docs/user/advanced_examples/FullyConnectedNeuralNetwork.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fully Connected Neural Network\n",
    "\n",
    "In this example, we show how one can train a neural network on a specific task (here, Iris Classification) and use Concrete-Numpy to make the model work in FHE settings."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import torch\n",
    "from torch import nn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define our neural network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class FCIris(torch.nn.Module):\n",
    "    \"\"\"Neural network for Iris classification\n",
    "\n",
    "    We define a fully connected network with three (3) fully connected (fc) layers that\n",
    "    perform feature extraction and one (fc) layer to produce the final classification.\n",
    "    We will use 3 neurons on all layers to ensure that the FHE accumulators\n",
    "    do not overflow (we are currently only allowed a maximum of 7 bits-width).\n",
    "    More information on this is available at\n",
    "    https://docs.zama.ai/concrete-numpy/main/user/howto/reduce_needed_precision.html#limitations-for-fhe-friendly-neural-network.\n",
    "\n",
    "    Due to accumulator limits, we have to design a network with only a few neurons on each layer.\n",
    "    This is in contrast to a traditional approach where the number of neurons increases after\n",
    "    each layer or block.\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self, input_size):\n",
    "        super().__init__()\n",
    "\n",
    "        # The first layer processes the input data, in our case 4 dimensional vectors\n",
    "        self.linear1 = nn.Linear(input_size, 3)\n",
    "        self.sigmoid1 = nn.Sigmoid()\n",
    "        # Next, we add a one intermediate layer\n",
    "        self.linear2 = nn.Linear(3, 3)\n",
    "        self.sigmoid2 = nn.Sigmoid()\n",
    "        # Finally, we add the decision layer for 3 output classes encoded as one-hot vectors\n",
    "        self.decision = nn.Linear(3, 3)\n",
    "\n",
    "    def forward(self, x):\n",
    "\n",
    "        x = self.linear1(x)\n",
    "        x = self.sigmoid1(x)\n",
    "        x = self.linear2(x)\n",
    "        x = self.sigmoid2(x)\n",
    "        x = self.decision(x)\n",
    "\n",
    "        return x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define all required variables to train the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get iris dataset\n",
    "from sklearn.datasets import load_iris\n",
    "\n",
    "X, y = load_iris(return_X_y=True)\n",
    "\n",
    "# Split into train and test\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.25, random_state=42)\n",
    "\n",
    "# Convert to tensors\n",
    "X_train = torch.tensor(X_train).float()\n",
    "X_test = torch.tensor(X_test).float()\n",
    "y_train = torch.tensor(y_train)\n",
    "y_test = torch.tensor(y_test)\n",
    "\n",
    "# Initialize our model\n",
    "model = FCIris(X.shape[1])\n",
    "\n",
    "# Define our loss function\n",
    "criterion = nn.CrossEntropyLoss()\n",
    "\n",
    "# Define our optimizer\n",
    "optimizer = torch.optim.SGD(model.parameters(), lr=0.1)\n",
    "\n",
    "# Define the number of iterations\n",
    "n_iters = 50001\n",
    "\n",
    "# Define the batch size\n",
    "batch_size = 16"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train():\n",
    "    for i in range(n_iters):\n",
    "        # Get a random batch of training data\n",
    "        idx = torch.randperm(X_train.size()[0])\n",
    "        X_batch = X_train[idx][:batch_size]\n",
    "        y_batch = y_train[idx][:batch_size]\n",
    "\n",
    "        # Forward pass\n",
    "        y_pred = model(X_batch)\n",
    "\n",
    "        # Compute loss\n",
    "        loss = criterion(y_pred, y_batch)\n",
    "\n",
    "        # Backward pass\n",
    "        optimizer.zero_grad()\n",
    "        loss.backward()\n",
    "\n",
    "        # Update weights\n",
    "        optimizer.step()\n",
    "\n",
    "        if i % 1000 == 0:\n",
    "            # Print epoch number, loss and accuracy\n",
    "            accuracy = torch.sum(torch.argmax(y_pred, dim=1) == y_batch).item() / y_batch.size()[0]\n",
    "            print(f\"Iterations: {i:02} | Loss: {loss.item():.4f} | Accuracy: {100*accuracy:.2f}%\")\n",
    "            if accuracy == 1:\n",
    "                break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compile the model\n",
    "\n",
    "The `compile_torch_model` first applies a quantization to `model` with `n_bits` of precision using `X_train` as the calibration dataset and compile the model to its FHE counterparts. Here we use 3 bits of precision. In some edge cases, the network accumulators can overflow (i.e. extreme quantized values in both input and weights, which is unlikely). In such a case, we need to retrain the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training a FHE friendly quantized network.\n",
      "Iterations: 00 | Loss: 1.0572 | Accuracy: 25.00%\n",
      "Iterations: 1000 | Loss: 0.3317 | Accuracy: 100.00%\n",
      "Compiling the model to FHE.\n",
      "The network is trained and FHE friendly.\n"
     ]
    }
   ],
   "source": [
    "from concrete.ml.torch.compile import compile_torch_model\n",
    "\n",
    "print(\"Training a FHE friendly quantized network.\")\n",
    "for _ in range(10):\n",
    "    try:\n",
    "        train()\n",
    "        print(\"Compiling the model to FHE.\")\n",
    "        quantized_compiled_module = compile_torch_model(\n",
    "            model,\n",
    "            X_train,\n",
    "            n_bits=3,\n",
    "        )\n",
    "        print(\"The network is trained and FHE friendly.\")\n",
    "        break\n",
    "    except RuntimeError as e:\n",
    "        if str(e).startswith(\"max_bit_width of some nodes is too high\"):\n",
    "            print(\"The network is not fully FHE friendly, retraining.\")\n",
    "            continue\n",
    "        raise e\n",
    "else:\n",
    "    raise RuntimeError(\n",
    "        \"Could not compile the model to FHE.\"\n",
    "        \"You may need to decrease the n_bits parameter to avoid potential overflows.\"\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Predict with the torch model in clear"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = model(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Predict with the quantized model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We now have a module in full numpy.\n",
    "# Convert data to a numpy array.\n",
    "X_train_numpy = X_train.numpy()\n",
    "X_test_numpy = X_test.numpy()\n",
    "y_train_numpy = y_train.numpy()\n",
    "y_test_numpy = y_test.numpy()\n",
    "q_X_test_numpy = quantized_compiled_module.quantize_input(X_test_numpy)\n",
    "quant_model_predictions = quantized_compiled_module(q_X_test_numpy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Predict in FHE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|█████████████████████████████████████████████████████████████████████████████████████████████| 38/38 [05:05<00:00,  8.05s/it]\n"
     ]
    }
   ],
   "source": [
    "from tqdm import tqdm\n",
    "\n",
    "fhe_x_test = quantized_compiled_module.quantize_input(X_test_numpy)\n",
    "homomorphic_quant_predictions = []\n",
    "for x_q in tqdm(fhe_x_test):\n",
    "    homomorphic_quant_predictions.append(\n",
    "        quantized_compiled_module.forward_fhe.encrypt_run_decrypt(np.array([x_q]).astype(np.uint8))\n",
    "    )\n",
    "homomorphic_predictions = quantized_compiled_module.dequantize_output(\n",
    "    np.array(homomorphic_quant_predictions, dtype=np.float32).reshape(quant_model_predictions.shape)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Print the accuracy of both models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test Accuracy: 97.37%\n",
      "Test Accuracy Quantized Inference: 65.79%\n",
      "Test Accuracy Homomorphic Inference: 68.42%\n"
     ]
    }
   ],
   "source": [
    "acc_0 = 100 * (y_pred.argmax(1) == y_test).float().mean()\n",
    "acc_1 = 100 * (quant_model_predictions.argmax(1) == y_test_numpy).mean()\n",
    "acc_2 = 100 * (homomorphic_predictions.argmax(1) == y_test_numpy).mean()\n",
    "\n",
    "print(f\"Test Accuracy: {acc_0:.2f}%\")\n",
    "print(f\"Test Accuracy Quantized Inference: {acc_1:.2f}%\")\n",
    "print(f\"Test Accuracy Homomorphic Inference: {acc_2:.2f}%\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca = PCA(n_components=2)\n",
    "X_train_2d = pca.fit_transform(X_train_numpy)\n",
    "\n",
    "b_min = np.min(X_train_2d, axis=0)\n",
    "b_max = np.max(X_train_2d, axis=0)\n",
    "\n",
    "grid_dims = tuple(np.linspace(b_min[i], b_max[i], 128) for i in range(X_train_2d.shape[1]))\n",
    "ndgrid_tuple = np.meshgrid(*grid_dims)\n",
    "grid_2d = np.vstack([g.ravel() for g in ndgrid_tuple]).transpose()\n",
    "\n",
    "grid_test = pca.inverse_transform(grid_2d)\n",
    "grid_test_quantized = quantized_compiled_module.quantize_input(grid_test)\n",
    "\n",
    "grid_pred_all = quantized_compiled_module(grid_test_quantized)\n",
    "grid_pred_all_original = model(torch.tensor(grid_test).float()).detach().numpy()\n",
    "\n",
    "pred_classes = np.argmax(grid_pred_all, axis=1).astype(np.int32)\n",
    "pred_classes_original = np.argmax(grid_pred_all_original, axis=1).astype(np.int32)\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "cmap = \"autumn\"\n",
    "# Create two subplots and set their locations\n",
    "plt.clf()\n",
    "fig, axs = plt.subplots(1, 2, figsize=(12, 6))\n",
    "\n",
    "# Plot original model contour plot\n",
    "axs[0].contourf(\n",
    "    ndgrid_tuple[0],\n",
    "    ndgrid_tuple[1],\n",
    "    pred_classes_original.reshape(ndgrid_tuple[0].shape),\n",
    "    cmap=cmap,\n",
    ")\n",
    "\n",
    "# Plot the scatter with marker borders\n",
    "axs[0].scatter(X_train_2d[:, 0], X_train_2d[:, 1], c=y_train_numpy, s=50, edgecolors=\"k\", cmap=cmap)\n",
    "\n",
    "# Add title and axis labels\n",
    "axs[0].set_title(\"Original Inference\")\n",
    "\n",
    "\n",
    "# Plot quantized model contour plot\n",
    "axs[1].contourf(\n",
    "    ndgrid_tuple[0], ndgrid_tuple[1], pred_classes.reshape(ndgrid_tuple[0].shape), cmap=cmap\n",
    ")\n",
    "\n",
    "# Plot the scatter with marker borders\n",
    "axs[1].scatter(X_train_2d[:, 0], X_train_2d[:, 1], c=y_train_numpy, s=50, edgecolors=\"k\", cmap=cmap)\n",
    "\n",
    "# Add title and axis labels\n",
    "axs[1].set_title(\"Quantized Inference\")\n",
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the above plot, we show the decision boundaries for both the original and quantized model. The quantized model has it's decision boundaries (colored regions) slightly shifted compared to the original model. This is due to the low-bit quantization applied to the model in post-training.\n",
    "\n",
    "Here we do not compute the contour plot for the FHE inference as this would be really costly but it should be pretty close to the quantized model.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "In this notebook, we presented a few steps to have a model (torch neural network) inference in over homomorphically encrypted data: \n",
    "- We first trained a fully connected neural network yielding ~97% accuracy\n",
    "- Then, we quantized it using Concrete-Numpy. We observed a small decrease in accuracy here due to the strong quantization applied(accuracy = ~94%).\n",
    "- We then used the compiled inference into its FHE equivalent to get our FHE predictions over the test set\n",
    "\n",
    "The homomorphic inference achieves a similar accuracy as the quantized model inference.\n",
    "\n",
    "Disclaimer: post-training quantization with such a low bit width (<=3) can yield different results for the quantized model which will mainly depend on the range of the learned weights."
   ]
  }
 ],
 "metadata": {
  "execution": {
   "timeout": 10800
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}