, 0, 2, 1] = -0.02333333343\n",
    "W[4, 0, 2, 2] = -0.006666666828\n",
    "W[4, 1, 0, 0] = 0.02666666731\n",
    "W[4, 1, 0, 2] = 0.02666666731\n",
    "W[4, 1, 1, 1] = 0.02999999933\n",
    "W[4, 1, 2, 0] = 0.02666666731\n",
    "W[4, 1, 2, 2] = 0.02666666731\n",
    "W[4, 2, 0, 0] = 0.02666666731\n",
    "W[4, 2, 0, 2] = 0.02666666731\n",
    "W[4, 2, 1, 1] = 0.02999999933\n",
    "W[4, 2, 2, 0] = 0.02666666731\n",
    "W[4, 2, 2, 2] = 0.02666666731\n",
    "W[4, 3, 0, 0] = 0.02666666731\n",
    "W[4, 3, 0, 2] = 0.02666666731\n",
    "W[4, 3, 1, 1] = 0.02999999933\n",
    "W[4, 3, 2, 0] = 0.02666666731\n",
    "W[4, 3, 2, 2] = 0.02666666731\n",
    "W[4, 5, 0, 0] = 0.02666666731\n",
    "W[4, 5, 0, 2] = 0.02666666731\n",
    "W[4, 5, 1, 1] = 0.02999999933\n",
    "W[4, 5, 2, 0] = 0.02666666731\n",
    "W[4, 5, 2, 2] = 0.02666666731\n",
    "W[4, 6, 0, 0] = 0.02666666731\n",
    "W[4, 6, 0, 2] = 0.02666666731\n",
    "W[4, 6, 1, 1] = 0.02999999933\n",
    "W[4, 6, 2, 0] = 0.02666666731\n",
    "W[4, 6, 2, 2] = 0.02666666731\n",
    "W[4, 7, 0, 0] = 0.02666666731\n",
    "W[4, 7, 0, 2] = 0.02666666731\n",
    "W[4, 7, 1, 1] = 0.02999999933\n",
    "W[4, 7, 2, 0] = 0.02666666731\n",
    "W[4, 7, 2, 2] = 0.02666666731\n",
    "W[4, 8, 0, 0] = 0.02666666731\n",
    "W[4, 8, 0, 2] = 0.02666666731\n",
    "W[4, 8, 1, 1] = 0.02999999933\n",
    "W[4, 8, 2, 0] = 0.02666666731\n",
    "W[4, 8, 2, 2] = 0.02666666731\n",
    "W[4, 9, 0, 0] = 0.02666666731\n",
    "W[4, 9, 0, 2] = 0.02666666731\n",
    "W[4, 9, 1, 1] = 0.02999999933\n",
    "W[4, 9, 2, 0] = 0.02666666731\n",
    "W[4, 9, 2, 2] = 0.02666666731\n",
    "W[5, 1, 0, 2] = -0.01999999955\n",
    "W[5, 1, 2, 0] = -0.01999999955\n",
    "W[5, 2, 0, 2] = -0.01999999955\n",
    "W[5, 2, 2, 0] = -0.01999999955\n",
    "W[5, 3, 0, 0] = -0.01999999955\n",
    "W[5, 3, 2, 2] = -0.01999999955\n",
    "W[5, 5, 1, 1] = 0.01999999955\n",
    "W[5, 6, 0, 2] = -0.01999999955\n",
    "W[5, 6, 2, 0] = -0.01999999955\n",
    "W[5, 7, 0, 0] = -0.01999999955\n",
    "W[5, 7, 2, 2] = -0.01999999955\n",
    "W[5, 8, 2, 0] = -0.01999999955\n",
    "W[5, 8, 2, 2] = -0.01999999955\n",
    "W[5, 9, 0, 0] = -0.01999999955\n",
    "W[5, 9, 2, 2] = -0.01999999955\n",
    "W[6, 1, 0, 2] = -0.01999999955\n",
    "W[6, 1, 2, 0] = -0.01999999955\n",
    "W[6, 2, 0, 2] = -0.01999999955\n",
    "W[6, 2, 2, 0] = -0.01999999955\n",
    "W[6, 3, 0, 0] = -0.01999999955\n",
    "W[6, 3, 2, 2] = -0.01999999955\n",
    "W[6, 5, 0, 2] = -0.01999999955\n",
    "W[6, 5, 2, 0] = -0.01999999955\n",
    "W[6, 6, 1, 1] = 0.01999999955\n",
    "W[6, 7, 0, 0] = -0.01999999955\n",
    "W[6, 7, 2, 2] = -0.01999999955\n",
    "W[6, 8, 0, 2] = -0.01999999955\n",
    "W[6, 8, 2, 0] = -0.01999999955\n",
    "W[6, 9, 0, 2] = -0.01999999955\n",
    "W[6, 9, 2, 0] = -0.01999999955\n",
    "W[7, 1, 0, 2] = -0.01999999955\n",
    "W[7, 1, 2, 0] = -0.01999999955\n",
    "W[7, 2, 0, 2] = -0.01999999955\n",
    "W[7, 2, 2, 0] = -0.01999999955\n",
    "W[7, 3, 0, 0] = -0.01999999955\n",
    "W[7, 3, 2, 2] = -0.01999999955\n",
    "W[7, 5, 0, 2] = -0.01999999955\n",
    "W[7, 5, 2, 0] = -0.01999999955\n",
    "W[7, 6, 0, 2] = -0.01999999955\n",
    "W[7, 6, 2, 0] = -0.01999999955\n",
    "W[7, 7, 1, 1] = 0.01999999955\n",
    "W[7, 8, 0, 2] = -0.01999999955\n",
    "W[7, 8, 2, 0] = -0.01999999955\n",
    "W[7, 9, 0, 2] = -0.01999999955\n",
    "W[7, 9, 2, 0] = -0.01999999955\n",
    "W[8, 1, 0, 2] = -0.01999999955\n",
    "W[8, 1, 2, 0] = -0.01999999955\n",
    "W[8, 2, 0, 2] = -0.01999999955\n",
    "W[8, 2, 2, 0] = -0.01999999955\n",
    "W[8, 3, 0, 0] = -0.01999999955\n",
    "W[8, 3, 2, 2] = -0.01999999955\n",
    "W[8, 5, 0, 2] = -0.01999999955\n",
    "W[8, 5, 2, 2] = -0.01999999955\n",
    "W[8, 6, 0, 0] = -0.01999999955\n",
    "W[8, 6, 2, 2] = -0.01999999955\n",
    "W[8, 7, 0, 2] = -0.01999999955\n",
    "W[8, 7, 2, 0] = -0.01999999955\n",
    "W[8, 8, 1, 1] = 0.01999999955\n",
    "W[8, 9, 0, 0] = -0.01999999955\n",
    "W[8, 9, 2, 2] = -0.01999999955\n",
    "W[9, 1, 0, 2] = -0.01999999955\n",
    "W[9, 1, 2, 0] = -0.01999999955\n",
    "W[9, 2, 0, 2] = -0.01999999955\n",
    "W[9, 2, 2, 0] = -0.01999999955\n",
    "W[9, 3, 0, 0] = -0.01999999955\n",
    "W[9, 3, 2, 2] = -0.01999999955\n",
    "W[9, 5, 0, 2] = -0.01999999955\n",
    "W[9, 5, 2, 0] = -0.01999999955\n",
    "W[9, 6, 0, 2] = -0.01999999955\n",
    "W[9, 6, 2, 0] = -0.01999999955\n",
    "W[9, 7, 0, 0] = -0.01999999955\n",
    "W[9, 7, 2, 2] = -0.01999999955\n",
    "W[9, 8, 0, 2] = -0.01999999955\n",
    "W[9, 8, 2, 0] = -0.01999999955\n",
    "W[9, 9, 1, 1] = 0.01999999955\n",
    "\n",
    "B = np.array([-0.01, -0.01, -0.01, -0.01, -0.01333333333,\n",
    "              -0.01, -0.01, -0.01, -0.01, -0.01], dtype=np.float32)\n",
    "\n",
    "print(\"Bias vector (10 output channels):\")\n",
    "for i, (name, val) in enumerate(zip(\n",
    "    ['black','blue','red','green','yellow','gray','magenta','orange','teal','maroon'], B)):\n",
    "    print(f\"  [{i}] {name:8s}: {val:+.4f}\")\n",
    "\n",
    "input_info = helper.make_tensor_value_info('input', TensorProto.FLOAT, [1, 10, 30, 30])\n",
    "output_info = helper.make_tensor_value_info('output', TensorProto.FLOAT, [1, 10, 30, 30])\n",
    "W_init = helper.make_tensor('W', TensorProto.FLOAT, [10, 10, 3, 3], W.flatten().tolist())\n",
    "B_init = helper.make_tensor('B', TensorProto.FLOAT, [10], B.tolist())\n",
    "conv_node = helper.make_node('Conv', ['input', 'W', 'B'], ['output'],\n",
    "                             kernel_shape=[3, 3], pads=[1, 1, 1, 1])\n",
    "graph = helper.make_graph([conv_node], 'task151', [input_info], [output_info], [W_init, B_init])\n",
    "model151 = helper.make_model(graph, opset_imports=[helper.make_operatorsetid('', 11)])\n",
    "onnx.save(model151, 'task151_demo.onnx')\n",
    "print(f\"\\nTotal params: {900 + B.size} (900 weights + 10 biases)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "2381497d",
   "metadata": {
    "_kg_hide-input": true,
    "execution": {
     "iopub.execute_input": "2026-05-31T09:46:19.694141Z",
     "iopub.status.busy": "2026-05-31T09:46:19.693837Z",
     "iopub.status.idle": "2026-05-31T09:46:20.318831Z",
     "shell.execute_reply": "2026-05-31T09:46:20.318206Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "papermill": {
     "duration": 0.635494,
     "end_time": "2026-05-31T09:46:20.320206+00:00",
     "exception": false,
     "start_time": "2026-05-31T09:46:19.684712+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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7bunjE088Merq6iIi4vLLL49Ro0aVPrexRW3FihXRrVu3Ft1vaxbIlqiqqoovf/nLMXbs2HjjjTfiwgsvjOeeey7Wrl0b5557bsr/PAAgL+t9Y2eccUYcfvjhpY+vueaamDZtWkREHHXUUXHeeeeVPte3b9/NHmtrHj8AcrN+N091dXUURRFPP/10fPe7343ly5fHSy+9FP/4j/8YV1xxxfvetj3W52HDhsWwYcO2yLErKytj7NixW+TY8IFUAC0ycODAIiKKiCgeeuih0uULFy4sXT5u3Lhi7ty5xYEHHlh06dKlmDhxYlEURXHVVVcVn/zkJ4v+/fsXXbt2LSorK4vdd9+9OPvss4vXXnutwf2MGzeudLyFCxc2eR/z5s0rxo8fX2y33XZF3759i/PPP79Ys2bNJudQXV1drFixosFlTzzxROnYEVG88sor73uM+mOp/62kpWOcNm1a6fqTJ08urr/++mKvvfYqKisriz333LO48cYbG9zvxIkTm3z8NzxOUTR8rjZ8W38dAGiK9b6xyZMnl263fq7r/fCHPyzGjRtX7LrrrkWXLl2K7bbbrthzzz2L888/v9EY6j+2ixYtKk444YSiR48exaBBg0rXmTNnTrH//vsXlZWVxZAhQ4qpU6c2udav9+KLLxaTJk0qBgwYUFRUVBR9+vQpTjrppOKZZ55pcvwbvg0cOLDZjwMAWy/rd+P5bvhff1OmTCldvs8++zT78SmKonjyySeLCRMmFFVVVUXnzp2Lfv36FV/+8peLxYsXNxrDggULinHjxhVdunQpdt1112LKlCnFAw880OReYmM/5xdFUTz66KPF5z73uWKXXXYpOnfuXPTt27c46qijigULFhQPPfTQRtf29c/NhnOrb/ny5cV5551XDB8+vOjSpUvRvXv34oADDiiuvPLKYu3atQ2uW3/P8PzzzxfHHnts0a1bt2LHHXcszjzzzOKdd9553+cEthX+sgC2gD/84Q9x5JFHNvgNh4iI6dOnx+zZsxtc9sILL8QVV1wRDz74YMyfPz+6dOnSrPt4/vnnY9y4cfHOO+9ERMQ777wTF198cQwaNKj053sb01RV37Did+3atVnjaMsx3nLLLfHcc8+VPv79738fp5xySnTo0CFOPvnkzR4PALQl6/1fXHvttQ3W8Ih16/jFF18cjzzySPzqV79q8naHHXZYvPjiixERseOOO0ZExG9/+9s48sgjY9WqVRER8eKLL8Y3vvGN+OhHP9rkMebPnx+f+MQnGpyj+LXXXovbbrstZs2aFQ8++GAccMABmztFAD4gsq/f9U/Fs3r16kaf39jjc++998ZnPvOZ0vocEVFbWxtXX311zJw5Mx555JEYPHhwRKx73MaPH186VdPLL78cU6ZMiX322adFY502bVp85StfiTVr1pQue+WVV+Lee++Nk046KQYNGtSi49X3xhtvxJgxY+LZZ59tcPm8efNi3rx5MWfOnLj55pubvN1BBx0Ur7/+ekSs+8uLn//859G7d+/4wQ9+0OrxwNbCCxzDFlBbWxu77bZb3HDDDTFr1qw4/vjjIyLi85//fFxzzTUxc+bMmDNnTsycOTNOPfXUiFj3A/Udd9zR7Pv485//HPvuu2/cfffdcc4555Qu3/Dchs11++23l94/5JBDonv37q06zuaM8bnnnou//uu/jpkzZ8YXv/jF0uXnnntuvPfeey2+/xkzZjQ4RcLpp58e1dXVUV1dHWeccUaLjwcA9Vnv/+Kss86K66+/PmbNmhVz5syJ//zP/4yjjz46IiIeeuiheOSRR5q83SuvvBI//vGPY/bs2aU1+9xzzy39R8Rhhx0Wv/zlL+PCCy+Mp556qtHti6KIiRMnlkLBt7/97Zg9e3Zccskl8aEPfSjefvvtOP3006MoijjjjDMavDBkVVVVaV8wY8aMNnkcANj6ZV2/i6KIZ555Jn72s5+VLmvqdEpNPT4rV66MiRMnxqpVq6JTp05x8cUXx+zZs+Pv/u7vIiKirq4uvva1r5WOccEFF5RCwahRo+Kuu+6KqVOnxgsvvNDs8b788svx1a9+tRQKjj/++LjzzjtjxowZ8ZWvfCUqKipi1KhRUV1dHSNHjizdbvr06aX1/f1eT+K8884rhYIRI0bEHXfcEVdddVXplxduueWWuPXWWxvd7s0334w+ffrE7bffHt///vdLl7f2uYWtTpn/sgG2Oc35s8aOHTsWzz77bKPb/ulPfyq+8pWvFIMHDy4qKysb/Ynct771rdJ1N/VnjRUVFUVdXV1RFEWxZs2aomvXrkVEFD179mzxnB5//PFihx12KCKiqKysLB5//PFN3qY5pyFqzhjrn1Lg4IMPLl3+f//3f8WAAQNKn3v44YeLomjZaYje73IAeD/W+8be7zRE//u//1tMmDCh2G233YrOnTs3mvNPfvKT0nXrP7b//u//3uA4r7zySulzlZWVxZIlS0qfmzBhQqM1fcGCBaXLRo4cWVRXV5feDjrooNLn6s91/WVOPQTwwWP9bjzfjb1VVFQU8+bNa9bjc+edd5Y+f9RRRzVYbwcNGlRERNGhQ4fitddeK9asWVN07969dP2nn366dJzzzz+/2achuvTSS0uXjRkz5n3n29Tz0dRjsf40RGvWrCl23HHH0uVPPfVU6fpTp04tXX7ccceVLq//2C1YsKB0+fDhw0uXL1u2bBPPDGz9nIYItoBhw4bFHnvs0eCyt956K8aMGRMvvfTSRm9X/8/nN2X48OGlFxPs2LFj7LjjjrFy5coWHSMi4te//nV8+tOfjjfffDM6deoUN998c+y3334tOkZbjfFjH/tY6f0PfehDsd9++8Wf/vSniFh3CoJDDjmkTcYFAG3Ber/OokWLYsyYMfHmm29u9DobG++xxx7b4OP1pySKiBg6dGjstNNOpY8POuiguOWWWxpc//nnny+9/8QTT2x0r/D73/++zeYLwLbN+h0xcuTI+PGPfxyjR49u9LmmHp/66+29994b9957b6PbFUURzz77bOy+++7x9ttvR0REt27dYq+99ipdpyWnBax/n5/+9KebfbvmeO211+KNN96IiHWndNp7771Ln6s/xvpjWK9Hjx4N/pKh/l5l2bJlDU7zBNsipyGCLWD9pqC+O++8s7TxGD58eNx6661RXV0dl156aek6a9eubfZ9rP/TuPU6dWp5+5s9e3YceeSR8eabb0ZlZWXMmDEjPvOZz7T4OBuzuWPs0KHD+15W/7yFS5YsaeHoAGDzWO/X+Y//+I9SKDjooIPirrvuiurq6tKpCSI2PuemHsP1mtoHtNaKFSva7FgAbNsyrt/rT8szb968+POf/xwLFiyIww47rMnrvt/avCmbWm/bcm1vKxuOaVNjfL/ntiiKthsYlIlYAFtAU4vLyy+/XHr/61//epx00kkxduzYRi8a1F7uvPPOOPbYY2PlypXRrVu3mDlzZhx33HFlGct68+bNK72/Zs2aePzxx0sfDxkyJCIavhhTXV1d6f377ruvyWN27PiXb3Mt2dwBwKZY79epP+fzzjsvjjvuuBg7dmzpXMXvZ8PHcOjQoaX3//jHP5Z+6y8i4tFHH210+w9/+MOl98eNGxdFUTR6W7FiRZx55pmN7tO+ACCnjOv32LFjY+zYsTF69Oioqqp63+s29fjUX28nTpy40fX2yCOPjJ133jm6desWEeviwe9///vSbR977LFmj7n+fc6aNet9r9vSn/v79OkTPXv2LI3x6aefbnKM9ccAWTgNEbSTgQMHlt6/5pprYsiQIfHCCy/ED37wg3Yfy/Tp0+Pkk0+ONWvWRIcOHWLy5MlRWVkZv/71r0vXGT16dFRWVrbruH7961/HueeeG0cccUTccsstpVMQ9e3bNw488MCIiNh9991L1//7v//7WLZsWTzyyCPx4IMPNnnM+tX/vvvui0MPPTS6dOkSI0aM8OeBALS5jOt9/TlffvnlUVFREY899lhcffXVLT5Wnz59YsyYMfHII4/Eu+++GxMmTIhzzjkn5s+fH7fddluj63/0ox+NvffeO/73f/835s6dG6eeemqceOKJ0blz56ipqYl58+bFnXfe2SA67LjjjrF06dKora2NG2+8MQYOHBh9+/aNYcOGte4BAGCbl3H9bokjjjgi+vTpE6+99lpcd9110atXrzjiiCNizZo1UVNTE7/5zW/iySefjGeeeSY6duwYxxxzTOnFgb/0pS/FBRdcEC+//HJcdtllzb7PE088Mb773e/GqlWr4je/+U189rOfjVNPPTXWrl0bDzzwQBx88MFxyimnRETDn/t/8YtfxNFHHx3bbbdd7L///k0eu2PHjjFhwoS48sorIyLilFNOicmTJ8cbb7wRkydPLl3v5JNPbulDBdu+8rxUAmy7mvOCSetfNKe+N998s9hll10avajQwQcf3OQL/GzqBZM2vI/649qU+i8etLG3DV8UaEPNeYHj5oyx/gsQjxgxosmxXH/99aXrL1mypMGLJa1/23PPPRu96GFRFMVrr73W5ItT1X/uAGBD1vvGNvYCx4sWLSq9cOPG5lx/bd7UHB599NGioqKi0fH22WefJo/33//930XPnj3fd571ffazn230+Q1fsBmAbZP1u/F8m3Ofm3p8iqIoZs6c2eTP1uvfBg4cWLru888/X/To0aPRdYYNG9bk49nUCxwXRVH84he/KDp27Njk/U2bNq10vfovSrzheDY2t9dff73BixNv+DZhwoRi7dq1pes3Nc+ieP8XV4ZtkdMQQTvZfvvt44EHHoiPf/zj0b1799h1113joosuiosuuqjcQ9tqnHDCCXHrrbfGRz7ykaioqIg99tgjrr/++vjiF79Yus5OO+0Ud911V+yzzz5RUVERQ4cOjZ/+9KcNzotcX+/eveOuu+6KUaNGxXbbbddeUwEgqYzr/YABA2L27NlxwAEHxHbbbRdDhw6Nf/u3f4tJkya16ngHHnhg3H///bH//vt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      "text/plain": [
       "<Figure size 1560x1320 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1560x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results on ARC-AGI examples: 4 pass, 0 fail\n",
      "Results on ARC-GEN examples: 262 pass, 0 fail\n",
      "\n",
      "Your network IS READY for submission!\n",
      "\n",
      "Performance stats (memory values reported here are approximate):\n",
      "Name    Type    Forward_MACs    FPercent    Memory    MPercent      Params  PPercent    InShape     OutShape\n",
      "------  ------  --------------  ----------  --------  ----------  --------  ----------  ----------  ----------\n",
      "Conv_0  Conv    819,000         100.00%     39,640    100.00%          910  100.00%     1x10x30x30  1x10x30x30\n",
      "Total   _       819,000         100%        39,640    100%             910  100%        _           _\n",
      "\n",
      "It appears to require 0 bytes + 910 params, yielding 18.187 points.\n",
      "\n",
      "Next steps:\n",
      " * Click the link below to download task151.onnx onto your local machine.\n",
      " * Create a zip file containing that network along with all others.\n",
      " * Submit that zip file to the Kaggle competition so that it can be officially scored.\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<a href='task151.onnx' target='_blank'>task151.onnx</a><br>"
      ],
      "text/plain": [
       "/kaggle/working/task151.onnx"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Test on all train examples\n",
    "fig, axes = plt.subplots(2, 3, figsize=(13, 11))\n",
    "for i in range(2):\n",
    "    inp = task151['train'][i]['input']\n",
    "    target = task151['train'][i]['output']\n",
    "    pred = run_inference(inp, 'task151_demo.onnx')\n",
    "    H, W = len(inp), len(inp[0])\n",
    "    plot_arc_grid(inp, axes[i, 0], f'Train {i+1} Input')\n",
    "    plot_arc_grid(target, axes[i, 1], f'Train {i+1} Target')\n",
    "    plot_arc_grid(pred[:H, :W], axes[i, 2], f'Train {i+1} Prediction')\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# Test on test example\n",
    "test_inp = task151['test'][0]['input']\n",
    "test_tgt = task151['test'][0]['output']\n",
    "test_pred = run_inference(test_inp, 'task151_demo.onnx')\n",
    "fig, axes = plt.subplots(1, 3, figsize=(13, 4))\n",
    "plot_arc_grid(test_inp, axes[0], 'Test Input')\n",
    "plot_arc_grid(test_tgt, axes[1], 'Test Target')\n",
    "plot_arc_grid(test_pred[:len(test_inp), :len(test_inp[0])], axes[2], 'Test Prediction')\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# Verify with official checker\n",
    "passed = verify_network(model151, 151, task151)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "806f8e91",
   "metadata": {
    "papermill": {
     "duration": 0.007983,
     "end_time": "2026-05-31T09:46:20.336574+00:00",
     "exception": false,
     "start_time": "2026-05-31T09:46:20.328591+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "# Summary\n",
    "- **Spatial Locality:** Kernel size 3x3 is enough to detect a pixel and its neighbors.\n",
    "- **Cross-Channel Power:** The 4D weights allow us to say 'If I see Color A, I should write Color B at this offset'.\n",
    "- **Competition via Negative Weights:** For every 'create' kernel (+1.0 for the target color), we add a matching 'suppress' kernel (−1.0 for Black) so the new color wins against the background.\n",
    "- **The Bias Term:** A learnable scalar per output channel that shifts the baseline activation. Used in trained models like task151 to fine-tune when a color activates.\n",
    "- **Trained vs Hand-Designed:** Both task015 and task151 share the exact same Conv 3×3 architecture — the only difference is whether weights are hand-crafted or learned."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "a5f3e3e2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-31T09:46:20.354180Z",
     "iopub.status.busy": "2026-05-31T09:46:20.353913Z",
     "iopub.status.idle": "2026-05-31T09:46:22.515898Z",
     "shell.execute_reply": "2026-05-31T09:46:22.515033Z"
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     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "import shutil\n",
    "import os\n",
    "import zipfile\n",
    "\n",
    "# --- CONFIGURATION ---\n",
    "SOURCE_FOLDER = '/kaggle/input/datasets/massimilianoghiotto/neurogolf2026-6112/submission'\n",
    "OUTPUT_ZIP = '/kaggle/working/submission.zip'\n",
    "\n",
    "# Package the ZIP (Ensuring files are at the root)\n",
    "with zipfile.ZipFile(OUTPUT_ZIP, 'w', zipfile.ZIP_DEFLATED) as zipf:\n",
    "    for root, dirs, files in os.walk(SOURCE_FOLDER):\n",
    "        for file in files:\n",
    "            if file.endswith('.onnx'):\n",
    "                file_path = os.path.join(root, file)\n",
    "                zipf.write(file_path, os.path.relpath(file_path, SOURCE_FOLDER))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b55edb8b",
   "metadata": {
    "papermill": {
     "duration": 0.008256,
     "end_time": "2026-05-31T09:46:22.534193+00:00",
     "exception": false,
     "start_time": "2026-05-31T09:46:22.525937+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "### **This is the best that we are able to do for the moment, if anyone has any suggestion, please write it in the comments, we are happy to have some brainstorning between people.**"
   ]
  }
 ],
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