Tutorial 3.3 Solution_Normalizing_Flows_2D_Scalar_Field_Theory.ipynb

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        "**Normalizing Flows for Lattice Field Theory**\n",
        "----\n",
        "\n",
        ">Code courtesy: 100% of the code is taken from the paper [Introduction to Normalizing Flows for Lattice Field Theory](https://arxiv.org/abs/2101.08176).\n",
        "\n",
        "Given below is a snippet from the same paper.\n",
        "![picture](https://drive.google.com/uc?export=view&id=1axWOeSJC7j4WOwnBLIyNIiCYQySmyVAi)\n",
        "In this tutorial, we will consider the map $f: z \\to \\phi$, contrary to the convention above.\n",
        "\n",
        "\n",
        "Consider a Neural Network that we want to train, to obtain a target output  $\\phi$ with a probability distribution function\n",
        "$$P[\\phi] = \\frac{1}{Z}e^{-S[\\phi]} = \\frac{1}{Z} \\exp\\big( - \\int d^dx (\\partial_\\mu \\phi(x) )^2 + m^2 \\phi(x)^2 + \\lambda \\phi(x)^4 \\big).$$\n",
        "$Z$ is the partition function or the overall normalization of this theory. Here, $d$ is the dimension of a lattice of inputs for this Neural Network. In scalar field theory language, this lattice is discretized (Euclidean) space-time. For simplicity, let us consider the case $d=2$, then the target output density is given as\n",
        "$$P_{\\text{lattice}}[\\phi] = \\frac{1}{Z} e^{-S_{\\text{lattice}}[\\phi]} \\\\\n",
        "= \\frac{1}{Z} \\exp \\Big( - \\sum_{\\vec{n}} \\phi(\\vec{n}) \\Big[\\sum_{\\mu \\in \\{1,2 \\} } 2\\phi(\\vec{n}) - \\phi(\\vec{n} + {\\mu} ) - \\phi(\\vec{n}- {\\mu}) \\Big] + m^2 \\phi(\\vec{n})^2 + \\lambda \\phi(\\vec{n})^4 \\Big). $$\n",
        "The $2$ dimensional lattice of inputs is given as $L_x \\times L_y$, with number of lattice sites $\\vec{n} = (n_x,n_y)$. The field $\\phi(\\vec{n})$ is defined only on the lattice sites, and $n_x,n_y$ are integers. Lattice spacing is taken as $1$, in appropriate units.\n",
        "\n",
        "The Neural Network takes in lattice points $x ,y \\in \\{L_x, L_y\\}$, and trainable priors (a.k.a. stochastic parameters) $z$. Let $r(z)$ denote the prior density. The actual output density of this Network is denoted by $Q[\\phi]$. *Normalizing Flows* $f: z \\to \\phi$ are differentiable and invertible maps from the space of priors to the space of outputs.\n",
        "\n",
        "* Let us choose the convention that $L_x = L_y = L$, and $n_x, n_y \\in [0, L-1]$.\n",
        "* Let us also introduce alternate notions $P[\\phi]:= P(\\alpha)$ and $Q[\\phi] := Q(\\alpha)$ for the target density and actual output density, respectively.\n",
        "* Neural Network output $\\alpha$ is a random variable, which in this case, corresponds to the value of the scalar field $\\phi(\\vec{n})$ evaluated on a single lattice site in $2$ dimensions.\n",
        "* Notations $\\phi(\\vec{n})$ and $\\phi_{\\vec{n}}$ respectively denote the field configuration that lives on the sites of the lattice, and the unraveled one-dimensional vector of lattice degrees of freedom.\n",
        "* Field $\\phi(\\vec{n}):= \\phi_1(\\vec{n}_x) \\times \\phi_2(\\vec{n}_y)$ can be thought of as some $(L \\times L)$ dimensional tensor.\n",
        "* Field action $S_{\\text{lattice}}[\\phi] \\in \\mathbb{R}$, and the path integral measure is a product over discretized ones $D\\phi(\\vec{n}) = \\prod_{\\vec{n}} d \\phi_{\\vec{n}}$.  \n",
        "* The partition function $Z = \\int \\prod_{\\vec{n}} d\\phi(\\vec{n}) \\, e^{- S_{\\text{lattice}}[\\phi]}$ is difficult to calculate, and obtaining the target density $P_{\\text{lattice}}[\\phi]$ up to some arbitrary constant is fine, for this tutorial.\n",
        "* *There is a curse of dimensionality here*. The dimensionality of the field density depends on the number of lattice sites, and grows with the volume of the lattice.\n",
        "\n",
        "*Reguralizing the scalar field theory on such a $2$ dimensional lattice, with one real degree of freedom per each lattice site, lets us access the non-perturbative physics in the strong coupling regime of the same theory.*\n",
        "\n",
        "**Let us introduce Normalizing Flows**\n",
        "----\n",
        "*A normalizing flow describes the transformation of a probability density through a sequence of invertible, differentiable mappings.*\n",
        "\n",
        "Any invertible, differentiable function $f(z)$ will transform the prior density $r(z)$ on random variable $z$ to a output density $Q(x):= Q(\\alpha)$ on variable $\\alpha = f(z)$; both $z$ and $\\alpha$ can be multi-dimensional random variables.\n",
        "* Let $f^{-1} = g$, then $z = g \\circ f(z)$.\n",
        "* The normalizing flow $f$ induces a change of variable(s) from $z$ to $\\alpha$.\n",
        "* The output density $Q(\\alpha)$ can be obtained from $r(z)$, if we can compute the Jacobian factor $J(z) = \\big|\\det_{kl} \\partial f(z_k)/\\partial z_l \\big|$ for this transformation. $$Q(\\alpha) = r(z)\\big[ J(z)\\big]^{-1} = r(z) \\Bigg|\\det_{kl} \\frac{\\partial f_k(z)}{\\partial z_l} \\Bigg|^{-1} $$\n",
        "\n",
        "**Let us introduce Coupling Layers**\n",
        "----\n",
        "\n",
        "An invertible, differentiable expressive function $f$ can be constructed as a composition of multiple simpler invertible, differentiable functions $f_i$\n",
        "$$f = f_k \\circ f_{k-1} \\circ \\cdots f_1.$$\n",
        "Coupling layers are one of the approaches to define the simpler mappings $f_i$, in a way such that only a subset of the input variables are updated through each $f_i$, conditioned on the complimentary (\"frozen\") subset.\n",
        "* As a simple example, if the inputs to a set of coupling layers is a lattice with one real number per each lattice site, then the first two coupling layers $f_1$ and $f_2$ can be designed to update only the even and odd sites, respectively.\n",
        "* The transformation applied by each coupling layer is manifestly invertible, e.g. a scaling transformation $x \\to e^s x$, or an affine transformation $x \\to e^s x + t$.\n",
        "* Next, a coupling layer generating outputs $x_1', x'_2 = f_i(x_1,x_2)$ via a scaling transformation is defined below\n",
        "$$x'_1 = e^{s(x_2)} x_1, \\\\\n",
        "x'_2 = x_2, $$ where $x_1, x_2$ are subsets of the layer input $x$.\n",
        "* The coupling layer in the above example keeps $x_2$ frozen, and $x_1$ is updated based on frozen $x_2$.\n",
        "* The product in $e^{s(x_2)}x_1$ is elementwise, and $e^{s(x_2)}$ is defined elementwise on $x_2$, and therefore, has the same shape as $x_1$.\n",
        "* The transformation inducing parameters in $s(x_2)$ can be complicated non-invertible functions of frozen $x_2$.\n",
        "* Such choices are not a problem as the inverse transformation can easily be defined, using the same functions $s(x_2)$, as\n",
        "$$x_1 = e^{-s(x'_2)} x'_1, \\\\\n",
        "x_2 = x'_2. $$\n",
        "* The Jacobian of the forward transformation\n",
        "$$J_{\\text{forward}}(x) = \\Bigg|\\det_{kl} \\frac{\\partial \\big[ f_i(x_1, x_2) \\big]_k }{\\partial x_l} \\Bigg| = \\prod_k e^{[s(x_2)]_k} ,$$\n",
        "is the inverse of the Jacobian of the reverse transformation associated with $f^{-1}_{i}$, i.e. $J_{\\text{reverse}}(x') = 1/J_{\\text{forward}}(x)$.\n",
        "\n",
        "*The Jacobian for the normalizing flow $f$ is obtained by composing all Jacobians of all coupling layers together, $$Q(\\alpha) = r(z)\\prod_{i=1}^{k} J_{i}^{-1}(z) = r(z) \\Bigg|\\det \\frac{\\partial f(z)}{\\partial z} \\Bigg|^{-1} .$$*\n",
        "\n",
        "\n",
        "\n",
        "**Coupling Layers for Scalar Field Theory on $2$D Lattice**\n",
        "---\n",
        "\n",
        "Previously, we defined scalar field theory on a $2$ dimensional lattice of size $L \\times L$. We will now define coupling layers for this problem, such that the real degrees of freedom on each lattice site $\\phi$ can be divided into two subsets $\\phi_1, \\phi_2$, and the coupling layers will induce affine and / or scaling transformations on one subset, while keeping the other frozen.\n",
        "\n",
        "We choose the same set of affine transformations as before. Then, each coupling layer of the form $f_i: (\\phi_1, \\phi_2) \\mapsto (\\phi_1' , \\phi_2') $ induces the following transformation\n",
        "$$ \\phi'_1 = e^{s(\\phi_2)}\\phi_1 + t(\\phi_2), \\\\\n",
        "\\phi'_2 = \\phi_2,$$\n",
        "on its inputs. The inverse of this layer is given by $f_i^{-1}(\\phi'_1, \\phi'_2) = \\big( (\\phi'_1 - t(\\phi'_2) )\\, e^{-s(\\phi'_2) } , \\phi'_2 \\big) .$\n",
        "* Here, $s(\\phi_2), t(\\phi_2)$ are vectors of the same size as $\\phi_1$, and all operations are elementwise.\n",
        "* Later, we will define functions $s,t$ using Neural Networks.\n",
        "* The logarithm of Jacobians for $f_i$ (forward) and its inverse $f^{-1}_{i}$ (reverse) transformations are respectively\n",
        "$$\\log J_{\\text{forward}}(\\phi) = \\sum_k \\big[s(\\phi_2) \\big]_k, \\\\\n",
        "\\log J_{\\text{reverse}}(\\phi') = \\sum_k - \\big[s(\\phi'_2) \\big]_k. $$\n",
        "* For implimentations in Neural Networks, we will define subsets $\\phi_1, \\phi_2$ using a mask $m(\\vec{n}) \\in \\{0,1 \\}$. When $m(\\vec{n})=1$, $\\phi_1$ is updated using functions $s,t$, while $\\phi_2$ is kept frozen.\n",
        "\n",
        "\n",
        "**KL Divergence Loss for Normalizing Flow**\n",
        "----\n",
        "Once we implement the coupling layers $f_i$ for scalar field theory on a $2$ dimensional lattice using a Neural Network, it will result in output distribution $Q[\\phi']$ on transformed variable $\\phi'$. A priori, there is no reason to believe that $Q[\\phi']$ would be close to target scalar field density $P_{\\text{lattice}}[\\phi']$ on $\\phi'$. We need a good loss function to minimize the differences between the approximate and true distributions $Q[\\phi']$ and $P_{\\text{lattice}}[\\phi']$, respectively.\n",
        "\n",
        "Recall [Tutorial 3.1 KL_divergence.ipynb](https://github.com/iaifi/summer-school-2023/blob/main/Tutorial%203.1%20KL_divergence.ipynb) from earlier today. Target output data $\\phi'$ from target distribution $P_{\\text{lattice}}[\\phi']$ can be scarce, which may pose a problem to training. To avoid this, we define the reverse Kullback-Leibler diveregnce between $Q[\\phi']$ and $P_{\\text{lattice}}[\\phi']$, under the assumption that output $\\phi'$ is a continuous random variable. Then, the reverse KL divergence loss is\n",
        "$$D_{KL}(Q||P_{\\text{lattice}}) = \\int d\\phi \\, Q(\\phi') \\big( \\log Q(\\phi') - \\log P_{\\text{lattice}}(\\phi')  \\big) .$$\n",
        "Actual outputs $\\phi'$ from the coupling layers would be discrete multidimensional random variables. Then, a trainable KL divergence loss would require some modifications of the above equation.\n",
        "\n",
        "Let's redefine the reverse KL divergence for approximate and true distributions $Q[\\phi']$ and $P_{\\text{lattice}}[\\phi']$ as\n",
        "$$\\tilde{D}_{KL}(Q||P_{\\text{lattice}}) = \\frac{1}{N} \\sum_{i=1}^{N} \\big( \\log Q[\\phi'_i]  - \\log P_{\\text{lattice}}[\\phi'_i] \\big) ,$$\n",
        "for $N$ samples $\\phi'_i$ drawn from target distribution $P_{\\text{lattice}}$. A problem with this choice may be the mode-seeking or zero-forcing behavior of reverse KL diveregnce, we will not discuss it here.\n",
        "\n",
        "\n",
        "**Effective Sample Size**\n",
        "---\n",
        "\n",
        "Defined below is Effective Sample Size or ESS for a batch of samples $\\phi'_i$. It's a measure of the model quality that does not require overall normalization of $P_{\\text{lattice}}[\\phi']$,\n",
        "$$ESS = \\frac{\\Big(\\frac{1}{N}\\sum_i \\frac{ P_{\\text{lattice}}[\\phi'_i] }{ Q[\\phi'_i]} \\Big)^2 }{ \\frac{1}{N}\\sum_i \\Big( \\frac{ P_{\\text{lattice}}[\\phi'_i] }{ Q[\\phi'_i]} \\Big)^2 } .$$\n",
        "It can be seen that ESS lies in the range $[0,1]$; larger values indicate better effective sampling, and a perfect value of $ESS = 1$ indicates perfect independent draw from target distribution $P_{\\text{lattice}}$ for each sample.\n",
        "\n",
        "ESS is a noisier quantity than KL divergence, and therefore, is not used as a loss function.\n"
      ],
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      "cell_type": "markdown",
      "source": [
        "\n",
        "**It's time to implement everything in codes.**\n",
        "----\n",
        "\n",
        "At this point, we will import all requires libraries, and define functions that we may need to call at a later point."
      ],
      "metadata": {
        "id": "mxk4LNiLBDoK"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# import libraries\n",
        "import base64\n",
        "import io\n",
        "import pickle\n",
        "import numpy as np\n",
        "import torch\n",
        "print(f'TORCH VERSION: {torch.__version__}')\n",
        "import packaging.version\n",
        "if packaging.version.parse(torch.__version__) < packaging.version.parse('1.5.0'):\n",
        "    raise RuntimeError('Torch versions lower than 1.5.0 not supported')\n",
        "\n",
        "%matplotlib inline\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "sns.set_style('whitegrid')\n",
        "\n",
        "# set up environmet for pytorch\n",
        "if torch.cuda.is_available():\n",
        "    torch_device = 'cuda'\n",
        "    float_dtype = np.float32 # single\n",
        "    torch.set_default_tensor_type(torch.cuda.FloatTensor)\n",
        "else:\n",
        "    torch_device = 'cpu'\n",
        "    float_dtype = np.float64 # double\n",
        "    torch.set_default_tensor_type(torch.DoubleTensor)\n",
        "print(f\"TORCH DEVICE: {torch_device}\")\n",
        "\n",
        "# define two functions for mod and remainder\n",
        "def torch_mod(x):\n",
        "    return torch.remainder(x, 2*np.pi)\n",
        "def torch_wrap(x):\n",
        "    return torch_mod(x+np.pi) - np.pi\n",
        "\n",
        "# a function to detach tensors from the computational graph and pull them to CPU as a numpy array\n",
        "def grab(var):\n",
        "    return var.detach().cpu().numpy()\n",
        "\n",
        "#####\n",
        "# the set of functions defined below make a live-updating plot during training\n",
        "from IPython.display import display\n",
        "\n",
        "def init_live_plot(dpi=125, figsize=(8,4)):\n",
        "    fig, ax_ess = plt.subplots(1,1, dpi=dpi, figsize=figsize)\n",
        "    plt.xlim(0, N_era*N_epoch)\n",
        "    plt.ylim(0, 1)\n",
        "\n",
        "    ess_line = plt.plot([0],[0], alpha=0.5) # dummy\n",
        "    plt.grid(False)\n",
        "    plt.ylabel('ESS')\n",
        "\n",
        "    ax_loss = ax_ess.twinx()\n",
        "    loss_line = plt.plot([0],[0], alpha=0.5, c='orange') # dummy\n",
        "    plt.grid(False)\n",
        "    plt.ylabel('Loss')\n",
        "\n",
        "    plt.xlabel('Epoch')\n",
        "\n",
        "    display_id = display(fig, display_id=True)\n",
        "\n",
        "    return dict(\n",
        "        fig=fig, ax_ess=ax_ess, ax_loss=ax_loss,\n",
        "        ess_line=ess_line, loss_line=loss_line,\n",
        "        display_id=display_id\n",
        "    )\n",
        "\n",
        "def moving_average(x, window=10):\n",
        "    if len(x) < window:\n",
        "        return np.mean(x, keepdims=True)\n",
        "    else:\n",
        "        return np.convolve(x, np.ones(window), 'valid') / window\n",
        "\n",
        "def update_plots(history, fig, ax_ess, ax_loss, ess_line, loss_line, display_id):\n",
        "    Y = np.array(history['ess'])\n",
        "    Y = moving_average(Y, window=15)\n",
        "    ess_line[0].set_ydata(Y)\n",
        "    ess_line[0].set_xdata(np.arange(len(Y)))\n",
        "    Y = history['loss']\n",
        "    Y = moving_average(Y, window=15)\n",
        "    loss_line[0].set_ydata(np.array(Y))\n",
        "    loss_line[0].set_xdata(np.arange(len(Y)))\n",
        "    ax_loss.relim()\n",
        "    ax_loss.autoscale_view()\n",
        "    fig.canvas.draw()\n",
        "    display_id.update(fig) # need to force colab to update plot\n",
        "#####"
      ],
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        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "iy57N9X2e8h6",
        "outputId": "b6e4e442-c8c0-4a3d-c945-d81e051840bd"
      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "TORCH VERSION: 2.0.1+cu118\n",
            "TORCH DEVICE: cpu\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Exercise 0: Compute the Jacobian for the transformation $f:(Z_1, Z_2) \\to (U_1, U_2)$ where $$Z_1 = \\sqrt{-2 \\ln U_1}\\cos(\\pi U_2), \\\\ Z_2 = \\sqrt{-2 \\ln U_1}\\sin(\\pi U_2).$$**\n",
        "---\n"
      ],
      "metadata": {
        "id": "k7_jddgSclso"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Solution (to be remove before GitHub upload): $\\frac{\\pi}{U_1}.$**\n",
        "---\n",
        "\n"
      ],
      "metadata": {
        "id": "Czz1cw-wdPFn"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "**Exercise 1: Sample $U_1, U_2 \\sim \\text{unif}(0,1)$ for a batch size of $2^{12}$. Write a code in python to plot transformed variables $Z_2$ against $Z_1$, and original variables $U_2$ against $U_1$, separately.**\n",
        "---"
      ],
      "metadata": {
        "id": "L9iTSIa4dNMt"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Solution (to be removed before GitHub upload)**\n",
        "----"
      ],
      "metadata": {
        "id": "vcliZOF8efAY"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "batch_size = 2**12\n",
        "u = np.random.random(size=(batch_size, 2))\n",
        "z = np.sqrt(-2*np.log(u[:,0]))[:,np.newaxis] * np.stack(\n",
        "    (np.cos(np.pi*u[:,1]), np.sin(np.pi*u[:,1])), axis=-1)\n",
        "\n",
        "fig, ax = plt.subplots(1,2, dpi=200, figsize=(3,3))\n",
        "for a in ax:\n",
        "    a.set_xticks([-2, 0, 2])\n",
        "    a.set_yticks([-2, 0, 2])\n",
        "    a.set_aspect('equal')\n",
        "ax[0].hist2d(u[:,0], u[:,1], bins=30, range=[[-3.0,3.0], [-3.0,3.0]])\n",
        "ax[0].set_xlabel(r\"$U_1$\")\n",
        "ax[0].set_ylabel(r\"$U_2$\", rotation=0, y=.46)\n",
        "ax[1].hist2d(z[:,0], z[:,1], bins=30, range=[[-3.0,3.0], [-3.0,3.0]])\n",
        "ax[1].set_yticklabels([])\n",
        "ax[1].set_xlabel(r\"$Z_1$\")\n",
        "ax[1].set_ylabel(r\"$Z_2$\", rotation=0, y=.53)\n",
        "ax[1].yaxis.set_label_position(\"right\")\n",
        "ax[1].yaxis.tick_right()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 356
        },
        "id": "GTeKu46CgIvX",
        "outputId": "d97c9351-a654-443b-90ae-8523ee543a30"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 600x600 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Next, let us implement a simple Coupling Layer using a feedforward Neural Network.**\n",
        "---\n",
        "\n",
        "Consider two random variables $x_1, x_2 \\sim \\text{unif}[0,1)$, and a map $f: (x_1, x_2) \\to (x'_1, x'_2)$ with\n",
        "$$x'_1 = e^{s(x_2)} x_1, \\\\\n",
        "x'_2 = x_2.$$\n",
        "\n",
        "* First, we define the coupling layer as a class called ```SimpleCouplingLayer```. There are two different functions in this class, one of them is $f: (x_1, x_2) \\to (x'_1, x'_2)$, called ```forward(self, x)```, and the other one is its inverse ```reverse(self, fx)```. Here, ```fx``` is the transformed output $f(x_1, x_2)$.\n",
        "* Then, priors are initialized in a way to give interesting behaviour without training.\n",
        "* Next, we evaluate $f(x_1, x_2)$, and $f^{-1}\\big(f(x_1, x_2) \\big)$.\n",
        "* Lastly, we plot (a)  $(x_1, x_2)$, (b) $f(x_1, x_2)$, and (c) $f^{-1}\\big(f(x_1, x_2) \\big)$ in three different plots.\n",
        "\n",
        "\n",
        "**Exercise 2: Write a function ```reverse(self, fx)``` in the class ```SimpleCouplingLayer``` to return $f^{-1}\\big(f(x_1, x_2) \\big)$. If it is properly defined, the plots (a) and (c) in the last step of this example would be identical.**\n",
        "---"
      ],
      "metadata": {
        "id": "-sKBXYcDKkL6"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# let's first define the class for the Coupling Layer\n",
        "\n",
        "class SimpleCouplingLayer(torch.nn.Module):\n",
        "    def __init__(self):\n",
        "        super().__init__()\n",
        "        self.s = torch.nn.Sequential(\n",
        "            torch.nn.Linear(1, 8),\n",
        "            torch.nn.ReLU(),\n",
        "            torch.nn.Linear(8, 8),\n",
        "            torch.nn.ReLU(),\n",
        "            torch.nn.Linear(8, 1),\n",
        "            torch.nn.Tanh()\n",
        "        )\n",
        "\n",
        "    # the map f: x --> x' is defined below\n",
        "    def forward(self, x):\n",
        "        x1, x2 = x[:,0], x[:,1]\n",
        "        s = self.s(x2.unsqueeze(-1)).squeeze(-1)\n",
        "        fx1 = torch.exp(s) * x1\n",
        "        fx2 = x2\n",
        "        logJ = s\n",
        "        return torch.stack((fx1, fx2), dim=-1), logJ\n",
        "\n",
        "\n",
        "    # Solution for exercise 2 (to be removed before GitHub upload)\n",
        "    def reverse(self, fx):\n",
        "        fx1, fx2 = fx[:,0], fx[:,1]\n",
        "        x2 = fx2\n",
        "        s = self.s(x2.unsqueeze(-1)).squeeze(-1)\n",
        "        logJ = -s\n",
        "        x1 = torch.exp(-s) * fx1\n",
        "        return torch.stack((x1, x2), dim=-1), logJ\n",
        "\n",
        "coupling_layer = SimpleCouplingLayer()\n",
        "\n",
        "# init weights in a way that gives interesting behavior without training\n",
        "def set_weights(m):\n",
        "    if hasattr(m, 'weight') and m.weight is not None:\n",
        "        torch.nn.init.normal_(m.weight, mean=1, std=2)\n",
        "    if hasattr(m, 'bias') and m.bias is not None:\n",
        "        m.bias.data.fill_(-1)\n",
        "torch.manual_seed(1234)\n",
        "coupling_layer.s.apply(set_weights);\n",
        "\n",
        "# we generate x, f(x), and f^{-1} (f(x))\n",
        "batch_size = 750\n",
        "np_x = (2*np.random.random(size=(batch_size, 2)) - 1).astype(float_dtype)\n",
        "x = torch.from_numpy(np_x).to(torch_device)\n",
        "\n",
        "gx, fwd_logJ = coupling_layer.forward(x)\n",
        "xp, bwd_logJ = coupling_layer.reverse(gx)\n",
        "\n",
        "# lastly, we plot x, f(x), and f^{-1} (f(x)). Expect first and last plots to be identical.\n",
        "fig, ax = plt.subplots(1,3, dpi=125, figsize=(6,2.3), sharex=True, sharey=True)\n",
        "np_gx, np_xp = grab(gx), grab(xp)\n",
        "for a in ax:\n",
        "    a.set_xlim(-1.1,1.1)\n",
        "    a.set_ylim(-1.1,1.1)\n",
        "ax[0].scatter(np_x[:,0], np_x[:,1], marker='.')\n",
        "ax[0].set_title(r'$x$')\n",
        "ax[1].scatter(np_gx[:,0], np_gx[:,1], marker='.', color='tab:orange')\n",
        "ax[1].set_title(r'$f(x)$')\n",
        "ax[2].scatter(np_xp[:,0], np_xp[:,1], marker='.')\n",
        "ax[2].set_title(r\"$f^{-1}(f(x))$\")\n",
        "fig.set_tight_layout(True)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 292
        },
        "id": "3WrX3bEvmFYX",
        "outputId": "3cf643dc-5318-400c-aec0-07384845b098"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 750x287.5 with 3 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Next, let us encode the $2$D scalar field theory on lattice.**\n",
        "---\n",
        "\n",
        "Let us go step by step.\n",
        "* First, we will define a $8 \\times 8$  lattice, and randomly initialize $\\phi(\\vec{n})$ on each lattice site, as a real number drawn from Gaussian distribution $\\text{Normal}(0,1)$.\n",
        "* There are two independent field configurations $\\phi_1, \\phi_2$ in two orthogonal directions. We will call this scalar field $\\vec{\\phi} = \\phi_1 \\times \\phi_2$, defined over all lattice sites, as ```cfgs```.\n",
        "* Then, we will define a class called ```ScalarPhi4Action``` to compute and return scalar field theory action $S_{\\text{lattice}}[\\phi]$, given each $\\phi(\\vec{n})$. This class takes in the values for scalar field mass $m$ and quartic coupling constant $\\lambda$.\n",
        "\n",
        "**Exercise 3: Write a callable object in class ```ScalarPhi4Action``` that will evaluate actions  $S_{\\text{lattice}}[\\phi_1], S_{\\text{lattice}}[\\phi_2]$ for each independent field configuration, and return them in an array format. Note that each $S_{\\text{lattice}}[\\phi_i]$ is a scalar.**\n",
        "----"
      ],
      "metadata": {
        "id": "zIjSabdCrM5O"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# first, we define a 8x8 lattice\n",
        "L = 8\n",
        "lattice_shape = (L,L)\n",
        "\n",
        "# then, we initialize a real values d.o.f. on each lattice site. Overall, these are two independent field configurations.\n",
        "phi_ex1 = np.random.normal(size=lattice_shape).astype(float_dtype)\n",
        "phi_ex2 = np.random.normal(size=lattice_shape).astype(float_dtype)\n",
        "cfgs = torch.from_numpy(np.stack((phi_ex1, phi_ex2), axis=0)).to(torch_device)\n",
        "\n",
        "# here, we define a class to return the action for each real d.o.f. on each lattice site.\n",
        "class ScalarPhi4Action:\n",
        "    def __init__(self, M2, lam):\n",
        "        self.M2 = M2\n",
        "        self.lam = lam\n",
        "\n",
        "    # Solution to Exercise 3 (to be removed before GitHub upload)\n",
        "    def __call__(self, cfgs):\n",
        "        # potential term\n",
        "        action_density = self.M2*cfgs**2 + self.lam*cfgs**4\n",
        "        # kinetic term (discrete Laplacian)\n",
        "        Nd = len(cfgs.shape)-1\n",
        "        dims = range(1,Nd+1)\n",
        "        for mu in dims:\n",
        "            action_density += 2*cfgs**2\n",
        "            action_density -= cfgs*torch.roll(cfgs, -1, mu)\n",
        "            action_density -= cfgs*torch.roll(cfgs, 1, mu)\n",
        "        return torch.sum(action_density, dim=tuple(dims))\n",
        "\n",
        "# We can choose different values for square of mass and the quartic coupling.\n",
        "M2 = -4.0\n",
        "lam = 8.0\n",
        "phi4_action = ScalarPhi4Action(M2=M2, lam=lam)\n",
        "print(phi4_action(cfgs))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MLzUZz2SvVVc",
        "outputId": "f464eeeb-8001-4647-f618-da4777937288"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([1296.7954, 1508.7099])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "* Next, we will define a class ```SimpleNormal``` that initializes priors drawn from uncorrelated Gaussian distributions.\n",
        "* Using this, we will generate priors for this $8 \\times 8$ lattice.\n",
        "* Lastly, we will use ```draw``` function, defined in the beginning, to acquire samples from this prior and plot them.  "
      ],
      "metadata": {
        "id": "H2dy_jnQ2RKE"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# first, let's define a class for uncorrelated Gaussians for prior distributions\n",
        "class SimpleNormal:\n",
        "    def __init__(self, loc, var):  # attributes 'loc' and 'var' determine the shape of the samples drawn\n",
        "        self.dist = torch.distributions.normal.Normal(\n",
        "            torch.flatten(loc), torch.flatten(var))\n",
        "        self.shape = loc.shape\n",
        "    def log_prob(self, x):\n",
        "        logp = self.dist.log_prob(x.reshape(x.shape[0], -1))\n",
        "        return torch.sum(logp, dim=1)\n",
        "    def sample_n(self, batch_size):\n",
        "        x = self.dist.sample((batch_size,))\n",
        "        return x.reshape(batch_size, *self.shape)\n",
        "\n",
        "# we use this to initialize the priors on the lattice\n",
        "prior = SimpleNormal(torch.zeros(lattice_shape), torch.ones(lattice_shape))\n",
        "\n",
        "# draw samples from this prior and plot them\n",
        "torch_z = prior.sample_n(1024)\n",
        "z = grab(torch_z)\n",
        "\n",
        "fig, ax = plt.subplots(4,4, dpi=125, figsize=(4,4))\n",
        "for i in range(4):\n",
        "    for j in range(4):\n",
        "        ind = i*4 + j\n",
        "        ax[i,j].imshow(np.tanh(z[ind]), vmin=-1, vmax=1, cmap='viridis')\n",
        "        ax[i,j].axes.xaxis.set_visible(False)\n",
        "        ax[i,j].axes.yaxis.set_visible(False)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 427
        },
        "id": "nRDonw0SlrP0",
        "outputId": "aebeaa9e-ed9d-44f9-f3ec-6a4a8a825dab"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 16 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "* Given below is a code to plot two-way histograms between lattice sites. The plots show that the priors are uncorrelated."
      ],
      "metadata": {
        "id": "V4CjiwzQ4FsG"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "fig, ax = plt.subplots(4,4, dpi=125, figsize=(4,4))\n",
        "for x1 in range(2):\n",
        "    for y1 in range(2):\n",
        "        i1 = x1*2 + y1\n",
        "        for x2 in range(2):\n",
        "            for y2 in range(2):\n",
        "                i2 = x2*2 + y2\n",
        "                ax[i1,i2].hist2d(z[:,x1,y1], z[:,x2,y2], range=[[-3,3],[-3,3]], bins=20)\n",
        "                ax[i1,i2].set_xticks([])\n",
        "                ax[i1,i2].set_yticks([])\n",
        "                if i1 == 3:\n",
        "                    ax[i1,i2].set_xlabel(rf'$\\phi({x2},{y2})$')\n",
        "                if i2 == 0:\n",
        "                    ax[i1,i2].set_ylabel(rf'$\\phi({x1},{y1})$')\n",
        "fig.suptitle(\"Correlations in Various Lattice Sites\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 505
        },
        "id": "vlZTKG4W4Npe",
        "outputId": "ce2be60d-6a84-419d-9e5e-85aff867ac85"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 16 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "* Finally, we evaluate scalar field theory action $S_{\\text{lattice}}[z]$ on these uncorrelated priors as\n",
        "$$S_{\\text{lattice}}[z] = \\sum_{\\vec{n}} z(\\vec{n}) \\Big[\\sum_{\\mu \\in \\{1,2 \\} } 2z(\\vec{n}) - z(\\vec{n} + {\\mu} ) - z(\\vec{n}- {\\mu}) \\Big] + m^2 z(\\vec{n})^2 + \\lambda z(\\vec{n})^4,$$\n",
        "and compare it against the actual action associated with prior distribution $r(z)$. The actual action is given as $S_{\\text{eff}} = - \\log r(z)$. The plot shows differences between the actual and scalar field theory actions on $z$.\n"
      ],
      "metadata": {
        "id": "ycwmKqoJx6kr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "S_eff = -grab(prior.log_prob(torch_z))\n",
        "S = grab(phi4_action(torch_z))\n",
        "fit_b = np.mean(S) - np.mean(S_eff)\n",
        "print(f'slope 1 linear regression S = -logr + {fit_b:.4f}')\n",
        "fig, ax = plt.subplots(1,1, dpi=125, figsize=(4,4))\n",
        "ax.hist2d(S_eff, S, bins=20, range=[[-800, 800], [200,1800]])\n",
        "xs = np.linspace(-800, 800, num=4, endpoint=True)\n",
        "ax.plot(xs, xs + fit_b, ':', color='w', label='slope 1 fit')\n",
        "ax.set_xlabel(r'$S_{\\mathrm{eff}} \\equiv -\\log~r(z)$')\n",
        "ax.set_ylabel(r'$S(z)$')\n",
        "ax.set_aspect('equal')\n",
        "plt.legend(prop={'size': 6})\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 510
        },
        "id": "YGfQTx0APtEA",
        "outputId": "ff544dea-91f0-4ab3-b7f0-0913cc17fd3e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "slope 1 linear regression S = -logr + 1455.4647\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## The prior distribution is expected to change due to training, such that the slope of this plot would become $\\sim 1$.\n"
      ],
      "metadata": {
        "id": "zI6yRSW35wtA"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Next, let us encode affine Coupling Layers for this lattice field theory problem.**\n",
        "---\n",
        "\n",
        "The steps are given below.\n",
        "* We start by designing a checkerboard masking for $m(\\vec{n}) \\in \\{0,1 \\}$, defined earlier in the tutorial.\n",
        "* Then, we define a class ```AffineCoupling``` for transformations given by $f: \\phi \\to \\phi^{-1}$ and its inverse transformation $f^{-1}$.\n",
        "* Later, when we will set up affine transformations on priors on the $2$D lattice using Neural Networks, we will let functions $s(\\phi_2), t(\\phi_2)$ transform both $\\phi_2$ and $\\phi_1$, and then use the masking to get\n",
        "$$ \\phi'_1 = e^{s(\\phi_2)}\\phi_1 + t(\\phi_2), \\\\\n",
        "\\phi'_2 = \\phi_2.$$\n",
        "* A single Neural Network will be used to define both $s,t$. The shared parameters in $s$ amd $t$ do not add to formal complexities.\n",
        "* We will use Convolutional Neural Nets for this $2$D lattice field theory problem. The implementation of Pytorch's $2$D CNNs require inputs in the shape ```(batch_size, n_input_channels, L_x, L_y)```.\n",
        "* To ensure that, we use ```.unsqueeze(1)``` in the class ```AffineCoupling```, to add a fake ```n_input_channels``` dimension of length $1$.\n",
        "* The outputs of the CNNs are shaped as ```(batch_size,n_output_channels,L_x, L_y)```. We will choose ```n_output_channels=2```, one for $s(x_2)$ and $t(x_2)$ each.\n",
        "\n",
        "**Exercise 4: Define a function called ```reverse(self, fx)``` in class ```AffineCoupling``` that induces inverse affine transformation $f^{-1}$. Get outputs as tuples of the form $\\big(f^{-1}\\big( f(\\phi)\\big), \\log J\\big) $, where $J$ denotes the Jacobian for $f^{-1}: \\phi' \\to \\phi$.**\n",
        "----"
      ],
      "metadata": {
        "id": "JaczZ4WZ6X3q"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# define checkerboard maskig first\n",
        "def make_checker_mask(shape, parity):\n",
        "    checker = torch.ones(shape, dtype=torch.uint8) - parity\n",
        "    checker[::2, ::2] = parity\n",
        "    checker[1::2, 1::2] = parity\n",
        "    return checker.to(torch_device)\n",
        "\n",
        "#print(\"For example this is the mask for an 8x8 configuration:\\n\", make_checker_mask(lattice_shape, 0))\n",
        "\n",
        "# define the class for affine coupling layer\n",
        "class AffineCoupling(torch.nn.Module):\n",
        "    def __init__(self, net, *, mask_shape, mask_parity):\n",
        "        super().__init__()\n",
        "        self.mask = make_checker_mask(mask_shape, mask_parity)\n",
        "        self.net = net\n",
        "\n",
        "    def forward(self, x):\n",
        "        x_frozen = self.mask * x\n",
        "        x_active = (1 - self.mask) * x\n",
        "        net_out = self.net(x_frozen.unsqueeze(1))\n",
        "        s, t = net_out[:,0], net_out[:,1]\n",
        "        fx = (1 - self.mask) * t + x_active * torch.exp(s) + x_frozen\n",
        "        axes = range(1,len(s.size()))\n",
        "        logJ = torch.sum((1 - self.mask) * s, dim=tuple(axes))\n",
        "        return fx, logJ\n",
        "\n",
        "    # Solution to exercise 4 (to be removed before GitHub upload)\n",
        "    def reverse(self, fx):\n",
        "        fx_frozen = self.mask * fx\n",
        "        fx_active = (1 - self.mask) * fx\n",
        "        net_out = self.net(fx_frozen.unsqueeze(1))\n",
        "        s, t = net_out[:,0], net_out[:,1]\n",
        "        x = (fx_active - (1 - self.mask) * t) * torch.exp(-s) + fx_frozen\n",
        "        axes = range(1,len(s.size()))\n",
        "        logJ = torch.sum((1 - self.mask)*(-s), dim=tuple(axes))\n",
        "        return x, logJ\n",
        "\n",
        "# both function s,t associated with each coupling layer are defined using a CNN\n",
        "def make_conv_net(*, hidden_sizes, kernel_size, in_channels, out_channels, use_final_tanh):\n",
        "    sizes = [in_channels] + hidden_sizes + [out_channels]\n",
        "    assert packaging.version.parse(torch.__version__) >= packaging.version.parse('1.5.0')\n",
        "    assert kernel_size % 2 == 1, 'kernel size must be odd for PyTorch >= 1.5.0'\n",
        "    padding_size = (kernel_size // 2)\n",
        "    net = []\n",
        "    for i in range(len(sizes) - 1):\n",
        "        net.append(torch.nn.Conv2d(\n",
        "            sizes[i], sizes[i+1], kernel_size, padding=padding_size,\n",
        "            stride=1, padding_mode='circular'))\n",
        "        if i != len(sizes) - 2:\n",
        "            net.append(torch.nn.LeakyReLU())\n",
        "        else:\n",
        "            if use_final_tanh:\n",
        "                net.append(torch.nn.Tanh())\n",
        "    return torch.nn.Sequential(*net)"
      ],
      "metadata": {
        "id": "Eg2LWLuE_-3n"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## The goal here is to obtain output $\\phi'$ from target density $P_{\\text{lattice}}[\\phi']$. Variable $\\phi'$ is obtained from lattice degrees of freedom $\\phi$, after affine transformation by $f$.\n",
        "* We hope to achieve this by composing a sequence of affine coupling layers.\n",
        "* We will use $16$ affine coupling layers, while embedding alternate lattice sites with checkerboard parity.\n",
        "* We will define a function ```make_phi4_affine_layers```, that imposes class ```AffineCoupling``` on the CNN defined above.\n",
        "* The function ```make_phi4_affine_layers``` will ensure that this CNN is transformed according to all $16$ affine coupling layers, in appropriate order of sequence.\n",
        "* CNN kernel size is kept at a minimum $3 \\times 3$ to induce correlations between neighboring sites. Larger kernel size will require more compute power.\n",
        "\n",
        "**Exercise 5: Fill in the missing parts in function ```make_phi4_affine_layers``` which ensures that this function returns appropriately transformed CNN layers.**\n",
        "---"
      ],
      "metadata": {
        "id": "VJxYeXvdD8FM"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# define the function to induce affine transformations on CNN layers\n",
        "def make_phi4_affine_layers(*, n_layers, lattice_shape, hidden_sizes, kernel_size):\n",
        "    layers = []\n",
        "    for i in range(n_layers):\n",
        "        parity = i % 2\n",
        "        net = make_conv_net(\n",
        "            in_channels=1, out_channels=2, hidden_sizes=hidden_sizes,\n",
        "            kernel_size=kernel_size, use_final_tanh=True)\n",
        "        # Solution to exercise 5 (to be removed before GitHub upload)\n",
        "        coupling = AffineCoupling(net, mask_shape=lattice_shape, mask_parity=parity)\n",
        "        layers.append(coupling)\n",
        "    return torch.nn.ModuleList(layers)\n",
        "\n",
        "# get the transformed CNN\n",
        "n_layers = 8\n",
        "hidden_sizes = [8,8]\n",
        "kernel_size = 3\n",
        "layers = make_phi4_affine_layers(\n",
        "    lattice_shape=lattice_shape, n_layers=n_layers,\n",
        "    hidden_sizes=hidden_sizes, kernel_size=kernel_size)\n",
        "model = {'layers': layers, 'prior': prior}"
      ],
      "metadata": {
        "id": "Ehxe8fCFHZim"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Next, we define a function called ```apply_flow_to_prior``` that returns the transformed prior density $Q[\\phi']$.\n",
        "* This is used to define a function for the the training step, called ```train_step```.\n",
        "* The function ```train_step``` calls in reverse Kl divergence loss.\n",
        "\n",
        "**Exercise 6: Define a function called ```calc_dkl```, that takes in $\\log Q$ and $\\log P_{\\text{lattice}}$ as arguments, computes reverse KL divergence, and returns a scalar valued loss.**\n",
        "---\n",
        "\n",
        "**Exercise 7: Write a function called ```compute_ess``` that takes in $\\log Q$ and $\\log P_{\\text{lattice}}$ as arguments, and returns the ESS for each batch of samples $\\phi'_i$.**\n",
        "---\n"
      ],
      "metadata": {
        "id": "Ts59OQCoKvHH"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# given below is the function that computes the transformed priors\n",
        "def apply_flow_to_prior(prior, coupling_layers, *, batch_size):\n",
        "    x = prior.sample_n(batch_size)\n",
        "    logq = prior.log_prob(x)\n",
        "    for layer in coupling_layers:\n",
        "        x, logJ = layer.forward(x)\n",
        "        logq = logq - logJ\n",
        "    return x, logq\n",
        "\n",
        "\n",
        "# solution to exercise 6 (to be removed before GitHub upload)\n",
        "def calc_dkl(logp, logq):\n",
        "    return (logq - logp).mean()\n",
        "\n",
        "\n",
        "# the function below defines the training step\n",
        "def train_step(model, action, loss_fn, optimizer, metrics):\n",
        "    layers, prior = model['layers'], model['prior']\n",
        "    optimizer.zero_grad()\n",
        "\n",
        "    x, logq = apply_flow_to_prior(prior, layers, batch_size=batch_size)\n",
        "    logp = -action(x)\n",
        "    loss = calc_dkl(logp, logq)\n",
        "    loss.backward()\n",
        "\n",
        "    optimizer.step()\n",
        "\n",
        "    metrics['loss'].append(grab(loss))\n",
        "    metrics['logp'].append(grab(logp))\n",
        "    metrics['logq'].append(grab(logq))\n",
        "    metrics['ess'].append(grab( compute_ess(logp, logq) ))\n",
        "\n",
        "# solution to exercise 7 (to be removed before GitHub upload)\n",
        "def compute_ess(logp, logq):\n",
        "    logw = logp - logq\n",
        "    log_ess = 2*torch.logsumexp(logw, dim=0) - torch.logsumexp(2*logw, dim=0)\n",
        "    ess_per_cfg = torch.exp(log_ess) / len(logw)\n",
        "    return ess_per_cfg\n",
        "\n",
        "# a function to print training history\n",
        "def print_metrics(history, avg_last_N_epochs):\n",
        "    print(f'== Era {era} | Epoch {epoch} metrics ==')\n",
        "    for key, val in history.items():\n",
        "        avgd = np.mean(val[-avg_last_N_epochs:])\n",
        "        print(f'\\t{key} {avgd:g}')"
      ],
      "metadata": {
        "id": "TEAEKcAU4fAU"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Next, let's train this model.\n"
      ],
      "metadata": {
        "id": "R1BkliUiQMkn"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Training specifications\n",
        "base_lr = .001\n",
        "optimizer = torch.optim.Adam(model['layers'].parameters(), lr=base_lr)\n",
        "use_pretrained = False\n",
        "\n",
        "# if not pretrained, then use the code below. If you have pretrained weights for similar lattice field configurations, that can be loaded here too.\n",
        "N_era = 25\n",
        "N_epoch = 100\n",
        "batch_size = 64\n",
        "print_freq = N_epoch\n",
        "plot_freq = 1\n",
        "\n",
        "history = {\n",
        "    'loss' : [],\n",
        "    'logp' : [],\n",
        "    'logq' : [],\n",
        "    'ess' : []\n",
        "}\n",
        "\n",
        "if not use_pretrained:\n",
        "    [plt.close(plt.figure(fignum)) for fignum in plt.get_fignums()] # close all existing figures\n",
        "    live_plot = init_live_plot()\n",
        "\n",
        "    for era in range(N_era):\n",
        "        for epoch in range(N_epoch):\n",
        "            train_step(model, phi4_action, calc_dkl, optimizer, history)\n",
        "\n",
        "            if epoch % print_freq == 0:\n",
        "                print_metrics(history, avg_last_N_epochs=print_freq)\n",
        "\n",
        "            if epoch % plot_freq == 0:\n",
        "                update_plots(history, **live_plot)\n",
        "else:\n",
        "    print('Skipping training')\n",
        "\n",
        "\n",
        "# next, the weights are serialized to distribute the model in this state\n",
        "print('Model weights blob:\\n===')\n",
        "serialized_model = io.BytesIO()\n",
        "torch.save(model['layers'].state_dict(), serialized_model)\n",
        "print(base64.b64encode(serialized_model.getbuffer()).decode('utf-8'))\n",
        "print('===')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "O7S91AvWQmeT",
        "outputId": "e4b45f22-b2e2-4b18-d5c5-9de089b097df"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Skipping pre-trained model\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "== Era 0 | Epoch 0 metrics ==\n",
            "\tloss 207.635\n",
            "\tlogp -264.479\n",
            "\tlogq -56.8442\n",
            "\tess 0.015625\n",
            "== Era 1 | Epoch 0 metrics ==\n",
            "\tloss -0.0839333\n",
            "\tlogp -16.8045\n",
            "\tlogq -16.8884\n",
            "\tess 0.0924834\n",
            "== Era 2 | Epoch 0 metrics ==\n",
            "\tloss -6.78759\n",
            "\tlogp -11.9234\n",
            "\tlogq -18.711\n",
            "\tess 0.127396\n",
            "== Era 3 | Epoch 0 metrics ==\n",
            "\tloss -7.27312\n",
            "\tlogp -11.9071\n",
            "\tlogq -19.1803\n",
            "\tess 0.159158\n",
            "== Era 4 | Epoch 0 metrics ==\n",
            "\tloss -7.67416\n",
            "\tlogp -11.6838\n",
            "\tlogq -19.3579\n",
            "\tess 0.179355\n",
            "== Era 5 | Epoch 0 metrics ==\n",
            "\tloss -7.86716\n",
            "\tlogp -11.5638\n",
            "\tlogq -19.4309\n",
            "\tess 0.21189\n",
            "== Era 6 | Epoch 0 metrics ==\n",
            "\tloss -8.06292\n",
            "\tlogp -11.4868\n",
            "\tlogq -19.5497\n",
            "\tess 0.219936\n",
            "== Era 7 | Epoch 0 metrics ==\n",
            "\tloss -8.19564\n",
            "\tlogp -11.3889\n",
            "\tlogq -19.5846\n",
            "\tess 0.223926\n",
            "== Era 8 | Epoch 0 metrics ==\n",
            "\tloss -8.23039\n",
            "\tlogp -11.3516\n",
            "\tlogq -19.582\n",
            "\tess 0.216062\n",
            "== Era 9 | Epoch 0 metrics ==\n",
            "\tloss -8.3569\n",
            "\tlogp -11.2825\n",
            "\tlogq -19.6394\n",
            "\tess 0.273863\n",
            "== Era 10 | Epoch 0 metrics ==\n",
            "\tloss -8.34248\n",
            "\tlogp -11.2865\n",
            "\tlogq -19.6289\n",
            "\tess 0.272031\n",
            "== Era 11 | Epoch 0 metrics ==\n",
            "\tloss -8.40113\n",
            "\tlogp -11.2481\n",
            "\tlogq -19.6492\n",
            "\tess 0.297204\n",
            "== Era 12 | Epoch 0 metrics ==\n",
            "\tloss -8.47775\n",
            "\tlogp -11.2158\n",
            "\tlogq -19.6936\n",
            "\tess 0.290421\n",
            "== Era 13 | Epoch 0 metrics ==\n",
            "\tloss -8.52232\n",
            "\tlogp -11.1786\n",
            "\tlogq -19.7009\n",
            "\tess 0.316205\n",
            "== Era 14 | Epoch 0 metrics ==\n",
            "\tloss -8.51364\n",
            "\tlogp -11.1997\n",
            "\tlogq -19.7134\n",
            "\tess 0.303031\n",
            "== Era 15 | Epoch 0 metrics ==\n",
            "\tloss -8.56361\n",
            "\tlogp -11.1941\n",
            "\tlogq -19.7577\n",
            "\tess 0.316682\n",
            "== Era 16 | Epoch 0 metrics ==\n",
            "\tloss -8.57724\n",
            "\tlogp -11.1444\n",
            "\tlogq -19.7216\n",
            "\tess 0.308409\n",
            "== Era 17 | Epoch 0 metrics ==\n",
            "\tloss -8.612\n",
            "\tlogp -11.2265\n",
            "\tlogq -19.8385\n",
            "\tess 0.331744\n",
            "== Era 18 | Epoch 0 metrics ==\n",
            "\tloss -8.57419\n",
            "\tlogp -11.1248\n",
            "\tlogq -19.699\n",
            "\tess 0.332467\n",
            "== Era 19 | Epoch 0 metrics ==\n",
            "\tloss -8.627\n",
            "\tlogp -11.1236\n",
            "\tlogq -19.7506\n",
            "\tess 0.344194\n",
            "== Era 20 | Epoch 0 metrics ==\n",
            "\tloss -8.64075\n",
            "\tlogp -11.165\n",
            "\tlogq -19.8057\n",
            "\tess 0.367612\n",
            "== Era 21 | Epoch 0 metrics ==\n",
            "\tloss -8.64381\n",
            "\tlogp -11.1416\n",
            "\tlogq -19.7855\n",
            "\tess 0.359901\n",
            "== Era 22 | Epoch 0 metrics ==\n",
            "\tloss -8.67351\n",
            "\tlogp -11.1209\n",
            "\tlogq -19.7944\n",
            "\tess 0.354235\n",
            "== Era 23 | Epoch 0 metrics ==\n",
            "\tloss -8.67469\n",
            "\tlogp -11.1173\n",
            "\tlogq -19.792\n",
            "\tess 0.384741\n",
            "== Era 24 | Epoch 0 metrics ==\n",
            "\tloss -8.67637\n",
            "\tlogp -11.1137\n",
            "\tlogq -19.7901\n",
            "\tess 0.360468\n",
            "Model weights blob:\n",
            "===\n",
            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//BlDU6NscL85j7hX+ESjP4fq3e8Q87c/a6EQphrIpj8myMvt/3Kiv/ABDOjQJKs/CYivq+wGnb/KdgjIMK+4P023lmNlCL0/RIUfn4pDur9j8wXgNPKQP+aisyTNt1K/kySNpULfpT94n7DUjtjBv4kGlEhrZmc/J6YGWBI9mb+RouZ0zfqtP23KYA1THGe/uU3Hy3sLsr8BdWjags6/P3ssTYmjIKa/ourbyMwGpr8DlAPudEWwPwJ4n6kn8qU/rWpp+Q4/sD8mJjdKIf6ivy91kj0DAHk/kYzesqeEpr8NGtExtnrDP7N8wenyWrA/Yzuhdvlxrz8gv0Qw+iWtP5e70EuF1q2/i9aMw+XItD8cVUKiBsqCP1C/bsj3Vkk/gJpQFOmnu79T25I0C5ikPzSUAlQPzqq/yi/EeVMWpz8oRDqXZ4Sgv3uccgGUioy/pnwc6IaEtD94osFK3sC2v13XldlRXYo/1Tb29nSek7/mqcGuRE60v4AhUiiM9bk/oHhCqk/RnT+yI7Gf2dWzP9v7M5HOd7m/B6jMPBTnfr8NtLptVkiIP5KgW+nULKS/UmWNg0pOor/4ulQbR9myPzx19cMrBbG/+gRRlQ3HsT962X3j3VS7v/+k+KH296C/XEJUM0Unqj+Z0dTfzTmrvzXR/y8xZ56/RWNSI9Djtj/evv704SOHPwR8QqcgerQ/itxszlj/sb/eZvGvIOSNv1irNnSGy6K/s19qwgE6gz+GpUH0OhOhP8E9PMTE9qg/SdGOi66buT8DynJBGIS/P4BF77fI/5E/OM8YdKxSjT/s+jvqXX+XP2pkc0+buqE/95nkBv7JuT9tqN1p7eGzP0EyK32X2qU/b2tbsxd1d7/8LWtvGZCGP+XWucIqi7i/7BMOiRX7qb+o9lsGrWW6P0AaCHVasbA/TgHAoAM1cD/syT8pR1WlvwUpm19477S/+qiPOEwwu7+/NtF2YvHDP7PevwG78ba/fhQLS+Vfwz9ZqdHwnK6oPxUA8MaYRrE/kW05pOi1pj+Kmiyp+jWmv14bsMx+ObI/I3Xa+fWun7+y9u2ZT1O1v+W9x+TACn8/rUuduFX5sL/GdqL9jqlrv7x8QPZrx4A/YN4tTre+rb+Q2HST8/K+P3N0AqEGW6W/zh7GkzFiwb+TpZxRE8Gvv0y6lM19g6o/1NASCS4ixL9Y2BnQ4OCnP7EhIht+ebu/LwW67g97uD+xqEVUwzOrvz96gZdE84s/D4BnAn+mtT/9AG1GUZWQPxb2Kh7hrsc/AcA8ut1is79+DWB2rEWkv1ksWSLBhLk/QbSzCSDtsT+YGscofsqUv3VC4BS/vtA/dMTx2/5LfT+hb5pF5IOqPwVcmTECGMs/9GKdrGePvD/79MNX2qXQP/jnrfjtPKu/uXn3exFEqL+r0GfGaHqFv56uX6YvULe/wA4yAAzatr/OnSTq2Gy5P7EkMfNffIk/+EOzomUaYj9htoQKdXOgP+pHClckqcE/b7AbPrXZqD9WLk/6CA6dvwyAYawKd6a/ohJl/RH6qT97XtNcQHyJP8kzNqL1QrY/Yb+CfH/lv78qOm6BQ+2wv64GM3sYBZk/Tf5CH7o4Y7/EJzbyIwrJvzfVfRKIeMo/ZMfUTfsNsj8EcqI+YTatv4bCFaps8bq/8cKCAMK2sT9PKj/t7dDFP+40UewmatW/XoWfySCWwL9UmpiL1sycv+j461xZx5S/01SFmkmiwb/THIRDZJ2hv8t5AVH1d5k/t4hsqX22wb+ID7V5grK+P7KgXnIar6U/WuCeLmexrD93F3eBeDVxv+jAnPloDKy/AK6CBIYakD9IxGrjwbq+P1XzvrzADrK/acUmhfy5pL+tfVlQ31iyP8EdoF63mKI/oaVDV0dDhT8V1L6cgJWjPzta4OaeCq2/pwPFbSbfwT/e1MN6Jq68P6SXcN+X+pw/FZKKAtI5xT8KcTnTNNmWv4/QThbCr6o/F75ROnLGlr/APBkx5xm0P/I2mUffJbI/xfAiQrwcsT8XF1wVhLuvP6GCTGHTtau/9EDnY187oj+S2NJA7A2fv9exvvQuO7Q/LWh1C/BWs79M0OJ8j1+vP+imtc6nTqE/VmP+xBeFLb84yAjJgQOlv9TZIW+fBMY/T7TXZm3Gxb/lp/1rWTC0P9XszTME6rW/BQA4DD3hpT/v17OAXjKmvypNlTMe8bw/iAvNx+n3vD+mtwbqfZ+7P3D+c0Iy+cC/f/gFiwNWv7+f8Vw0ZnGwv4B50qHJWaW/aMCNlENbr7+KFWQ2luTFP4JVCctKpqY/3nsaK7WEWL/n/i2cqgq4vyqEAP8LM7M/aJEmzdN7s7/BTY8IQUePv5+uvsPy4aS/ReXG3CYGvz8hFHYs1VXLP6cnX0YOvqY/eSBtPKOPnj9zyi5qHCrEPzsnbd/M97Q/ld1Ya9C9wT9S1PwPwMGivx8mYN3LK4Y/AgLo2KwvZD8GmjBuA0eiP7qq3NIIN5a/Vw6uraSFl7+RQ/F4fQSYv+LRPBi7L7k/fPg4fWYRvz9ssuouSZKTP3QwwFScYZu/pOIKM6tgaz8dnQSfLcm2PzEhrOPZmLE/Ml3mbwp4nL/BKwmOGUrEP7P+uor65ZS/RNYSb/Fhfb+y7QFORwOgv3GHoEJFNX0/9rau94qucj9mXW6lLyvCPz1d3cQaY3M/VZnM/lJtnT+NU3KPoHvAP2dQ9v5siIc/NSkYJwd1tD+EIL0v6zKyvxcX2flbWL0/bptD/oPZoj8m/5u5t8ihP251BV4h5KU/p9G7PM/Trj/F3tXyxB27PygopIiC7Ju/neddpBgIib9QdUZjXiXDP8ndViwBJHw/c6kBgwVchL97Ir3Vi2KiP42YxxKrhsI/Wf9WGLBTvT860Ccm87HPvzPtTG+w8sE/Ksr9dGBuo79wtW10YOHCv7niDEOVJ6K/eCLtINv3Fr+pjzHCtKCxv7G9PXhCQcC/Q6AU4oPioj+pDzQTlyzAv7bMI/kD62k/JUrjfa6akb/Xm8O2lvOgv89/SCk1kb2/W8wIg7IZq7+hOPUE5UB/v0fwvmnNfoq/BK+Qb65Ruz//a7HDUtCdv7Pny7ZYwaU/owVtAFRetj/YrpwirA+jP8DLVRmrAbI/rzW6nmX1vj+YvQ5guIGtP82U0zDzVqO/WGnk5gZPuL+kaEjK0KKpP1KWzXzpTs2/Mh/wVFvClr9CVuoGuSDAP0NOCZdRwaW/qdgl1+8TlD9aH7DKGjq9v4udlNIN6Lw/abwT4BHEsz9NjZtA82ydP1jAmVEijLU/pIgdhM6xLL/QiZzs3aC0P/XudSh0I7W/KyqWUOMfej8kgB8yzv68v1UqNSDdUXW/yLySzVVpuj82xLPwsrWzv9VnFTKlTrs//tqP+jQTqr+W9ZqTr0mXP69sG4DreoG/nvWBUc1Hgj9rI0eNgZCmv0bwGxKLq5w/puJYiqfdtL+VNX4TCaeJvyfpygXtAbA/pKFP7n0reL/8scKByiXCP6Eya1s3cKU/TYJt+gKwn7/0OrlHT2zCv8/sNWpEGlm/SpxQlogwq7/i47PF7ZSwP4Hv3k7q7KU/mzMklKMqpL+82YDP0fC7v1d2cslkTr2/ZT2Zx04otL9yZaSAHHqjvzbeltdYUsK/8tpZQ2Kyur8SuJaAqiqOP7rn5hdbPbc/fnCrexKJsL88C6LvByykvz93efBaVIo/7twL6NBSsD9ZSwztBX20P3UIHsQZQqS/EJkcRXICtD9omF4g5SSgP1x1bVDsxsC/KtAbcoijk7+fBMMNTC+yvxz+5n3CQrG/yzU5C4REuL8xwDL5Gp66vwoMsfSWR8O/4c+EMYpsqr91oBboilGPP1IuPe80JaE/yGLCCRUBr7/lr0hxccOyv4p4JjpYI6E/eUuQ/OW9oD8mLfs8OiGoP62t0OQz2aq/TsDNT6tYjL+CDljU1+2cP/5Rhs8RhKa/ebtLcA/rsD9VvQgQDfiKP5XGF1m9t5a/jsWwDYcEfD9BoWRKu7myvyX1TZPGUra/ODzQ5jPSqr/heWHSJzOov0PxZJMHibi/szAv3/Z+kb8AfmjcFza9vyghCrrY+LA/ZJ80kwdYt79y0ql+Kfmsv9xBXVs9o8C/NHAMKNbWtz8McplfH5SzP8AY86v9WrI/vYEWSjgNsb/tlm7aYPeoP9hzgVkEvbc/54TMqePbnr+tf3kvmneoP6PNBs50OKi/frYJo/sNiz+oRK/sy121v5wkiirIzGc/MHcVlQWHsj8iTwQge4OlP4xhJddL150/UEsHCBNU/pgAEgAAABIAAFBLAwQAAAgIAAAAAAAAAAAAAAAAAAAAAAAADwBDAGFyY2hpdmUvZGF0YS8yN0ZCPwBaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpPjXiwJDCzPxyuJzPHiLm/iSpI7jrVfD/DfF+PBwmzv4CipUlEMsG/VUYcaOw5pj9CcMBKDfehP8s+aFXSdZG/UEsHCF78GJ5AAAAAQAAAAFBLAwQAAAgIAAAAAAAAAAAAAAAAAAAAAAAADwBDAGFyY2hpdmUvZGF0YS8yOEZCPwBaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWloG0gcAHSy1v1WyLZTiibI/kl2G5OdlsL/ZfNhgTuqmv1nkNpQy+7G/WD5Hkdtqoj8JjH/qtDbBv5dEwKlg1KI/EuX3YSiUtL+BfxAuCxeHvypJqoGp9Hy/PQqFxHmhYD9i0tFUbXmxP5Jshx74Jq6/zwRc9ZO5o78KhH/9fnaTPz/COZ3Ftr4/x0odbbAmnD8PIL9H2EmVv+nOUy0LI7I/JnYgRx2MpL8zphapcmG0PxxrCjcNacK/O+Amo4NBrT8Jhtk1fmyXv3VyML5Sb7u/aGyFnqr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LF16TPw3CyUhbyqC/wEhOi7q8cj/0NK3zactov7mQ68zlA7y/ZcGGdW+2qz+gmO2ZPSWoP/7moJ1Z7cE/U02N28XvlT/w8/KY78OhPz3Ks4WJwp6/LH8Izba0rT/xGSLvHN27vyGsoEmKxa8/+kuX/8Ajcj8AO3ezeGjIvxkb6TP46cq/0mXZjCLXz79/Vb/2pXHCv2/Gj37HDLO/4VNrHIi5bz9j+p336/mrv5D6IAL0+dO/rVPNq6HUzD9+G+R3YCWsP8CkGKlKwq4/JIiH0x48sD8S5KArjiiSP4ysQdyH1ZE/GxiatSeVfz/e7zTtL76tv/TVAyeMc7A/iaAW7i34qr+W7m9ZgfS3P7v4PRVKGq8/X7vWH5QRuj/DNhJ5GeuvP/CUr1WQ7KS/e9PL/0Ghlj+FSWl4LLS2P+i9rGDiraw/Vnkk0R5Xur9kC7FOkdmwvyaq0Vm0AL4/7TFEeQtdp7+p4eIEthG2P8CFxoizkb8/5OPOD0I6tj9yI+BIc861v0fV+Ad8W6s/3GL9m6Dprb/m5RkiQEiQP/3GrPRflKs/C2PKKk0bsz+CQCyTeUWaP0f1WVEye6q/ehlCZsKxsz+Mlqnrh9GjP/TJ+lHRLKa/8z9CcvfLuD9Qi31KUf6jP3u0jhCjSbg/GtwwAtnXrb/k5lzHPBC0vwuDeZhFFoG/oPe7F1jTqT/PlIo1dvuVP9PXRy7v9bO/7ysUa5M7cj910xQvjzyzP+8fgIk3ZrA/gGSfNQN9gb99xS22PBCFPwoXMoau3Ye/Yp4GBKYpvz//Y7KUtLuyPwgMXHadZ7q/4Vck7aTyj7+L43Jni0d3P2v4kE0mQLe/Wip2J9drsD/NZmLBz1u0P6xBqTxF+ao/WG5m0rR5vT9JkH68X3asP3onHfBqsLw//vVQKDcKvz92ZvCKlP2lv0ecTttDXdS/Ni4To6MLmT+OqfwW0uSpP8IFAyKLhcW/6GkY/cB/sr8I6yyhwoHSv3cTuNO6FMe/oo2I507sob9L9k3drRq5P1HncqGHmXo/FmuvGsXOl7/By3kpSgy0v0sViiM+TpU/X6Nigsh/pj/KgxSyKmzAPwhn6xjOE6k/P8HSFmi6lj8llj1GF4Wxv3gP1wwszWW/cnUmB8lJj78Vi162XJrBP9FOzTgBvaA/fBO3XxZOrD9mwJL73QGYv4ZNc9h0s7Q/9wvpnZKCYT8K6HgUTUGeP1iMAjXJyaI/bQ/auD4gwb8lYZ4au5C+P2XWxTUeJjY/ZGOpo16yxz/40Mx8WP7AP+ptkG5ZdGA/6c1kHm5nrb+5iVXvQSO4P9o7ZxRMrqW/HW0y7BWkrz+TJb5NbazSP14/wZEHv7y/qas912X/ur/E1Z353Ml3PzDrsyWCMLo/ILse8XrBuT8q7olXWOGsP0BLWNC4fK6/v3A8QoVrq78yAwVzbsRxP3dN8kHfS7G/GP/sQWaE0z/YcYC2hY+NP9W3HVcRGq8/524KdRaPwL80MlmIYwCtvxu0dN7Lyr4/420G1M+2oD8F1IntdJjAP7Iznq9IoJi/6lB7F7+oib+GSe1QLxaqv6DBFyWuebm/Gfhc0TXYlL9VmBXcpqCuv23RhyCXZbq/B4fIY8aUvj9ukl6OV8W8P74BiUjMWqO/C3oywcBMxL/KDZz/sDLCPw2mLKfpR5C/r8uC0Q1NuT9NGGim6pKsv/HC9cB6ZrG/mC30uHqPs78+Tja0mEqRvxYyPjiSkK2/j57M3AGhwD8zNS8udze2vxIHX9aG/te/xF/5r6Anxz+fu1jh3CmdvxBpchS6XMQ/8auoQBlKtr/gyU4OPO/Dv+M8fcmHj7e/fJM5jLqAnD+dXSQkq9S0P0e5bQqNUrq/iUaXJiHObT/+ivGfEbuxv8WWQq5o366/wR5dTc0wyL+QkO5qW6DHP5lT/jJbwKE/aO5LzhQZrD9WBW/ml5eyv3EITds+zLA/vAQE3TGGlj9bg1FqLxC4v0E66RZC4YM/IfPeDKCmmj98fU+R9XKyv++oaJxqxJU/J1IqIS3LyD9JG0IlDRuNv8MzkmpP/5i/G808YsNNsr/uPDe4PLizP4mTphSrW7k/Q22nwBfroz8KlWYmyqy/Pxg9JvQeGGm/i/OC59+8xb/VrqsRNeCvv0gkErqcTLo/Zzo0+UXawb8vVKvw6Rd3v0xbsNLKxqE/711bgxBttb9uoHp4iOKCP4dwkSYOt6w/dWm8plehwT8pIJ9dth2LPxx9bT4Sg40/CDYhSziYsj+/8LDuiWS3v1C+QLmpiZM/jVE746RFur8KLe68vLSZP2+PZvJBx7i/q/p2jlNYvj+DNkRLOPa2v37LDQGiS7m/rHuhA3ZtqT94dinOlBuiv1Kzq8bvTou/+JAGXay6hj/QlfGUtU+4Py+h3Nv/1LM/1HN5bh/jwL9w3Rg5XkGmPxrWGZLlWb2/r6f9aA6pxD+OqWeDkWe4P5ZqdsjIybM/juqstW74qb/I+LPTmFHAPzY+CuNxps0/QxS7yJAC0z9cHTd12M26P6nUBbzhCcM/nN490m79vr+2k/7E4Xykv1BoOwh2MLS/bW1yOsPupL8GNVALhma9P7ysxMakMK+/6ie04c0csL/bTMKS75q1PzdhEIsGfMK/63PsLzc4u79/XqFrpcOuvwJoyfquo7U//3m+oiFgYT+8UHlIIu6hPzDk5AEyq8K/3iWp+FPssz9TrOQkPzHAv3HnxmYp75m/EMn5s7avtr/DRgvf+AWyP3+UzQFhOr0/KrIUfmuNx79JjufVqbS0v1UZyOuPS7E//kd1ChUIrb9jpMfLVDa5P0OxlAuaTZw/Whzjq86GYL91AryF1iy4PxsPW7X/rsO/ReJaZjTirz+b38PQQvm1P+K7gBYKhtK/aqbBfTvwsL9+of4BO6CkP06pp2+/TIq/SahHQtDGxb/vhs0F1FSuP/7btVlHmbI/kz7aHoXYkb8UXSnxkq2ovxRbrnHQ5Ly/Zcpcblctmr8OVUKej1ymP7K63z+ku6Q/RcVjdCg6rb/xKrhv5R+2P9NjztvbLMI/3ru9pyLRc7/5NMWPUTqyPxVHQC/2MsI/e/R8dP1Vlj9ENevsXv7AP6Polz7MrpS/3QpdoD4SsD/c/urmf7ejP/4UwPHKI62/8RYLU/VVsb93h92jHcxGP2Jl7GJSN8U/5gbycXJqvj9B8gkIZX2iP8ssZFd2J52/yE5q7FPYiL+YEPHoLMWFPzOFK9QfRa2/hLBIlBIxpL9vF6IJdPBgP51/tGPl372/Qzx1mMMU2L+vSKNJwGKwP2VOukGQfsC/WikdDCo/z7/IDVxCfca0v3TA0ERpE6E/pmyYR9uouT+v2E/6PNXDv7YXgJrQq6k/CSljr3VAwb9Kr6dh/FGUv/jKrEVhYKG/du+J4iikkT8M45ueKO3Bv5nvDlqPxqA/D2p/VIPCS7/KKqnQZ6GYP3y8C8tBWrm/OaSPDhgTub8D0aVUcyKsv6tf3YK8k1w/t86wm50toT9fL6a0tLl9v7zoGIUY3We/QeA4JMbggL+ZwBNa5xO0PxL620ac6LQ/hw5kDa1QkL9th+IEeqq0P1lgyXPM5Yq/CktrTcQBej8FaPfUb12XP/hmk+H1lqE/PkegWflnh79xxFkKSUnEPzZNSi1EUpy/g69/b+kDmb/0iXfDNPjAP8QDRZP4vKm/jkhFQqrDiL8oBcs4ndaxPwxEDcjTc6q/5PbMWZDxtL8Be9CRLTK0v6uVMoNQzLI/skCQUIvGwz/W9fuZTnWlv3ylhTRwFrS/TT8WyJAGsT8A/UYL08J3v4WQbmUvF7E/hdaMO/xKrL+3CLCsq+LFP/UC4DfHKsQ/eou6r5WJtD9vLFZe7tfBP+bdvxxUUbA/LIkMEMZHnT+ph3Bbo29+vx/2Bj0sTWy/E1nh4fuDsj/Zg2y7fGWqvzj1RiejmKu/SmXQdwmpcz+1YLrlbV27P3gvmfqwSLK/X5EtvTUXtL8dkVgENlK1v5ktVWqw8co/S3Wr/cf2x78uDZeJ1ny6PwWWRXBBTcY/Xvdy2qNJsL/2EuS6S2bGP37KJQ9qPN2/QdwMwSspdD8uROXRgsWxP5Ek6hE8o7M/VgBmA3MysD/eOoYFmpmxvxVS+Omc/ae/mcLFR7xAmD8Nj57+LFG7P2Iv31qUCXW/4qC7ZRD6jj9QSwcI40CUWwASAAAAEgAAUEsDBAAACAgAAAAAAAAAAAAAAAAAAAAAAAAPAEMAYXJjaGl2ZS9kYXRhLzMzRkI/AFpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWjgdwNr0dKq/ELgRyeOKub9+bhj0ey2zP09GNr4pZLa/a8ak7fh2sj8dx3XtMwHEv41NTkLN/LA/OMBlzSflgL9QSwcIQvMDHUAAAABAAAAAUEsDBAAACAgAAAAAAAAAAAAAAAAAAAAAAAAPAEMAYXJjaGl2ZS9kYXRhLzM0RkI/AFpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWlpaWqHbBUQiNqm/aII1tGkBrD+LBv2ZWT+3vxKYpl/xtHs/PdD1k8Jmo79j5xPwI86mP0aurSBcOcW/BKCKtXYGor9uOCq+3za1v39d3tGLSra/wbvkYSLTgL9Nn8HI9vm+v7b8gPoSRb2/kCvgO2f6sb9OdlM0ljmuP3mJZ+eyOq+/BwWzqJYVob/uOFubBA2LP8u3m9DW5nM/8QhI/5wYYj/XZHVsscm/v3DjePUj9b6/GEVPzjq3rL/SMLBvwtyHv7iOU1zzHoM/KNT8WJfqsb+Swx3XfmWCv1S5cVZd3Le/qeMXyCByur+CSkz2uuK/v+m87PBapr2/htdp7muURr8Nb80iOPauPycq6JKXRoE/ohMl1gOWmz+CQUtz/bmtv8K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            "===\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Now that we have a trained model at hand, let us draw samples from this, and check the quality.\n",
        "* We plot the drawn samples below. These have regions with smoother, largely correlated fluctuations, in comparison to untrained priors.\n",
        "* Output distribution $Q[\\phi']$ is an approximate one, and can be used for reweighting or resampling.\n",
        "* As we do not know what $1/Z$ is, there is a finite offset between approximate and true actions $- \\log Q[\\phi']$ and $S_{\\text{lattice}}[\\phi']$.\n",
        "\n",
        "**Exercise 8: Find an expression for the offset between approximate and target actions $- \\log Q[\\phi']$ and $S_{\\text{lattice}}[\\phi']$. Use it to correct the approximate action, call it $-\\log Q'[\\phi']$. Plot and compare $-\\log Q'[\\phi']$ against target action $S_{\\text{lattice}}[\\phi']$.**\n",
        "---"
      ],
      "metadata": {
        "id": "RZzOuTk3bRxK"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# we draw samples from this trained weight distribution and plot below\n",
        "torch_x, torch_logq = apply_flow_to_prior(prior, layers, batch_size=1024)\n",
        "x = grab(torch_x)\n",
        "\n",
        "fig, ax = plt.subplots(4,4, dpi=125, figsize=(4,4))\n",
        "for i in range(4):\n",
        "    for j in range(4):\n",
        "        ind = i*4 + j\n",
        "        ax[i,j].imshow(np.tanh(x[ind]), vmin=-1, vmax=1, cmap='viridis')\n",
        "        ax[i,j].axes.xaxis.set_visible(False)\n",
        "        ax[i,j].axes.yaxis.set_visible(False)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 427
        },
        "id": "GZd3WmEwSGqr",
        "outputId": "4eaaad7c-5df9-45ef-b4a5-cbb27c22c8b7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 16 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Solution to Exercise 8 (to be removed before GitHub upload)."
      ],
      "metadata": {
        "id": "B2KDpGbYd0mx"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "S_eff = -grab(torch_logq)\n",
        "S = grab(phi4_action(torch_x))\n",
        "# the finite offset between target and approximate actions are evaluated below\n",
        "fit_b = np.mean(S) - np.mean(S_eff)\n",
        "print(f'slope 1 linear regression S = S_eff + {fit_b:.4f}')\n",
        "fig, ax = plt.subplots(1,1, dpi=125, figsize=(4,4))\n",
        "ax.hist2d(S_eff, S, bins=20, range=[[5, 35], [-5, 25]])\n",
        "ax.set_xlabel(r'$S_{\\mathrm{eff}} = -\\log~q(x)$')\n",
        "ax.set_ylabel(r'$S(x)$')\n",
        "ax.set_aspect('equal')\n",
        "xs = np.linspace(5, 35, num=4, endpoint=True)\n",
        "ax.plot(xs, xs + fit_b, ':', color='w', label='slope 1 fit') # we use the finite offset to get a closer match between target and approximate actions of priors.\n",
        "plt.legend(prop={'size': 6})\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 510
        },
        "id": "W5gCdLWNSO17",
        "outputId": "c07b4d6a-8cf8-4d09-f7ca-746145d61466"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "slope 1 linear regression S = S_eff + -8.7196\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "References\n",
        "* [Introduction to Normalizing Flows for Lattice Field Theory](https://arxiv.org/abs/2101.08176) by Boyda et. al.\n",
        "* [Learning Lattice Quantum Field Theories with Equivariant Continuous Flows](https://arxiv.org/abs/2207.00283) by Gerdes et. al.\n",
        "* [Quantum Field Theory](https://www.cambridge.org/highereducation/books/quantum-field-theory/718DD037728FB3745F48A40A6D9A8A1C#overview), Mark Srednicki, Cembridge University Press, Chapter 9.\n",
        "* [Quantum Field on a Lattice](https://www.cambridge.org/core/books/quantum-fields-on-a-lattice/4401A88CD232B0AEF1409BF6B260883A), Istvan Montvay and Gernot Munster, Cambridge University Press, Chapters 1, 2."
      ],
      "metadata": {
        "id": "1INQfCC8d9Wm"
      }
    }
  ]
}