notebooks/CL_via_PNN.ipynb

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      "source": [
        "\n",
        "One way to eleminate forgetting while keeping the benefits of transfer learning is to expand the network architecture with every task. By doing this, one can increase the capacity of the network to learn new tasks while retaining its perfromance on older ones. An example approach to achieve CL via architecture expansion is [Progressive Neural Networks(PNN)](https://arxiv.org/abs/1606.04671.pdf).\n",
        "\n",
        "**PNN**\n",
        "\n",
        "PNN works by having a part of the network (a column) dedicated to each task. Upon adding new tasks the previous columns weights get frozen so the network perfromance on those columns is fixed. To make the new columns benefit from the old columns knowledge through transfer learning, lateral connections `a` are added. By having a seperate lateral connections, the new column can learn from previous columns without decreasing the performance on the old tasks. \n",
        "\n",
        "The image below shows a network of 3 tasks upon adding the third task. The dashed lines are frozen weights to fix task 1 & 2 performance and `a` connections are used to link old tasks knowledge to the new task.\n",
        "\n",
        "<img src=\"https://qph.fs.quoracdn.net/main-qimg-c1e7ad14cca99e0b97475ad014e02397.webp\" align=\"center\"> </img>\n",
        "\n",
        "This network offers one the architecture-based techniques to solve CL. That being said, the expansion per task can be limiting when the number of tasks increases. This in addition to that the network expects to have the task-id at inference time are important drawbacks of this architecture. It's still intuitive and an important benchmark so we'll discuss how to make a simple PNN.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5b4uH__YeIuE"
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      "source": [
        "# some initial imports\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "\n",
        "import torch\n",
        "import torch.nn as nn\n",
        "import torchvision.datasets as datasets\n",
        "import torchvision.transforms as transforms\n",
        "import torch.optim as optim\n",
        "import torch.nn.functional as F"
      ],
      "execution_count": null,
      "outputs": []
    },
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        "id": "U4A2qeef4EGq"
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        "# switch to False to use CPU\n",
        "use_cuda = True\n",
        "\n",
        "use_cuda = use_cuda and torch.cuda.is_available()\n",
        "device = torch.device(\"cuda\" if use_cuda else \"cpu\");\n",
        "torch.manual_seed(1);"
      ],
      "execution_count": null,
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        "id": "eK7EoyUC4Hum",
        "outputId": "d6efd1fa-fef2-4855-cb41-f2002205ddc1"
      },
      "source": [
        "# Get MNIST data\n",
        "!git clone https://github.com/ContinualAI/colab.git continualai/colab\n",
        "\n",
        "from continualai.colab.scripts import mnist\n",
        "mnist.init()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Cloning into 'continualai/colab'...\n",
            "remote: Enumerating objects: 124, done.\u001b[K\n",
            "remote: Counting objects: 100% (124/124), done.\u001b[K\n",
            "remote: Compressing objects: 100% (78/78), done.\u001b[K\n",
            "remote: Total 244 (delta 67), reused 88 (delta 41), pack-reused 120\u001b[K\n",
            "Receiving objects: 100% (244/244), 10.23 MiB | 39.09 MiB/s, done.\n",
            "Resolving deltas: 100% (109/109), done.\n",
            "Downloading train-images-idx3-ubyte.gz...\n",
            "Downloading t10k-images-idx3-ubyte.gz...\n",
            "Downloading train-labels-idx1-ubyte.gz...\n",
            "Downloading t10k-labels-idx1-ubyte.gz...\n",
            "Download complete.\n",
            "Save complete.\n",
            "Downloading https://storage.googleapis.com/cvdf-datasets/mnist/train-images-idx3-ubyte.gz to data/mnist/MNIST/raw/train-images-idx3-ubyte.gz\n"
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            "\n",
            "Extracting data/mnist/MNIST/raw/train-images-idx3-ubyte.gz to data/mnist/MNIST/raw\n",
            "Downloading https://storage.googleapis.com/cvdf-datasets/mnist/train-labels-idx1-ubyte.gz to data/mnist/MNIST/raw/train-labels-idx1-ubyte.gz\n"
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          "text": [
            "\n",
            "Extracting data/mnist/MNIST/raw/train-labels-idx1-ubyte.gz to data/mnist/MNIST/raw\n",
            "Downloading https://storage.googleapis.com/cvdf-datasets/mnist/t10k-images-idx3-ubyte.gz to data/mnist/MNIST/raw/t10k-images-idx3-ubyte.gz\n"
          ],
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        {
          "output_type": "stream",
          "text": [
            "\n",
            "Extracting data/mnist/MNIST/raw/t10k-images-idx3-ubyte.gz to data/mnist/MNIST/raw\n",
            "Downloading https://storage.googleapis.com/cvdf-datasets/mnist/t10k-labels-idx1-ubyte.gz to data/mnist/MNIST/raw/t10k-labels-idx1-ubyte.gz\n"
          ],
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        },
        {
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          "text": [
            "\n",
            "Extracting data/mnist/MNIST/raw/t10k-labels-idx1-ubyte.gz to data/mnist/MNIST/raw\n",
            "Processing...\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/torchvision/datasets/mnist.py:479: UserWarning: The given NumPy array is not writeable, and PyTorch does not support non-writeable tensors. This means you can write to the underlying (supposedly non-writeable) NumPy array using the tensor. You may want to copy the array to protect its data or make it writeable before converting it to a tensor. This type of warning will be suppressed for the rest of this program. (Triggered internally at  /pytorch/torch/csrc/utils/tensor_numpy.cpp:143.)\n",
            "  return torch.from_numpy(parsed.astype(m[2], copy=False)).view(*s)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Done!\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "o2jv9bAh4J1o"
      },
      "source": [
        "# we will construct 5 tasks of MNIST, where every task is responsible for 2 digits\n",
        "x_train, t_train, x_test, t_test = mnist.load()\n",
        "# tasks to use\n",
        "task_classes_arr = [(0, 1), (2, 3), (4, 5), (6, 7), (8, 9)]\n",
        "tasks_num = len(task_classes_arr) # 5\n",
        "\n",
        "task_data = []\n",
        "for i, task_classes in enumerate(task_classes_arr):\n",
        "  train_mask = np.isin(t_train, task_classes)\n",
        "  test_mask = np.isin(t_test, task_classes)\n",
        "  x_train_task, t_train_task = x_train[train_mask], t_train[train_mask]\n",
        "  x_test_task, t_test_task = x_test[test_mask], t_test[test_mask]\n",
        "\n",
        "  task_data.append((x_train_task, t_train_task - (i * 2), \n",
        "                    x_test_task, t_test_task - (i * 2)))\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "j_KR19pu4G_g"
      },
      "source": [
        "First we need to build a network for each column and combine those later in the main network. A column is just like an ordinary network with the exception of the lateral connections from the previous columns. An important part is that all the previous columns need to be infered before the current column, so that it can use the output with the lateral connections.\n",
        "\n",
        "To limit the expansion of the network we'll decrease the size on the columns of tasks that come after the first task. In the code we use a hidden layer of size `128` for task#1 and `32` for all the subsequent tasks.    "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jcgvm1oy4N_H"
      },
      "source": [
        "class Column(nn.Module):\n",
        "  def __init__(self,  col_id=0, hsize=128):\n",
        "    super().__init__()\n",
        "    # new layers per column\n",
        "    self.l1 = nn.Linear(784, hsize)\n",
        "    self.l2 = nn.Linear(hsize, 2)\n",
        "    # lateral connections for old intermediate outputs\n",
        "    # a set of connections per layer\n",
        "    self.Us = nn.ModuleList()\n",
        "    self.col_id = col_id\n",
        "    for col_i in range(self.col_id):\n",
        "      h = 128 if col_i == 0 else 32\n",
        "      lateral = nn.Linear(h, 2)\n",
        "      self.Us.append(lateral)\n",
        "\n",
        "  def add_lateral(self, x, prev_cols, lateral_weights):\n",
        "    \"\"\"Compute the o/p of lateral connections.\n",
        "     Returns zeros tensor for first column.\n",
        "     lateral_weights ([int]): list of weights to control\n",
        "     the lateral connections\"\"\"\n",
        "    outputs = torch.zeros_like(x)\n",
        "    for col_id, col in enumerate(prev_cols):\n",
        "      input = col.outputs\n",
        "      if lateral_weights:\n",
        "        input = input * lateral_weights[col_id]\n",
        "      layer = self.Us[col_id]\n",
        "      outputs += layer(input)\n",
        "    return outputs\n",
        "\n",
        "  def freeze(self):\n",
        "    \"freezes all parameters of the column. To be used when adding new columns.\"\n",
        "    for param in self.parameters():\n",
        "      param.requires_grad = False\n",
        "\n",
        "  def forward(self, x, prev_cols, lateral_weights):\n",
        "    \"lateral_weights ([int]): list of weights to control the lateral connections\"\n",
        "    # 1- Transfer Learning\n",
        "    # for all previous columns, compute old transfered knowledge\n",
        "    # and save it to the instance of the column\n",
        "    for i, col in enumerate(prev_cols):\n",
        "      # compute all layers first\n",
        "      l_w = lateral_weights[:i+1]\n",
        "      col(x, prev_cols[:i], l_w)\n",
        "\n",
        "    # 2- New Knowledge\n",
        "    # input/1st layer\n",
        "    x = x.view(x.size(0), -1)\n",
        "    x = F.relu(self.l1(x))\n",
        "    # save intermediate outputs of current col\n",
        "    self.outputs = x\n",
        "    # last/2nd layer\n",
        "    x = self.l2(x)\n",
        "    # add lateral connextion o/p from all previous columns\n",
        "    x += self.add_lateral(x, prev_cols=prev_cols,\n",
        "                          lateral_weights=lateral_weights)\n",
        "\n",
        "    return x"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mvevuQUR7yMQ"
      },
      "source": [
        "To create the whole network, we'll have a ModuleList that holds the columns. Upon adding a new task, all the columns are freezed and a new column with proper lateral connections is instantiated. For the forward pass we need to indicate which column to compute and it automatically computes all its previous columns. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Gyy_QkD_Jcpz"
      },
      "source": [
        "class Net(nn.Module):\n",
        "  def __init__(self):\n",
        "    super().__init__()\n",
        "    self.cols = nn.ModuleList()\n",
        "  \n",
        "  def add_column(self, hsize=128):\n",
        "    # freeze all previous columns\n",
        "    for col in self.cols:\n",
        "      col.freeze()\n",
        "    # create new column\n",
        "    col_id = len(self.cols)\n",
        "    col = Column(col_id, hsize)\n",
        "    self.cols.append(col)\n",
        "\n",
        "  def forward(self, x, id, lateral_weights=None):\n",
        "    if lateral_weights is None:\n",
        "      # all lateral connections are on by default\n",
        "      lateral_weights = [1 for _ in range(id)]\n",
        "    col = self.cols[id]\n",
        "    return col(x, self.cols[:id], lateral_weights)\n",
        "    "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QAXUWl1HKPFH"
      },
      "source": [
        "# basic training and testing loops\n",
        "def train(model, task_id, device, x_train, t_train,\n",
        "          optimizer, epochs=10, log_training=False):\n",
        "    for epoch in range(epochs):\n",
        "      model.train()\n",
        "      \n",
        "      for start in range(0, len(t_train)-1, 256):\n",
        "        end = start + 256\n",
        "        x, y = torch.from_numpy(x_train[start:end]), torch.from_numpy(t_train[start:end]).long()\n",
        "        x, y = x.to(device), y.to(device)\n",
        "        \n",
        "        optimizer.zero_grad()\n",
        "\n",
        "        output = model(x, task_id)\n",
        "        loss = F.cross_entropy(output, y)\n",
        "        loss.backward()\n",
        "        optimizer.step()\n",
        "        if log_training:\n",
        "          print('Train Epoch: {} \\tLoss: {:.6f}'.format(epoch, loss.item()))\n",
        "\n",
        "def test(model, task_id, device, x_test, t_test, lateral_weights=None):\n",
        "    model.eval()\n",
        "    test_loss = 0\n",
        "    correct = 0\n",
        "    for start in range(0, len(t_test)-1, 256):\n",
        "      end = start + 256\n",
        "      with torch.no_grad():\n",
        "        x, y = torch.from_numpy(x_test[start:end]), torch.from_numpy(t_test[start:end]).long()\n",
        "        x, y = x.to(device), y.to(device)\n",
        "        output = model(x, task_id, lateral_weights=lateral_weights)\n",
        "        test_loss += F.cross_entropy(output, y).item() # sum up batch loss\n",
        "        pred = output.max(1, keepdim=True)[1] # get the index of the max logit\n",
        "        correct += pred.eq(y.view_as(pred)).sum().item()\n",
        "\n",
        "    test_loss /= len(t_test)\n",
        "    return test_loss, 100. * correct / len(t_test)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rNnoPQau-2I1"
      },
      "source": [
        "In the next step we'll have a function that adds a column per task. In order to investigate how much the network have used old columns' output, we'll test once with turning on all the lateral connections and another with them off."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kLST74EoKqxM"
      },
      "source": [
        "def train_PNN(epochs=10):\n",
        "  \"Train all 5 taks using PNN\"\n",
        "  accs_grid_a = []\n",
        "  accs_grid_no_a = []\n",
        "\n",
        "  # to track the increase of the number of parameters\n",
        "  parameters = []\n",
        "  grad_parameters = []\n",
        "\n",
        "  net = Net()\n",
        "  for task_id in range(tasks_num):\n",
        "    # train on current task\n",
        "    x_train, t_train, _, _ = task_data[task_id]\n",
        "    # smaller column sizes from 2nd task inwards to limit expansion\n",
        "    if task_id > 0:\n",
        "      net.add_column(hsize=32)\n",
        "    else: net.add_column()\n",
        "    optimizer = optim.SGD(net.parameters(), lr=0.01, momentum=0.9)\n",
        "    # increase of parameters over time\n",
        "    parameters.append(sum(p.numel() for p in net.parameters()))\n",
        "    grad_parameters.append(sum(p.numel() for p in net.parameters() if p.requires_grad))\n",
        "    train(net, task_id, device, x_train, t_train, optimizer,\n",
        "          epochs=epochs, log_training=False)\n",
        "\n",
        "    # test on all tasks with lateral connections `a`\n",
        "    \n",
        "    accs_a = []\n",
        "    for id in range(0, task_id + 1):\n",
        "      _, _, x_test, t_test = task_data[id]\n",
        "      # we'll have the lateral weights as fully-on here\n",
        "      l_w = [1] * id\n",
        "      _, test_acc = test(net, id, device, x_test, t_test, lateral_weights=l_w)\n",
        "      accs_a.append(test_acc)\n",
        "  \n",
        "    if task_id < (tasks_num - 1):\n",
        "      accs_a.extend([np.nan] * (4 - task_id))\n",
        "    accs_grid_a.append(accs_a)\n",
        "\n",
        "\n",
        "    # test on all tasks without lateral connections `a`\n",
        "    accs_no_a = []\n",
        "    for id in range(0, task_id + 1):\n",
        "      _, _, x_test, t_test = task_data[id]\n",
        "      # we'll have the lateral weights as fully-off here\n",
        "      l_w = [0] * id\n",
        "      _, test_acc = test(net, id, device, x_test, t_test, lateral_weights=l_w)\n",
        "      accs_no_a.append(test_acc)\n",
        "  \n",
        "    if task_id < (tasks_num - 1):\n",
        "      accs_no_a.extend([np.nan] * (4 - task_id))\n",
        "    accs_grid_no_a.append(accs_no_a)\n",
        "\n",
        "  # return accuracies with and without lateral connections \n",
        "  return accs_grid_a, accs_grid_no_a, parameters, grad_parameters"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "f-qYfSd4M-xF"
      },
      "source": [
        "accs_a, accs_no_a, parameters, grad_parameters= train_PNN(epochs=15)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4CwebvEDBy0M"
      },
      "source": [
        "We can see from the below figure that the network uses some of the knowledge learnt from previous tasks to learn new tasks. As task number increases, its dependance on lateral connections increases (due to having more more connections as the task# progresses.) MNIST problem with multi-head setting is relatively simple though and with more complex tasks we can see more prononced releance on transfer learning from previous columns and can have a proxy for task similarity. A deeper analysis can be found in [the original paper](https://arxiv.org/pdf/1606.04671.pdf)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vcIdCFHkUkk3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 351
        },
        "outputId": "e85b13a3-a008-4c21-93d0-06d2d28e137f"
      },
      "source": [
        "fig, ax = plt.subplots(1, 2, figsize=(10, 5))\n",
        "\n",
        "ax[0].plot(range(1, 6), np.nanmean(accs_a, axis=1))\n",
        "ax[0].plot(range(1, 6), np.nanmean(accs_no_a, axis=1))\n",
        "ax[0].legend(['With lateral connections', 'Without lateral connections'])\n",
        "ax[0].set_ylabel('Accumulated Accuracy for Seen Tasks')\n",
        "ax[0].set_xlabel('Task Number')\n",
        "\n",
        "ax[1].plot(range(1, 6), accs_a[-1])\n",
        "ax[1].plot(range(1, 6), accs_no_a[-1])\n",
        "ax[1].legend(['With lateral connections', 'Without lateral connections'])\n",
        "ax[1].set_ylabel('Task Accuracy')\n",
        "ax[1].set_xlabel('Task Number')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 0, 'Task Number')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x360 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "beU_K_ViGtXd"
      },
      "source": [
        "Since we add new column for every task, the number of parameters expands. The number of learnable parameters expands in more modest rate though as we are freezing old columns. In the figure below we can see the rate at which the parameters expands. Note that since we use smaller column size starting from task 2 (32 neurons vs. 128) the learnable parameters decrease at first then increases very slowly afterwards."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Ku2oKU9AL_ij",
        "outputId": "97e6b013-f164-45b9-835e-2e69f0e062af"
      },
      "source": [
        "# Number of learnable paramters decreases after task#1, increase by just 66 after task#2\n",
        "print(grad_parameters)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[100738, 25444, 25510, 25576, 25642]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 351
        },
        "id": "hfksKzteFbFf",
        "outputId": "055b03b0-4953-48dd-eece-34a2326cf46f"
      },
      "source": [
        "fig, ax = plt.subplots(1, 1, figsize=(5, 5))\n",
        "ax.plot(range(1, 6), parameters)\n",
        "ax.plot(range(1, 6), grad_parameters)\n",
        "ax.set_yscale('log')\n",
        "ax.legend(['All model parameters', 'Learnable Model Parameters'])\n",
        "ax.set_ylabel('Number of Parameters')\n",
        "ax.set_xlabel('Task Number')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 0, 'Task Number')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 360x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xdyFPVX7DOXr",
        "outputId": "38d3c6d7-93fb-4520-8ef7-4a07e68038f3",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "!git status\n"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "fatal: not a git repository (or any of the parent directories): .git\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_LM2sqT_p06h"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}