AlexNet-pytorch-MPFit.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ESD for Pytorch pretrained models\n",
    "http://pytorch.org/docs/master/torchvision/models.html\n",
    "\n",
    "Try to auto-fit MP using Kernel Density Estimator (KDE) and Optimizer (i.e LM Fit)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T05:24:44.617534Z",
     "start_time": "2018-08-11T05:24:43.522561Z"
    }
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "import torchvision.models as models\n",
    "import torchvision.transforms as transforms\n",
    "import torch.nn as nn\n",
    "\n",
    "import numpy as np\n",
    "import scipy as sp\n",
    "from scipy.linalg import svd\n",
    "\n",
    "import powerlaw\n",
    "\n",
    "import matplotlib\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T05:24:46.806272Z",
     "start_time": "2018-08-11T05:24:44.619580Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "importing notebook from RMT_Util.ipynb\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/charlesmartin14/anaconda3/lib/python3.6/importlib/_bootstrap.py:219: RuntimeWarning: compiletime version 3.5 of module 'tensorflow.python.framework.fast_tensor_util' does not match runtime version 3.6\n",
      "  return f(*args, **kwds)\n",
      "/Users/charlesmartin14/.local/lib/python3.6/site-packages/h5py/__init__.py:34: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
      "  from ._conv import register_converters as _register_converters\n",
      "Using TensorFlow backend.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.6.5 |Anaconda custom (64-bit)| (default, Apr 26 2018, 08:42:37) \n",
      "[GCC 4.2.1 Compatible Clang 4.0.1 (tags/RELEASE_401/final)]\n",
      "numpy version 1.14.2\n",
      "scipy version 1.0.1\n",
      "tensforflow version 1.5.0-dev20171116\n",
      "keras version 2.1.5\n",
      "sklearn version 0.19.1\n",
      "powerlaw version 1.4.3\n"
     ]
    }
   ],
   "source": [
    "import import_ipynb\n",
    "import RMT_Util"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T05:24:46.812407Z",
     "start_time": "2018-08-11T05:24:46.808860Z"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['figure.figsize'] = [5, 5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T05:24:48.723394Z",
     "start_time": "2018-08-11T05:24:46.814199Z"
    }
   },
   "outputs": [],
   "source": [
    "alexnet = models.alexnet(pretrained=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Marchenko Pastur Fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## FC1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T05:27:38.647884Z",
     "start_time": "2018-08-11T05:24:48.725563Z"
    }
   },
   "outputs": [],
   "source": [
    "this_im = 17\n",
    "\n",
    "for im, m in enumerate(alexnet.modules()):\n",
    "    if im == this_im:\n",
    "        W17 = np.array(m.weight.data.clone().cpu()) \n",
    "        Q = RMT_Util.get_Q(W17)\n",
    "        \n",
    "        u, sv, sh = svd(W17)\n",
    "        \n",
    "        evals17 = sv*sv\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T05:27:39.506729Z",
     "start_time": "2018-08-11T05:27:38.650072Z"
    }
   },
   "outputs": [
    {
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v7n8a8PE+1zMT2Lvu6a/Ia54vnx4aES8CjdNDx7SIuIZlf0u7J3B2fn42sFcf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\nSUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(evals17, bins=200,  alpha=0.25, color='blue', density=True);\n",
    "plt.title(r\"Empirical Spectral Density $\\rho(\\lambda)$ for AlexNet, FC1\")\n",
    "plt.ylabel(r\"Spectral Density\")\n",
    "plt.xlabel(r\"Eigenvalues ($\\lambda$) of $\\mathbf{X}=\\mathbf{W}_{FC1}^{T}\\mathbf{W}_{FC1}$\")\n",
    "plt.savefig(\"img/alexnet-fc1-full.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T05:27:39.872515Z",
     "start_time": "2018-08-11T05:27:39.508560Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "RMT_Util.ipynb:7: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  \"## RMT Util\\n\",\n",
      "RMT_Util.ipynb:7: RuntimeWarning: invalid value encountered in sqrt\n",
      "  \"## RMT Util\\n\",\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "% spikes outside bulk 11.13\n",
      "% sigma 0.6057\n"
     ]
    },
    {
     "data": {
      "image/png": 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ZAeWaNCW9XdJfJM2T9MU6z39I0gJJs9PbCbkF022VJiSDQddfD8uWdToSM8so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\nTTOzJjhpmpk1wUnTzKwJ/x/3AALVxwctvAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sigma = RMT_Util.plot_ESD_and_fit(model=None,eigenvalues=evals17[evals17<5], weightfile=None, layer=None, \n",
    "                            Q=Q, num_spikes = 400, sigma=None, color='blue')\n",
    "plt.title(r\"ESD $\\rho(\\lambda)$ for AlexNet, FC1, zoomed in\")\n",
    "plt.ylabel(r\"Spectral Density\")\n",
    "plt.xlabel(r\"Eigenvalues ($\\lambda$) of $\\mathbf{X}=\\mathbf{W}_{FC1}^{T}\\mathbf{W}_{FC1}$\")\n",
    "plt.savefig(\"img/alexnet-fc1.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T03:10:48.674479Z",
     "start_time": "2018-08-11T03:10:48.671978Z"
    }
   },
   "source": [
    "### AutoMated Fits\n",
    "\n",
    "FC1 = Layer 17\n",
    "\n",
    "Recall we zoomed in A LOT to fit this, but only dropped 3% of the eigenvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T05:27:40.119368Z",
     "start_time": "2018-08-11T05:27:39.875374Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'FC1 layer 17')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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6YP/8TknOA94GXFRV31roRFW1vapmq2p2ZmbmaOqVpF6ME353AacnOS3J8cAlwI7hDknO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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(evals17, bins=100, density=True);\n",
    "plt.title(\"FC1 layer 17\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T05:27:40.347221Z",
     "start_time": "2018-08-11T05:27:40.120979Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3993, 4096, 97.4853515625)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Y6FGWJK2NPtcYs0RbLdkx+TFgFnjzQPPlVXUsyfcBn07yeFX979MOWLUX2AswOzu75PEl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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(evals17[evals17<5], bins=100,density=True);\n",
    "len(evals17[evals17<5]), len(evals17), 100.0*len(evals17[evals17<5])/len(evals17)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T03:21:53.204803Z",
     "start_time": "2018-08-11T03:21:53.202482Z"
    }
   },
   "source": [
    "### KDE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T05:27:40.351327Z",
     "start_time": "2018-08-11T05:27:40.349001Z"
    }
   },
   "outputs": [],
   "source": [
    "from scipy import optimize\n",
    "from sklearn.neighbors import KernelDensity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T05:27:40.637825Z",
     "start_time": "2018-08-11T05:27:40.353026Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "% spikes outside bulk 7.90\n",
      "% sigma 0.7069\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "RMT_Util.ipynb:7: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  \"## RMT Util\\n\",\n",
      "RMT_Util.ipynb:7: RuntimeWarning: invalid value encountered in sqrt\n",
      "  \"## RMT Util\\n\",\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x13480ac88>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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wfzC2tUFxsXPfWozGmAzwfzC2t0NJiXN/6lRoaHBakcYYkyb+D8a2tgPBmJ/vdMJs25bd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\nRK5CYII=\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "evals = evals17\n",
    "RMT_Util.plot_ESD_and_fit(model=None, eigenvalues=evals, Q=Q, num_spikes=300)\n",
    "plt.xlim(0,5)\n",
    "\n",
    "kde = KernelDensity(kernel='linear', bandwidth=0.25).fit(evals.reshape(-1, 1))\n",
    "X_plot = np.linspace(0, np.max(evals), 1000)[:, np.newaxis]\n",
    "log_dens = kde.score_samples(X_plot)\n",
    "plt.plot(X_plot[:, 0], np.exp(log_dens))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T05:27:41.027982Z",
     "start_time": "2018-08-11T05:27:40.640381Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "% spikes outside bulk 21.26\n",
      "% sigma 0.5358\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "RMT_Util.ipynb:7: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  \"## RMT Util\\n\",\n",
      "RMT_Util.ipynb:7: RuntimeWarning: invalid value encountered in sqrt\n",
      "  \"## RMT Util\\n\",\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1348b2f28>]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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iJ7hohV9bEH7ZGPYCLK6to6SggLvL64ONHp7y/AwicgKIVvgd7fllJ/xKCgpY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\nRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "evals = evals17[evals17<5]\n",
    "sigma = RMT_Util.plot_ESD_and_fit(model=None, eigenvalues=evals, Q=Q, num_spikes=700)\n",
    "plt.title(\"ALexNet FC1 KDE (blue) vs MP (red)\")\n",
    "\n",
    "kde = KernelDensity(kernel='linear', bandwidth=0.25).fit(evals.reshape(-1, 1))\n",
    "X_plot = np.linspace(0, np.max(evals), 1000)[:, np.newaxis]\n",
    "log_dens = kde.score_samples(X_plot)\n",
    "plt.plot(X_plot[:, 0], np.exp(log_dens))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T05:27:41.970078Z",
     "start_time": "2018-08-11T05:27:41.725933Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "% spikes outside bulk 2.57\n",
      "% sigma 0.6852\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "RMT_Util.ipynb:7: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  \"## RMT Util\\n\",\n",
      "RMT_Util.ipynb:7: RuntimeWarning: invalid value encountered in sqrt\n",
      "  \"## RMT Util\\n\",\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'MP fit to FC1, sigma auto-fit')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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zq8SAg1HS3pKUvp+WrvNl4GFgqqQpkkYCZwBzBrq9PnV1bXfLsUK+k7eZVaKPkYqEpBuB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\n0cysiIPRzKyIg9HMrIiD0cysyP8H/iz2b7T2qMMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s1 = RMT_Util.fit_mp(evals17, Q)\n",
    "RMT_Util.plot_ESD_and_fit(model=None, eigenvalues=evals, Q=Q, num_spikes=100, sigma=s1)\n",
    "plt.title(\"MP fit to FC1, sigma auto-fit\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T05:34:40.754035Z",
     "start_time": "2018-08-11T05:34:40.685182Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.03698511617935258"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RMT_Util.calc_mp_soft_rank(evals=evals17,Q=Q, sigma=s1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### FC2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T05:36:53.434661Z",
     "start_time": "2018-08-11T05:34:43.370043Z"
    }
   },
   "outputs": [],
   "source": [
    "this_im = 20\n",
    "\n",
    "for im, m in enumerate(alexnet.modules()):\n",
    "    if im == this_im:\n",
    "        W20 = np.array(m.weight.data.clone().cpu()) \n",
    "        Q = RMT_Util.get_Q(W20)\n",
    "        \n",
    "        u, sv, sh = svd(W20)\n",
    "        \n",
    "        evals20 = sv*sv\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T05:36:54.387145Z",
     "start_time": "2018-08-11T05:36:53.442555Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "RMT_Util.ipynb:6: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  \"source\": [\n",
      "RMT_Util.ipynb:6: RuntimeWarning: invalid value encountered in sqrt\n",
      "  \"source\": [\n",
      "RMT_Util.ipynb:6: RuntimeWarning: invalid value encountered in multiply\n",
      "  \"source\": [\n"
     ]
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T05:36:55.436557Z",
     "start_time": "2018-08-11T05:36:55.211617Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "% spikes outside bulk 2.57\n",
      "% sigma 0.7045\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "RMT_Util.ipynb:7: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  \"## RMT Util\\n\",\n",
      "RMT_Util.ipynb:7: RuntimeWarning: invalid value encountered in multiply\n",
      "  \"## RMT Util\\n\",\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0, 5)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ceGaWjeYGnm/IMLMWcgvPzLLhwDOzbDjwzCwbDjwzy4YDz8yy4cAzs2w48MwsGw48M8uG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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s1 = RMT_Util.fit_mp(evals20, Q)\n",
    "RMT_Util.plot_ESD_and_fit(model=None, eigenvalues=evals, Q=Q, num_spikes=100)\n",
    "plt.xlim(0,5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T05:36:56.057926Z",
     "start_time": "2018-08-11T05:36:55.438566Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "% spikes outside bulk 0.00\n",
      "% sigma 0.5159\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "RMT_Util.ipynb:7: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  \"## RMT Util\\n\",\n",
      "RMT_Util.ipynb:7: RuntimeWarning: invalid value encountered in sqrt\n",
      "  \"## RMT Util\\n\",\n",
      "RMT_Util.ipynb:7: RuntimeWarning: invalid value encountered in multiply\n",
      "  \"## RMT Util\\n\",\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0, 4)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Q40sOfz35YdaYun34ATz/6e8z8NkZ7PgH/0fnZpZoiPDb1Kcfc7/+W3b/8ef9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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "RMT_Util.plot_ESD_and_fit(model=None, eigenvalues=evals, Q=Q, sigma=s1)\n",
    "plt.xlim(0,5)\n",
    "plt.ylim(0,4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T05:36:56.063988Z",
     "start_time": "2018-08-11T05:36:56.059897Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.030190051669856464"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RMT_Util.calc_mp_soft_rank(evals=evals17,Q=Q, sigma=s1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### FC3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T05:37:03.546382Z",
     "start_time": "2018-08-11T05:36:56.065832Z"
    }
   },
   "outputs": [],
   "source": [
    "this_im = 22\n",
    "\n",
    "for im, m in enumerate(alexnet.modules()):\n",
    "    if im == this_im:\n",
    "        W22 = np.array(m.weight.data.clone().cpu()) \n",
    "        Q = RMT_Util.get_Q(W22)\n",
    "        \n",
    "        u, sv, sh = svd(W22)\n",
    "        \n",
    "        evals22 = sv*sv\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T05:37:03.794877Z",
     "start_time": "2018-08-11T05:37:03.549670Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "% spikes outside bulk 11.11\n",
      "% sigma 1.1007\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "RMT_Util.ipynb:7: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  \"## RMT Util\\n\",\n",
      "RMT_Util.ipynb:7: RuntimeWarning: invalid value encountered in sqrt\n",
      "  \"## RMT Util\\n\",\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0, 10)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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0ShuEbXe4iS/zaVZapQ7CaKcgPOIIWLfOF383K6HyBiFB24wRQjqBxCmnwK23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\nOQjNrOM5CM2s4/0POZW8g7yA7FIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "RMT_Util.plot_ESD_and_fit(model=None, eigenvalues=evals22, Q=Q, num_spikes=100)\n",
    "plt.xlim(0,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T05:37:05.523405Z",
     "start_time": "2018-08-11T05:37:03.886022Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "RMT_Util.ipynb:7: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  \"## RMT Util\\n\",\n",
      "RMT_Util.ipynb:7: RuntimeWarning: invalid value encountered in sqrt\n",
      "  \"## RMT Util\\n\",\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "% spikes outside bulk 0.00\n",
      "% sigma 0.9866\n"
     ]
    },
    {
     "data": {
      "image/png": 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H4bgj+9nTMTr/wnnzFIQiUhFBB+HIY4c5MHR4/oUXXwxPPFHbgkSkIYUdhD1HOFgoCM86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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s1 = RMT_Util.fit_mp(evals22, Q)\n",
    "RMT_Util.plot_ESD_and_fit(model=None, eigenvalues=evals22, Q=Q, sigma=s1)\n",
    "plt.xlim(0,10)\n",
    "plt.hist(evals22,bins=1000, density=True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-08-11T05:37:05.530388Z",
     "start_time": "2018-08-11T05:37:05.525307Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.061624154661628676"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RMT_Util.calc_mp_soft_rank(evals=evals17,Q=Q, sigma=s1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}