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   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 0, Loss: 0.0\n",
      "Iteration 20, Loss: 0.0\n",
      "Iteration 40, Loss: 0.0\n",
      "Iteration 60, Loss: 0.0\n",
      "Iteration 80, Loss: 0.0\n",
      "Iteration 100, Loss: 0.0\n",
      "Iteration 120, Loss: 0.0\n",
      "Iteration 140, Loss: 0.0\n",
      "Iteration 160, Loss: 0.0\n",
      "Iteration 180, Loss: 0.0\n",
      "Final weights:\n",
      " [[0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]]\n",
      "Final biases:\n",
      " [0. 0. 0.]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "# Initial inputs\n",
    "inputs = np.array([1, 2, 3, 4])\n",
    "\n",
    "# Initial weights and biases\n",
    "weights = np.array([\n",
    "    [0.1, 0.2, 0.3, 0.4],\n",
    "    [0.5, 0.6, 0.7, 0.8],\n",
    "    [0.9, 1.0, 1.1, 1.2]\n",
    "])\n",
    "\n",
    "biases = np.array([0.1, 0.2, 0.3])\n",
    "\n",
    "# Learning rate\n",
    "learning_rate = 0.001\n",
    "\n",
    "# ReLU activation function and its derivative\n",
    "def relu(x):\n",
    "    return np.maximum(0, x)\n",
    "\n",
    "def relu_derivative(x):\n",
    "    return np.where(x > 0, 1, 0)\n",
    "\n",
    "# Training loop\n",
    "for iteration in range(200):\n",
    "    # Forward pass\n",
    "    z = np.dot(weights, inputs) + biases\n",
    "    a = relu(z)\n",
    "    y = np.sum(a)\n",
    "\n",
    "    # Calculate loss\n",
    "    loss = y ** 2\n",
    "\n",
    "    # Backward pass\n",
    "    # Gradient of loss with respect to output y\n",
    "    dL_dy = 2 * y\n",
    "\n",
    "    # Gradient of y with respect to a\n",
    "    dy_da = np.ones_like(a)\n",
    "\n",
    "    # Gradient of loss with respect to a\n",
    "    dL_da = dL_dy * dy_da\n",
    "\n",
    "    # Gradient of a with respect to z (ReLU derivative)\n",
    "    da_dz = relu_derivative(z)\n",
    "\n",
    "    # Gradient of loss with respect to z\n",
    "    dL_dz = dL_da * da_dz\n",
    "\n",
    "    # Gradient of z with respect to weights and biases\n",
    "    dL_dW = np.outer(dL_dz, inputs)\n",
    "    dL_db = dL_dz\n",
    "\n",
    "    # Update weights and biases\n",
    "    weights -= learning_rate * dL_dW\n",
    "    biases -= learning_rate * dL_db\n",
    "\n",
    "    # Print the loss every 20 iterations\n",
    "    if iteration % 20 == 0:\n",
    "        print(f\"Iteration {iteration}, Loss: {loss}\")\n",
    "\n",
    "# Final weights and biases\n",
    "print(\"Final weights:\\n\", weights)\n",
    "print(\"Final biases:\\n\", biases)\n",
    "\n"
   ]
  }
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