ho ja bhai

main@@.ipynb

@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 43,
+   "execution_count": 4,
    "id": "90418142-03d2-4803-b187-f112f426a008",
    "metadata": {},
    "outputs": [],
@@ -17,7 +17,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 44,
+   "execution_count": 5,
    "id": "03498927-394e-4438-98f3-27d71e3a8920",
    "metadata": {},
    "outputs": [
@@ -35,7 +35,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 45,
+   "execution_count": 6,
    "id": "65ffc9ef-eeb4-4318-b648-d257d3bb4b34",
    "metadata": {},
    "outputs": [],
@@ -45,7 +45,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 46,
+   "execution_count": 7,
    "id": "670c7b49-01f3-446a-bd60-b1e1710a30a6",
    "metadata": {},
    "outputs": [
@@ -5581,7 +5581,7 @@
        "4         0  "
       ]
      },
-     "execution_count": 46,
+     "execution_count": 7,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5592,7 +5592,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 47,
+   "execution_count": 8,
    "id": "b6de1f03-d0bd-48d2-96f6-cfb5bdca6819",
    "metadata": {},
    "outputs": [],
@@ -5611,7 +5611,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 48,
+   "execution_count": 9,
    "id": "5aa2c7da-e7e6-426d-9867-86937a76892c",
    "metadata": {},
    "outputs": [],
@@ -5622,19 +5622,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 49,
+   "execution_count": 10,
    "id": "2fa2a087-fec8-4a7a-8c94-95520e87e83c",
    "metadata": {},
    "outputs": [],
    "source": [
     "data_dev = data[0:1000].T\n",
     "X_dev = data_dev[1:n]\n",
-    "y_dev = data_dev[0]"
+    "y_dev = data_dev[0]\n",
+    "X_dev = X_dev / 255."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 50,
+   "execution_count": 11,
    "id": "b00b5e87-6762-4d9d-9089-268ab82cdfee",
    "metadata": {},
    "outputs": [],
@@ -5648,7 +5649,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 65,
+   "execution_count": 12,
    "id": "3dfbc08b-676c-424f-9620-5a15716a291a",
    "metadata": {},
    "outputs": [],
@@ -5663,7 +5664,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 79,
+   "execution_count": 20,
    "id": "cddd98b0-9287-4398-a0e1-dc985efccbf2",
    "metadata": {},
    "outputs": [],
@@ -5672,13 +5673,14 @@
     "   return np.maximum(0, Z)\n",
     "    \n",
     "def softmax(Z):\n",
-    "    return exp(Z)/ sum(np.exp(Z))\n",
+    "    exp_Z = np.exp(Z - np.max(Z, axis=0, keepdims=True))\n",
+    "    return exp_Z / np.sum(exp_Z, axis=0, keepdims=True)\n",
     "    \n",
     "def forward_prop(W1, b1 , W2, b2, X):\n",
     "    Z1 = W1.dot(X)  + b1\n",
     "    A1 = ReLu(Z1)\n",
     "    Z2 = W2.dot(A1) + b2 \n",
-    "    A2 = softmax(A1)\n",
+    "    A2 = softmax(Z2)\n",
     "    \n",
     "    return Z1 , Z2  , A1 , A2\n",
     "    "
@@ -5686,17 +5688,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 80,
+   "execution_count": 21,
    "id": "90c76872-2a23-4756-8d04-dfecce8fbcd0",
    "metadata": {},
    "outputs": [],
    "source": [
     "def one_hot(Y):\n",
-    "    one_hot_Y = np.zeroes((Y.size, Y.max() + 1))\n",
+    "    one_hot_Y = np.zeros((Y.size, Y.max() + 1))\n",
     "    one_hot_Y[np.arange(Y.size) , Y] = 1\n",
     "    return one_hot_Y.T\n",
     "\n",
-    "def deriv_ReLU():\n",
+    "def deriv_ReLU(Z):\n",
     "    return Z > 0\n",
     "    \n",
     "def back_prop(Z1 , Z2 , A1 , A2, W2 ,X, Y ):\n",
@@ -5706,29 +5708,30 @@
     "    dW2 = 1/m * dZ2.dot(A1.T)\n",
     "    db2 = 1/m * np.sum(dZ2)\n",
     "    dZ1 = W2.T.dot(dZ2) *deriv_ReLU(Z1)\n",
-    "    dW1 = 1/m * dZ2.dot(X.T)\n",
+    "    dW1 = 1/m * dZ1.dot(X.T)\n",
     "    db1 = 1/m * np.sum(dZ1)\n",
     "    return dW2 ,dW1, db1, db2"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 81,
+   "execution_count": 22,
    "id": "2735f3d3-df5a-465f-aa59-a247ecb27343",
    "metadata": {},
    "outputs": [],
    "source": [
-    "def update_params(W1, b1, W2 , b2 ,dW2 ,dW1, db1, db2, alpha):\n",
-    "    W1 = W1 - alpha * dW1\n",
+    "def update_params(W1, b1, W2, b2, dW2, dW1, db1, db2, alpha):\n",
+    "  \n",
+    "    W1 = W1 - alpha * dW2\n",
     "    b1 = b1 - alpha * db1\n",
-    "    W2 = W1 - alpha * dW2\n",
-    "    b2 = b1 - alpha * db2\n",
-    "    return W1 , b1 , W2 , b2 \n"
+    "    W2 = W2 - alpha * dW1\n",
+    "    b2 = b2 - alpha * db2\n",
+    "    return W1, b1, W2, b2\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 82,
+   "execution_count": 23,
    "id": "9b2e810f-9911-445b-944b-6a7488647b80",
    "metadata": {},
    "outputs": [],
@@ -5757,22 +5760,164 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 83,
+   "execution_count": 24,
    "id": "543f85cc-6171-4d5d-80c4-3206e44e1714",
    "metadata": {},
    "outputs": [
     {
-     "ename": "TypeError",
-     "evalue": "only length-1 arrays can be converted to Python scalars",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
-      "Cell \u001b[0;32mIn[83], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m W1, b1, W2, b2 \u001b[38;5;241m=\u001b[39m \u001b[43mgradient_descent\u001b[49m\u001b[43m(\u001b[49m\u001b[43mX_train\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mY_train\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m500\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m0.10\u001b[39;49m\u001b[43m)\u001b[49m\n",
-      "Cell \u001b[0;32mIn[82], line 11\u001b[0m, in \u001b[0;36mgradient_descent\u001b[0;34m(X, Y, iter, alpha)\u001b[0m\n\u001b[1;32m      9\u001b[0m W1, b1 , W2 , b2 \u001b[38;5;241m=\u001b[39m init_params()\n\u001b[1;32m     10\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(\u001b[38;5;28miter\u001b[39m):\n\u001b[0;32m---> 11\u001b[0m     Z1 , Z2  , A1 , A2\u001b[38;5;241m=\u001b[39m \u001b[43mforward_prop\u001b[49m\u001b[43m(\u001b[49m\u001b[43mW1\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mb1\u001b[49m\u001b[43m \u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mW2\u001b[49m\u001b[43m \u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mb2\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mX\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     12\u001b[0m     dW1 , dW2, db1 , db2 \u001b[38;5;241m=\u001b[39mback_prop(Z1 , Z2  , A1 , A2, W2, X , Y)\n\u001b[1;32m     13\u001b[0m     W1, b1 , W2, b2 \u001b[38;5;241m=\u001b[39m update_params(W1, b1, W2 , b2 ,dW2 ,dW1, db1, db2, alpha)\n",
-      "Cell \u001b[0;32mIn[79], line 11\u001b[0m, in \u001b[0;36mforward_prop\u001b[0;34m(W1, b1, W2, b2, X)\u001b[0m\n\u001b[1;32m      9\u001b[0m A1 \u001b[38;5;241m=\u001b[39m ReLu(Z1)\n\u001b[1;32m     10\u001b[0m Z2 \u001b[38;5;241m=\u001b[39m W2\u001b[38;5;241m.\u001b[39mdot(A1) \u001b[38;5;241m+\u001b[39m b2 \n\u001b[0;32m---> 11\u001b[0m A2 \u001b[38;5;241m=\u001b[39m \u001b[43msoftmax\u001b[49m\u001b[43m(\u001b[49m\u001b[43mA1\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     13\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m Z1 , Z2  , A1 , A2\n",
-      "Cell \u001b[0;32mIn[79], line 5\u001b[0m, in \u001b[0;36msoftmax\u001b[0;34m(Z)\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21msoftmax\u001b[39m(Z):\n\u001b[0;32m----> 5\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mexp\u001b[49m\u001b[43m(\u001b[49m\u001b[43mZ\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241m/\u001b[39m \u001b[38;5;28msum\u001b[39m(np\u001b[38;5;241m.\u001b[39mexp(Z))\n",
-      "\u001b[0;31mTypeError\u001b[0m: only length-1 arrays can be converted to Python scalars"
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Iteration:  0\n",
+      "[4 4 4 ... 4 7 2] [2 6 4 ... 2 6 0]\n",
+      "0.10421951219512195\n",
+      "Iteration:  10\n",
+      "[4 4 4 ... 6 4 4] [2 6 4 ... 2 6 0]\n",
+      "0.1402439024390244\n",
+      "Iteration:  20\n",
+      "[2 4 4 ... 6 4 4] [2 6 4 ... 2 6 0]\n",
+      "0.18260975609756097\n",
+      "Iteration:  30\n",
+      "[2 4 4 ... 6 4 2] [2 6 4 ... 2 6 0]\n",
+      "0.22639024390243903\n",
+      "Iteration:  40\n",
+      "[2 4 4 ... 6 4 2] [2 6 4 ... 2 6 0]\n",
+      "0.27358536585365856\n",
+      "Iteration:  50\n",
+      "[2 4 4 ... 6 4 0] [2 6 4 ... 2 6 0]\n",
+      "0.3517073170731707\n",
+      "Iteration:  60\n",
+      "[2 4 4 ... 6 4 0] [2 6 4 ... 2 6 0]\n",
+      "0.40836585365853656\n",
+      "Iteration:  70\n",
+      "[2 4 4 ... 6 4 0] [2 6 4 ... 2 6 0]\n",
+      "0.4554878048780488\n",
+      "Iteration:  80\n",
+      "[2 4 4 ... 6 4 0] [2 6 4 ... 2 6 0]\n",
+      "0.49997560975609756\n",
+      "Iteration:  90\n",
+      "[2 4 4 ... 6 4 0] [2 6 4 ... 2 6 0]\n",
+      "0.5408780487804878\n",
+      "Iteration:  100\n",
+      "[2 4 4 ... 6 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.5816341463414634\n",
+      "Iteration:  110\n",
+      "[2 4 4 ... 6 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.6165121951219512\n",
+      "Iteration:  120\n",
+      "[2 4 4 ... 6 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.6435853658536586\n",
+      "Iteration:  130\n",
+      "[2 4 4 ... 6 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.6667073170731708\n",
+      "Iteration:  140\n",
+      "[2 4 4 ... 6 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.6854634146341464\n",
+      "Iteration:  150\n",
+      "[2 4 4 ... 6 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.7005121951219512\n",
+      "Iteration:  160\n",
+      "[2 6 4 ... 6 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.7150487804878048\n",
+      "Iteration:  170\n",
+      "[2 6 4 ... 6 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.7254146341463414\n",
+      "Iteration:  180\n",
+      "[2 6 4 ... 7 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.7356585365853658\n",
+      "Iteration:  190\n",
+      "[2 6 4 ... 7 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.7440243902439024\n",
+      "Iteration:  200\n",
+      "[2 6 4 ... 7 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.7522926829268293\n",
+      "Iteration:  210\n",
+      "[2 6 4 ... 7 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.759609756097561\n",
+      "Iteration:  220\n",
+      "[2 6 4 ... 7 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.766\n",
+      "Iteration:  230\n",
+      "[2 6 4 ... 7 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.7719268292682927\n",
+      "Iteration:  240\n",
+      "[2 6 4 ... 7 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.777\n",
+      "Iteration:  250\n",
+      "[2 6 4 ... 7 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.781829268292683\n",
+      "Iteration:  260\n",
+      "[2 6 4 ... 7 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.7859756097560976\n",
+      "Iteration:  270\n",
+      "[2 6 4 ... 7 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.7901951219512195\n",
+      "Iteration:  280\n",
+      "[2 6 4 ... 7 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.7943902439024391\n",
+      "Iteration:  290\n",
+      "[2 6 4 ... 7 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.7986829268292683\n",
+      "Iteration:  300\n",
+      "[2 6 4 ... 7 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.8016341463414635\n",
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+      "[2 6 4 ... 7 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.8048780487804879\n",
+      "Iteration:  320\n",
+      "[2 6 4 ... 7 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.8074878048780488\n",
+      "Iteration:  330\n",
+      "[2 6 4 ... 7 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.810829268292683\n",
+      "Iteration:  340\n",
+      "[2 6 4 ... 7 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.8133170731707317\n",
+      "Iteration:  350\n",
+      "[2 6 4 ... 7 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.8162682926829268\n",
+      "Iteration:  360\n",
+      "[2 6 4 ... 7 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.8192926829268292\n",
+      "Iteration:  370\n",
+      "[2 6 4 ... 7 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.8213170731707317\n",
+      "Iteration:  380\n",
+      "[2 6 4 ... 7 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.8239024390243902\n",
+      "Iteration:  390\n",
+      "[2 6 4 ... 7 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.8258048780487804\n",
+      "Iteration:  400\n",
+      "[2 6 4 ... 7 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.8281219512195122\n",
+      "Iteration:  410\n",
+      "[2 6 4 ... 7 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.8301463414634146\n",
+      "Iteration:  420\n",
+      "[2 6 4 ... 7 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.8321951219512195\n",
+      "Iteration:  430\n",
+      "[2 6 4 ... 7 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.8337317073170731\n",
+      "Iteration:  440\n",
+      "[2 6 4 ... 7 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.8355853658536585\n",
+      "Iteration:  450\n",
+      "[2 6 4 ... 7 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.8376585365853658\n",
+      "Iteration:  460\n",
+      "[2 6 4 ... 7 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.8391463414634146\n",
+      "Iteration:  470\n",
+      "[2 6 4 ... 9 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.840780487804878\n",
+      "Iteration:  480\n",
+      "[2 6 4 ... 9 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.8422682926829268\n",
+      "Iteration:  490\n",
+      "[2 6 4 ... 9 6 0] [2 6 4 ... 2 6 0]\n",
+      "0.8439512195121951\n"
      ]
     }
    ],
@@ -5782,16 +5927,229 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 25,
    "id": "4a6a9819-bf7f-443b-b654-8b4a94c07d4f",
    "metadata": {},
    "outputs": [],
+   "source": [
+    "def make_predictions(X, W1, b1, W2, b2):\n",
+    "    _, _, _, A2 = forward_prop(W1, b1, W2, b2, X)\n",
+    "    predictions = get_predictions(A2)\n",
+    "    return predictions\n",
+    "\n",
+    "def test_prediction(index, W1, b1, W2, b2):\n",
+    "    current_image = X_train[:, index, None]\n",
+    "    prediction = make_predictions(X_train[:, index, None], W1, b1, W2, b2)\n",
+    "    label = Y_train[index]\n",
+    "    print(\"Prediction: \", prediction)\n",
+    "    print(\"Label: \", label)\n",
+    "    \n",
+    "    current_image = current_image.reshape((28, 28)) * 255\n",
+    "    plt.gray()\n",
+    "    plt.imshow(current_image, interpolation='nearest')\n",
+    "    plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "id": "430ac2c1-f81c-488c-9b94-433d750d459e",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Prediction:  [2]\n",
+      "Label:  2\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Prediction:  [6]\n",
+      "Label:  6\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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dkW4r7Kqqqtz8/HzX5/O5o0ePdidOnOgWFxe7H330UaRbC6lp06a5kvod33zzTc92H3/8sXvjjTe648aNc5OTk92lS5e6x44di1zjw+xyx6GlpcUtLi52p0+f7iYkJLhjxoxxs7Ky3LKyMvf777+PdPtDdsMNNwz4+//0z1osnwuDOQ7RdC7wfUgAABOi6j0kAEDsIpAAACYQSAAAEwgkAIAJBBIAwAQCCQBgAoEEADCBQAIAmEAgAQBMIJAAACYQSAAAEwgkAIAJ/w8caFvydw4z2gAAAABJRU5ErkJggg==",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Prediction:  [4]\n",
+      "Label:  4\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Prediction:  [3]\n",
+      "Label:  8\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": "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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "test_prediction(0, W1, b1, W2, b2)\n",
+    "test_prediction(1, W1, b1, W2, b2)\n",
+    "test_prediction(2, W1, b1, W2, b2)\n",
+    "test_prediction(3, W1, b1, W2, b2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "id": "fdb878e1-cd7c-48c8-bbab-2407dcc41eab",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "from PIL import Image\n",
+    "\n",
+    "def preprocess_image(image_path, target_size=(28, 28)):\n",
+    "    try:\n",
+    "        # Load the image\n",
+    "        img = Image.open(image_path)\n",
+    "        \n",
+    "        # Convert to RGB if the image has an alpha channel (PNG)\n",
+    "        if img.mode == 'RGBA':\n",
+    "            img = img.convert('RGB')\n",
+    "        \n",
+    "        # Convert to grayscale\n",
+    "        img = img.convert('L')\n",
+    "        \n",
+    "        # Resize the image\n",
+    "        img = img.resize(target_size)\n",
+    "        \n",
+    "        # Convert to numpy array and normalize\n",
+    "        img_array = np.array(img).reshape(1, 28*28) / 255.0\n",
+    "        \n",
+    "        return img_array.T  # Transpose to match the shape (784, 1)\n",
+    "    \n",
+    "    except Exception as e:\n",
+    "        print(f\"Error processing image {image_path}: {str(e)}\")\n",
+    "        return None\n",
+    "    return img_array.T  # Transpose to match the shape (784, 1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "id": "723d31e8-33dd-438b-8b6a-21d3cde7eace",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def predict_custom_image(image_path, W1, b1, W2, b2):\n",
+    "    # Preprocess the image\n",
+    "    X = preprocess_image(image_path)\n",
+    "    \n",
+    "    # Forward propagation\n",
+    "    _, _, _, A2 = forward_prop(W1, b1, W2, b2, X)\n",
+    "    \n",
+    "    # Get the prediction\n",
+    "    prediction = get_predictions(A2)\n",
+    "    \n",
+    "    return prediction[0]  # Return the single prediction"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "id": "a9aa8b02-edd4-477f-a74e-8b63c77eb51e",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The predicted digit is: 6\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Assuming you have already trained your model and have W1, b1, W2, b2\n",
+    "\n",
+    "# Path to your custom image\n",
+    "custom_image_path = \"images.png\"\n",
+    "\n",
+    "# Make prediction\n",
+    "predicted_digit = predict_custom_image(custom_image_path, W1, b1, W2, b2)\n",
+    "\n",
+    "print(f\"The predicted digit is: {predicted_digit}\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "id": "2e02ae63-cdff-4b57-ab45-4906693645eb",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import pickle\n",
+    "\n",
+    "model_params = {\n",
+    "    'W1': W1,\n",
+    "    'b1': b1,\n",
+    "    'W2': W2,\n",
+    "    'b2': b2\n",
+    "}\n",
+    "\n",
+    "with open('model.pkl', 'wb') as f:\n",
+    "    pickle.dump(model_params, f)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "f5b72124-7465-46ee-8bc7-72e2ab756b1b",
+   "metadata": {},
+   "outputs": [],
    "source": []
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "430ac2c1-f81c-488c-9b94-433d750d459e",
+   "id": "e50817d2-c0a4-4564-8afc-c570526ab8fa",
    "metadata": {},
    "outputs": [],
    "source": []