single-neuron-experiments.ipynb

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      "source": [
        "# Single Neuron Experiments\n",
        "\n",
        "This tutorial introduces [Norse](norse.ai) and the concept of spiking neurons.\n",
        "In the next 5-10 minutes or so you will learn about\n",
        "\n",
        "- Spiking Neuron Models\n",
        "- Gradient based learning with Spiking Neurons"
      ]
    },
    {
      "source": [
        "## Step 0: Installation\n",
        "\n",
        "First of all, we will need to install Norse. Please run the cell below. Read on while it's running."
      ],
      "cell_type": "markdown",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {},
      "outputs": [
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          "name": "stdout",
          "text": [
            "Requirement already satisfied: norse in /Users/cpehle/opt/miniconda3/lib/python3.8/site-packages (0.0.6)\nRequirement already satisfied: absl-py in /Users/cpehle/opt/miniconda3/lib/python3.8/site-packages (from norse) (0.10.0)\nRequirement already satisfied: matplotlib in /Users/cpehle/opt/miniconda3/lib/python3.8/site-packages (from norse) (3.3.2)\nRequirement already satisfied: torchvision>=0.6.0 in /Users/cpehle/opt/miniconda3/lib/python3.8/site-packages (from norse) (0.8.2)\nRequirement already satisfied: torch>=1.5.0 in /Users/cpehle/opt/miniconda3/lib/python3.8/site-packages (from norse) (1.7.1)\nRequirement already satisfied: numpy in /Users/cpehle/opt/miniconda3/lib/python3.8/site-packages (from norse) (1.19.2)\nRequirement already satisfied: six in /Users/cpehle/opt/miniconda3/lib/python3.8/site-packages (from absl-py->norse) (1.15.0)\nRequirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.3 in /Users/cpehle/opt/miniconda3/lib/python3.8/site-packages (from matplotlib->norse) (2.4.7)\nRequirement already satisfied: cycler>=0.10 in /Users/cpehle/opt/miniconda3/lib/python3.8/site-packages (from matplotlib->norse) (0.10.0)\nRequirement already satisfied: python-dateutil>=2.1 in /Users/cpehle/opt/miniconda3/lib/python3.8/site-packages (from matplotlib->norse) (2.8.1)\nRequirement already satisfied: pillow>=6.2.0 in /Users/cpehle/opt/miniconda3/lib/python3.8/site-packages (from matplotlib->norse) (7.2.0)\nRequirement already satisfied: certifi>=2020.06.20 in /Users/cpehle/opt/miniconda3/lib/python3.8/site-packages (from matplotlib->norse) (2020.6.20)\nRequirement already satisfied: kiwisolver>=1.0.1 in /Users/cpehle/opt/miniconda3/lib/python3.8/site-packages (from matplotlib->norse) (1.2.0)\nRequirement already satisfied: typing-extensions in /Users/cpehle/opt/miniconda3/lib/python3.8/site-packages (from torch>=1.5.0->norse) (3.7.4.3)\n"
          ]
        }
      ],
      "source": [
        "!pip install --quiet norse\n",
        "\n",
        "import torch\n",
        "import norse\n",
        "import numpy as np\n",
        "import matplotlib as mpl\n",
        "\n",
        "mpl.rcParams['ytick.left'] = True\n",
        "mpl.rcParams['ytick.labelleft'] = True\n",
        "mpl.rcParams['axes.spines.left'] = True\n",
        "mpl.rcParams['axes.spines.right'] = False\n",
        "mpl.rcParams['axes.spines.top'] = False\n",
        "mpl.rcParams['axes.spines.bottom'] = True\n",
        "mpl.rcParams['legend.frameon'] = False"
      ]
    },
    {
      "source": [
        "## Step 1: A simple neuron model\n",
        "\n",
        "The point neuron models supported by Norse are almost all variants of the Leaky-Integrate and Fire neuron model. It is however relatively easy to implement your own model. The library\n",
        "is build in layers, here I show an example of how to use the functional API directly. To\n",
        "build large scale machine learning models, you should check out the tutorial on [PyTorch\n",
        "lightning + Norse](high-performance-computing.ipynb).\n"
      ],
      "cell_type": "markdown",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {},
      "outputs": [],
      "source": [
        "from norse.torch.functional.lif import lif_step, LIFParameters, LIFState\n",
        "\n",
        "class Neurons(torch.nn.Module):\n",
        "    def __init__(self, weights, alpha):\n",
        "        super(Neurons, self).__init__()\n",
        "        self.hidden_size = hidden_size\n",
        "        self.w_in = torch.nn.Parameter(torch.tensor(weights).float())\n",
        "        self.w_rec = torch.zeros(hidden_size, hidden_size) # no recurrent connections\n",
        "        \n",
        "        self.lambda_vs = []\n",
        "        self.lambda_is = []\n",
        "        self.p = LIFParameters(alpha=alpha)\n",
        "\n",
        "    def reset_lambda_recording(self):\n",
        "        self.lambda_vs = []\n",
        "        self.lambda_is = []\n",
        "\n",
        "    def forward(self, z_in):\n",
        "        seq_length, batch_size, _ = z_in.shape\n",
        "        hidden_size = self.hidden_size\n",
        "\n",
        "        s = LIFState(\n",
        "            v = torch.zeros(batch_size, hidden_size, requires_grad=True),\n",
        "            i = torch.zeros(batch_size, hidden_size, requires_grad=True),\n",
        "            z = torch.zeros(batch_size, hidden_size)\n",
        "        )\n",
        "        voltages = torch.zeros(seq_length, batch_size, hidden_size)\n",
        "        currents = torch.zeros(seq_length, batch_size, hidden_size)\n",
        "        z_s = torch.zeros(seq_length, batch_size, hidden_size)\n",
        "\n",
        "        def save_lambda_v(grad):\n",
        "            if grad is not None:\n",
        "                self.lambda_vs.append(grad)\n",
        "\n",
        "        def save_lambda_i(grad):\n",
        "            if grad is not None:\n",
        "                self.lambda_is.append(grad)\n",
        "\n",
        "        for ts in range(seq_length):\n",
        "            z, s = lif_step(z_in[ts], s, self.w_in, self.w_rec, p=self.p)\n",
        "\n",
        "            # record the gradient in the backward pass\n",
        "            s.v.register_hook(save_lambda_v)\n",
        "            s.i.register_hook(save_lambda_i)\n",
        "\n",
        "            # save the voltage + synaptic input current state\n",
        "            voltages[ts,:] = s.v\n",
        "            currents[ts, :] = s.i\n",
        "            z_s[ts,:] = z\n",
        "\n",
        "        return z_s, voltages, currents"
      ]
    },
    {
      "source": [
        "## Step 2.1: Optimizing for a fixed number of spikes\n",
        "\n",
        "A simple task to consider is a single neuron stimulated at different times by $k$ fixed poisson distributed spike trains, with synaptic weights distributed according to a gaussian distribution. The goal is for the neuron to respond to these fixed spike trains with a certain number of spikes $n_\\text{target}$ within a time $T$. The loss in this case is\n",
        "$$\n",
        "l = -n_\\text{target}/T + \\sum_i \\delta(t - t_i) \n",
        "$$\n",
        "so\n",
        "$$\n",
        "S = \\int_0^T (-n_\\text{target}/T + \\sum_i \\delta(t - t_i)) dt = n_\\text{actual} - n_\\text{target}\n",
        "$$"
      ],
      "cell_type": "markdown",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {},
      "outputs": [],
      "source": [
        "from tqdm.notebook import trange\n",
        "\n",
        "def run_training(\n",
        "    w_in,\n",
        "    z_in,\n",
        "    alpha=100.0,\n",
        "    max_epochs=100,\n",
        "    target_spikes=6,\n",
        "    target_spike_offset=10\n",
        "):\n",
        "    neurons = Neurons(w_in, alpha=torch.tensor(alpha))\n",
        "    optim = torch.optim.SGD(neurons.parameters(), lr=0.1)\n",
        "\n",
        "    lambda_vs = []\n",
        "    lambda_is = []\n",
        "    spikes_out = []\n",
        "    vs = []\n",
        "    cs = []\n",
        "\n",
        "    pbar = trange(max_epochs)\n",
        "    for e in pbar:\n",
        "        optim.zero_grad()\n",
        "        z_s, voltages, currents = neurons(z_in)\n",
        "\n",
        "        # compute the loss according to the formula above\n",
        "        loss = torch.sum(torch.abs((torch.sum(z_s, axis=0) - target_spikes)))\n",
        "        loss.backward()\n",
        "\n",
        "        pbar.set_postfix({\"spike difference\": loss.detach().item()})\n",
        "\n",
        "        # keep track of the experiment data\n",
        "        vs.append(voltages.detach().data)\n",
        "        cs.append(currents.detach().data)     \n",
        "        spikes_out.append(z_s.detach().data)\n",
        "        lambda_vs.append(torch.stack(neurons.lambda_vs))\n",
        "        lambda_is.append(torch.stack(neurons.lambda_is))\n",
        "        neurons.reset_lambda_recording()\n",
        "\n",
        "        if loss.data == torch.tensor([0.0]):\n",
        "            break\n",
        "\n",
        "        # do a gradient optimisation step\n",
        "        optim.step()\n",
        "\n",
        "    return spikes_out, vs, cs, lambda_vs, lambda_is"
      ]
    },
    {
      "source": [],
      "cell_type": "markdown",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {},
      "outputs": [
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          "text": [
            "\n"
          ]
        }
      ],
      "source": [
        "seq_length = 1000\n",
        "input_size = 20\n",
        "hidden_size = 1\n",
        "batch_size = 1\n",
        "epochs = 100\n",
        "alpha = 100.0\n",
        "\n",
        "spikes = torch.distributions.bernoulli.Bernoulli(probs=0.04*torch.ones(seq_length, batch_size, input_size))\n",
        "z_in = spikes.sample()\n",
        "w_in = np.random.randn(hidden_size,input_size) * np.sqrt(2/hidden_size)\n",
        "spikes, vs, cs, lambda_vs, lambda_is = run_training(z_in=z_in, w_in=w_in, alpha=alpha, target_spikes=6, max_epochs=epochs)"
      ]
    },
    {
      "source": [
        "Don't worry that the progress bar turned red, in this case it means that the optimisation\n",
        "finished early. We can plot the error signals that are propagated backwards in time as follows. At each spike that reaches the neuron at synapse the variable $\\lambda_i$ is accumulated to the gradient\n",
        "of the synaptic weight."
      ],
      "cell_type": "markdown",
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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "epoch_from_last = 2\n",
        "plt.plot(lambda_vs[-epoch_from_last][:,0], label='$\\lambda_v$')\n",
        "plt.plot(lambda_is[-epoch_from_last][:,0], label='$\\lambda_i$')\n",
        "plt.xlabel('Time [ms]')\n",
        "plt.legend()"
      ]
    },
    {
      "source": [
        "Exercises:\n",
        "- Change the epoch_from_last variable to plot the error traces at different times in the optimisation\n",
        "  procedure.\n",
        "- Change the value alpha. What do you observe?\n",
        "- Repeat the experiment with more biologically realistic parameters\n"
      ],
      "cell_type": "markdown",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {},
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\u001b[0;31mInit signature:\u001b[0m\n",
            "\u001b[0mnorse\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfunctional\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlif\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mLIFParameters\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\u001b[0m\n",
            "\u001b[0;34m\u001b[0m    \u001b[0mtau_syn_inv\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mTensor\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtensor\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m200.\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
            "\u001b[0;34m\u001b[0m    \u001b[0mtau_mem_inv\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mTensor\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtensor\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m100.\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
            "\u001b[0;34m\u001b[0m    \u001b[0mv_leak\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mTensor\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtensor\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0.\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
            "\u001b[0;34m\u001b[0m    \u001b[0mv_th\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mTensor\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtensor\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1.\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
            "\u001b[0;34m\u001b[0m    \u001b[0mv_reset\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mTensor\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtensor\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0.\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
            "\u001b[0;34m\u001b[0m    \u001b[0mmethod\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mstr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m'super'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
            "\u001b[0;34m\u001b[0m    \u001b[0malpha\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mfloat\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtensor\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m100.\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
            "\u001b[0;34m\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mDocstring:\u001b[0m     \n",
            "Parametrization of a LIF neuron\n",
            "\n",
            "Parameters:\n",
            "    tau_syn_inv (torch.Tensor): inverse synaptic time\n",
            "                                constant (:math:`1/\\tau_\\text{syn}`) in 1/ms\n",
            "    tau_mem_inv (torch.Tensor): inverse membrane time\n",
            "                                constant (:math:`1/\\tau_\\text{mem}`) in 1/ms\n",
            "    v_leak (torch.Tensor): leak potential in mV\n",
            "    v_th (torch.Tensor): threshold potential in mV\n",
            "    v_reset (torch.Tensor): reset potential in mV\n",
            "    method (str): method to determine the spike threshold\n",
            "                  (relevant for surrogate gradients)\n",
            "    alpha (float): hyper parameter to use in surrogate gradient computation\n",
            "\u001b[0;31mFile:\u001b[0m           ~/Documents/Code/norse/norse/torch/functional/lif.py\n",
            "\u001b[0;31mType:\u001b[0m           type\n",
            "\u001b[0;31mSubclasses:\u001b[0m     \n"
          ],
          "name": "stdout"
        }
      ],
      "source": [
        "norse.torch.functional.lif.LIFParameters?"
      ]
    },
    {
      "source": [
        "## Step 2.2: Learning target spike times\n",
        "\n",
        "Another task is for one neuron to spike at specific spike times $t_0, \\ldots, t_N$ given that it stimulated \n",
        "by a fixed set of poisson distributed spikes. We can choose as a loss in this case\n",
        "$$\n",
        "l = \\sum_i \\lvert v - v_{\\text{th}} \\rvert^2 \\delta(t - t_i) + l_N\n",
        "$$\n",
        "that is we require the membrane voltages to be close to the threshold $v_{th}$ at the required spike times $t_i$\n",
        "and penalise the neuron if it spikes more or less than the required number of times."
      ],
      "cell_type": "markdown",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "execution_count": 42,
      "metadata": {},
      "outputs": [],
      "source": [
        "from tqdm.notebook import trange\n",
        "\n",
        "def run_target_spike_time_training(\n",
        "    w_in,\n",
        "    z_in,\n",
        "    alpha=100.0,\n",
        "    epochs=4000,\n",
        "    target_times=[100, 300, 500, 700]\n",
        "):\n",
        "    neurons = Neurons(w_in, alpha=torch.tensor(alpha))\n",
        "    optim = torch.optim.SGD(neurons.parameters(), lr=0.1)\n",
        "\n",
        "    lambda_vs = []\n",
        "    lambda_is = []\n",
        "    spikes_out = []\n",
        "    vs = []\n",
        "    cs = []\n",
        "    \n",
        "\n",
        "    v_target = torch.zeros(seq_length, batch_size, hidden_size)\n",
        "    target_spikes = len(target_times)\n",
        "\n",
        "    for time in target_times:  \n",
        "        v_target[time,:] = 1.1 * torch.ones(hidden_size)\n",
        "    \n",
        "    pbar = trange(epochs)\n",
        "    for e in pbar:\n",
        "        optim.zero_grad()\n",
        "\n",
        "        z_s, voltages, currents = neurons(z_in)\n",
        "        loss = torch.zeros(1,1)\n",
        "        for time in target_times:    \n",
        "            loss += 1/2 * 1/10 * (voltages[time,:] - v_target[time,:])**2\n",
        "\n",
        "        dspikes = torch.sum(torch.abs(torch.sum(z_s, axis=0) - target_spikes))\n",
        "        loss += dspikes\n",
        "        loss.backward()\n",
        "\n",
        "        pbar.set_postfix({\"loss\": loss.detach().item(), \"spike difference\": dspikes.detach().item()})\n",
        "\n",
        "        vs.append(voltages.detach().data)\n",
        "        cs.append(currents.detach().data)\n",
        "        spikes_out.append(z_s.detach().data)\n",
        "        lambda_vs.append(torch.stack(neurons.lambda_vs))\n",
        "        lambda_is.append(torch.stack(neurons.lambda_is))\n",
        "\n",
        "        neurons.lambda_vs = []\n",
        "        neurons.lambda_is = []\n",
        "        if loss.data == torch.tensor([0.0]):\n",
        "            break\n",
        "\n",
        "        optim.step()\n",
        "\n",
        "    return spikes_out, vs, vs, lambda_vs, lambda_is"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 43,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "HBox(children=(HTML(value=''), FloatProgress(value=0.0), HTML(value='')))",
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "acd881b50b474f349a31ec5d60c9ecf6"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n"
          ]
        }
      ],
      "source": [
        "seq_length = 1000\n",
        "input_size = 50\n",
        "hidden_size = 1\n",
        "batch_size = 1\n",
        "epochs = 100\n",
        "alpha = 100.0\n",
        "target_times = [100, 300, 500, 700]\n",
        "\n",
        "\n",
        "w_in = np.random.randn(hidden_size,input_size)* np.sqrt(2/hidden_size)\n",
        "spikes = torch.distributions.bernoulli.Bernoulli(probs=0.04*torch.ones(seq_length, batch_size, input_size))\n",
        "z_in = spikes.sample()\n",
        "result = run_target_spike_time_training(\n",
        "    w_in=w_in, \n",
        "    z_in=z_in,\n",
        "    alpha=alpha, \n",
        "    epochs=epochs, \n",
        "    target_times=target_times\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 45,
      "metadata": {},
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fa8edd5d160>"
            ]
          },
          "metadata": {},
          "execution_count": 45
        },
        {
          "output_type": "display_data",
          "data": {
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          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "spikes, vs, cs, lambda_vs, lambda_is = result\n",
        "\n",
        "actual_times = spikes[-1][:,0,0].to_sparse().indices()[0]\n",
        "\n",
        "\n",
        "for ts in target_times:\n",
        "    plt.axvline(x=ts, color='red', linestyle='--')\n",
        "\n",
        "for ts in list(actual_times):\n",
        "    plt.axvline(x=ts, color='red', linestyle='-')\n",
        "\n",
        "plt.plot(vs[-1][:,0], label='$v$')\n",
        "plt.xlabel('Time [ms]')\n",
        "plt.legend()"
      ]
    },
    {
      "source": [
        "We again visualise the error traces over time."
      ],
      "cell_type": "markdown",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {},
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fa8f50619d0>"
            ]
          },
          "metadata": {},
          "execution_count": 24
        },
        {
          "output_type": "display_data",
          "data": {
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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "plt.plot(lambda_vs[-2][:,0], label='$\\lambda_v$')\n",
        "plt.xlabel('Time [ms]')\n",
        "plt.legend()"
      ]
    },
    {
      "source": [
        "Exercises:\n",
        "- This task doesn't actually great, can you think of ways to improve it?\n",
        "- What additions to the loss could one consider to make the task more stable?\n",
        "- Explore different values for alpha, target_times and input size, what do you observe?\n",
        "- Consider a different optimiser\n",
        "- Consider using biologically plausible neuron parameters"
      ],
      "cell_type": "markdown",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    }
  ]
}