Batchnorm.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook, we will show how to compute the GP kernel of a mutilayer perceptron with batchnorm+ReLU."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Setup"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Software prereqs:\n",
    "\n",
    "- `quadpy`\n",
    "\n",
    "`quadpy` is a package for fast, vectorized integration, which will be essential for speeding up the computation of the V-transform of batch normalization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-31T13:52:36.973908Z",
     "start_time": "2019-10-31T13:52:34.272895Z"
    }
   },
   "outputs": [],
   "source": [
    "import scipy as sp\n",
    "from scipy.optimize import root_scalar\n",
    "import numpy as np\n",
    "import quadpy as qp\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-31T13:52:37.058895Z",
     "start_time": "2019-10-31T13:52:36.978896Z"
    }
   },
   "outputs": [],
   "source": [
    "from utils import J1, VReLU"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose one has a batch of $B$ samples $x_1, \\ldots, x_B \\in \\mathbb{R}^n$, consider their kernel\n",
    "$$\\Sigma = (x_i^\\top x_j / d)_{ij} \\in \\mathbb{R}^{B \\times B}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "If $f(x) = \\mathrm{ReLU}(W x)$ represents a dense matrix multiplication followed by ReLU, then the matrix $(f(x_i)^\\top f(x_j) / n')_{ij}$ converges almost surely to a deterministic positive semidefinite matrix $V_{\\mathrm{ReLU}}(\\Sigma)$ if $W \\in \\mathbb{R}^{n' \\times n}$ is sampled as $W_{ij} \\sim \\mathcal{N}(0, 1/n)$ and as $n' \\to \\infty$.\n",
    "By [Cho & Saul 2009](http://papers.nips.cc/paper/3628-kernel-methods-for-deep-learning), \n",
    "$$V_\\mathrm{ReLU}(\\Sigma) = D^{1/2} J_1(D^{-1/2} \\Sigma D^{-1/2}) D^{1/2}$$\n",
    "where $D = \\mathrm{Diag}(\\Sigma)$ and\n",
    "$$\\begin{align*}\n",
    "    J_1(c)\n",
    "        &=\n",
    "            \\frac 1 \\pi (\\sqrt{1 - c^2} + (\\pi - \\arccos(c))c), \\forall c \\in [-1, \n",
    "            1]\n",
    "\\end{align*}$$\n",
    "\n",
    "The function `VReLU` applies $V_\\mathrm{ReLU}$ to a sequence of matrices represented in the form of a tensor whose last 2 dimensions represent the matrices."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mean Field Theory of Batchnorm: Single Batch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now suppose $f(x_1, \\ldots, x_B) = \\mathrm{ReLU}(\\mathcal{B}(W x_1, \\ldots, W x_B)) =: (y_1, \\ldots, y_B)$ represents a dense matrix multiplication followed by batchnorm and ReLU.\n",
    "Then the matrix $(y_i^\\top y_j / n')_{ij}$ converges almost surely to a deterministic positive semidefinite matrix\n",
    "$$V_{\\mathcal{B}_\\mathrm{ReLU}}(\\Sigma)$$\n",
    "if $W \\in \\mathbb{R}^{n' \\times n}$ is sampled as $W_{ij} \\sim \\mathcal{N}(0, 1/n)$ and as $n' \\to \\infty$, just like the above.\n",
    "According to Theorem 3.2 of [Yang et al. 2019](https://arxiv.org/pdf/1902.08129.pdf), by the Laplace method,\n",
    "$$\\begin{equation}\n",
    "V_{\\mathcal{B}_\\mathrm{ReLU}}(\\Sigma) = B \\int_0^\\infty\n",
    "    \\frac{V_\\mathrm{ReLU}(\\Sigma^G (I + 2s\\Sigma^G)^{-1})}\n",
    "    {\\sqrt{\\det(I + 2 s \\Sigma^G)}} ds\n",
    "\\end{equation}$$\n",
    "where\n",
    "\n",
    "$$\\begin{align*}\n",
    "    \\Sigma^G &= G \\Sigma G\\\\\n",
    "    G &= I_B - \\frac 1 B \\mathbf 1 \\mathbf 1^T\n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-31T13:52:37.069897Z",
     "start_time": "2019-10-31T13:52:37.061898Z"
    }
   },
   "outputs": [],
   "source": [
    "def Gmatrix(B):\n",
    "    return np.eye(B) - np.ones([B, B]) / B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will compute the integrand of $V_{\\mathcal{B}_\\mathrm{ReLU}}$ efficiently as follows:\n",
    "\n",
    "- Obtain eigenvalues of $\\Sigma^G$.\n",
    "$$\\Sigma^G = A \\Lambda A^\\top$$\n",
    "where $A$ is orthogonal and $\\Lambda$ is diagonal.\n",
    "Note that the smallest eigenvalue of $\\Lambda$ is 0, since $\\Sigma^G$ has nullity with dimension at least 1.\n",
    "WLOG, assume the diagonal values of $\\Lambda$ are nondecreasing, so that $\\Lambda_{11} = 0$.\n",
    "- Then for each $s$, compute\n",
    "    - $\\Sigma^G(I + 2s \\Sigma^G)^{-1} = A \\Lambda(I + 2s \\Lambda)^{-1} A^\\top$.\n",
    "    - Similarly, $\\det(I + 2s\\Sigma^G) = \\prod_{i=1}^B (1 + 2 s \\Lambda_{ii})\n",
    "        = \\prod_{i=2}^B (1 + 2 s \\Lambda_{ii})$\n",
    "    \n",
    "For each $s$, the most heavy computation will be the two matrix multiplications by $A$ and $A^\\top$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-31T13:52:37.091912Z",
     "start_time": "2019-10-31T13:52:37.076903Z"
    }
   },
   "outputs": [],
   "source": [
    "def VBNReLUIntegrand(Sigma):\n",
    "    '''Returns the integrand function of VBNRelU(Sigma)\n",
    "    '''\n",
    "    B = Sigma.shape[0]\n",
    "    G = Gmatrix(B)\n",
    "    eigvals, eigvecs = np.linalg.eigh(G @ Sigma @ G)\n",
    "    def f(s, multfactor=1, eps=1e-10):\n",
    "        # Ueigvals.shape = [..., B]\n",
    "        Ueigvals = (1 + 2 * s[..., None] * eigvals)\n",
    "        # inteigvals.shape = [..., B]\n",
    "        inteigvals = eigvals / Ueigvals\n",
    "        # divide by sqrt(det)\n",
    "        inteigvals /= np.sqrt(np.prod(Ueigvals, axis=-1, keepdims=True))\n",
    "        # the eigenspace corresponding to (1, ..., 1) is zeroed out\n",
    "        inteigvals[..., 0] = 0\n",
    "        inteigvals *= multfactor\n",
    "        return VReLU(np.einsum('ij,...j,jk->...ik', eigvecs, inteigvals, eigvecs.T), eps)\n",
    "    return f"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To compute $V_{\\mathcal{B}_\\mathrm{ReLU}}$ numerically, we first transform its integral via an exponential substitution\n",
    "$$\\begin{equation}\n",
    "V_{\\mathcal{B}_\\mathrm{ReLU}}(\\Sigma) = B \\int_{-\\infty}^\\infty\n",
    "    \\frac{V_\\mathrm{ReLU}(\\Sigma^G (I + 2e^r \\Sigma^G)^{-1})}\n",
    "    {\\sqrt{\\det(I + 2 e^r \\Sigma^G)}} e^r\\ dr.\n",
    "\\end{equation}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-31T13:52:37.110897Z",
     "start_time": "2019-10-31T13:52:37.095898Z"
    }
   },
   "outputs": [],
   "source": [
    "def VBNReLUIntegrandExp(Sigma):\n",
    "    '''Returns the integrand function of VBNRelU(Sigma), reparametrized exponentially\n",
    "    '''\n",
    "    B = Sigma.shape[0]\n",
    "    G = Gmatrix(B)\n",
    "    eigvals, eigvecs = np.linalg.eigh(G @ Sigma @ G)\n",
    "    # remove the 1st (smallest) eigenvalue, which is 0\n",
    "    logeigvals = np.log(eigvals[1:])\n",
    "    eigvecs = eigvecs[:, 1:]\n",
    "    def f(logs, logmultfactor=0, eps=1e-10):\n",
    "        # Ueigvals.shape = [..., B]\n",
    "        logUeigvals = np.logaddexp(0, np.log(2) + logs[..., None] + logeigvals)\n",
    "        # inteigvals.shape = [..., B]\n",
    "        loginteigvals = logeigvals - logUeigvals\n",
    "        # divide by sqrt(det)\n",
    "        loginteigvals -= 0.5 * np.sum(logUeigvals, axis=-1, keepdims=True)\n",
    "        loginteigvals += logmultfactor\n",
    "        inteigvals = np.exp(loginteigvals)\n",
    "        return VReLU(np.einsum('ij,...j,jk->...ik', eigvecs, inteigvals, eigvecs.T), eps)\n",
    "    return f"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that as $r \\to -\\infty$, the integrand drops like $e^{-|r|}$, whereas for $r \\to \\infty$, it drops like $e^{-r(B-2)/2}$.\n",
    "This suggests splitting the integral above and approximating each piece via Gaussian-Laguerre quadrature.\n",
    "We split at the \"argmax\" of the integrand, as given in the following\n",
    "$$\\begin{align*}\n",
    "&\\phantom{{}={}}\n",
    "    \\argmax_r \\frac{\\lambda_B e^r}{(1 + 2 e^r \\lambda_B)\\sqrt{\\prod_i (1 + 2 e^r \\lambda_i)}}\n",
    "    \\\\\n",
    "&=\n",
    "    \\argmax_r \\log \\frac{\\lambda_B e^r}{(1 + 2 e^r \\lambda_B)\\sqrt{\\prod_i (1 + 2 e^r \\lambda_i)}}\n",
    "    \\\\\n",
    "&=\n",
    "    \\argmax_r r - \\log(1 + 2 e^r \\lambda_B) - \\frac 1 2 \\sum_i \\log(1 + 2 e^r \\lambda_i)\n",
    "\\end{align*}$$\n",
    "where $\\lambda_i$ are the eigenvalues of $\\Sigma^G$ and $\\lambda_B$ is the largest eigenvalue of $\\Sigma^G$.\n",
    "This is a monotonic function, so we just need to find the root of its derivative, which is\n",
    "$$\\begin{align*}\n",
    "f(r)\n",
    "&=\n",
    "    1 - \\frac 1 2 \\frac{2\\lambda_B e^r}{1 + 2 e^r \\lambda_B} - \\frac 1 2 \\sum_{i=2}^B \\frac{2\\lambda_i e^r}{1 + 2 e^r \\lambda_i}\n",
    "    \\\\\n",
    "&=\n",
    "    -\\frac{B-1}{2} + \\frac{1}{1 + 2 e^r \\lambda_B} + \\frac 1 2 \\sum_{i=2}^B \\frac{1}{1 + 2 e^r \\lambda_i}\n",
    "    .\n",
    "\\end{align*}$$\n",
    "\n",
    "For the Newton method of root-finding, we also need another derivative, which is\n",
    "$$f'(r) = -\\frac 1 2 \\sum_{i=2}^B \\frac{2 e^r \\lambda_i}{(1 + 2 e^r \\lambda_i)^2} - \\frac{2 e^r \\lambda_B}{(1 + 2 e^r \\lambda_B)^2}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that when $\\Sigma = I$, $f$ is maximized at $-\\log(B-1)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-31T13:52:37.135897Z",
     "start_time": "2019-10-31T13:52:37.114894Z"
    }
   },
   "outputs": [],
   "source": [
    "def sigmoid(x):\n",
    "    return (1 + np.tanh(x/2))/2\n",
    "def VBNReLUIntegrandExpArgmax(Sigma, method='brentq'):\n",
    "    '''find r that \"maximizes\" the exponentially parametrized integrand of VBNReLU(Sigma).\n",
    "    The numerical integral will be split around this argmax.'''\n",
    "    B = Sigma.shape[0]\n",
    "    G = Gmatrix(B)\n",
    "    eigvals = np.linalg.eigvalsh(G @ Sigma @ G)\n",
    "    eigvals = eigvals[1:]\n",
    "    logeigvals = np.log(eigvals)\n",
    "    def f(r):\n",
    "        return -(B-1)/2 + 0.5 * np.sum((1 + 2 * eigvals * np.exp(r))**-1) \\\n",
    "            + (1 + 2 * eigvals[-1] * np.exp(r))**-1\n",
    "    def fprime(r):\n",
    "        '''numerically stable version of f' '''\n",
    "        return -0.5 * np.sum(sigmoid(np.log(2) + logeigvals + r) * (1 + 2 * eigvals * np.exp(r))**-1) \\\n",
    "            - sigmoid(np.log(2) + logeigvals[-1] + r) * (1 + 2 * eigvals[-1] * np.exp(r))**-1\n",
    "    if method=='newton':\n",
    "        return root_scalar(f, x0=-np.log(B - 1),\n",
    "                           fprime=fprime,\n",
    "                           method='newton')\n",
    "    else:\n",
    "        return root_scalar(f, bracket=[-1000, 0], method='brentq')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use `quadpy` package for fast, vectorized integration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-31T13:52:37.155903Z",
     "start_time": "2019-10-31T13:52:37.138897Z"
    }
   },
   "outputs": [],
   "source": [
    "def VBNReLU(Sigma, npos=10, nneg=10, alpha=1/8):\n",
    "    '''Computes BN+ReLU kernel for a single batch.\n",
    "    Inputs:\n",
    "        Sigma: input kernel (shape = batchsize x batchsize)\n",
    "        npos: number of points for integrating the big s side of the VBNReLU integral\n",
    "        nneg: number of points for integrating the small s side of the VBNReLU integral\n",
    "        alpha: reparametrize the integral by s = exp(alpha r)\n",
    "    Outputs:\n",
    "        VBNReLU(Sigma)\n",
    "    '''\n",
    "    schemepos = qp.e1r.gauss_laguerre(npos, alpha=0)\n",
    "    schemeneg = qp.e1r.gauss_laguerre(nneg, alpha=0)\n",
    "    intargmax = VBNReLUIntegrandExpArgmax(Sigma).root\n",
    "    dim = Sigma.shape[0]\n",
    "    f = VBNReLUIntegrandExp(Sigma)\n",
    "    integrandpos = lambda xs: np.rollaxis(\n",
    "        np.rollaxis(\n",
    "            alpha * f(intargmax + alpha * xs,\n",
    "                logmultfactor=(intargmax + (1 + alpha) * xs)[..., None]),\n",
    "            2, 0),\n",
    "        3, 1)\n",
    "    integrandneg = lambda xs: np.rollaxis(\n",
    "        np.exp(intargmax) * np.rollaxis(f(intargmax - xs),\n",
    "            2, 0),\n",
    "        3, 1)\n",
    "    return dim * (\n",
    "        schemepos.integrate(integrandpos) + schemeneg.integrate(integrandneg)).squeeze(-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mean Field Theory of Batchnorm: Multi-Batch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now suppose one has a batch of $B_1$ samples\n",
    "$x_{11}, \\ldots, x_{1B_1} \\in \\mathbb{R}^n$\n",
    "and a batch of $B_2$ samples\n",
    "$x_{21}, \\ldots, x_{2B_2} \\in \\mathbb{R}^n$.\n",
    "Consider their kernel arranged in block matrix form\n",
    "$$\\tilde \\Sigma = \\begin{pmatrix} \\Sigma_1 & \\Xi\\\\ \\Xi^\\top & \\Sigma_2 \\end{pmatrix} \\in \\mathbb R^{(B_1+B_2) \\times (B_1+B_2)}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again suppose $(y_{11}, \\ldots, y_{1B_1}) = \\mathrm{ReLU}(\\mathcal{B}(W x_{11}, \\ldots, W x_{1B_1}))$ represents a dense matrix multiplication followed by batchnorm and ReLU, applied to the first batch.\n",
    "Likewise, let $(y_{21}, \\ldots, y_{2B_2}) = \\mathrm{ReLU}(\\mathcal{B}(W x_{21}, \\ldots, W x_{2B_2}))$ be the same applied to the second batch.\n",
    "Then the block matrix\n",
    "$$\\begin{pmatrix}\n",
    "(y_{1i}^\\top y_{1j}^\\top)_{ij}/n' & (y_{1i}^\\top y_{2j}^\\top)_{ij}/n'\\\\\n",
    "(y_{2i}^\\top y_{1j}^\\top)_{ij}/n' & (y_{2i}^\\top y_{2j}^\\top)_{ij}/n'\n",
    "\\end{pmatrix}$$\n",
    "converges almost surely to a deterministic limit \n",
    "$$V_{\\mathcal{B}_\\mathrm{ReLU}^{\\oplus2}}(\\tilde\\Sigma)$$\n",
    "if $W \\in \\mathbb{R}^{n' \\times n}$ is sampled as $W_{ij} \\sim \\mathcal{N}(0, 1/n)$ and as $n' \\to \\infty$, just like before."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Calculating $V_{\\mathcal{B}_\\mathrm{ReLU}^{\\oplus2}}(\\tilde\\Sigma)$.**\n",
    "\n",
    "$V_{\\mathcal{B}_\\mathrm{ReLU}^{\\oplus2}}(\\tilde\\Sigma)$ has the same block structure as $\\tilde \\Sigma$, and its diagonal blocks are given by $V_{\\mathcal{B}_\\mathrm{ReLU}}(\\Sigma_1)$ and $V_{\\mathcal{B}_\\mathrm{ReLU}}(\\Sigma_2)$, which can be computed according to the last section.\n",
    "Its off-diagonal block can be expressed as\n",
    "$$[V_{\\mathcal{B}_\\mathrm{ReLU}}(\\tilde \\Sigma)]_{12} = \n",
    "\\sqrt{B_1 B_2} \\pi^{-1} \\int_0^\\infty d s \\int_0^\\infty d t\\ \n",
    "(st)^{-1/2} \\det(I_{B_1+B_2} + 2 \\Omega)^{-1/2}\n",
    "V_\\mathrm{ReLU}(\\Pi)_{12}$$\n",
    "by equation (56) of [Yang et al. 2019](https://arxiv.org/pdf/1902.08129.pdf),\n",
    "where\n",
    "$$\\begin{align*}\n",
    "    \\Omega &=\n",
    "        D^{1/2}\\begin{pmatrix} G_1 \\Sigma_1 G_1 & G_1 \\Xi G_2\\\\ G_2 \\Xi^\\top G_1 & G_2 \\Sigma_2 G_2 \\end{pmatrix} D^{1/2}\n",
    "            \\\\\n",
    "    \\Pi &=\n",
    "        D^{-1/2} \\Omega (I + 2 \\Omega)^{-1} D^{-1/2}\n",
    "            \\\\\n",
    "    D &=\n",
    "        s I_{B_1} \\oplus t I_{B_2}\n",
    "        = \\begin{pmatrix} s I_{B_1} & 0 \\\\ 0 & t I_{B_2} \\end{pmatrix}\n",
    "            \\\\\n",
    "    G_i &= I - B_i^{-1} \\mathbf{1}\\mathbf{1}^\\top\n",
    "\\end{align*}$$\n",
    "and $V_\\mathrm{ReLU}(\\Pi)_{12}$ is the block of $V_\\mathrm{ReLU}(\\Pi)$ on the first row, second column, of size $B_1 \\times B_2$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We apply a similar diagonalization trick as in the single batch case to efficiently evaluate the integrand."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**We define some new matrices $A_1, \\Delta_1, A_2, \\Delta_2, \\dot \\Xi, \\dot \\Omega, A$ below.**\n",
    "Let $A_1 \\in \\mathbb R^{B_1 \\times (B_1-1)}$ contain an orthonormal basis of the the image of $G_1$ in its columns such that we have the diagonalization\n",
    "$$G_1 \\Sigma_1 G_1 = A_1 \\Delta_1 A_1^\\top$$\n",
    "where $\\Delta_1$ is a diagonal matrix.\n",
    "Likewise, let $A_2 \\in \\mathbb R^{B_2 \\times (B_2-1)}$ satisfy $A_2^\\top A_2 = I_{B_2-1}$ such that\n",
    "$$G_2 \\Sigma_2 G_2 = A_2 \\Delta_2 A_2^\\top$$\n",
    "where $\\Delta_2$ is a diagonal matrix.\n",
    "Let $\\dot \\Xi \\in \\mathbb R^{(B_1-1) \\times (B_2-1)}$ be the unique matrix such that\n",
    "$$G_1 \\Xi G_2 = A_1 \\dot \\Xi A_2^\\top.$$\n",
    "Define\n",
    "$$\\dot \\Omega = \\begin{pmatrix} \\Delta_1 & \\dot \\Xi\\\\ \\dot \\Xi^\\top & \\Delta_2 \\end{pmatrix}$$\n",
    "so that $\\Omega = \\sqrt D A \\dot \\Omega A^\\top \\sqrt D$ where $A = \\begin{pmatrix} A_1 & 0\\\\ 0 & A_2 \\end{pmatrix} \\in \\mathbb{R}^{(B_1+B_2) \\times (B_1+B_2-2)}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Then we can simplify $\\Pi$ as \n",
    "$$\\begin{align*}\n",
    "\\Pi\n",
    "    &=\n",
    "        D^{-1/2} D^{1/2} A \\dot \\Omega A^\\top D^{1/2} D^{-1/2} (D^{-1} + 2 A\\dot \\Omega A^\\top)^{-1} D^{-1/2} D^{-1/2}\n",
    "        \\\\\n",
    "    &=\n",
    "        A \\dot \\Omega A^\\top (D^{-1} + 2 A \\dot \\Omega A^\\top)^{-1} D^{-1}\n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Calculating $\\Pi$.**\n",
    "\n",
    "Note that $(D^{-1} + 2 A \\dot \\Omega A^\\top)^{-1}$ has two eigenspaces given by the two eigenspaces projected away by $G_1$ and $G_2$, and it has resp. $s$ and $t$ for their eigenvalues.\n",
    "However, these eigenvalues are zeroed out by the multiplication of $A \\dot \\Omega A^\\top$, so, assuming $\\dot \\Omega$ is invertible, the above expression for $\\Pi$ is equivalent to\n",
    "$$\\begin{align*}\n",
    "    \\Pi\n",
    "        &=\n",
    "            G(D^{-1} A \\dot \\Omega^{-1} A^\\top + 2 I_{B_1+B_2})^{-1} D^{-1}G\n",
    "            \\\\\n",
    "        &=\n",
    "            G (A \\dot \\Omega^{-1} A^\\top + 2 D)^{-1} G\n",
    "\\end{align*}$$\n",
    "where $G = \\begin{pmatrix} G_1 & 0\\\\ 0 & G_2 \\end{pmatrix}$.\n",
    "This can be further simplified as\n",
    "$$\\Pi = A (\\dot \\Omega^{-1} + 2 \\dot D)^{-1} A^\\top$$\n",
    "where $\\dot D = \\begin{pmatrix} s I_{B_1-1} & 0\\\\ 0 & t I_{B_2-1} \\end{pmatrix}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Calculating the determinant.**\n",
    "\n",
    "Similarly, the determinant above can be expressed as\n",
    "$$\\begin{align*}\n",
    "\\det(I_{B_1+B_2} + 2 \\Omega)\n",
    "    &=\n",
    "        s^{B_1-1} t^{B_2-1} \\det(\\dot D^{-1} + 2 \\dot \\Omega).\n",
    "\\end{align*}$$\n",
    "> *N.B.* We will not use this formula below, but using the block matrix formula for determinant, we can express the above as\n",
    "$$\\begin{align*}\n",
    "\\det(I_{B_1+B_2} + 2 \\Omega)\n",
    "    &=\n",
    "        s^{B_1-1} t^{B_2-1} \\det(s^{-1} I + 2 \\Delta_1) \\det(t^{-1} I + 2 \\Delta_2 - \\dot \\Xi^\\top (s^{-1} + 2 \\Delta_1)^{-1} \\dot \\Xi)\n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Tie it all together.**\n",
    "\n",
    "Thus the integrand of $V_{\\mathcal{B}_\\mathrm{ReLU}^{\\oplus 2}}(\\tilde \\Sigma)$ can be calculated as\n",
    "$$s^{-B_1/2} t^{-B_2/2} \\det(\\dot D^{-1} + 2 \\dot \\Omega)^{-1/2} V_\\mathrm{ReLU}(A (\\dot \\Omega^{-1} + 2 \\dot D)^{-1} A^\\top)_{12}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-31T13:52:37.189899Z",
     "start_time": "2019-10-31T13:52:37.160903Z"
    }
   },
   "outputs": [],
   "source": [
    "def VBNReLUCrossBatchIntegrand(Xi, Sigma1, Sigma2):\n",
    "    '''Computes the off diagonal block of the BN+ReLU kernel over 2 batches\n",
    "    Input:\n",
    "        Xi: covariance between batch1 and batch2\n",
    "        Sigma1: autocovariance of batch1\n",
    "        Sigma2: autocovariance of batch2\n",
    "    Output:\n",
    "        f: integrand function in the integral for computing cross batch VBNReLU \n",
    "    '''\n",
    "    n1 = Sigma1.shape[0]\n",
    "    n2 = Sigma2.shape[0]\n",
    "    G1 = Gmatrix(n1)\n",
    "    G2 = Gmatrix(n2)\n",
    "    Delta1, A1 = np.linalg.eigh(G1 @ Sigma1 @ G1)\n",
    "    Delta2, A2 = np.linalg.eigh(G2 @ Sigma2 @ G2)\n",
    "    # kill first 0 eigenval\n",
    "    Delta1 = Delta1[1:]\n",
    "    Delta2 = Delta2[1:]\n",
    "    A1 = A1[:, 1:]\n",
    "    A2 = A2[:, 1:]\n",
    "    \n",
    "    Xidot = A1.T @ Xi @ A2\n",
    "    Omegadot = np.block([[np.diag(Delta1), Xidot], [Xidot.T, np.diag(Delta2)]])\n",
    "    Omegadotinv = np.linalg.inv(Omegadot)\n",
    "    \n",
    "    def f(s, t, multfactor=1):\n",
    "        # Ddot.shape = (..., n1+n2-2, n1+n2-2)\n",
    "        Ddot = s[..., None, None] * np.eye(n1-1+n2-1)\n",
    "        Ddot[..., np.arange(n1-1, n1+n2-2), np.arange(n1-1, n1+n2-2)] = t[..., None]\n",
    "        \n",
    "        ## Compute off-diagonal block of VReLU(Pi)\n",
    "        Pitilde = Omegadotinv + 2 * Ddot\n",
    "        Pitilde = np.linalg.inv(Pitilde)\n",
    "        Pi11diag = np.einsum('ij,...jk,ki->...i',\n",
    "                            A1,\n",
    "                            Pitilde[..., :n1-1, :n1-1],\n",
    "                            A1.T)\n",
    "        Pi22diag = np.einsum('ij,...jk,ki->...i',\n",
    "                            A2,\n",
    "                            Pitilde[..., n1-1:, n1-1:],\n",
    "                            A2.T)\n",
    "        Pi12 = np.einsum('ij,...jk,kl->...il',\n",
    "                        A1,\n",
    "                        Pitilde[..., :n1-1, n1-1:],\n",
    "                        A2.T)\n",
    "        C = J1(np.einsum('...i,...ij,...j->...ij',\n",
    "                        Pi11diag**-0.5,\n",
    "                        Pi12,\n",
    "                        Pi22diag**-0.5))\n",
    "        VReLUPi12 = 0.5 * np.einsum('...i,...ij,...j->...ij',\n",
    "                                Pi11diag**0.5,\n",
    "                                C,\n",
    "                                Pi22diag**0.5)\n",
    "        \n",
    "        \n",
    "        ## Compute determinant\n",
    "        ind = np.arange(n1+n2-2)\n",
    "        # Ddot <- matrix inverse of Ddot\n",
    "        Ddot[..., ind, ind] = Ddot[..., ind, ind]**-1\n",
    "        logdet = np.linalg.slogdet(Ddot + 2 * Omegadot)[1]\n",
    "        return np.exp(\n",
    "                    (np.log(multfactor)\n",
    "                      + (-n1/2) * np.log(s)\n",
    "                      + (-n2/2) * np.log(t)\n",
    "                      - 1/2 * logdet)[..., None, None] + np.log(VReLUPi12))\n",
    "    return f"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We reparametrize the integrand above via the exponential function, just like in the single batch case, and integrate via `quadpy`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-31T13:52:37.229898Z",
     "start_time": "2019-10-31T13:52:37.194899Z"
    }
   },
   "outputs": [],
   "source": [
    "def VBNReLUCrossBatch(Xi, Sigma1, Sigma2, npos=10, nneg=5,\n",
    "                      alphapos1=1/3, alphaneg1=1,\n",
    "                     alphapos2=1/3, alphaneg2=1):\n",
    "    '''Compute VBNReLU for two batches.\n",
    "    \n",
    "    Inputs:\n",
    "        Xi: covariance between batch1 and batch2\n",
    "        Sigma1: autocovariance of batch1\n",
    "        Sigma2: autocovariance of batch2\n",
    "        npos: number of points for integrating the big s side of the VBNReLU integral\n",
    "            (effective for both dimensions of integration)\n",
    "        nneg: number of points for integrating the small s side of the VBNReLU integral\n",
    "            (effective for both dimensions of integration)\n",
    "        alphapos1: reparametrize the large s integral by s = exp(alpha r) in the 1st dimension\n",
    "        alphaneg1: reparametrize the small s integral by s = exp(alpha r) in the 1st dimension\n",
    "        alphapos2: reparametrize the large s integral by s = exp(alpha r) in the 2nd dimension\n",
    "        alphaneg2: reparametrize the small s integral by s = exp(alpha r) in the 2nd dimension\n",
    "            By tuning the `alpha` parameters, the integrand is closer to being well-approximated by \n",
    "            low-degree Laguerre polynomials, which makes the quadrature more accurate in approximating the integral.\n",
    "    Outputs:\n",
    "        The (batch1, batch2) block of block matrix obtained by\n",
    "        applying VBNReLU^{\\oplus 2} to the kernel of batch1 and batch2\n",
    "    '''\n",
    "    # We will do the integration explicitly ourselves:\n",
    "    #     We obtain sample points and weights via `quadpy`'s Gauss Laguerre quadrature\n",
    "    #     and do the sum ourselves\n",
    "    schemepos = qp.e1r.gauss_laguerre(npos, alpha=0)\n",
    "    schemeneg = qp.e1r.gauss_laguerre(nneg, alpha=0)\n",
    "    dim1 = Sigma1.shape[0]\n",
    "    dim2 = Sigma2.shape[0]\n",
    "    intargmax = (-np.log(2*(dim1-1)), -np.log(2*(dim2-1)))\n",
    "    f = VBNReLUCrossBatchIntegrand(Xi, Sigma1, Sigma2)\n",
    "    # Get the points manually for each dimension\n",
    "    scheme1dpoints = np.concatenate([schemepos.points, -schemeneg.points])\n",
    "    # Get the weights manually for each dimension\n",
    "    scheme1dwts = np.concatenate([schemepos.weights, schemeneg.weights])\n",
    "    # Obtain the points for the whole 2d integration\n",
    "    scheme2dpoints = np.meshgrid(scheme1dpoints, scheme1dpoints)\n",
    "    # Obtain the weights for the whole 2d integration\n",
    "    scheme2dwts = scheme1dwts[:, None] * scheme1dwts[None, :]\n",
    "\n",
    "    def applyalpha(x, alphapos, alphaneg):\n",
    "        xx = np.copy(x)\n",
    "        xx[xx > 0] *= alphapos\n",
    "        xx[xx <= 0] *= alphaneg\n",
    "        return xx\n",
    "    def alphafactor(x, y):\n",
    "        a = np.zeros_like(x)\n",
    "        a[(x > 0) & (y > 0)] = alphapos1 * alphapos2\n",
    "        a[(x > 0) & (y <= 0)] = alphapos1 * alphaneg2\n",
    "        a[(x <= 0) & (y > 0)] = alphaneg1 * alphapos2\n",
    "        a[(x <= 0) & (y <= 0)] = alphaneg1 * alphaneg2\n",
    "        return a\n",
    "        \n",
    "    integrand = lambda inp: \\\n",
    "        f(np.exp(applyalpha(inp[0], alphapos1, alphaneg1) + intargmax[0]), \n",
    "          np.exp(applyalpha(inp[1], alphapos2, alphaneg2) + intargmax[1]),\n",
    "          multfactor=alphafactor(inp[0], inp[1])\n",
    "              * np.pi**-1\n",
    "              * np.exp(applyalpha(inp[0], alphapos1, alphaneg1) + intargmax[0]\n",
    "                     + applyalpha(inp[1], alphapos2, alphaneg2) + intargmax[1]\n",
    "                     + np.abs(inp[0]) + np.abs(inp[1])\n",
    "                      )\n",
    "         )\n",
    "\n",
    "    return np.sqrt(dim1 * dim2) * np.einsum('ij...,ij->...',\n",
    "              integrand(scheme2dpoints),\n",
    "              scheme2dwts\n",
    "             )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Verification of Theory with Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-31T13:52:38.028893Z",
     "start_time": "2019-10-31T13:52:37.232897Z"
    }
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "import torchvision\n",
    "import torchvision.transforms as transforms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll work with a 2-layer ReLU+BN neural network over 64 samples from CIFAR10."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-31T13:52:38.033896Z",
     "start_time": "2019-10-31T13:52:38.030900Z"
    }
   },
   "outputs": [],
   "source": [
    "nsamples = 64\n",
    "depth = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-31T13:52:39.436760Z",
     "start_time": "2019-10-31T13:52:38.035896Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Files already downloaded and verified\n"
     ]
    }
   ],
   "source": [
    "transform = transforms.Compose(\n",
    "    [transforms.ToTensor(),\n",
    "     transforms.Normalize((0.5, 0.5, 0.5), (0.5, 0.5, 0.5))])\n",
    "\n",
    "trainset = torchvision.datasets.CIFAR10(root='./data', train=True,\n",
    "                                        download=True, transform=transform)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-31T13:52:49.095341Z",
     "start_time": "2019-10-31T13:52:39.439762Z"
    }
   },
   "outputs": [],
   "source": [
    "myimages = list(trainset)[:nsamples]\n",
    "myimages = np.array([im[0].numpy() for im in myimages])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-31T13:52:49.101268Z",
     "start_time": "2019-10-31T13:52:49.096237Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(64, 3, 32, 32)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "myimages.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-31T13:52:49.131243Z",
     "start_time": "2019-10-31T13:52:49.103237Z"
    }
   },
   "outputs": [],
   "source": [
    "inker = myimages.reshape(nsamples, -1) @ myimages.reshape(nsamples, -1).T / (3 * 32 * 32)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We divide the 64 samples into 2 batches of 32, so that `ker11` denotes the \"autocovariance\" of the 1st batch, `ker22` denotes that of the 2nd batch, and `ker12` denotes the \"covariance\" between the 1st and the 2nd."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-31T13:52:49.138243Z",
     "start_time": "2019-10-31T13:52:49.133241Z"
    }
   },
   "outputs": [],
   "source": [
    "myimages1 = myimages[:nsamples//2]\n",
    "myimages2 = myimages[nsamples//2:]\n",
    "ker11 = inker[:nsamples//2, :nsamples//2]\n",
    "ker22 = inker[nsamples//2:, nsamples//2:]\n",
    "ker12 = inker[:nsamples//2, nsamples//2:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We finally apply our functions `VBNReLU` and `VBNReLUCrossBatch`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-31T13:52:50.258243Z",
     "start_time": "2019-10-31T13:52:49.140239Z"
    }
   },
   "outputs": [],
   "source": [
    "Sigma1s = [ker11]\n",
    "Sigma2s = [ker22]\n",
    "Xis = [ker12]\n",
    "for _ in range(depth):\n",
    "    Sigma1 = Sigma1s[-1]\n",
    "    Sigma2 = Sigma2s[-1]\n",
    "    Xi = Xis[-1]\n",
    "    Sigma1s.append(VBNReLU(Sigma1))\n",
    "    Sigma2s.append(VBNReLU(Sigma2))\n",
    "    Xis.append(VBNReLUCrossBatch(Xi, Sigma1, Sigma2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-31T13:52:50.266239Z",
     "start_time": "2019-10-31T13:52:50.260242Z"
    }
   },
   "outputs": [],
   "source": [
    "ker = np.block(\n",
    "    [\n",
    "        [Sigma1s[-1], Xis[-1]],\n",
    "        [Xis[-1].T, Sigma2s[-1]]\n",
    "    ]\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For example, this is what our 2-layer BN+ReLU NNGP kernel looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-31T13:52:51.007236Z",
     "start_time": "2019-10-31T13:52:50.269242Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 8 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from utils import getCor, colorbar\n",
    "\n",
    "plt.figure(figsize=(8, 8))\n",
    "\n",
    "plt.subplot(221)\n",
    "ax = plt.gca()\n",
    "im_thcov = plt.imshow(ker, cmap='PuBu_r')\n",
    "plt.title('BN+ReLU covariances (theory)')\n",
    "plt.grid()\n",
    "colorbar(im_thcov)\n",
    "\n",
    "plt.subplot(222)\n",
    "ax = plt.gca()\n",
    "im_thcor = plt.imshow(getCor(ker), cmap='viridis')\n",
    "plt.title('BN+ReLU correlations (theory)')\n",
    "plt.grid()\n",
    "colorbar(im_thcor)\n",
    "\n",
    "\n",
    "plt.subplot(223)\n",
    "ax = plt.gca()\n",
    "im_input = plt.imshow(inker, cmap='PuBu_r')\n",
    "plt.title('Input covariances')\n",
    "plt.grid()\n",
    "colorbar(im_input)\n",
    "\n",
    "plt.subplot(224)\n",
    "ax = plt.gca()\n",
    "im_inputcor = plt.imshow(getCor(inker), cmap='viridis')\n",
    "plt.title('Input correlations')\n",
    "plt.grid()\n",
    "colorbar(im_inputcor)\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-31T13:52:51.014237Z",
     "start_time": "2019-10-31T13:52:51.008237Z"
    }
   },
   "outputs": [],
   "source": [
    "with open('BN.kernel', 'wb') as f:\n",
    "    np.save(f, ker)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compute Simulations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-31T13:55:31.311924Z",
     "start_time": "2019-10-31T13:55:31.304930Z"
    }
   },
   "outputs": [],
   "source": [
    "from torch import nn\n",
    "from torch.autograd import Variable\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-31T13:55:31.347483Z",
     "start_time": "2019-10-31T13:55:31.336483Z"
    }
   },
   "outputs": [],
   "source": [
    "class MyNet(nn.Module):\n",
    "    def __init__(self, nonlin, width=500, depth=2, inputdim=None):\n",
    "        super(MyNet, self).__init__()\n",
    "        self.nonlin = nonlin\n",
    "        self.width = width\n",
    "        self.depth = depth\n",
    "        self.params = nn.ParameterList()\n",
    "        self.BNs = nn.ModuleList()\n",
    "        self.nonlins = nn.ModuleList()\n",
    "        for i in range(depth):\n",
    "            if i == 0:\n",
    "                if inputdim is None:\n",
    "                    inputdim = width\n",
    "                w = Variable(torch.randn(width, inputdim) / np.sqrt(width), requires_grad=True)\n",
    "            else:\n",
    "                w = Variable(torch.randn(width, width) / np.sqrt(width), requires_grad=True)\n",
    "            self.params.append(nn.Parameter(w))\n",
    "            self.BNs.append(nn.BatchNorm1d(width, eps=0, momentum=None, affine=False, track_running_stats=False))\n",
    "            self.nonlins.append(nonlin())\n",
    "    def forward(self, x):\n",
    "        for i in range(self.depth):\n",
    "            w = self.params[i]\n",
    "            h = torch.einsum('ij,kj->ki', w, x)\n",
    "            x = self.nonlins[i](self.BNs[i](h))\n",
    "        return x\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We randomly initialize 100 BN+ReLU networks for each width among $[2^5, 2^6, \\ldots, 2^{13}]$ and run them on the two batches defined above.\n",
    "We calculate the empirical Gram matrix of the network outputs as well as its Frobenius distance to the infinite-width theoretical kernel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-31T13:56:59.092531Z",
     "start_time": "2019-10-31T13:55:31.354483Z"
    }
   },
   "outputs": [],
   "source": [
    "widths = [2**i for i in range(5, 13)]\n",
    "frobs = []\n",
    "V11 = Sigma1s[-1]\n",
    "V22 = Sigma2s[-1]\n",
    "V12 = Xis[-1]\n",
    "V11frob = np.sum(V11**2)\n",
    "V22frob = np.sum(V22**2)\n",
    "V12frob = np.sum(V12**2)\n",
    "Vfrob = V11frob + V22frob + 2 * V12frob\n",
    "batch1 = torch.from_numpy(myimages1.reshape(nsamples//2, -1))\n",
    "batch2 = torch.from_numpy(myimages2.reshape(nsamples//2, -1))\n",
    "for width in widths:\n",
    "    for _ in range(100):\n",
    "        mynet = MyNet(nn.ReLU,\n",
    "                      width=width,\n",
    "                      depth=depth, inputdim=3072)\n",
    "        out = []\n",
    "        simbatch1 = mynet(batch1)\n",
    "        simbatch2 = mynet(batch2)\n",
    "        simV11 = simbatch1 @ simbatch1.t() / simbatch1.shape[-1]\n",
    "        simV22 = simbatch2 @ simbatch2.t() / simbatch2.shape[-1]\n",
    "        simV12 = simbatch1 @ simbatch2.t() / simbatch1.shape[-1]\n",
    "        diffV11 = simV11 - torch.from_numpy(V11).float()\n",
    "        diffV22 = simV22 - torch.from_numpy(V22).float()\n",
    "        diffV12 = simV12 - torch.from_numpy(V12).float()\n",
    "        difffrob11 = torch.sum(diffV11**2).item()\n",
    "        difffrob22 = torch.sum(diffV22**2).item()\n",
    "        difffrob12 = torch.sum(diffV12**2).item()\n",
    "        frobs.append(\n",
    "        {\n",
    "            'relfrob11': difffrob11 / V11frob,\n",
    "            'relfrob22': difffrob22 / V22frob,\n",
    "            'relfrob12': difffrob12 / V12frob,\n",
    "            'relfrob': (difffrob11 + difffrob22 + 2 * difffrob12) / Vfrob,\n",
    "            'width': width\n",
    "        })"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We store the results in a dataframe `frob_df`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-31T13:56:59.105531Z",
     "start_time": "2019-10-31T13:56:59.094531Z"
    }
   },
   "outputs": [],
   "source": [
    "frob_df = pd.DataFrame(frobs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-31T13:56:59.150534Z",
     "start_time": "2019-10-31T13:56:59.108532Z"
    }
   },
   "outputs": [],
   "source": [
    "frob_df.to_pickle('BN.df')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compare Theory with Simulations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The deviation from infinite-width theory drops with width, as expected."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-31T13:56:59.961530Z",
     "start_time": "2019-10-31T13:56:59.153532Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(x='width', y='relfrob12', data=frob_df)\n",
    "plt.semilogy()\n",
    "plt.title('Deviation From Infinite-width Theory')\n",
    "_ = plt.ylabel(u'Relative Squared Frob. Norm\\n $\\|K_{\\infty} - K_{width}\\|_F^2/\\|K_{\\infty}\\|_F^2$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The deviation from theory in *squared* Frobenius norm scales like $\\frac{1}{width}$ (so, in Frobenius norm, the deviation scales like $width^{-1/2}$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-31T13:57:00.507299Z",
     "start_time": "2019-10-31T13:56:59.962530Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "frob_df.groupby('width', as_index=False).mean().plot.line(x='width', y='relfrob')\n",
    "plt.plot(widths, np.array(widths, dtype='float')**-1, '--', label=u'${width}^{-1}$')\n",
    "plt.ylabel(u'Mean Relative Squared Frob. Norm\\n $\\|K_{\\infty} - K_{width}\\|_F^2/\\|K_{\\infty}\\|_F^2$')\n",
    "plt.loglog()\n",
    "plt.legend()\n",
    "_ = plt.title(u'Deviation from Theory in (Frobenius norm)$^2$ drops like $width^{-1}$')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
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   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}