day_3/3_didrik/bnn_solution.ipynb

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        "## Tasks\n",
        "We will implement a Bayesian Neural Network (BNN) and fit it to toy data.\n",
        "\n",
        "#### Todo:\n",
        "* Implement the `VariationalLinear` class (in **Create Layers** section)\n",
        "* Implement the `VariationalFlow` class (in **Create Flow Layers** section)\n",
        "* Train mean-field & flow-based BNNs and compare\n",
        "* **Bonus:** Study the effect of some parameter (e.g. flow architecture, NN architecture, initialization, etc.) and improve performance."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G28jER-pjMil"
      },
      "source": [
        "## Create Dataset"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install einops\n",
        "\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.nn.functional as F\n",
        "from torch.distributions import Normal\n",
        "from torch.utils.data import Dataset, DataLoader\n",
        "from einops import rearrange, reduce, repeat\n",
        "import plotly.express as px\n",
        "import plotly.graph_objects as go\n",
        "\n",
        "device = 'cuda' if torch.cuda.is_available() else 'cpu'\n",
        "\n",
        "def plot_preds(dataset, model=None, title=None):\n",
        "    fig = go.Figure()\n",
        "    fig.update_layout(title=title, title_x=0.5)\n",
        "    fig.add_trace(go.Scatter(x=dataset.x[:,0], y=dataset.y[:,0], mode='markers', name='data'))\n",
        "    if model:\n",
        "      x = torch.linspace(-5,5,steps=200).to(device)\n",
        "      ys = [model(x.unsqueeze(-1))[0].detach()[:,0] for _ in range(10)]\n",
        "      for y in ys: fig.add_trace(go.Scatter(x=x, y=y, mode='lines', name='pred', marker = {'color' : '#EF553B'}))\n",
        "    return fig"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nwL6k5ngjWom",
        "outputId": "07afa018-42db-44f5-9d9b-553e9d2a0e4d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Requirement already satisfied: einops in /usr/local/lib/python3.7/dist-packages (0.4.1)\n"
          ]
        }
      ]
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        "id": "2_fpR-TFjMil",
        "outputId": "ef759266-07e1-4276-ea6f-87756763a3b1"
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      "source": [
        "class ToyData(Dataset):\n",
        "  def __init__(self, num, sigma=0.5):\n",
        "      self.x = 8 * torch.rand(num, 1) - 4\n",
        "      self.y  = 0.1 * self.x**3 - self.x + sigma * torch.randn(num, 1)\n",
        "      self.num = num\n",
        "      self.sigma = sigma\n",
        "\n",
        "  def __getitem__(self, i):\n",
        "      return self.x[i], self.y[i]\n",
        "\n",
        "  def __len__(self):\n",
        "      return len(self.x)\n",
        "\n",
        "torch.manual_seed(42)\n",
        "dataset = ToyData(128)\n",
        "testset = ToyData(1024)\n",
        "train_loader = DataLoader(dataset, batch_size=32, shuffle=True)\n",
        "plot_preds(dataset)"
      ]
    },
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        "id": "12vNrsrjjMin"
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      "source": [
        "## Create Layers"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "NJ-u_AKQjMin"
      },
      "outputs": [],
      "source": [
        "class StandardGaussian(nn.Module):\n",
        "\n",
        "    def __init__(self, dim):\n",
        "        super().__init__()\n",
        "        self.register_buffer('loc', torch.zeros(dim))\n",
        "        self.register_buffer('scale', torch.ones(dim))\n",
        "\n",
        "    def log_prob(self, x):\n",
        "        return Normal(self.loc, self.scale).log_prob(x).sum(1)\n",
        "\n",
        "    def sample(self, num_samples):\n",
        "        return Normal(self.loc, self.scale).sample((num_samples,))\n",
        "\n",
        "    def sample_with_log_prob(self, num_samples):\n",
        "        x = self.sample(num_samples)\n",
        "        return x, self.log_prob(x)\n",
        "\n",
        "\n",
        "class Gaussian(nn.Module):\n",
        "\n",
        "    def __init__(self, dim, mean_std_init=0.05, std_init=0.05):\n",
        "        super().__init__()\n",
        "        self.loc = nn.Parameter(mean_std_init*torch.randn(dim))\n",
        "        self.log_scale = nn.Parameter(np.log(std_init)*torch.ones(dim))\n",
        "\n",
        "    def sample_with_log_prob(self, num_samples):\n",
        "        d = Normal(self.loc, self.log_scale.exp())\n",
        "        x = d.rsample((num_samples,))\n",
        "        return x, d.log_prob(x).sum(1)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def split_wb(wb, i, o):\n",
        "    w, b = torch.split_with_sizes(wb, (i*o, o))\n",
        "    return w.reshape(o, i), b\n",
        "\n",
        "\n",
        "class VariationalLinear(nn.Module):\n",
        "\n",
        "    def __init__(self, q, p, dim_in, dim_out):\n",
        "        super().__init__()\n",
        "        self.q = q # Variational distribution\n",
        "        self.p = p # Prior distribution\n",
        "        self.dim_in = dim_in\n",
        "        self.dim_out = dim_out\n",
        "\n",
        "    def forward(self, x):\n",
        "        wb, log_qwb = self.q.sample_with_log_prob(1)\n",
        "        kl = log_qwb - self.p.log_prob(wb)\n",
        "        w, b = split_wb(wb.squeeze(0), self.dim_in, self.dim_out)\n",
        "        return F.linear(x, w, b), kl\n",
        "\n",
        "    \n",
        "# Test VariationalLinear\n",
        "m = VariationalLinear(Gaussian(10*5+5), StandardGaussian(10*5+5), 10, 5)\n",
        "m(torch.randn(1, 10))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YXSQF1rk9V6W",
        "outputId": "8fce37a4-b0e9-4b58-bda2-9448d080a7af"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([[-0.2881,  0.1345,  0.3139, -0.2588,  0.6795]],\n",
              "        grad_fn=<AddmmBackward0>), tensor([137.3688], grad_fn=<SubBackward0>))"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Create Flow Layers"
      ],
      "metadata": {
        "id": "nOzJEru9luGA"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def build_mask(in_dim, out_dim, ar_dim, causal=False):\n",
        "    assert in_dim % ar_dim == 0; assert out_dim % ar_dim == 0\n",
        "    base = torch.ones(ar_dim, ar_dim)\n",
        "    base = base.tril(-1) if causal else base.tril(0)\n",
        "    return repeat(base, 'h w -> (o h) (i w)', i=in_dim // ar_dim, o=out_dim // ar_dim)\n",
        "\n",
        "\n",
        "class MaskedLinear(nn.Module):\n",
        "\n",
        "    def __init__(self, in_dim, out_dim, ar_dim, causal=False):\n",
        "        super().__init__()\n",
        "        self.register_buffer('mask', build_mask(in_dim, out_dim, ar_dim, causal))\n",
        "        self.weight = nn.Parameter(torch.empty(out_dim, in_dim))\n",
        "        self.bias = nn.Parameter(torch.empty(out_dim))\n",
        "        self.reset_parameters()\n",
        "\n",
        "    def reset_parameters(self):\n",
        "        nn.init.kaiming_normal_(self.weight)\n",
        "        nn.init.zeros_(self.bias)\n",
        "\n",
        "    def forward(self, x):\n",
        "        return F.linear(x, self.weight * self.mask, self.bias)\n",
        "\n",
        "\n",
        "def make_net(dim): \n",
        "    return nn.Sequential(\n",
        "        MaskedLinear(dim,   dim*4, ar_dim=dim), nn.GELU(),\n",
        "        MaskedLinear(dim*4, dim*4, ar_dim=dim), nn.GELU(),\n",
        "        MaskedLinear(dim*4, dim*2, ar_dim=dim, causal=True),\n",
        "    )"
      ],
      "metadata": {
        "id": "O8Em_3mDltEt"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "class Reverse(nn.Module):\n",
        "\n",
        "    def forward(self, x):\n",
        "        return x.flip(-1), x.new_zeros(x.shape[0])\n",
        "\n",
        "    def inverse(self, z):\n",
        "        return z.flip(-1)\n",
        "\n",
        "\n",
        "class IAF(nn.Module):\n",
        "\n",
        "    def __init__(self, ar_net):\n",
        "        super().__init__()\n",
        "        self.ar_net = ar_net\n",
        "\n",
        "    def forward(self, x):\n",
        "        p = self.ar_net(x)\n",
        "        m, u = torch.chunk(p, 2, dim=1)\n",
        "        u = u + 1.0 # Improve initialization\n",
        "        s, log_s = torch.sigmoid(u), F.logsigmoid(u)\n",
        "        z = s * x + (1-s) * m\n",
        "        ldj = log_s.sum(1)\n",
        "        return z, ldj\n",
        "\n",
        "\n",
        "class VariationalFlow(nn.Module):\n",
        "\n",
        "    def __init__(self, base_dist, bijections):\n",
        "        super().__init__()\n",
        "        self.base_dist = base_dist\n",
        "        self.bijections = nn.ModuleList(bijections)\n",
        "\n",
        "    def sample_with_log_prob(self, num_samples):\n",
        "        z, log_prob = self.base_dist.sample_with_log_prob(num_samples)\n",
        "        for bijection in self.bijections:\n",
        "            z, ldj = bijection(z)\n",
        "            log_prob -= ldj\n",
        "        return z, log_prob\n",
        "\n",
        "\n",
        "def make_flow(dim):\n",
        "    return VariationalFlow(\n",
        "        base_dist=StandardGaussian(dim=dim),\n",
        "        bijections=[\n",
        "            IAF(make_net(dim)), Reverse(),\n",
        "            IAF(make_net(dim)), Reverse(),\n",
        "            IAF(make_net(dim)), Reverse(),\n",
        "            IAF(make_net(dim)),\n",
        "        ],\n",
        "    )\n",
        "\n",
        "# Test VariationalFlow\n",
        "flow = make_flow(5)\n",
        "flow.sample_with_log_prob(2)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "H_0qK_Z6l0r2",
        "outputId": "cb066ea3-cb6e-4c35-9a30-b09827f615be"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([[ 0.0887, -0.1286,  0.3598, -0.1486, -0.0394],\n",
              "         [ 0.0592,  0.1806, -0.2329, -0.0417, -0.1132]], grad_fn=<AddBackward0>),\n",
              " tensor([0.4505, 1.0394], grad_fn=<SubBackward0>))"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Create BNN"
      ],
      "metadata": {
        "id": "vRQn8lVb5Y20"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "UxAovOxfjMiq"
      },
      "outputs": [],
      "source": [
        "class BNN(nn.Module):\n",
        "\n",
        "    def __init__(self, I, O, H, scale, num, mean_field=True):\n",
        "        super().__init__()\n",
        "        D = lambda i,o: i*o+o\n",
        "        q = lambda i,o: Gaussian(D(i,o), mean_std_init=1/np.sqrt(i)) if mean_field else make_flow(D(i,o))\n",
        "        self.layer0 = VariationalLinear(q(I,H), StandardGaussian(D(I,H)), I, H)\n",
        "        self.layer1 = VariationalLinear(q(H,O), StandardGaussian(D(H,O)), H, O)\n",
        "        self.scale = scale\n",
        "        self.num = num\n",
        "\n",
        "    def forward(self, x):\n",
        "        h, kl0 = self.layer0(x)\n",
        "        h = F.gelu(h)\n",
        "        h, kl1 = self.layer1(h)\n",
        "        return h, kl0+kl1\n",
        "\n",
        "    def elbo(self, x, y):\n",
        "        yhat, kl = self(x)\n",
        "        return Normal(yhat, self.scale).log_prob(y).mean() - kl/self.num\n",
        "\n",
        "get_model = lambda mean_field: BNN(1, 1, 32, scale=dataset.sigma, num=dataset.num, mean_field=mean_field).to(device)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def train(model, epochs=1000):\n",
        "  optimizer = torch.optim.Adam(model.parameters(), lr=1e-3)\n",
        "\n",
        "  print('Training...')\n",
        "  model = model.train()\n",
        "  elbos = []\n",
        "  for epoch in range(epochs):\n",
        "      loss_sum = 0.0\n",
        "      for i, (x,y) in enumerate(train_loader):\n",
        "          x, y = x.to(device), y.to(device)\n",
        "          optimizer.zero_grad()\n",
        "          loss = -model.elbo(x, y)\n",
        "          loss.backward()\n",
        "          optimizer.step()\n",
        "          loss_sum += loss.detach().cpu().item()\n",
        "      elbos.append(loss_sum/len(train_loader))\n",
        "      if (epoch+1) % 100 == 0:\n",
        "        print('Epoch: {}/{}, Loss: {:.3f}'.format(epoch+1, epochs, elbos[-1]))\n",
        "  model = model.eval()\n",
        "  return model, elbos"
      ],
      "metadata": {
        "id": "YcrtU857x6xK"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Train Mean-Field BNN"
      ],
      "metadata": {
        "id": "X533DKq5pBC9"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vIadGCejjMir",
        "outputId": "c1c34221-1003-4ef0-db4a-d957ef1d642f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Training...\n",
            "Epoch: 100/1000, Loss: 3.846\n",
            "Epoch: 200/1000, Loss: 3.224\n",
            "Epoch: 300/1000, Loss: 3.468\n",
            "Epoch: 400/1000, Loss: 3.192\n",
            "Epoch: 500/1000, Loss: 2.953\n",
            "Epoch: 600/1000, Loss: 2.868\n",
            "Epoch: 700/1000, Loss: 2.715\n",
            "Epoch: 800/1000, Loss: 2.686\n",
            "Epoch: 900/1000, Loss: 2.816\n",
            "Epoch: 1000/1000, Loss: 2.597\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
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          },
          "metadata": {}
        }
      ],
      "source": [
        "torch.manual_seed(42)\n",
        "model_mf, elbos_mf = train(get_model(True))\n",
        "plot_preds(dataset, model_mf, title='Mean-Field BNN')"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Train Flow-Based BNN"
      ],
      "metadata": {
        "id": "buOaaNOOpdut"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "torch.manual_seed(42)\n",
        "model_flow, elbos_flow = train(get_model(False))\n",
        "plot_preds(dataset, model_flow, title='Flow-Based BNN')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AqyKbTRGpjta",
        "outputId": "1b0c7ad2-fc09-46b8-8201-e003a21158e0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Training...\n",
            "Epoch: 100/1000, Loss: 4.131\n",
            "Epoch: 200/1000, Loss: 3.409\n",
            "Epoch: 300/1000, Loss: 3.519\n",
            "Epoch: 400/1000, Loss: 3.165\n",
            "Epoch: 500/1000, Loss: 2.081\n",
            "Epoch: 600/1000, Loss: 2.000\n",
            "Epoch: 700/1000, Loss: 2.063\n",
            "Epoch: 800/1000, Loss: 2.551\n",
            "Epoch: 900/1000, Loss: 2.136\n",
            "Epoch: 1000/1000, Loss: 1.939\n"
          ]
        },
        {
          "output_type": "display_data",
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    {
      "cell_type": "markdown",
      "source": [
        "## Compare Models"
      ],
      "metadata": {
        "id": "taCLBdHtrI58"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "df = pd.DataFrame({'mean_field':elbos_mf, 'flow':elbos_flow})\n",
        "px.line(df, y=['mean_field','flow'])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        },
        "id": "HwcVa3PMxF2C",
        "outputId": "38bae67d-de5e-4c06-d43d-755ce87baa27"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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      "cell_type": "code",
      "source": [
        "print(f'Mean-Field: Avg. loss over last 100 epochs: {np.mean(elbos_mf[-100:]):.4f}')\n",
        "print(f'Flow:       Avg. loss over last 100 epochs: {np.mean(elbos_flow[-100:]):.4f}')"
      ],
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      "execution_count": null,
      "outputs": [
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          "name": "stdout",
          "text": [
            "Mean-Field: Avg. loss over last 100 epochs: 2.6132\n",
            "Flow:       Avg. loss over last 100 epochs: 1.9368\n"
          ]
        }
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      "source": [
        "test_mse_mf = [F.mse_loss(model_mf(testset.x)[0], testset.y).detach().item() for _ in range(100)]\n",
        "test_mse_flow = [F.mse_loss(model_flow(testset.x)[0], testset.y).detach().item() for _ in range(100)]\n",
        "\n",
        "print(f'Mean-Field: Test MSE: {np.mean(test_mse_mf):.4f}')\n",
        "print(f'Flow:       Test MSE: {np.mean(test_mse_flow):.4f}')"
      ],
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      "execution_count": null,
      "outputs": [
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          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mean-Field: Test MSE: 0.4393\n",
            "Flow:       Test MSE: 0.3836\n"
          ]
        }
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