pyTorch-models-VGG-drilldown.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  Drilldown into pretrained models in PyTorch\n",
    "\n",
    "This notebook only has the default pyTorch models\n",
    "\n",
    "- VGG and VGG BN \n",
    "- We only want the initial Conv layers since we know how the  larger layers behave"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-14T00:30:38.661447Z",
     "start_time": "2018-11-14T00:30:32.603760Z"
    }
   },
   "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 pandas as pd\n",
    "\n",
    "import numpy as np\n",
    "import powerlaw\n",
    "\n",
    "from tqdm import tqdm_notebook as tqdm\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": "2018-11-14T00:30:38.688707Z",
     "start_time": "2018-11-14T00:30:38.671565Z"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['figure.figsize'] = [5,5]\n",
    "matplotlib.rcParams.update({'font.size': 16})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-14T00:31:33.925132Z",
     "start_time": "2018-11-14T00:31:33.915351Z"
    }
   },
   "outputs": [],
   "source": [
    "MIN_DIM = 50"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### All Linear Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-14T00:31:34.326560Z",
     "start_time": "2018-11-14T00:31:34.308908Z"
    }
   },
   "outputs": [],
   "source": [
    "def get_conv2D_Wmats(Wtensor):\n",
    "    \"\"\"Extract W slices from a 4 index conv2D tensor of shape: (N,M,i,j) or (M,N,i,j).  Return ij (N x M) matrices\"\"\"\n",
    "    Wmats = []\n",
    "    s = Wtensor.shape\n",
    "    N, M, imax, jmax = s[0],s[1],s[2],s[3]\n",
    "    #print(\"tensor shape\", N,M,imax,jmax)\n",
    "    for i in range(imax):\n",
    "        for j in range(jmax):\n",
    "            W = Wtensor[:,:,i,j]\n",
    "            if N < M:\n",
    "                W = W.T\n",
    "            Wmats.append(W)\n",
    "    return Wmats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-14T00:31:34.582477Z",
     "start_time": "2018-11-14T00:31:34.552800Z"
    }
   },
   "outputs": [],
   "source": [
    "def count_layers(model):\n",
    "    \"\"\"Loops over a pytorch model and counts all the weight matrices, linear, conv2d, and conv2d-slices\"\"\"\n",
    "    num_linear, num_conv2d, num_conv2d_slices = 0, 0, 0\n",
    "    \n",
    "    for im, m in enumerate(model.modules()):\n",
    "        #print(im,m)\n",
    "        if isinstance(m, nn.Linear):    \n",
    "            #print(\"linear\")\n",
    "            W = np.array(m.weight.data.clone().cpu())\n",
    "            if W is not None:\n",
    "                #print(im,m, W.shape)\n",
    "                num_linear += 1\n",
    "        elif isinstance(m, nn.Conv2d):\n",
    "            #print(\"conv2d\")\n",
    "            Wtensor = np.array(m.weight.data.clone().cpu())\n",
    "            #print(Wtensor.shape)\n",
    "            Wmats = get_conv2D_Wmats(Wtensor)\n",
    "            #print(im,m)\n",
    "            num_conv2d += 1\n",
    "            for W in Wmats:\n",
    "                #print(W.shape)\n",
    "                if (np.min(W.shape) >= MIN_DIM):\n",
    "                    num_conv2d_slices += 1\n",
    "                \n",
    "    return num_linear, num_conv2d, num_conv2d_slices\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-14T00:31:36.101817Z",
     "start_time": "2018-11-14T00:31:36.079511Z"
    }
   },
   "outputs": [],
   "source": [
    "def iter_pytotch_layers(model, min_dim=MIN_DIM):\n",
    "    \"\"\"Iterate over a pytorch layers and  weight matrix.  \n",
    "    Supports linear, conv2d, and conv2d-slices\"\"\"\n",
    "    for im, m in enumerate(model.modules()):\n",
    "        if isinstance(m, nn.Linear):     \n",
    "            W = np.array(m.weight.data.clone().cpu())\n",
    "            if W is not None:\n",
    "                yield W\n",
    "        elif isinstance(m, nn.Conv2d):\n",
    "            Wtensor = np.array(m.weight.data.clone().cpu())\n",
    "            Wmats = get_conv2D_Wmats(Wtensor)\n",
    "            for W in Wmats:\n",
    "                if (np.min(W.shape) >= min_dim):\n",
    "                    yield W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-14T03:14:47.483684Z",
     "start_time": "2018-11-14T03:14:47.452136Z"
    }
   },
   "outputs": [],
   "source": [
    "def calc_model_alphas(model):\n",
    "    try:\n",
    "        alphas, norms, lmaxs = [], [], []\n",
    "\n",
    "        for W in tqdm(iter_pytotch_layers(model)):\n",
    "            M, N = W.shape[0], W.shape[1]\n",
    "            print(M,N)\n",
    "            if M > 1024:\n",
    "                break\n",
    "                \n",
    "           # correct for glorot normalization\n",
    "            glorot_correction = np.sqrt(np.average(W.shape))\n",
    "            W = W*glorot_correction\n",
    "            normW = np.linalg.norm(W)\n",
    "\n",
    "            if (M>N):\n",
    "                X=np.dot(W.T,W)/N\n",
    "            else:\n",
    "                X=np.dot(W,W.T)/N\n",
    "\n",
    "            evals = np.linalg.eigvals(X)\n",
    "            \n",
    "            l_max = np.max(evals)\n",
    "            if (l_max > 1):\n",
    "  \n",
    "                fit = powerlaw.Fit(evals, xmax=l_max, verbose=False)\n",
    "               \n",
    "\n",
    "                print(N, M, X.shape, fit.alpha, np.max(evals), fit.D)\n",
    "\n",
    "                alphas.append(fit.alpha)\n",
    "                norms.append(normW)\n",
    "                lmaxs.append(l_max)\n",
    "            \n",
    "           \n",
    "    except Exception as e: \n",
    "\n",
    "        print(\"skipping \", model_name)\n",
    "        print(e)\n",
    "\n",
    "        pass\n",
    "    \n",
    "    return  np.array(alphas),  np.array(norms), np.array(lmaxs)"
   ]
  },
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      "128 64\n",
      "64 128 (64, 64) 1.6501380557141414 6.738295 0.1694855053362465\n",
      "128 64\n"
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     "text": [
      "/Users/charleshmartin/anaconda3/lib/python3.6/site-packages/powerlaw.py:700: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  (Theoretical_CDF * (1 - Theoretical_CDF))\n",
      "/Users/charleshmartin/anaconda3/lib/python3.6/site-packages/powerlaw.py:700: RuntimeWarning: invalid value encountered in true_divide\n",
      "  (Theoretical_CDF * (1 - Theoretical_CDF))\n"
     ]
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      "64 128 (64, 64) 1.5729749512187854 8.271922 0.1797384350918581\n",
      "128 64\n",
      "64 128 (64, 64) 1.4121035942309466 6.4598393 0.19428117596452105\n",
      "128 64\n",
      "64 128 (64, 64) 1.4345913109436141 6.8347855 0.18133933322787987\n",
      "128 64\n",
      "64 128 (64, 64) 1.6184989159677603 13.821855 0.16232586138055982\n",
      "128 64\n",
      "64 128 (64, 64) 1.3854852949105274 8.080619 0.18905146934229966\n",
      "128 64\n",
      "64 128 (64, 64) 1.569204110777663 5.6521955 0.1819836181454877\n",
      "128 64\n",
      "64 128 (64, 64) 1.4466121577534141 7.4524913 0.18158004314008436\n",
      "128 64\n",
      "64 128 (64, 64) 1.6136188055006313 6.271439 0.17297128682994922\n",
      "256 128\n",
      "128 256 (128, 128) 2.6822107696456925 3.8933222 0.15839166995063148\n",
      "256 128\n",
      "128 256 (128, 128) 1.6245755183676356 6.0587945 0.15038343403592247\n",
      "256 128\n",
      "128 256 (128, 128) 1.7481681533160724 3.8148115 0.15976226159856022\n",
      "256 128\n",
      "128 256 (128, 128) 2.576076637045816 6.5674796 0.13313312865838484\n",
      "256 128\n",
      "128 256 (128, 128) 2.53372629580107 11.5017805 0.1260402015887302\n",
      "256 128\n",
      "128 256 (128, 128) 1.615083227571029 6.9235363 0.12912552961625856\n",
      "256 128\n",
      "128 256 (128, 128) 1.6649286743131322 3.616818 0.15493786547581134\n",
      "256 128\n",
      "128 256 (128, 128) 1.6911655918967212 6.020543 0.13113799986198876\n",
      "256 128\n",
      "128 256 (128, 128) 2.0503663998537642 3.9268982 0.14425817438514243\n",
      "256 256\n",
      "256 256 (256, 256) 2.210368745155713 2.4806092 0.12885939357138032\n",
      "256 256\n"
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     "text": [
      "/Users/charleshmartin/anaconda3/lib/python3.6/site-packages/powerlaw.py:1160: RuntimeWarning: invalid value encountered in log\n",
      "  return 1 + len(data)/sum(log(data / (self.xmin)))\n",
      "/Users/charleshmartin/anaconda3/lib/python3.6/site-packages/powerlaw.py:701: RuntimeWarning: overflow encountered in double_scalars\n",
      "  )[1:]\n"
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      "256 256 (256, 256) 2.025263614368387 3.2093854 0.12252819152531846\n",
      "256 256\n",
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      "256 256\n",
      "256 256 (256, 256) 2.658269352938596 3.1404648 0.12169916242995937\n",
      "256 256\n",
      "256 256 (256, 256) 1.80045362839399 5.752889 0.11590080291933835\n",
      "256 256\n",
      "256 256 (256, 256) 2.042517458656814 3.498113 0.12374506755489251\n",
      "256 256\n",
      "256 256 (256, 256) 2.6040953714076167 2.5047364 0.1242841322676077\n",
      "256 256\n",
      "256 256 (256, 256) 1.9744266107780324 3.1301105 0.12141228533720927\n",
      "256 256\n",
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      "512 256\n",
      "256 512 (256, 256) 2.651723173693334 4.4681783 0.10811342580002525\n",
      "512 256\n",
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      "512 256\n",
      "256 512 (256, 256) 2.689082947115983 4.4894295 0.09975517998639649\n",
      "512 256\n",
      "256 512 (256, 256) 2.055719116616769 6.160263 0.11025216122298409\n",
      "512 256\n",
      "256 512 (256, 256) 3.8241504066156065 10.704096 0.09906479789549272\n",
      "512 256\n",
      "256 512 (256, 256) 2.8416611827561247 6.0866494 0.10146027459959384\n",
      "512 256\n",
      "256 512 (256, 256) 2.542659814119495 4.4176507 0.11033066753708382\n",
      "512 256\n",
      "256 512 (256, 256) 2.899488643525573 5.4885507 0.11620853677603127\n",
      "512 256\n",
      "256 512 (256, 256) 2.267162106588364 4.6350164 0.1139875896941433\n",
      "512 512\n",
      "512 512 (512, 512) 3.149647634021204 4.4045234 0.05121067426138748\n",
      "512 512\n",
      "512 512 (512, 512) 3.517971430799456 5.955502 0.06635106684967362\n",
      "512 512\n",
      "512 512 (512, 512) 3.14703617782465 4.2881646 0.053711047697071634\n",
      "512 512\n",
      "512 512 (512, 512) 2.746993968597777 6.009544 0.05741509111718701\n",
      "512 512\n",
      "512 512 (512, 512) 2.407422086928957 9.346973 0.06230395538241612\n",
      "512 512\n",
      "512 512 (512, 512) 3.3026564220463714 5.8348856 0.05007001768887687\n",
      "512 512\n",
      "512 512 (512, 512) 3.1959309618379086 4.043213 0.05217699012617483\n",
      "512 512\n",
      "512 512 (512, 512) 3.3540202532355265 6.2737813 0.04650963426798005\n",
      "512 512\n",
      "512 512 (512, 512) 2.9671913538492407 4.122296 0.06097226530563982\n",
      "512 512\n",
      "512 512 (512, 512) 2.7750606719344155 3.2470713 0.08158068000202795\n",
      "512 512\n",
      "512 512 (512, 512) 3.650766704993771 4.073695 0.07941534203937883\n",
      "512 512\n",
      "512 512 (512, 512) 3.1718414815826237 3.4678502 0.07556438481879812\n",
      "512 512\n",
      "512 512 (512, 512) 3.8758834201794343 4.1151123 0.07539029460337274\n",
      "512 512\n",
      "512 512 (512, 512) 2.2345614890607224 6.928325 0.07883965691243294\n",
      "512 512\n",
      "512 512 (512, 512) 3.202318400881362 4.291187 0.0716379436702485\n",
      "512 512\n",
      "512 512 (512, 512) 2.886601316522584 3.3769126 0.07947003485385556\n",
      "512 512\n",
      "512 512 (512, 512) 2.99332469375034 4.0992336 0.0726039100280117\n",
      "512 512\n",
      "512 512 (512, 512) 2.9316354735511987 3.5009003 0.07331764675014818\n",
      "512 512\n",
      "512 512 (512, 512) 3.717479114758237 7.219969 0.039757802932680886\n",
      "512 512\n",
      "512 512 (512, 512) 3.654137402866977 9.933048 0.04704426218614155\n",
      "512 512\n",
      "512 512 (512, 512) 3.738463946042499 7.9021263 0.03906618483555874\n",
      "512 512\n",
      "512 512 (512, 512) 3.5153681816708193 8.617064 0.02941176470588236\n",
      "512 512\n",
      "512 512 (512, 512) 2.7753493967200598 11.887598 0.0553579802685219\n",
      "512 512\n",
      "512 512 (512, 512) 3.4376685122647532 8.740241 0.03492494441390337\n",
      "512 512\n",
      "512 512 (512, 512) 3.7856459656595094 7.015336 0.03172588384241744\n",
      "512 512\n",
      "512 512 (512, 512) 3.409722203594513 9.44295 0.044012325882756165\n",
      "512 512\n",
      "512 512 (512, 512) 3.6552996700656064 7.094127 0.03151366442008108\n",
      "4096 25088\n"
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      "64 64\n",
      "64 64 (64, 64) 1.9985712884332631 1.8433783 0.18598422179219143\n",
      "64 64\n",
      "64 64 (64, 64) 1.5227655339759387 2.8955903 0.15918360530739062\n",
      "64 64\n",
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      "64 64\n",
      "64 64 (64, 64) 1.4775761922756745 2.806978 0.1607357277400564\n",
      "64 64\n",
      "64 64 (64, 64) 1.5488979444861908 3.6493485 0.14938154760902123\n",
      "64 64\n",
      "64 64 (64, 64) 1.5522514471998385 2.5130134 0.1676523014457032\n",
      "64 64\n",
      "64 64 (64, 64) 1.4229916653090868 1.9675564 0.19553246299845828\n",
      "64 64\n",
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      "64 64\n",
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      "128 64\n",
      "64 128 (64, 64) 1.8107390944974115 4.111668 0.14500306011210584\n",
      "128 64\n",
      "64 128 (64, 64) 1.7729934951098707 5.8248873 0.14534382943605173\n",
      "128 64\n",
      "64 128 (64, 64) 1.8114717938224976 4.1783004 0.15762427369838505\n",
      "128 64\n",
      "64 128 (64, 64) 1.780424518798032 4.903387 0.15575138431642704\n",
      "128 64\n",
      "64 128 (64, 64) 1.7223669763223055 8.304812 0.14315039990089018\n",
      "128 64\n",
      "64 128 (64, 64) 1.7330243641616834 5.0326734 0.14202296160749794\n",
      "128 64\n",
      "64 128 (64, 64) 1.8129091950080776 5.5952535 0.13809799434280756\n",
      "128 64\n",
      "64 128 (64, 64) 1.7591481643265667 5.3180976 0.1393480718288136\n",
      "128 64\n",
      "64 128 (64, 64) 1.8891459748320187 4.089856 0.1665013053940465\n",
      "128 128\n",
      "128 128 (128, 128) 1.8570223420975212 1.693869 0.15544385422725138\n",
      "128 128\n",
      "128 128 (128, 128) 1.9010925354345887 2.068852 0.1509024032914092\n",
      "128 128\n",
      "128 128 (128, 128) 3.653603573349746 1.9483969 0.1535131672894195\n",
      "128 128\n",
      "128 128 (128, 128) 1.7262486218808317 1.7554779 0.17243250239171626\n",
      "128 128\n",
      "128 128 (128, 128) 4.822064420126715 2.9500155 0.14172951445724258\n",
      "128 128\n",
      "128 128 (128, 128) 2.0045949525880253 1.9631392 0.16553385785598068\n",
      "128 128\n",
      "128 128 (128, 128) 1.9531349326132257 1.823063 0.15664835805515098\n",
      "128 128\n",
      "128 128 (128, 128) 1.9591051354884952 1.6766865 0.16397833625466707\n",
      "128 128\n",
      "128 128 (128, 128) 1.8342965663525972 1.7876014 0.16355886793901908\n",
      "256 128\n",
      "128 256 (128, 128) 2.515625481318409 3.9283516 0.10143100447604148\n",
      "256 128\n",
      "128 256 (128, 128) 2.4514525727993624 5.188679 0.11681627597714539\n",
      "256 128\n",
      "128 256 (128, 128) 3.0291397612711553 3.693216 0.12958638437700665\n",
      "256 128\n",
      "128 256 (128, 128) 2.8392641176399227 5.387222 0.10860286951991505\n",
      "256 128\n",
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    {
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      "4096 25088\n"
     ]
    }
   ],
   "source": [
    "\n",
    "alphas, norms, lmaxs = {}, {}, {}\n",
    "\n",
    "\n",
    "model_name = 'vgg11'\n",
    "model = models.vgg11(pretrained=True)\n",
    "alphas[model_name], norms[model_name], lmaxs[model_name]  =  calc_model_alphas(model)\n",
    "\n",
    "\n",
    "model_name = 'vgg13'\n",
    "model = models.vgg13(pretrained=True)\n",
    "alphas[model_name], norms[model_name], lmaxs[model_name]  =  calc_model_alphas(model)\n",
    "\n",
    "\n",
    "model_name = 'vgg16'\n",
    "model = models.vgg16(pretrained=True)\n",
    "alphas[model_name], norms[model_name], lmaxs[model_name]  =  calc_model_alphas(model)\n",
    "\n",
    "model_name = 'vgg19'\n",
    "model = models.vgg19(pretrained=True)\n",
    "alphas[model_name], norms[model_name], lmaxs[model_name] =  calc_model_alphas(model)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-14T03:15:50.917054Z",
     "start_time": "2018-11-14T03:14:47.767275Z"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "351bae4d859b41eaaae6ba9f04d4ffb0",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=1, bar_style='info', max=1), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "128 64\n",
      "64 128 (64, 64) 1.6496955282104455 3.4403384 0.2062696035013719\n",
      "128 64\n",
      "64 128 (64, 64) 1.5135117597221512 (5.114818+0j) 0.23009822969000904\n",
      "128 64\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/charleshmartin/anaconda3/lib/python3.6/site-packages/powerlaw.py:700: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  (Theoretical_CDF * (1 - Theoretical_CDF))\n",
      "/Users/charleshmartin/anaconda3/lib/python3.6/site-packages/powerlaw.py:700: RuntimeWarning: invalid value encountered in true_divide\n",
      "  (Theoretical_CDF * (1 - Theoretical_CDF))\n",
      "/Users/charleshmartin/anaconda3/lib/python3.6/site-packages/numpy/core/numeric.py:501: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return array(a, dtype, copy=False, order=order)\n",
      "/Users/charleshmartin/anaconda3/lib/python3.6/site-packages/powerlaw.py:104: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  self.xmax = float(self.xmax)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "64 128 (64, 64) 1.6653278881632256 3.427748 0.2209022207924561\n",
      "128 64\n",
      "64 128 (64, 64) 1.7353058922987887 5.5120263 0.22664930575535136\n",
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      "128 256 (128, 128) 2.024799553284514 3.9635642 0.11699078524667839\n",
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      "128 256 (128, 128) 2.1390733242753215 4.396853 0.10477085371029193\n",
      "256 256\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/charleshmartin/anaconda3/lib/python3.6/site-packages/powerlaw.py:1160: RuntimeWarning: invalid value encountered in log\n",
      "  return 1 + len(data)/sum(log(data / (self.xmin)))\n",
      "/Users/charleshmartin/anaconda3/lib/python3.6/site-packages/powerlaw.py:701: RuntimeWarning: overflow encountered in double_scalars\n",
      "  )[1:]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "256 256 (256, 256) 2.109953041505934 1.496708 0.14019921668944613\n",
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     ]
    },
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       "HBox(children=(IntProgress(value=1, bar_style='info', max=1), HTML(value='')))"
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     "text": [
      "64 64\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "512 512 (512, 512) 3.6033645446466744 8.161789 0.03748275102126153\n",
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      "4096 25088\n"
     ]
    }
   ],
   "source": [
    "\n",
    "alphas, norms, lmaxs = {}, {}, {}\n",
    "\n",
    "\n",
    "   \n",
    "model_name = 'vgg11_bn'\n",
    "model = models.vgg11_bn(pretrained=True)\n",
    "alphas[model_name], norms[model_name], lmaxs[model_name] =  calc_model_alphas(model)\n",
    "\n",
    "\n",
    "\n",
    "model_name = 'vgg13_bn'\n",
    "model = models.vgg13_bn(pretrained=True)\n",
    "alphas[model_name], norms[model_name], lmaxs[model_name] =  calc_model_alphas(model)\n",
    "\n",
    "\n",
    "model_name = 'vgg16_bn'\n",
    "model = models.vgg16_bn(pretrained=True)\n",
    "alphas[model_name], norms[model_name], lmaxs[model_name] =  calc_model_alphas(model)\n",
    "\n",
    "\n",
    "model_name = 'vgg19_bn'\n",
    "model = models.vgg19_bn(pretrained=True)\n",
    "alphas[model_name], norms[model_name], lmaxs[model_name] =  calc_model_alphas(model)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rcParams['figure.figsize'] = [4,4]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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2RxF6wLxMqGFeRPhSLSHJdGQ8TmGk688qlOeDyWfhWUJNcYiQi/0KI0dpVnrtTyAMylmZvMfPEFIMR6dsu6T0tS5Tvq0JA2t+n5Tvt8DHknUnEWp0y2r4DFf6rOR+PhnHL/c5zv19KHoNvk2oVBVGjx7Jpn7zH07ZZ3dK+iETOgI4Jd/R5LUYNXqXfP2ajyj63KaVY9ui9amjQqt8vM8Bz1T7frt7bYFaN92aeSM0GDlwWLvLolvT3uMfJ+/xninr0gL1OMIvrFkl295KymCtPIGzwc8nT6D+AaFL5otFt2/nOb7mo5aoJF3O/pqQyriuzcWROpnZ61OW7U+Y9fE3bEo/luVhaod7KOq5ZWEWu30JA0jGgmmEX1j7FN1Oz7Njra2/Ig2VfHlnEHon7Ayc4O4b2looaYQfJo2pdxJyvnuwKTf9pUIVFDb2iJnEpqmL9zSzfuBhd3+R0Bf/+2Z2N2F06z8S2qh+0aonU6uk8XUqYdxD1aMaFaglFu8jdFt7hjCqrt6GG4nDlYTc7BGEnO9aQkPiPHcvvcjIYYwck1H4RTUTWOLul1i4Gsq5hMbFW4BDPP/kbO00hdDg+utadtY1E0Wk45jZbGAfdz89mcNjBqGhe03ZHZv0eGZ2LKHysY3X0OtGgVpEpMnM7JvAdHcfNdAn1/4K1CIicVOvDxGRyClQi4hEToFaRCRyCtQiIpFToBYRiZwCtYhI5BSoRUQip0AtIhI5BWoRkcgpUIuIRE6BWkQkcgrUIiKRU6AWEYmcArWISOQUqEVEIqdALSISOQVqEZHIKVCLiEROgVpEJHIK1CIikVOgFhGJnAK1iEjkFKhFRCK3ebsLEKsdd9zRJ0+e3O5iiHSdu+6661l3n9DucsREgTrD5MmTGRwcbHcxRLqOma1sdxlio9SHiEjkFKhFRCKnQC0iEjkFahGRyClQi4hEToFaRCRy6p4nIk2zcNkQZ9+wgifXDLNLfx9zZ01h9rSJ7S7WmKNALSJNsXDZECdffR/D6zcAMLRmmJOvvg9AwbpKSn2ISFOcfcOKjUG6YHj9Bs6+YUWbSjR2KVCLSFM8uWa4quWSTYFaRJpil/6+qpZLNgVqEWmKubOm0NfbM2JZX28Pc2dNaVOJxi41JsqYp54FcSq8B3pv6qdALS1TT0DN2jfWngU6eQSzp03syufdaArU0hL1BNRy+5brWdCuABHryUPGLgVqaYl6Amq5ffP0LCjUbofWDNNjxgZ3JjaxlhvjyUPGNgVqaYl6umqV23eX/j6GUtYXehaU1m43uAObarmDK1ez+MFVDU1RqFuaNJp6fUhL1NNVq398b/oKgzUvvzJqcXHPgrTabcHw+g1cuvQxhtYM42wK3guXDVUsUznqliaNpkAtLVFrV61jf3g7z728PnWdO7z0ysgg3N/Xy7zDpwIwff6i1Nr2iGOU/N+IkXPqliaNNqZSH2b2c2AWcJa7n1ph29LvYME0d7+n4YWTsmrpqnXqwvu47ZHVNT1ecbqjWk+uGa6r14a6pUmjmXtWPIuLmX0U+BawM/kD9UXA+SWr7nX3lys93sDAgOvitu31ppOv35hTrsbEjLx1XtuN7+WP618bEej7enuYd/hUBdsWMLO73H2g3eWIyZioUZtZP3AucCJwWRW7Drn70uaUShqpuAbbP76Xdes31BSkoXyjXaHXhzE67QEhILujXhsSlTERqIFvAMvd/XIzqyZQS8SKu80Vy8pJ57Hd+F7Gb7F5ao260CXvK1f+OvMkMLx+Q2bKRL02pF2iD9Rmtj/wCWDvGnY/wczmAhuApcBp7n5LI8snI5XmdmfuMYHr7n1qVPAd37sZ619z1m9oXOptM4PTDt0LGJ2j7uvtYeYeEzj56vtqrqmr14a0S9SB2sx6CTnmb7p7tU3xC4D/Ap4EdgXmAovM7C/dfUlDCypA+oi8BUsfS9325fWvNfSx+/t6Of2wvUakJkob88p11aukHb02NAxdCqJuTDSzU4FPA3u5+3CyzMnRmJhyrK2B+4HH3X3/jG2OB44HmDRp0ttWrlxZT/G7Tp7ucM1gwKPzD6643eSTrqvp2K0OkguXDfH1a5eP+hXSjAbNUxfex+V3PM4Gd3rM+Og73sCZs6c27Pi1UGPiaNHWqM1sEnAK8FlgnJmNK1o9LmlgfMHdc1WR3P0FM7sO+EyZbS4ALoDQ66PmwnepduVw86QkFi4bymxAzNJjxiPzDqq5XLUo/VVSrFENmlltAxvcWbD0MX569xBnfVg9XGIS84CXNwJbElIYzxXdAOYkf1d76q/2uypVaGYOt2cz481/8rpRy/OmJM6+YUXqG29l9qk1l12PSumZek+GhRNBuV8+L72yoSEjNKVxYg7U9wAzU24QgvdM4OG8BzOzbYCDgTsaW0wpSBuRV85mFnppQKi9QuiZ8bH9JtHft2nY+HbjeznnyL258cszOO/ofZjY34cl2+ZJBSxcNpQZmDw5Tpqs5c1UKRDXezLMm6fXtQ3jEm3qw93XAEtKl1v4Qq8sNAia2a7AI8AZ7n5GsmwOMAVYzKbGxDmEwTLHNr/03SltRF5Wr4/txvdy2qF7ZQbZrDxptfMbF2qQWQpd9tJ6ibRjyHfWJFPQmDJVUyNXd8R4RBuoq2BADyN/HawAPpzctgWeB24DPuPud7a8hF0kLZC2s3GqXA2yEPhiGvKddtKA9F4ttSh3IkjbVuIw5gK1u1vJ/7+jJNXo7tcC17awWBKpcrXC4rRJLFciafZJI+tEUEqTSMVlzAVqkWpk1SAn9vdFEZjTNPOkkXUiSFsW6+vTjRSopaPFlH+ORdaJQIE5XgrU0tFiyj+L1EqBWjpeLPlnkVrF3I9aRERQoBYRiZ4CtYhI5BSoRUQip8ZEaSjNoSzSeArUUpfSax2++MdXWf9amHVuaM3wxnk2mh2sdYKQTqZA3QWaFcRK505Ou9ZhKy4Km3ZlmVadIERaQTnqDlc8/7CzKYg1Yq7hvFNmNnsWtrRyaJpO6SQK1B2umUEsbwBu9ixsWeXQNJ3SKRSoO1wzg1ieANyKeTWyyqFpOqVTKEfd4bJmj8sKYqX57Jl7TGDxg6tS89tpEx719hiv22Jz1g6vb1mjniZekk6nQN3hqgliaY1yC5Y+tnF9Ib89uHL1xuDdP76XcZtvNiIww6ZJkAoplmYGa028JJ3OvA0X8BwLBgYGfHBwsN3FaIi8vT6mz1+U6+ofpVcI7uvt2TgJf9pVtIvXi1RiZne5+0C7yxET1ai7QN7Z4/LmrUtP7cVd8Mo1XipQi9RGjYmyUT2Nb4Ugrx4YIo2nQC0bzZ01hb7enrLbWMbyQpBXDwyRxlOglo1mT5vIvMOnMrG/DyNcV/Bj+00a8f+x+00aFcyLGyfTgr16YIjURzlqGSFPPntg1+0zGyfVA0Ok8dTrI0Mn9foQGUvU62M0pT5ERCKnQC0iEjkFahGRyClQi4hEToFaRCRy6p4nEgldTkyyKFCLRECXE5NyxlTqw8x+bmZuZmfm2HZLMzvbzJ4ys2Ezu93M3tOKcopUS5cTk3LGTKA2s48Ce1exy4XAXwP/ABwCPAXcYGb7NKF4InXRZFZSzphIfZhZP3AucCJwWY7t9waOAT7t7j9Klt0MLAfOAA5rXmk7i/KmrVHtlXiku4yVGvU3gOXufnnO7Q8D1gNXFBa4+6vAT4BZZjau8UXsPM28grmMpMmspJzoA7WZ7Q98AvhCFbvtBTzq7i+XLF8ObAHs3qDidTTlTVsnbeZCXRVHCqJOfZhZL3A+8E13ryY6bA88l7J8ddF6qUB509bKeyUe6T6x16i/CvQBZ1W5X+ll/YqXZ+9kdryZDZrZ4KpVq6p8yM6jiwCIxCHaQG1mk4BTgP8LjDOz/qRRkaL/sy5Hspr0WvN2RetHcfcL3H3A3QcmTJhQT/E7gvKmInGINlADbwS2BBYQ0hiFG8Cc5O+pGfsuB3Yzs/Ely/cEXgEebnhpO5DypiJxiDlHfQ8wM2X5YkLwvpDsgHsN8HXgSOBiADPbHDga+IW7r2t4aTuU8qYi7RdtoHb3NcCS0uVmBrDS3Zck/+8KPAKc4e5nJPveY2ZXAOclDZKPAicAuwHHtqL8MpL6Y4vULtpAXQUDehidxvkUoRHyTKAf+DXwAXe/u7XFi08zgma5Y6bNYzH3P37N169dzpqX1ytwi1Qw5gK1u1vJ/78jpTeHuw8DX05ukmjG5D+VjpnWH3v9a85zL69vWBlEOlnMjYnSBM0YxFLpmHn6XWsgjUg2Beou04xBLJWOmbfftQbSiKQbc6kPKa9S/rkRk/+UPsb4LXp46ZUNo7brH98LhP7YxamRLBpII5JOgbpDLFw2xNevXb4x7wvpud+0oGnAzD3yDfBJy0dn8WRsaOGxC8F9275eXnrlVdZv2DR4VANpRLIpUHeA0uBZrJD7LQTL2dMmMrhyNZcufWzjGHsHrrpriIFdt6/YmJeWj86yZnjTSaO0P7a664nkp0DdASoFz9Lc7+IHV42aCKU4oJcLotXkkY0QkNMCsAbSiOSnxsQOUCl4luZ+yzX+VZqDetu+3tzlclBPDpEGUKDuAOUa4dJyv+VmxavU1c7Kzj84mnpyiNRPgXqMWbhsiOnzF7HbSdcxff4iFi4bSp3lDqC/rzd1EqVys+JlBdahpLa9pqixMg/15BCpnwL1GJKVlgBGzXJ33tH7cM9p78/MD2fNilcusJ589X0bu9zloZ4cIo1h7mnz68vAwIAPDg62uxgjTJ+/KLU73MT+Pm476cCGPEa5HiQQaunrXn1tVPc+T9aZofk7pC5mdpe7D7S7HDFRr48xpBWXxioE1r+74p7U9WuH13Pu0fuoa51ICylQjyGNGFWYR2EipazHUtc6kdZSjnoMaeWlsXQZLpF4qEY9hpQOxW5m2qGVjyUi5akxMUOMjYki3UCNiaMp9SEiEjkFahGRyClQi4hEToFaRCRy6vXRIpp/eRO9FiLVUaBugWZc+XssynsVmkrHUJCXbqPURws048rfY03hZPVcyux7eV+LSnNli3QqBeoWaMUcHbGr9io0eY/RbSc86U4K1C1QbqL+blHtVWiqOUY3nfCkOylQt4Dmzaj+KjTVHKObTnjSnRSoW6DcRP3dotqr0OQ9Rred8KQ7qddHi3T71KCNmORJE0VJt9KkTBk0KZNIe2hSptGU+hARiVzUgdrMZpnZIjN72szWmdkTZnalme1ZYb/JZuYZt/5WlV9EpBFiz1FvD9wFfA9YBUwCTgKWmtlUd19ZYf95wDUly15oeClbJPZRebWUL/bnJBKDqAO1u18OXF68zMzuBB4EjgDOqXCI37r70iYVr6ViH4ZeS/lif04isYg69ZHhD8n96LHIHSz2UXm1lC/25yQSizERqM2sx8y2MLM3A+cDTwM/ybHrPDN71czWmtk1Zja1uSVtnthH5dVSvrSrnJdbLtKtxkSgBu4A1gEPAX8OHOjuz5TZfh0hoH8OmAnMAaYC/2tmb21yWZsi9lF5tZSvx6yq5SLdaqwE6o8D+wHHAM8DN5rZ5KyN3f0pd/+8u1/t7re4+w+B9wAOnJK1n5kdb2aDZja4atWqhj6BesU+Kq+W8m3I6MOftVykW42JQO3uD7j7HUnj4nuBrQi9P6o5xuPArcC+Zba5wN0H3H1gwoQJdZW50WIfhl5L+SZm1Lazlot0q6h7faRx9zVm9jCwew27G6FWPSbFPgy92vLNnTVlRK8PiOtXgkgsxlygNrOdgD2AS6vcbxIwHfhpM8o1VrWzH7Pm7hDJJ+pAbWY/Be4G7iXkpt8CnAi8StKH2swOAG4CPu3ulyTLziGkdW4nDJSZApwMvAb8U2ufRbxi6Mcc+68EkRjEnqNeCswGLgauA74M3Azs4+4PJdsY0MPI57Ic2J/Q8+NG4HTgNuAd7q5Ougn1YxYZG6KuUbv7PwP/XGGbJYRgXbzs34F/b17JOkPsfbNFJIi9Ri1NFHvfbBEJFKi7WOx9s0UkiDr1Ic2lXhciY4MCdZdTrwuR+Cn1ISISOQVqEZHIKVCLiEROgVpEJHIK1CIikVOvD2kIXaRWpHkUqBssT8DqtKCWNbnT4MrVLH5wVcOfZ6e9fiKVKFA3UJ4N9zELAAAKA0lEQVTZ6GKYsa7RsiZ3unTpYxsn/27U8+zE10+kEuWoGyjPbHSdOGNd1iROpVdoaMTz7MTXT6QSBeoGyjMbXSfOWFfNJE71Ps9OfP1EKlGgbqA8s9F14ox1aZM7ZV1HvN7n2Ymvn0glCtQNlGc2uk6csS7twrbH7jepKc+zE18/kUrUmNhAeWaj69QZ69ImdxrYdfuGP89Off1EyjH3MXtR7qYaGBjwwcHBdhdDpOuY2V3uPtDucsREqQ8Rkcgp9SHSQhqsI7VQoBZpEQ3WkVop9SHSIhqsI7VSjboO+hkr1dBgHamVAnWNWj0RkYx9u/T3MZQSlDVYRypR6qNG5SYiGlozjLMpeC9cNtSeQkpUNFhHaqVAXaNWTkQknSFtBOe8w6fqF5dUpNRHjfrH9/Lcy+tzbZv2c1e6U9oITpFKVKOuUTUDOnssa4oiEZHKFKhrtHY4X20aYIOG6YtIHRSoa1RNS/1EteqLSB2iDtRmNsvMFpnZ02a2zsyeMLMrzWzPHPtuZ2b/ZmbPmtlLZvZLM5vaqLKlteD3bmb09oxMc6hVX0TqFXWgBrYH7gL+Bng/cDKwF7DUzHbN2snMDLgG+ADwt8BHgF5gsZn9aSMKltaCf/Tb38AWPZteUgM+8jY1HolIfcbcNKdmNgV4EJjj7udkbPMhYCFwoLsvTpZtCzwKLHD3L1V6nGqnOV24bIi5//lr1m8Y+Xr2bmacfeTeCtYiOWma09Fir1Gn+UNyX6417zDgyUKQBnD3tcC1wIeaUaizb1gxKkgDrH/Nq+5HvXDZENPnL2K3k65j+vxFGjAj0uXGRKA2sx4z28LM3gycDzwN/KTMLnsB96csXw5MMrOtGl3Gcn2lq5nLoTA0XaMbRaRgTARq4A5gHfAQ8OeElMYzZbbfHnguZfnq5H67xhavfF/panqIaIY1ESk1VgL1x4H9gGOA54EbzWxyme2N0aO5C8uzdzI73swGzWxw1apVVRWwXF/panp9aIY1ESk1JgK1uz/g7ne4++XAe4GtgJPK7LKaUKsuVahJp9W2cfcL3H3A3QcmTJhQVRmz+kpvN763qobErNq3ZlgT6V5jIlAXc/c1wMPA7mU2W07IU5faE3jM3V9sdLmyZkY77dC0YlR/HPXFFuleYy5Qm9lOwB7AI2U2uwaYaGYHFO23DXBosq7hGjUzmmZYE5FSUfejNrOfAncD9xJy028BTgR2Bt7u7g8lwfgm4NPufkmy32bArcAbgLmEVMfJhIbIvd398UqPXW0/ahFpDPWjHi32aU6XAkcBXwG2AB4HlgDz3P13yTYG9FD068DdXzOzQ4BvAt8DtgRuB2bmCdIiIjGJukbdTqpRi7SHatSjjbkctYhIt1GgFhGJnAK1iEjkFKhFRCKnQC0iEjkFahGRyClQi4hEToFaRCRyCtQiIpFToBYRiZwCtYhI5BSoRUQip0AtIhI5BWoRkcjFPh+11GHhsiHOvmEFT64ZZpf+PubOmqIrxYiMQQrUHWrhsiFOvvo+htdvAGBozTAnX30fgIK1yBij1EeHOvuGFRuDdMHw+g2cfcOKNpVIRGqlQN2hnlwzXNVyEYmXAnWH2qW/r6rlIhIvBeoONXfWFPp6e0Ys6+vtYe6sKW0qkYjUSo2JHarQYKheHyJjnwJ1B5s9baICs0gHUOpDRCRyCtQiIpFToBYRiZwCtYhI5BSoRUQip14fTRD7ZEixl09ERlKgbrDYJ0OKvXwiMppSHw0W+2RIsZdPREaLNlCb2RFmdpWZrTSzYTNbYWbzzGzrHPt6xm2fZpc79smQYi+fiIwWc+pjDvAY8DXgCWAacDow08ze5e6vVdj/IuD8kmUPNbiMo+zS38dQStCLZTKk2MsnIqPFHKgPdfdVRf/fbGargYuBGcCiCvsPufvSZhUuy9xZU0bkgCGuyZBaXb5WNFyqcVQ6XbSBuiRIF/wquY/2Wxj7ZEitLF8rGi7VOCrdwNy93WXIzcw+D3wf2NfdB8ts58BqYCtgA7AUOM3db8n7WAMDAz44mPkQksP0+YtS0ywT+/u47aQDx8xjSGuZ2V3uPtDucsQk2sbEUmY2ETgD+GW5IJ1YAHwBeB9wPLADsMjMZjS1kDJCKxou1Tgq3SDa1EcxM9sK+BnwKvCpStu7+8eL/r3FzH4G3A+cCexf5nGOJwR2Jk2aVE+RhXwNl/Xml9U4Kt0g+hq1mW0JXAO8EZjl7k9Uewx3fwG4Dti3wnYXuPuAuw9MmDChpvLKJpWuMlPILw+tGcbZlF9euGyoYY8h0gmiDtRm1gtcBbwdOMjd76vncMDYSch3gNnTJjLv8KlM7O/DCHnjeYdPHdGgWe/gm0qPIdIJok19mNlmwKXAe4GD6+lqZ2bbAAcDdzSoeJJTuavMNCq/rCvZSKeLNlAD/wocCZwFvGRm+xWte8LdnzCzXYFHgDPc/QwAM5sDTAEWA08CuxIGz+wMHNvC8ksFyi+L5BNz6uODyf0pwO0lt88m6wzoYeTzWAHsCfwLcCPwLeBRYP9quudJ4yxcNsT0+YvY7aTrmD5/0cYctPLLIvlEW6N298k5tvkdIVgXL7sWuLY5pZJq5RmQEuvgIJFYRBuopTOUazAs5JYVmEXKizn1IR1AA1JE6qdALU2V1TCoBkOR/BSopanUYChSP+WopanUYChSPwVqaTo1GIrUR6kPEZHIKVCLiEROgVpEJHIK1CIikVOgFhGJnAK1iEjkxtTFbVvJzFYBK9tcjB2BZ9tchm6n96D1dnV3XWKpiAJ1xMxsUFdjbi+9BxIDpT5ERCKnQC0iEjkF6rhd0O4CiN4DaT/lqEVEIqcatYhI5BSoI2JmR5jZVWa20syGzWyFmc0zs63bXbZuZmY/NzM3szPbXRbpTgrUcZkDbAC+BnwA+D5wAnCjmem9agMz+yiwd7vLId1N81HH5VB3X1X0/81mthq4GJgBLGpLqbqUmfUD5wInApe1uTjSxVRLi0hJkC74VXKvmfdb7xvAcne/vN0Fke6mGnX8DkjuH2hrKbqMme0PfAKlPSQCqlFHzMwmAmcAv3T3wXaXp1uYWS9wPvBNd1/R7vKIKFBHysy2An4GvAp8qs3F6TZfBfqAs9pdEBFQ6iNKZrYlcA3wRuAAd3+izUXqGmY2CTgF+CwwzszGFa0elzQwvuDuG9pSQOlKGpkYmeRn90JCbvp97r60zUXqKmY2A1hcYbNp7n5PC4ojAqhGHZWkr/SlwHuBgxWk2+IeYGbK8sXAAuBC4OGWlki6ngJ1XP4VOJKQG33JzPYrWveEUiDN5+5rgCWly80MYKW7j1on0mxqTIzLB5P7U4DbS26fbVehRKS9lKMWEYmcatQiIpFToBYRiZwCtYhI5BSoRUQip0AtIhI5BWoRkcgpUIuIRE6BWkQkcgrUIiKR+/9MYOQ58mIg9wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for model_name in alphas.keys():\n",
    "    x = alphas[model_name]\n",
    "    y =  2.0*np.log10(norms[model_name]) \n",
    "    plt.scatter(x,y,label=model_name )\n",
    "\n",
    "    plt.title(r\"VGG Conv2D Layers: $\\alpha$ vs $\\log_{10}\\Vert W\\Vert^{2}_{F}$\"+\"\\n\")\n",
    "    #plt.ylim(0,20)\n",
    "    plt.show()\n",
    "#plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 5.929604 +0.j  4.6931195+0.j  5.971523 +0.j  4.520993 +0.j\n",
      "  3.7068458+0.j  5.152868 +0.j  5.6546535+0.j  4.508826 +0.j\n",
      "  5.8888655+0.j  5.864708 +0.j  5.811292 +0.j  5.654266 +0.j\n",
      "  5.931505 +0.j  4.5487785+0.j  6.205372 +0.j  6.146463 +0.j\n",
      "  5.8557544+0.j  5.7229996+0.j 22.680511 +0.j 14.188918 +0.j\n",
      " 21.368351 +0.j 16.43204  +0.j  8.095457 +0.j 15.961493 +0.j\n",
      " 29.2464   +0.j 15.5990715+0.j 26.343027 +0.j  7.122927 +0.j\n",
      "  6.8792253+0.j  7.0196824+0.j  6.592838 +0.j  5.5063   +0.j\n",
      "  6.379893 +0.j  7.5649467+0.j  7.083263 +0.j  7.529225 +0.j\n",
      "  8.285846 +0.j  7.3490825+0.j  8.735851 +0.j  7.491218 +0.j\n",
      "  5.8857427+0.j  7.726602 +0.j  8.777016 +0.j  7.4794483+0.j\n",
      "  8.888229 +0.j  7.9346733+0.j  7.5858073+0.j  7.7440257+0.j\n",
      "  7.8949723+0.j  6.1741796+0.j  7.913988 +0.j  8.660063 +0.j\n",
      "  8.261002 +0.j  8.50092  +0.j  9.261727 +0.j  4.895664 +0.j\n",
      "  8.321861 +0.j  5.8720655+0.j  3.5274198+0.j  8.208531 +0.j\n",
      "  8.39288  +0.j  6.869202 +0.j  8.326038 +0.j]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/charleshmartin/anaconda3/lib/python3.6/site-packages/numpy/core/numeric.py:553: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return array(a, dtype, copy=False, order=order, subok=True)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[26.999765 +0.j  8.63951  +0.j 40.07446  +0.j 12.935834 +0.j\n",
      "  6.343679 +0.j  9.757742 +0.j 10.38117  +0.j 94.15326  +0.j\n",
      "  4.083693 +0.j  4.4038105+0.j  4.400308 +0.j  5.0933814+0.j\n",
      "  4.4070215+0.j  4.7217836+0.j  4.7724915+0.j  5.0028596+0.j\n",
      "  4.400046 +0.j 31.55798  +0.j 21.63236  +0.j 38.642826 +0.j\n",
      " 24.111395 +0.j 11.008227 +0.j 16.212646 +0.j 28.368654 +0.j\n",
      " 20.369219 +0.j 25.53473  +0.j  9.2299595+0.j  6.5657864+0.j\n",
      "  9.986277 +0.j  6.3942847+0.j  5.6218057+0.j  6.089336 +0.j\n",
      "  9.114944 +0.j  6.7018228+0.j  8.614622 +0.j 16.555817 +0.j\n",
      " 16.313128 +0.j 19.120626 +0.j 17.58926  +0.j  7.9236703+0.j\n",
      " 17.004587 +0.j 19.832993 +0.j 18.091106 +0.j 22.393139 +0.j\n",
      "  7.5819683+0.j  7.740692 +0.j  7.7835355+0.j  7.0996566+0.j\n",
      "  6.226126 +0.j  7.176657 +0.j  8.493855 +0.j  7.942962 +0.j\n",
      "  8.524557 +0.j  8.7949095+0.j  7.6420197+0.j  8.73871  +0.j\n",
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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  90.9553   +0.j    8.92251  +0.j   18.936579 +0.j   12.00307  +0.j\n",
      "    5.556061 +0.j    8.989115 +0.j    9.976247 +0.j    4.9567256+0.j\n",
      "    5.060269 +0.j    5.2233777+0.j    5.801559 +0.j    4.5106144+0.j\n",
      "    5.1466517+0.j    5.4149237+0.j    5.234576 +0.j    4.868527 +0.j\n",
      "   45.79294  +0.j   33.630733 +0.j   16.501362 +0.j   35.279865 +0.j\n",
      "   45.209614 +0.j  278.75433  +0.j   13.1891165+0.j    9.81904  +0.j\n",
      "   13.342287 +0.j    9.864887 +0.j    6.3683043+0.j    8.967791 +0.j\n",
      "   14.185524 +0.j    8.566534 +0.j   11.655867 +0.j  219.0846   +0.j\n",
      "   32.22936  +0.j 2804.1206   +0.j   22.595789 +0.j    7.6592684+0.j\n",
      "   25.595993 +0.j   29.416492 +0.j   71.07337  +0.j   29.27272  +0.j\n",
      "   69.051254 +0.j   41.316757 +0.j   11.1143875+0.j   26.25171  +0.j\n",
      "  218.47015  +0.j   49.1719   +0.j   67.66546  +0.j   11.245664 +0.j\n",
      "    9.966351 +0.j   11.492646 +0.j    9.008379 +0.j    8.068989 +0.j\n",
      "    8.856658 +0.j   11.552903 +0.j   10.024817 +0.j   11.631588 +0.j\n",
      "   14.7395935+0.j   13.4477   +0.j   14.542932 +0.j   12.824824 +0.j\n",
      "    7.3835106+0.j   12.703101 +0.j   16.79593  +0.j   14.401475 +0.j\n",
      "   16.053974 +0.j    8.747923 +0.j    8.108187 +0.j    8.905415 +0.j\n",
      "    8.752587 +0.j    6.8797264+0.j    8.91534  +0.j    9.048332 +0.j\n",
      "    8.736622 +0.j    9.228805 +0.j   12.498675 +0.j   19.98726  +0.j\n",
      "   13.232099 +0.j   21.057457 +0.j   10.576037 +0.j   22.530602 +0.j\n",
      "   14.702359 +0.j   29.933882 +0.j   14.394131 +0.j    6.758814 +0.j\n",
      "    7.0023313+0.j    6.6946425+0.j    7.2842283+0.j    7.59764  +0.j\n",
      "    7.2333474+0.j    6.983514 +0.j    7.314985 +0.j    7.0367403+0.j\n",
      "   13.718214 +0.j    8.779647 +0.j   13.603208 +0.j    5.162655 +0.j\n",
      "    4.3511157+0.j    5.124646 +0.j   12.662589 +0.j    9.37224  +0.j\n",
      "   13.099779 +0.j]\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 12.658638 +0.j   9.81783  +0.j   5.5831184+0.j  13.33723  +0.j\n",
      "  12.858327 +0.j   6.9511867+0.j   4.6540656+0.j   6.6249123+0.j\n",
      "   5.169563 +0.j   4.2515   +0.j   5.2052054+0.j   6.255904 +0.j\n",
      "   4.911939 +0.j   5.5400157+0.j  33.809654 +0.j  34.07222  +0.j\n",
      "  12.132316 +0.j  25.079962 +0.j  42.841972 +0.j  27.54047  +0.j\n",
      "  14.266405 +0.j  18.096752 +0.j  14.284351 +0.j   6.1166573+0.j\n",
      "  13.923773 +0.j  34.032658 +0.j  12.535436 +0.j  18.940096 +0.j\n",
      " 865.91455  +0.j   8.849391 +0.j 104.70388  +0.j  66.210335 +0.j\n",
      " 104.67729  +0.j 211.24841  +0.j  10.090178 +0.j  83.56945  +0.j\n",
      "  95.77449  +0.j  47.268833 +0.j  13.956962 +0.j  48.702297 +0.j\n",
      "  85.82841  +0.j  18.759235 +0.j  11.0007105+0.j  20.927753 +0.j\n",
      "   9.3631935+0.j   9.025997 +0.j   9.441727 +0.j  21.151669 +0.j\n",
      "  11.502442 +0.j  21.428452 +0.j  35.85581  +0.j  22.1313   +0.j\n",
      "  36.16875  +0.j  17.90934  +0.j   8.885736 +0.j  17.826483 +0.j\n",
      "  32.696934 +0.j  22.532017 +0.j  36.969406 +0.j  20.415035 +0.j\n",
      "  14.15898  +0.j  22.850653 +0.j  15.749638 +0.j   9.358475 +0.j\n",
      "  15.640633 +0.j  22.974789 +0.j  15.289107 +0.j  22.643475 +0.j\n",
      "  10.533554 +0.j   9.925884 +0.j  10.595342 +0.j  10.538097 +0.j\n",
      "   7.4217234+0.j  10.876589 +0.j  10.531925 +0.j  10.215228 +0.j\n",
      "  10.763882 +0.j  17.94534  +0.j  34.58332  +0.j  18.541079 +0.j\n",
      "  35.40919  +0.j  11.95336  +0.j  33.70481  +0.j  21.067524 +0.j\n",
      "  62.796658 +0.j  19.982492 +0.j  13.505162 +0.j  18.180378 +0.j\n",
      "  13.869509 +0.j  16.651606 +0.j  12.251287 +0.j  16.852842 +0.j\n",
      "  15.665264 +0.j  20.422596 +0.j  15.814443 +0.j   6.7042117+0.j\n",
      "   7.84006  +0.j   6.7604737+0.j   7.4015594+0.j   9.552985 +0.j\n",
      "   7.596407 +0.j   6.783977 +0.j   7.811853 +0.j   6.909615 +0.j\n",
      "  11.222551 +0.j   6.0677176+0.j  15.934676 +0.j   8.209865 +0.j\n",
      "   4.8748236+0.j  12.278732 +0.j  10.48976  +0.j   5.68557  +0.j\n",
      "  16.015919 +0.j]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for model_name in alphas.keys():\n",
    "    x = alphas[model_name]\n",
    "    y = np.divide( 2.0*np.log10(norms[model_name]) , np.log10(lmaxs[model_name]) )\n",
    "    print(y)\n",
    "    plt.scatter(x,y,label=model_name )\n",
    "\n",
    "    plt.title(model_name+r\" Conv2D Layers: $\\alpha$ vs $\\frac{\\log_{10}\\Vert W\\Vert^{2}_{F}}{\\log_{10}\\lambda_{max}}$\"+\"\\n\")\n",
    "    plt.xlabel(r\"$\\alpha$\")\n",
    "    plt.show()\n",
    "#plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/charleshmartin/anaconda3/lib/python3.6/site-packages/numpy/core/numeric.py:553: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return array(a, dtype, copy=False, order=order, subok=True)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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TqLSQbxzwtMdu9e7eSyilfdDMxiTytpqZ/YhQozLdY5OJu79OaFP/UPzu5tJ3Er57GwOPlfMdsDCTyo6EEzjxOEsI4z53LrLdXoTOg+e5++2JbRcRLmrTSprbE74TXyL0DP4k4aLqBsKQg8mEav/TclWeZrYm4ff5OULHre8TJvLYLu7zf1nZLm6E33ofoadpFiV/szEfmb9bZSj3vJTrD/CD5JCN2ITy8XIPXulnX0KuGvY4Qkn37Lz1uZLmMYQLrJ96mZMZ5MTv/RhCTcG7E4/JWbavpCh9MXAaK3sapZ3Ucv6DlVeDj5rZHOCvwD8JP9SdCbPYvEAY+D3Y7Yo5gfBhHEOYPu4mwokHwmwre5Fop4hy45j2A+aZ2R8Jg8MPIfTo/Ky7D7Z6FkInq58S2jxWJ71q9vuE6aR6CT2LT0rpBDPDV509aRtbOdnzcEIV0a6E0vdbwLe8/NmAPmBmMwqsu9FDD9WfEk4mt8cOEO8Q3uMOQk/JHdI2dvcXzez3hCqvd1jZszOZ5g9mNo3wmT5mZrMIV54jCSfInQm9G5/K+HquBt4ws9sI7a0jgH0JP6TTfGCP0ksI1Zl7EK7gU7l7v5ldQejpeJuZXUuoxtoFOJ4wm9VUM1vP3Qt2BjKzdYAtgWvzVp1I+N7cYWZXE6rHJhOCzqWs7EWcczbhwvHO+Hm8Tfiu9xCusu8vlIcCNiTUfOS3ib1EgYuBeLL6BeGzOiElyYPA3mb2HndPViVvH/P5GXfvi/t6nNC55bj4/8vx9W1E6CTzT0L1Yc4MMzuB8L1fED+f0wiTTmxCaEvd1Vd2cCwly28WyvtuZVXueekiQq/vg4HNzeyWePxDCCXNfSkveJf92WeQq56dANzmYSL1pNcS698kXHxWaiwh/3/ylD4BJWUpjqYUf68n/ND+mjH9hwjB9e/xBb9F+BFcT7gyWrua25XIy0TCl+5JwpVlH6Eq8XxgXEr6DsJwjgWEoN1L6MW4e0raSVRQPRvXXxPX95EYi5Rf5VDiMSmRfnTK+qXx/buJMD7uPWW+d2n7zH/8VyL9wYSexEsJJa8ZhB/VHApUz8btcjNM/a5Efj4RvwsvE4JAD6G96NsMnB2p1Ht/DGEChqfjZ/wSYQzYKrPjUN44zXUIkyj8I+bvCeBzcd3xhKvreSX2sVuhvBM65N3Dyhlh5gCHFtjPaoSqqufja1xA6LG6X9z/MQW2S62iI3Sqc/J+M/F7nDqLFeFCwYH9C6yfHtd/Im/5jcAZect6gf0S/48jXGStGf/fkjCLzCPxfX6DEBh2TmyzOiGALwK2KOe3kOU3W+53q8D2qd9dyjgvJb6L5xIKGrnZsz7NyvHR/68Wnz3Zq2cPYuU5JC0v6yXWp87IlPWYhKr5l8r9vFdsX+mGeuhRqwehhODAAY3OS6s/CFX0/cDGBdYXOnEOj0Fqct7y28gwUUaZeXyRxIQMrLx4e1di2eGEcawQSlGvEqr4JxH6SRwYg+baiW0OI1yIv0JiMoB2ehDalx3YthaffdagWeXXVCpo/oLQBv1G4nFu1v3rfprSVGL3/S8TSgDXNzg7LcHM1rBwQ4LksmFm9p+EYHKeuxcawpDKwyQL80n0SLdwx4mdCB1qqsLMRhJqJ5LDdnYAXvCBw2e2T6Q5gDBP6ZfdfY6HfhKTCe22b8T9TiTULu1HKGl+s1p5bkYWxvrmL9uNcJekv7Oyqaqken32NTSOUAO0Y+JxctaNK+0eLFJV8Qc8idDBYxNCdeGyhmaqdewAzIltX08Qet9+mFACm0PoQzBADLKjCL2AAbY1sy4SgYcw9vY8M7ufMMvTDwh9DG6sct7fYGDfhR1YdY7c7VnZMeVVYBMLd0LqIQzvOJQ4OYSFm3jPBL7p7jeZ2Q+Bc83sJx46WbWiC2OHtHsI7YPbsLIt8xu5Yhk01WdfdbHj1FjC+PZyZxICyh+nKVIrexF+eFsSZlAZTEO/DPQmIaDsRihRfYbQBvY1YG9Pv4/gAYR2r1wHpOvj/yumgXT3SwgTSvyYMARhbUI7Y1k3DihhLKHvhCeW7cCqsxclS5rXEO6t+DvCSfwVQrCYH3vXXg/8r7vnxv9eRmgX/1YV891sria0ZR5EmE1nV0InoN3dPX8qvWb57GthDKGzVMU3JrCB30UREZHqMLMpwI7ufrKF+WQnEToL1qxEX+yYZvZZwgX5ul7hPMsKmiIi0hbM7CzCpBq7lExcaB8KmiIiItmoTVNERCQjBU0REZGMFDRFREQyUtAUERHJSEFTREQkIwVNERGRjBQ0RUREMlLQFBERyUhBU0REJCMFTRERkYwUNEVERDJS0BQREclIQVNERCQjBU0REZGMFDRFREQyUtAUERHJSEFTREQkIwVNERGRjBQ0RUREMlLQFBERyUhBU0REJCMFTRERkYwUNEVERDJavdEZkNrZaKONfPTo0Y3Ohkjbue+++15295GNzodUn4JmCxs9ejRz585tdDZE2o6ZPd3oPEhtqHpWREQkIwVNERGRjBQ0RUREMlLQFBERyUhBU0REJCMFTRERkYw05EREGmLmvB6mz1rI8719bNrVydTJY5gyrrvR2RIpSkFTROpu5rweTrjmIfr6lwHQ09vHCdc8BKDAKU1N1bMiUnfTZy1cETBz+vqXMX3WwgblSCQbBU0Rqbvne/vKWi7SLFQ9K9IA7d6et2lXJz0pAXLTrs4G5EYkO5U0Reos157X09uHs7I9b+a8nkZnrW6mTh5DZ8ewAcs6O4YxdfKYBuVIJBsFTZE6U3te6Owz7cCxdHd1YkB3VyfTDhzbVqVtGZpUPStSZ8Xa89qp2nbKuO6WfW3SuhQ0ReqsUHveep0dGobRhNrpQkZKU/WsSJ2ltecZ0NvXn1pte/K1C+qYO0lS+7PkU9AUqbNkex6EgOlF0vf29esk3SBqf5Z8CpoiNTRzXg8Tz5jN5sdfz8QzZq8IflPGdXP78XvS3dVZNGDm6CTdGBpPKvkUNEVqZOa8Hqb+5oEBVXtTf/PAgFJj1pOvTtKNUWjcqMaTti91BBKpQK5zSE9vH8PMWObOagbLSxQb+5c5p1y3YEVHkkKdgvLpJN0YUyePGdA5CzSetN0paIqUKX+y8WUeImWpgJmzeGn/iv0sffudkumb7STdTr1Jc6+rXV6vlKagKVKmtM4h5coPvIWsP6KDk/bfDoCJZ8yu+Ym7VEAcancnqUaA13hSSVLQFClTNdoXT752QdGAacBndx7FaVPGlhWoBhMkshynWG/SZgssJ858iMvuemZFR6tmD/AyNChoipQpaztkMb19/UXXO3DrI4uAwoHqm1fN5+RrF2AGvUv76RrRwRv/fIf+WE9cbpDIEhCHSm/SmfN6BgTMnGYN8DJ0qPdsnZnZDWbmZnZahrRe4LFjPfIq6dImJ6iFXCAqFpB6+/pZvLQfJ7SV9uc1rJYzpjBLQBwqvUmnz1pYcChPswV4GVoUNOvIzA4FdihzsxnALnmPR6ubMylH/uQEw8wAWM1WTZuyCAhtlaUCby4QDTYgZS0VZwmIQ+XuJMUCY7MFeBlaVD1bJ2bWBfwYOBa4vIxNe9z9rtrkSiqVtXNIWoefzo5hKzr35Iat5M8KlAxEacMeypEL6qVkGV4xVHqTFqpCN2i6AC9Di4Jm/ZwJLHD3K8ysnKApQ1ipIJN7LtaBJ7mPStpSc0NiBpvXZLpmC5L50i4Acp2rmj3v0tzMM/6gpHJmthtwM7CDuy80MwdOd/cTS2znwKvA2sAy4C7gJHf/S5bjTpgwwefOnTu4zEtTyTpUJam7q5Pbj9+zhrlqTo0cT2pm97n7hLocTOpKJc0aM7MO4HzgLHcvdwLRS4HfA88DmwFTgdlmtre7z6lqRmVIyC8NQvHJ3puxvbFehkKJWIYelTRrzMxOBI4EtnP3vrgsU0kzZV/rAH8FnnX33QqkORo4GmDUqFHjn3766cFkX5rc5sdfXzBodjdpe2M7UEmzdamkWUNmNgr4HnAUMNzMhidWD4+dg15390x1be7+upldD3ypSJoLgAsgVM9WnHkZEgp1eGnXKlmRWtOQk9raAliTUM26OPEAOC7+PbbMfZa6/aK0kaEyBESkVaikWVvzgT1Slt9KCKQXAY9l3ZmZrQvsC9xdldzJkDdUhoCItAoFzRpy915gTv5yC+Pmns515jGzzYDHgVPd/dS47DhgDCHA5joCHQdsAny29rmXoUIdXkTqR0GzORgwjIHV5QuB/xcf6wGvAbcDX3L3e+qeQxERUdBsBHe3vP+fIm/GNXe/DriujtkSEZES1BFIREQkI5U0RaqkkTPQiEh9KGiKlCktOAKZbxRdrWNmnTBegVykejQjUAvT3LPVV+iuJcNXXy31xtLVmGSg0DGnHTi2aACsdDsZPM0I1LrUpimSYua8HiaeMZvNj7+eiWfMZua8HiCMh8yfLL2vf1lqwITq3PC40DFL3Vy60u1EpDBVz4rkyS+hJatayw2C1bjhcaFjlspLpduJSGEqaYrkKVZC6xrRkXk/1ZrOrlDgLRWQK91ORApT0BTJU6yEVqoLQHdXJxafq9V2WOn8spqXVqT6VD0rkqfQnUM27eosWbVZizuLVDq/rOalFak+9Z5tYeo9W5livU6nz1qYGlAB1h/Rwbzvf6xe2ZQmpt6zrUslTZE8pUpoU3/9AP3LB15sDlvNOGn/7eqeVxGpLwVNkRSF7hySW3bytQtWDDNZf0QHJ+2/nao9RdqAgqZImXQrLpH2pd6zIiIiGSloioiIZKSgKSIikpGCpoiISEYKmiIiIhkpaIqIiGSkoCkiIpKRgqaIiEhGCpoiIiIZKWiKiIhkpGn0ROpg5rwe3aJLpAUoaIrUWP6txnp6+zjhmocAFDhFhhhVz4rU2PRZCwfcmxOgr38Z02ctbFCORKRSCpoiNfZ8gZtWF1ouIs1LQVOkxjbt6ixruYg0LwVNkRqbOnkMnR3DBizr7BjG1MljGpQjEamUOgKJ1Fius496z4oMfQqadWZmNwCTgdPd/cQSadcEfgB8DugC5gPfcfc/1zyjUlVTxnUrSIq0AFXP1pGZHQrsUMYmFwFfBr4P7Ae8AMwysx1rkD0RESlBQbMIMzuiivvqAn4MfCtj+h2Aw4Bj3f1Cd78FOBh4Bji1WvkSEZHs2i5omtnmZnaLmT1hZufEKtDcunvykn8jse7IQR76TGCBu1+RMf0BQD9wVW6Bu78DXAlMNrPhg8xPw8yc18OOp9zI6OOvZ/Tx1zPu1BuZOa+n0dkSESmpHds0fw5cA9wFfB24xcw+7u6vAx15aS3x99eA/63kgGa2G/AFyqua3Q540t2X5i1fAKwBbBX/HlJmzuth6q8foH+5r1i2eGk/U3/zAFB4hpxi09BpijoRqZd2DJobu/vP4t9HmNkJhMC5N+B5aZP/GxUwsw7gfOAsdy9nCpgNgMUpy19NrB9yps9aOCBg5vQvc6bPWpga7IpNQwdoijoRqZu2q54FBlRruvs04GrgFmCdvLRjzOwqMzsOGGFmIyo43neATuD0MrczVg3iueWFNzI72szmmtncRYsWlXnI2is2C05Pbx8Tz5i9SlVtsWnoNEWdiNRTO5Y0HzWzvd39ptwCdz/LzJYDZ+WlnQSMj483gVfN7BngAeBBd/9BsQOZ2Sjge8BRwPC8dsjhsXPQ6+6+LGXzV4FRKcvXT6xfhbtfAFwAMGHChLSgWxP5VaR7bDOSWx9ZtEqV6aZdnfSUCJz5JcVKpqHTFHUiUgvtWNL8DLDKOEd3Pwd4b96ye939F+7+ZXf/ALAuoUfrzflpC9gCWBO4lFDVmnsAHBf/Hltg2wXA5iml222Bt4HHMhy/LnLVpz29fTgh8F161zMD/j/hmodCe2aGWXDyS4rFpqHTFHUiUk9tFzTd/S13f6vAuqJdON39bXef6+7nu/vRGQ43H9gj5QEhkO5B4eB3LaFj0qdzC8xsdeAQ4MZCr6ER0qpI8+UCYdZ2xmRJsdg0dJqirriZ83qYeMZsNj/++tSqbxEpTztWz9aNu/cCc/KXmxnA0+4+J/6/GfA4cKq7nxq3nW9mVwH/FTsTPQkcA2wOfLYe+c8qa1VoLl13iSpaGFhSzDINnXrPrkplISK2AAAZ6klEQVT38RSpvrYNmmb2JOkdbTJx9y2qmR1gGKuW/L9I6EB0GmEavQeAj7v7/VU89qCVaqdMpoNQckyezPOllRSLTUOnKerSFeskpfdLpDJtGzSBGY06sLtb3v9PkdIr1t37CDMIZZpFqFFKBUEYGAjzS45dIzpwhyV9/SopVpHu4ylSfe0cNJ9sdAZaRVr1aaHes8ltFBhrq1ANgDpJiVSunYPmjEFs68AlVcpHS1AQbD5pNQDqJCUyOG0bNN297XoOS3vRfTxFqq9tg6aZvdfdn210PkRqSTUAItXVzqWtJ8zsajOb2OiMiIjI0NDOQfM0YCLwZzO738y+YGZrNDpTIiLSvNo2aLr7KcBmhIkC+ggdg54xs1PMbJNG5k1ERJpT2wZNCDd1dvcr3X0iMAH4IzAVeMrMfmVmOzU2hyIi0kzaOmgmufv97v5FwkTspwAfAe4yszvN7DONzZ2IiDSDtu09m8/M1iLcxWQ9wr015wOHAwcRJle/snG5k6Eg//ZoueEdueU9vX0MM2OZO90a/iEyJLVt0DSz+YQAuR7h5tO5UndyOrt3gCXxIVJQocnR5z79Kr+9r2fF8mXuA9aDJk8XGUraNmgC28fnPwHnAYuA15KPOPertLlCJcikQpOjX3H3sysCZT5Nni4y9LRzm+aOhB6zHwJ+AkwCetz97+7+DwVMgfQbbOduqJ1UaBL0QgGz1HYi0pzaNmi6+4PufiSh48+5hNtwPWVml5jZBxqbO2kWxW6vlVRoEvRhtsrNazJtJyLNqW2DZo67v+LuPyTc3PkL8Xmumd1mZp8ys7Z/j9pZ1ttrTZ08hs6OYQOWdXYM49APvXeV5cn1mjxdZGhRQIjcfZm7X+3uHwbGA48Res0+YWbHNTZ30iiFSoL5y6eM62bagWPp7urEgO6uTqYdOJbTpoxdsRxWljxz69WeKTK0mJdoc2lVcdaf9QjDTAo9tgb2J7xP6cWFJjZhwgSfO3duo7NRkbTON5B+x44sHXUGk4+022sp4EkxZnafu09odD6k+to5aC4n3BcTBg4zIS5/gzDUpBdYEkugQ8pQDZppgSpNZ8cwPjW+e8CQjtzyaga1WgZlaU0Kmq2rnYPm14HFrByH2Zv4e4m3wBszVIPmxDNm05OxV2lusoB83V2d3H78ntXOmkgmCpqtq23Habr7TxqdB0lXzjCMQkM6NJRDRGpBHYGk6ZQzDKPQkA4N5RCRWlDQlKaTNnwjTaEhHRrKISK10rbVs2b2JCs7ApXN3beoYnYkIdfJ5pTrFrB4af+AdUb40JITnk/YbAN11BGRumjnjkAnDWb7eBPrpjZUOwIlqeeqDEXqCNS62rakCTzZ6AxIaVPGdStIikjTaOegOWMQ2zpwSZXyISIiQ0TbBk13VycoEREpiwKHiIhIRgqaIiIiGbVt9WwW8b6ao+K/z7j7/Y3Mj4iINJaCZgozGw9cRujw8wxheOBmFmafOczd7ytjX5OB7wDbAusDi4A7gJPd/W9FthtN4R6+67t7b9Y8iIhIdShoprsA+Jq735xcaGZ7AxcCHyhjXxsA9wE/JwTMUcDxwF1mNtbdny6x/TTg2rxlr5dxfBERqRIFzXRr5wdMAHe/ycx+Ws6O3P0K4IrkMjO7B3gEOAg4u8QunnD3u8o55lCliQxEpNmpI1C6l8zsi2a2YlJTMxtmZkcBL1dh/6/E5/6iqdpI7h6aPb19ONDT28cJ1zzEzHk9jc6aiMgKCprpDgcOBV41s4fN7GHgVeCQuK5sMeiuYWbvA84HXgSuzLDpNDN7x8yWmNm1Zja2kuM3u+mzFq5y0+m+/mVMn7WwQTkSEVmVqmdTuPsTwMfMbCMG9p4dTCnzbmB8/PsxYE93f6lI+rcIwfVGQlvoNsB3gTvM7IPu/nDaRmZ2NHA0wKhRo9KSNKVC97/UfTFFpJmopFmEu7/s7vfHx8sAZvauCnf3eWBn4DDgNeCm2EO20LFfcPevuPs17v4Xd78Q+AihR+/3imx3gbtPcPcJI0eOrDCr9Vfo/pe6L6aINBMFzfJVdNsQd3/Y3e+OHYM+CqxN6EVbzj6eBW4DdqokD80s7R6aui+miDQbVc+mMLMDiqxec7D7d/deM3sM2KqCzXO3lGwpuV6y6j0rIs1MQTPd/wF/IgSofOsMdudmtjGhjfKyMrcbBUyM+Ws5ug2YiDQ7Bc10fwe+5O6rzMhjZs+WsyMz+z/gfuBBQlvm1sCxwDvEMZpmtjtwC3Cku18Sl51NqD6/k9ARaAxwArAc+GFFr0pERAZFQTPdxcBGpE9j94sy93UXcDDwbWAN4FlgDjDN3Z+KaQwYxsA25gXAMcARhNLty8Bs4BR31zgMEZEGMPeWax6TaMKECT53bkX9lmpOs/9IKzOz+9x9QqPzIdWnkqbUXW72n9xkBrnZfwAFThFpagqagJnNLrJ6ObCEMOn6Re7+j/rkqnUVm/1nMEFTpVcRqTUFzcAIHXTeTWjH/AewMbA58EL8fx/gWDPbvdgtvVrVzHk9nHztAnr7wnS564/o4KT9t6soKNVi9h+VXkWkHjS5QXAO8E9gvLtv6e67uvuWhEkE/gmcAryP0Iv19MZlszFmzuth6q8fWBEwARYv7Wfqbx6oaEL1Wsz+o7lrRaQeFDSD0wg3hZ6XXBhvNn0KcJq7PwdMJ0xl11amz1pI//JVO4z1L/OKglItZv/R3LUiUg8KmsHWFL7l1yJWztzzOLBWXXLURIoFnkqC0pRx3Uw7cCzdXZ0Y0N3VybQDxw6qGlVz14pIPahNM3gKOAr4Y8q6o+N6CGM3X0lJ09I27eqkp0BwrDQoVXv2n6mTxwxo0wTNXSsi1aegGZwKXGpmDwK/BV4C3gV8Cng/4c4kAHsRbvHVFnK9UQsFzI5h1jRBqdpz16onroikUdAE3P0KM3uZ0H75XaAD6Cfc0eRj7n5zTPotYFn6XlpLfm/UfAYcstN7myqQVKv0qp64IlKI2jQjd7/J3XcFOoFNgE53n5gImLj7P929v+BOWkhab9QkB66699mKes82O/XEFZFCFDTzuPtyd3/J3Zc3Oi+NlKWDT6W9Z5udeuKKSCEKmpGZvdvMzjKze83scTO7x8zONLNNGp23RsjawacVA4l64opIIQqagJltDcwHvgG8AdwDvAn8OzDfzN7XwOw1RNYOPq0YSGoxjlREWoOCZvAj4r0u3X0Pdz/U3fcgjN9cEte3lSnjuunq7Ciappl6z1ZTLcaRikhr0K3BADPrBb7i7lemrDsU+Lm7r1//nA3OYG8NVqwH7WDmnhVpdbo1WOvSkJNgDeD1Autej+vbTrXHPtZS/rjKPbYZya2PLCqZb43HFJFyqKQJmNkdhOrZfZK9Zs3MgOuB9dx9YqPyV6lmvgl1NZUaU5rT1dnByQesLB2nbdfZMUxVsTJoKmm2LpU0g1OB3wMPm9lVhNuBbQJ8mnB3k30bmDcpodSY0pzevv4BkxTU6r6eItK61BEIcPcbgP0IVbHfA34GnEjoSbufu9/YwOxJCeUMe0lOUqDxmCJSLpU0oxg4bzCzEcD6wGJ3X9rgbEkGxSaUT5MLioW2a8VhNCJSHSpp5nH3pe7eo4A5dKSNqywmFxQ1HlNEytW2JU0zW06YQjULd/e2fa+aXVov3z22Gcn1D77A4qUDpwpOBsVyegcn7/gyzIxl7nSrt61I22nnQHAq2YOmNLm0O5ycNmXsoIeUzJzXwynXLRgQfJfFHue6+4lI+9GQkxbWLkNOKlVqyEnWoSzdXZ3cfvyetc6uDCEactK61KYpbavULcCyDmVRb1uR9qGgKW2r1JCTrMFQvW1F2oeCprStUrcAyxIM1dtWpL0oaErbKjXkpNBQFovPuvuJSPtp596z0uZKDTkZShPWi0h9qPdsjZnZZOA7wLaEmYYWAXcAJ7v730psuz4wHZgCdAJ3Ase6+0NZjq3esyKNod6zrUvVs7W3AXAf8DXgY8AJwHbAXWa2WaGN4h1WrgU+Dnwd+BTQAdxqZu+pdaZFRGRVqp6tMXe/ArgiuczM7gEeAQ4Czi6w6QHAbsCe7n5r3O5O4EngP4Bv1CrPIiKSTiXNxnglPvcXSXMA8HwuYAK4+xLgOuCTNcybiIgUoKBZJ2Y2zMzWMLP3AecDLwJXFtlkO+CvKcsXAKPMbO0aZFNERIpQ0Kyfu4G3gEeB7QnVri8VSb8BsDhl+avxef3qZk9EREpR0KyfzwM7A4cBrwE3mdnoIumN9AnlLWXZypVmR5vZXDObu2jRogqzKiIiaRQ068TdH3b3u2PHoI8CawPHF9nkVUJpM1+uhJlWCsXdL3D3Ce4+YeTIkYPKs4iIDKSg2QDu3gs8BmxVJNkCQrtmvm2BZ9z9jVrkTUREClPQbAAz2xjYBni8SLJrgW4z2z2x3brA/nGdiIjUmcZp1piZ/R9wP/AgoS1za+BY4B3iGM0YGG8BjnT3S+Km1xJmALrUzKYSqmNPILRpnlnP1yAiIoGCZu3dBRwMfBtYA3gWmANMc/enYhoDhpEo+bv7cjPbDzgL+DmwJiGI7uHuz9Yr8yIispLmnm1hmntWpDE092zrUpumiIhIRgqaIiIiGSloioiIZKSgKSIikpGCpoiISEYKmiIiIhkpaIqIiGSkoCkiIpKRZgQSqbKZ83qYPmshz/f2sWlXJ1Mnj2HKuO5GZ0tEqkBBU6SKZs7r4YRrHqKvfxkAPb19nHDNQwAKnCItQNWzIlU0fdbCFQEzp69/GdNnLWxQjkSkmhQ0Raro+d6+spaLyNCioClSRZt2dZa1XESGFgVNkSqaOnkMnR3DBizr7BjG1MljGpQjEakmdQQSqaJcZx/1nhVpTQqaIlU2ZVy3gqRIi1L1rIiISEYKmiIiIhkpaIqIiGSkNk1pOE07JyJDhYKmNJSmnRORoUTVs9JQmnZORIYSlTSlJrJWuWraOREZShQ0perKqXLdtKuTnpQAmWXaObWFiki9KWhK1RWrcp0yrntAsOsa0UHHakb/cl+RNsu0c2oLFZFGUJumVF2xKtdcsOvp7cOBxUv7waCrswMDurs6mXbg2JKBT22hItIIKmlK1RWrck0Ldv3LnLWGr878kz6W+RhqCxWRRlBJU6qu2J0+qhXsdAsuEWkEBU2puinjupl24Fi6uzpXqXKtVrDTLbhEpBFUPSs1UehOH1MnjxnQgQcqC3a6BZeINIKCZo2Z2UHAocAE4F3AM8A1wA/d/fUS23qBVePcfX5VM1on1Qx2ugWXiNSbgmbtHUcIlN8FngPGAScDe5jZru6+vMT2M4Dz85Y9WuU81pWCnYgMVQqatbe/uy9K/P8nM3sVuBiYBMwusX2Pu99Vq8yJiEh2Cpo1lhcwc+6Nzw0vbmlWHRGR7NR7tjF2j88PZ0h7jJm9ZWZLzWy2mX24WpnIn2igp7ePb141n3Gn3sjMeT3VOoyISMtQ0KwzM+sGTgVudve5JZJfCnwV2As4GtgQmG1mk6qRl7SJBiDM0nPCNQ8pcIqI5FHQrCMzWxv4HfAO8MVS6d398+5+lbv/xd0vBXYDngdOK3KMo81srpnNXbQorWZ4pWITCmhKOhGRVSlo1omZrQlcC2wBTHb358rdRxyicj2wU5E0F7j7BHefMHLkyKL7KzWhgKakExEZSEGzDsysA/gt8EFgH3d/aDC7AwqN3yxL2qw6SV0jOqpxGBGRlqHeszVmZqsBlwEfBfYdzPARM1sX2Be4uxp5y/WSPfaq+alR2KsSmkVEWodKmrX3M+DTwFnAm2a2c+LxHgAz28zM3jGz7+c2MrPjzOxCMzvMzCaZ2eHA7cAmwInVylyx4SVL+vqrdRgRkZagoFl7n4jP3wPuzHscFdcZMIyBn8dCYFvgv4GbgHOAJ4Hd3P0v1cyg7hgiIpKNqmdrzN1HZ0jzFCFwJpddB1xXm1wNVK1J1EVEWp2CpuiOISIiGSloCqBJ1EVEslCbpoiISEYKmiIiIhkpaIqIiGSkoCkiIpKRgqaIiEhGCpoiIiIZmWuC0ZZlZouAp1NWbQS8XOfsSOX0eQ0tGwFruXvx2wzJkKSg2YbMbK67T2h0PiQbfV5Diz6v1qbqWRERkYwUNEVERDJS0GxPFzQ6A1IWfV5Diz6vFqY2TRERkYxU0hQREclIQbNNmNl7zew3ZrbEzF4zs2vMbFSj8yWrMrODzOy3Zva0mfWZ2UIzm2Zm6zQ6b1Kamd1gZm5mpzU6L1J9CpptwMxGALOBbYDDgc8D7wNuNbO1Gpk3SXUcsAz4LvBx4DzgGOAmM9NvtomZ2aHADo3Oh9SO7qfZHr4MbAGMcffHAMzsQeDvwL8C5zQwb7Kq/d19UeL/P5nZq8DFwCTCBZA0GTPrAn4MHAtc3uDsSI3oqrU9HADclQuYAO7+JHA78MmG5UpS5QXMnHvjs+4U3rzOBBa4+xWNzojUjoJme9gO+GvK8gXAtnXOi1Rm9/j8cENzIanMbDfgC8BXG50XqS0FzfawAbA4ZfmrwPp1zouUycy6gVOBm919bqPzIwOZWQdwPnCWuy9sdH6kthQ020fagFyrey6kLGa2NvA74B3giw3OjqT7DtAJnN7ojEjtqSNQe1hMKG3mW5/0Eqg0ATNbE7iW0Ilrd3d/rsFZkjxx2Nb3gKOA4WY2PLF6eOwc9Lq7L2tIBqXqNCNQGzCz2cAa7r5b3vI5hO/A7qkbSsPEKr+ZhLbMvdz9rgZnSVKY2STg1hLJxrn7/DpkR+pAJc32cC1wlplt4e5PAJjZaGAicHwD8yUp4ljMy4CPAvsqYDa1+cAeKctvBS4FLgIeS1kvQ5RKmm0gTmDwANAHnEho3/wBsA6wvbu/0cDsSR4zOw/4CqGN7Pd5q59TNW3zMzMHTnf3ExudF6kudQRqA+7+JrAn8CjwK0Ip5klgTwXMpvSJ+Pw94M68x1GNypSIqKQpIiKSmUqaIiIiGSloioiIZKSgKSIikpGCpoiISEYKmiIiIhkpaIqIiGSkoCkiIpKRgqaIiEhGCpoiRZjZtmbmZvaxRuclCzPbPOb3JTP7UqPzI9JqFDRFivtAfL6/obnI7mVgb8It305tcF5EWo6Cpkhx44Gn3f3lRmckC3d/3d1vJtxdY1Mze1ej8yTSShQ0pS2YWYeZnWhmT5hZn5ndaWZjzGyCmS01s00LbDqevFKmma1mZt8wswfjvp4ws5PjPTCT6dYws1PN7OmY7mYz29LM3jKzb9XqtUYL4/MONT6OSFvR/TSl5cVg9kdge+AE4B/Az4HTgDWBn7n78ynbGbAj8KPEsmHA1YS7xvwAmEeowj0dGB73n9v2asK9Fk8nBN59gJuANahhdW88di4obx+PKSJVoKAp7eCrhCC3m7vfAWBmOwH/DhhwRIHttibcc/S+xLJvAgcAO7t7bvmtZrY1cDQxaAJfBvYFdnH3uXHZzWb2EWA0IdjWyleBXYA3UUlTpKpUPSvt4CvAjbmAGfUC6wHnuPsrBbYbH5/vhxUluG8CVycCZs5jwAZmtmb8/z9iurkp6R539yVxn981s4VmttzMpiQTxqrc28zsUTObZ2YTSr1QMxsNnEEo3d5NKGmKSJUoaEpLM7NNgG2AP+StWgN4FTinyOYfAJ5z95fi/1sD70nZF8B7gcXu/k8z2wLYEri+QLpkwL2FUG3755S0vwBmuPvWhCB8WQzcxVxICMw/BOYD/5Lf1ioilVPQlFa3VXx+Mrcgtkt+gVDie73ItuMZGOBGxucXk4liINuTEAABNi2QbkNCdemK9kx3v9vdH88/sJmNBHYGLo7pcu2S4/PTJrY5GtgdOMLd+wlBcw3CRUMuzalmdqWZXRc7MM00sx3N7Pfx/18l0o43sz+b2X1m9piZ/Wdi3flmdlb8e1Mz+5uZ7VUobyKtQkFTWt3y+LxBYtkxwLbAsEIbxUA4joEddp6Oz1vlJf8isB3w3/H/RfF5TF66/wTWYmAgLmQU8HwMfsnjjyqQ3/cA04HT3P2BuHh+fE5W0Y4HRgAHE4LproS23U8R3pP9zezdMe0TwJ7uPh4YC3zDzNZPvJYvmNkHCCXv78ShLiItTR2BpNU9ACwBvm9mSwjVq2cCvyUEiE8At7r7P/O225LQ5rkiwLn7s2Z2I3CSmS0FngMmE3qqnujuf4lJ/w4siOneBHqAQ4ADAafynrPFqmYvAB4HpiWWPQy8RSjdXhaXjQcmuXsfgJmtDnzf3d+KJfDVgddi2o8D/xoDpQFdwNsA7v6Smf0UuB043N2vq/A1iQwpCprS0tz9TTP7NPBjwhCQRYSerbMIpbbfA+umbDqgE1DCYcDZhFLd2oSg/Bl3vyZxzOVmdhBwPnAeYZaeS4ArgYnuvjhD1p8hTE7QkShtbhaXD2BmRwB7ATslS6bu/o6Z/ZVY0oyl0dXc/ZH4/+ZAr7s/Gzf5F+CZ+J7tCxwLfNLdXzCzPQlDc96M225IuAhYAuS2F2l5CprS8mJ74PtTVn2wyDZXAVelLH+FwkNUkukeIbQvAisC1FxCtWZJ7r7IzO6Jx7rQzPYmlPZWqdp19xnAjAL7Sfa4HR/zkLNT3v/J9eOB+TFgjiSUzu+Nr2U94AbgLOAdQmeqXbK8LpGhTm2aIlVmZrvEDjf7mNlHzWwqcAehVHpBXtoTzew5QtD5HzN7Lvb4hTBU5otm9iihZPtZd/dBZC0/aE6gcNC8BPiQmT1IKKU/Bcw1s7UIbZj/4+6XEi4sVjezzwwiXyJDhg3uNygi+czso4TS15ZAB6Gt8XJguru/1ci8icjgKGiKiIhkpOpZERGRjBQ0RUREMlLQFBERyUhBU0REJCMFTRERkYwUNEVERDJS0BQREclIQVNERCSj/w9qeSy7/A06JwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for model_name in alphas.keys():\n",
    "    x =  np.multiply(alphas[model_name], np.log10(lmaxs[model_name]) )\n",
    "    y =  2.0*np.log10(norms[model_name]) \n",
    "    plt.scatter(x,y,label=model_name )\n",
    "\n",
    "    plt.title(r\"VGG Conv2D Layers: $\\alpha\\;log_{10}\\;\\lambda_{max}$ vs $\\log_{10}\\Vert W\\Vert^{2}_{F}$\"+\"\\n\")\n",
    "    #plt.ylim(0,20)\n",
    "    plt.xlabel(r\"$\\alpha\\;log_{10}\\;\\lambda_{max}$\")\n",
    "    plt.ylabel(r\"$\\log_{10}\\Vert W\\Vert^{2}_{F}$\")\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Randomize Matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rand_model_alphas(model):\n",
    "    try:\n",
    "        alphas, norms, lmaxs = [], [], []\n",
    "\n",
    "        for W in tqdm(iter_pytotch_layers(model)):\n",
    "            M, N = W.shape[0], W.shape[1]\n",
    "            print(M,N)\n",
    "            if M > 1024:\n",
    "                break\n",
    "                \n",
    "           # correct for glorot normalization\n",
    "            glorot_correction = np.sqrt(np.average(W.shape))\n",
    "            W = W*glorot_correction\n",
    "            \n",
    "            # shuffle W\n",
    "            W = W.ravel()\n",
    "            np.random.shuffle(W)\n",
    "            W = W.reshape(N,M)\n",
    "            \n",
    "            normW = np.linalg.norm(W)\n",
    "\n",
    "            if (M>N):\n",
    "                X=np.dot(W.T,W)/N\n",
    "            else:\n",
    "                X=np.dot(W,W.T)/N\n",
    "\n",
    "            evals = np.linalg.eigvals(X)\n",
    "            \n",
    "            l_max = np.max(evals)\n",
    "            #if (l_max > 1):\n",
    "\n",
    "            fit = powerlaw.Fit(evals, xmax=l_max, verbose=False)\n",
    "\n",
    "\n",
    "            print(N, M, X.shape, fit.alpha, np.max(evals), fit.D)\n",
    "\n",
    "            alphas.append(fit.alpha)\n",
    "            norms.append(normW)\n",
    "            lmaxs.append(l_max)\n",
    "            \n",
    "           \n",
    "    except Exception as e: \n",
    "\n",
    "        print(\"skipping \", model_name)\n",
    "        print(e)\n",
    "\n",
    "        pass\n",
    "    \n",
    "    return  np.array(alphas),  np.array(norms), np.array(lmaxs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f0ea81b3c48f48b88f0ecbbc724bab69",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=1, bar_style='info', max=1), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "128 64\n",
      "64 128 (64, 64) 1.6501380557141414 6.738295 0.1694855053362465\n",
      "128 64\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/charleshmartin/anaconda3/lib/python3.6/site-packages/powerlaw.py:700: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  (Theoretical_CDF * (1 - Theoretical_CDF))\n",
      "/Users/charleshmartin/anaconda3/lib/python3.6/site-packages/powerlaw.py:700: RuntimeWarning: invalid value encountered in true_divide\n",
      "  (Theoretical_CDF * (1 - Theoretical_CDF))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "64 128 (64, 64) 1.5729749512187854 8.271922 0.1797384350918581\n",
      "128 64\n",
      "64 128 (64, 64) 1.4121035942309466 6.4598393 0.19428117596452105\n",
      "128 64\n",
      "64 128 (64, 64) 1.4345913109436141 6.8347855 0.18133933322787987\n",
      "128 64\n",
      "64 128 (64, 64) 1.6184989159677603 13.821855 0.16232586138055982\n",
      "128 64\n",
      "64 128 (64, 64) 1.3854852949105274 8.080619 0.18905146934229966\n",
      "128 64\n",
      "64 128 (64, 64) 1.569204110777663 5.6521955 0.1819836181454877\n",
      "128 64\n",
      "64 128 (64, 64) 1.4466121577534141 7.4524913 0.18158004314008436\n",
      "128 64\n",
      "64 128 (64, 64) 1.6136188055006313 6.271439 0.17297128682994922\n",
      "256 128\n",
      "128 256 (128, 128) 2.6822107696456925 3.8933222 0.15839166995063148\n",
      "256 128\n",
      "128 256 (128, 128) 1.6245755183676356 6.0587945 0.15038343403592247\n",
      "256 128\n",
      "128 256 (128, 128) 1.7481681533160724 3.8148115 0.15976226159856022\n",
      "256 128\n",
      "128 256 (128, 128) 2.576076637045816 6.5674796 0.13313312865838484\n",
      "256 128\n",
      "128 256 (128, 128) 2.53372629580107 11.5017805 0.1260402015887302\n",
      "256 128\n",
      "128 256 (128, 128) 1.615083227571029 6.9235363 0.12912552961625856\n",
      "256 128\n",
      "128 256 (128, 128) 1.6649286743131322 3.616818 0.15493786547581134\n",
      "256 128\n",
      "128 256 (128, 128) 1.6911655918967212 6.020543 0.13113799986198876\n",
      "256 128\n",
      "128 256 (128, 128) 2.0503663998537642 3.9268982 0.14425817438514243\n",
      "256 256\n",
      "256 256 (256, 256) 2.210368745155713 2.4806092 0.12885939357138032\n",
      "256 256\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/charleshmartin/anaconda3/lib/python3.6/site-packages/powerlaw.py:1160: RuntimeWarning: invalid value encountered in log\n",
      "  return 1 + len(data)/sum(log(data / (self.xmin)))\n",
      "/Users/charleshmartin/anaconda3/lib/python3.6/site-packages/powerlaw.py:701: RuntimeWarning: overflow encountered in double_scalars\n",
      "  )[1:]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "256 256 (256, 256) 2.025263614368387 3.2093854 0.12252819152531846\n",
      "256 256\n",
      "256 256 (256, 256) 2.048447913043735 2.502136 0.12204158382166175\n",
      "256 256\n",
      "256 256 (256, 256) 2.658269352938596 3.1404648 0.12169916242995937\n",
      "256 256\n",
      "256 256 (256, 256) 1.80045362839399 5.752889 0.11590080291933835\n",
      "256 256\n",
      "256 256 (256, 256) 2.042517458656814 3.498113 0.12374506755489251\n",
      "256 256\n",
      "256 256 (256, 256) 2.6040953714076167 2.5047364 0.1242841322676077\n",
      "256 256\n",
      "256 256 (256, 256) 1.9744266107780324 3.1301105 0.12141228533720927\n",
      "256 256\n",
      "256 256 (256, 256) 2.073195547557657 2.4406357 0.1321530823826083\n",
      "512 256\n",
      "256 512 (256, 256) 2.651723173693334 4.4681783 0.10811342580002525\n",
      "512 256\n",
      "256 512 (256, 256) 2.1681144770246012 5.461192 0.1237198549105295\n",
      "512 256\n",
      "256 512 (256, 256) 2.689082947115983 4.4894295 0.09975517998639649\n",
      "512 256\n",
      "256 512 (256, 256) 2.055719116616769 6.160263 0.11025216122298409\n",
      "512 256\n",
      "256 512 (256, 256) 3.8241504066156065 10.704096 0.09906479789549272\n",
      "512 256\n",
      "256 512 (256, 256) 2.8416611827561247 6.0866494 0.10146027459959384\n",
      "512 256\n",
      "256 512 (256, 256) 2.542659814119495 4.4176507 0.11033066753708382\n",
      "512 256\n",
      "256 512 (256, 256) 2.899488643525573 5.4885507 0.11620853677603127\n",
      "512 256\n",
      "256 512 (256, 256) 2.267162106588364 4.6350164 0.1139875896941433\n",
      "512 512\n",
      "512 512 (512, 512) 3.149647634021204 4.4045234 0.05121067426138748\n",
      "512 512\n",
      "512 512 (512, 512) 3.517971430799456 5.955502 0.06635106684967362\n",
      "512 512\n",
      "512 512 (512, 512) 3.14703617782465 4.2881646 0.053711047697071634\n",
      "512 512\n",
      "512 512 (512, 512) 2.746993968597777 6.009544 0.05741509111718701\n",
      "512 512\n",
      "512 512 (512, 512) 2.407422086928957 9.346973 0.06230395538241612\n",
      "512 512\n",
      "512 512 (512, 512) 3.3026564220463714 5.8348856 0.05007001768887687\n",
      "512 512\n",
      "512 512 (512, 512) 3.1959309618379086 4.043213 0.05217699012617483\n",
      "512 512\n",
      "512 512 (512, 512) 3.3540202532355265 6.2737813 0.04650963426798005\n",
      "512 512\n",
      "512 512 (512, 512) 2.9671913538492407 4.122296 0.06097226530563982\n",
      "512 512\n",
      "512 512 (512, 512) 2.7750606719344155 3.2470713 0.08158068000202795\n",
      "512 512\n",
      "512 512 (512, 512) 3.650766704993771 4.073695 0.07941534203937883\n",
      "512 512\n",
      "512 512 (512, 512) 3.1718414815826237 3.4678502 0.07556438481879812\n",
      "512 512\n",
      "512 512 (512, 512) 3.8758834201794343 4.1151123 0.07539029460337274\n",
      "512 512\n",
      "512 512 (512, 512) 2.2345614890607224 6.928325 0.07883965691243294\n",
      "512 512\n",
      "512 512 (512, 512) 3.202318400881362 4.291187 0.0716379436702485\n",
      "512 512\n",
      "512 512 (512, 512) 2.886601316522584 3.3769126 0.07947003485385556\n",
      "512 512\n",
      "512 512 (512, 512) 2.99332469375034 4.0992336 0.0726039100280117\n",
      "512 512\n",
      "512 512 (512, 512) 2.9316354735511987 3.5009003 0.07331764675014818\n",
      "512 512\n",
      "512 512 (512, 512) 3.717479114758237 7.219969 0.039757802932680886\n",
      "512 512\n",
      "512 512 (512, 512) 3.654137402866977 9.933048 0.04704426218614155\n",
      "512 512\n",
      "512 512 (512, 512) 3.738463946042499 7.9021263 0.03906618483555874\n",
      "512 512\n",
      "512 512 (512, 512) 3.5153681816708193 8.617064 0.02941176470588236\n",
      "512 512\n",
      "512 512 (512, 512) 2.7753493967200598 11.887598 0.0553579802685219\n",
      "512 512\n",
      "512 512 (512, 512) 3.4376685122647532 8.740241 0.03492494441390337\n",
      "512 512\n",
      "512 512 (512, 512) 3.7856459656595094 7.015336 0.03172588384241744\n",
      "512 512\n",
      "512 512 (512, 512) 3.409722203594513 9.44295 0.044012325882756165\n",
      "512 512\n",
      "512 512 (512, 512) 3.6552996700656064 7.094127 0.03151366442008108\n",
      "4096 25088\n"
     ]
    }
   ],
   "source": [
    "model_name = 'vgg11'\n",
    "model = models.vgg11(pretrained=True)\n",
    "alphas[model_name], norms[model_name], lmaxs[model_name] =  calc_model_alphas(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e45bead2a5b74820af5d46b31c51fedf",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=1, bar_style='info', max=1), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "128 64\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/charleshmartin/anaconda3/lib/python3.6/site-packages/powerlaw.py:1160: RuntimeWarning: invalid value encountered in log\n",
      "  return 1 + len(data)/sum(log(data / (self.xmin)))\n",
      "/Users/charleshmartin/anaconda3/lib/python3.6/site-packages/powerlaw.py:701: RuntimeWarning: overflow encountered in double_scalars\n",
      "  )[1:]\n",
      "/Users/charleshmartin/anaconda3/lib/python3.6/site-packages/powerlaw.py:700: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  (Theoretical_CDF * (1 - Theoretical_CDF))\n",
      "/Users/charleshmartin/anaconda3/lib/python3.6/site-packages/powerlaw.py:700: RuntimeWarning: invalid value encountered in true_divide\n",
      "  (Theoretical_CDF * (1 - Theoretical_CDF))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "64 128 (128, 128) 4.453579644181959 2.3707552 0.16097765772966544\n",
      "128 64\n",
      "64 128 (128, 128) 4.894451829033902 2.6759892 0.19516412287787172\n",
      "128 64\n",
      "64 128 (128, 128) 10.425422274398352 2.3500612 0.16769430755250392\n",
      "128 64\n",
      "64 128 (128, 128) 3.8545566742147903 2.2131994 0.23964150460957973\n",
      "128 64\n",
      "64 128 (128, 128) 3.28327221543609 3.8609643 0.16269810873033297\n",
      "128 64\n",
      "64 128 (128, 128) 2.509978484302864 2.3880465 0.2480845130575593\n",
      "128 64\n",
      "64 128 (128, 128) 3.377278692541899 1.9916152 0.20742060608238078\n",
      "128 64\n",
      "64 128 (128, 128) 3.2129977001089656 2.6557248 0.20448972049856495\n",
      "128 64\n",
      "64 128 (128, 128) 3.6680665442139655 2.0296023 0.2389631233537861\n",
      "256 128\n",
      "128 256 (256, 256) 9.502049934239333 1.2100102 0.16160576489192546\n",
      "256 128\n",
      "128 256 (256, 256) 5.013704801217314 1.6882031 0.1723492575983946\n",
      "256 128\n",
      "128 256 (256, 256) 4.009602165182082 1.1639392 0.20742915131593959\n",
      "256 128\n",
      "128 256 (256, 256) 4.936039579846135 1.6463104 0.1881639439661582\n",
      "256 128\n",
      "128 256 (256, 256) 7.911187143491673 3.6132288 0.10954957647402142\n",
      "256 128\n",
      "128 256 (256, 256) 14.381157675010751 1.6717331 0.2047422433499716\n",
      "256 128\n",
      "128 256 (256, 256) 5.598950636966801 1.1529675 0.20360689423134226\n",
      "256 128\n",
      "128 256 (256, 256) 5.0812118181362 1.6156969 0.1994209838520008\n",
      "256 128\n",
      "128 256 (256, 256) 6.690027971834139 1.2337029 0.17404013440151245\n",
      "256 256\n",
      "256 256 (256, 256) 8.041440959758702 0.7830199 0.19009085614773064\n",
      "256 256\n",
      "256 256 (256, 256) 8.368911086829858 1.1904308 0.1075381282794795\n",
      "256 256\n",
      "256 256 (256, 256) 10.616653516163726 0.85460037 0.18223691519170182\n",
      "256 256\n",
      "256 256 (256, 256) 8.904216036669123 1.1675652 0.09332183015351636\n",
      "256 256\n",
      "256 256 (256, 256) 5.575986064035552 3.2902822 0.06518043241010274\n",
      "256 256\n",
      "256 256 (256, 256) 12.128203432936674 1.1878887 0.11111111111111116\n",
      "256 256\n",
      "256 256 (256, 256) 7.763972647735439 0.79873544 0.1831618173686793\n",
      "256 256\n",
      "256 256 (256, 256) 6.043033731331991 1.2112749 0.10862349390902937\n",
      "256 256\n",
      "256 256 (256, 256) 4.276241270227722 0.80427915 0.21074398246040044\n",
      "512 256\n",
      "256 512 (512, 512) 5.403075749532013 1.2479848 0.173965946280765\n",
      "512 256\n",
      "256 512 (512, 512) 13.293647867447056 1.6289576 0.09999999999999998\n",
      "512 256\n",
      "256 512 (512, 512) 4.765742236906478 1.2185606 0.18571875881390698\n",
      "512 256\n",
      "256 512 (512, 512) 10.131431532223315 1.78857 0.07868169811088005\n",
      "512 256\n",
      "256 512 (512, 512) 9.228210096941526 2.8971403 0.06440586854811603\n",
      "512 256\n",
      "256 512 (512, 512) 10.265787854488964 1.8329647 0.06881156757318108\n",
      "512 256\n",
      "256 512 (512, 512) 8.693771254792406 1.1858503 0.18441543785969183\n",
      "512 256\n",
      "256 512 (512, 512) 14.93961055388105 1.5334288 0.11594435045242524\n",
      "512 256\n",
      "256 512 (512, 512) 6.71610209537834 1.2023419 0.1764219760045984\n",
      "512 512\n",
      "512 512 (512, 512) 7.724033357985307 1.3918284 0.08972526524297286\n",
      "512 512\n",
      "512 512 (512, 512) 6.8002163695073055 2.1368403 0.09863458480814036\n",
      "512 512\n",
      "512 512 (512, 512) 9.121345184150556 1.3278267 0.08814868829253453\n",
      "512 512\n",
      "512 512 (512, 512) 6.221754201400726 2.3404698 0.09807290180221373\n",
      "512 512\n",
      "512 512 (512, 512) 5.486394670161891 3.554844 0.09518791255727965\n",
      "512 512\n",
      "512 512 (512, 512) 6.2539831982210945 2.2087283 0.09036224962484318\n",
      "512 512\n",
      "512 512 (512, 512) 7.940385371599975 1.3408898 0.08015794503604623\n",
      "512 512\n",
      "512 512 (512, 512) 6.650192838634451 2.2700543 0.09558408064502388\n",
      "512 512\n",
      "512 512 (512, 512) 8.636768705053914 1.2984769 0.07231385918136335\n",
      "512 512\n",
      "512 512 (512, 512) 13.960070705283771 0.9237639 0.09090909090909094\n",
      "512 512\n",
      "512 512 (512, 512) 11.625384212775476 1.1848814 0.07897265473587245\n",
      "512 512\n",
      "512 512 (512, 512) 9.514305648254698 0.9815621 0.09684194808699953\n",
      "512 512\n",
      "512 512 (512, 512) 8.026245534776157 1.4566065 0.056948425071245645\n",
      "512 512\n",
      "512 512 (512, 512) 10.193421077341856 1.6908567 0.09927982184563389\n",
      "512 512\n",
      "512 512 (512, 512) 8.38686416037839 1.5157824 0.09203114049491046\n",
      "512 512\n",
      "512 512 (512, 512) 10.224666845542203 0.98028666 0.07912759087655086\n",
      "512 512\n",
      "512 512 (512, 512) 10.709127358085869 1.2480925 0.06571047666876517\n",
      "512 512\n",
      "512 512 (512, 512) 11.026362784715383 1.0151116 0.08582281234222033\n",
      "512 512\n",
      "512 512 (512, 512) 7.805219130941667 1.5658145 0.10304865930071272\n",
      "512 512\n",
      "512 512 (512, 512) 6.196126305874778 2.4923792 0.09235916701011349\n",
      "512 512\n",
      "512 512 (512, 512) 7.105406728240559 1.6364026 0.0903936652642009\n",
      "512 512\n",
      "512 512 (512, 512) 6.474199079984495 2.4566755 0.10049160379883804\n",
      "512 512\n",
      "512 512 (512, 512) 5.3934475256284085 3.9664412 0.10462349973696483\n",
      "512 512\n",
      "512 512 (512, 512) 6.129337849852691 2.575507 0.08380599610595363\n",
      "512 512\n",
      "512 512 (512, 512) 6.895125932154677 1.6602689 0.09053191049161069\n",
      "512 512\n",
      "512 512 (512, 512) 6.551613941872229 2.575071 0.10390512560265686\n",
      "512 512\n",
      "512 512 (512, 512) 7.6859648753825045 1.7179556 0.08767111577520226\n",
      "4096 25088\n"
     ]
    }
   ],
   "source": [
    "model_name = 'vgg11_rand'\n",
    "model = models.vgg11(pretrained=True)\n",
    "alphas[model_name], norms[model_name], lmaxs[model_name] =  rand_model_alphas(model)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rcParams['figure.figsize'] = [10,10]\n",
    "matplotlib.rcParams.update({'font.size': 24})\n",
    "legend_prop={'size':20}\n",
    "marker_size = 75\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'$\\\\log_{10}\\\\Vert W\\\\Vert^{2}_{F}$')"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "model_name = 'vgg11_rand'\n",
    "x = alphas[model_name]\n",
    "y =  2.0*np.log10(norms[model_name]) \n",
    "plt.scatter(x,y,label=model_name , color='red', s=marker_size)\n",
    "\n",
    "model_name = 'vgg11'\n",
    "x = alphas[model_name]\n",
    "y =  2.0*np.log10(norms[model_name]) \n",
    "#plt.scatter(x,y,label=model_name, color='blue' )\n",
    "\n",
    "\n",
    "plt.title(r\"$\\alpha$ vs $\\log_{10}\\Vert W\\Vert^{2}_{F}$\"+\"\\nVGG11 BN Randomized Conv2D Layers\")\n",
    "plt.legend(prop=legend_prop)\n",
    "plt.xlabel(r\"$\\alpha}$\")\n",
    "plt.ylabel(r\"$\\log_{10}\\Vert W\\Vert^{2}_{F}$\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_name = 'vgg11'\n",
    "x = alphas[model_name]\n",
    "y =  2.0*np.log10(norms[model_name]) \n",
    "plt.scatter(x,y,label=model_name, color='blue', s=marker_size)\n",
    "\n",
    "\n",
    "plt.title(r\"$\\alpha$ vs $\\log_{10}\\Vert W\\Vert^{2}_{F}$\"+\"\\nVGG 11 BN  Conv2D Layers\")\n",
    "plt.legend()\n",
    "plt.xlabel(r\"$\\alpha}$\")\n",
    "plt.ylabel(r\"$\\log_{10}\\Vert W\\Vert^{2}_{F}$\")\n",
    "\n",
    "plt.savefig(\"img/fro-vgg11.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'$\\\\lambda_{rand}^{max}$')"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "model_name = 'vgg11'\n",
    "x = lmaxs[model_name]\n",
    "\n",
    "model_name = 'vgg11_rand'\n",
    "y = lmaxs[model_name]\n",
    "\n",
    "\n",
    "plt.title(r\"VGG11 $\\lambda^{max}$ vs VGG11 Randomized $\\lambda_{rand}^{max}$\")\n",
    "plt.scatter(x,y, label='VGG 11', s=marker_size)\n",
    "\n",
    "plt.xlabel(r\"$\\lambda^{max}$\")\n",
    "plt.ylabel(r\"$\\lambda_{rand}^{max}$\")\n",
    "#plt.legend()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'$\\\\alpha^{rand}')"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "model_name = 'vgg11'\n",
    "x = alphas[model_name]\n",
    "\n",
    "model_name = 'vgg11_rand'\n",
    "y = alphas[model_name]\n",
    "\n",
    "\n",
    "plt.title(r\"VGG11 $\\alpha$ vs VGG11 Randomized $\\alpha^{rand}$\")\n",
    "plt.scatter(x,y, label='VGG 11', s=marker_size)\n",
    "\n",
    "plt.xlabel(r\"$\\alpha$\")\n",
    "plt.ylabel(r\"$\\alpha^{rand}\")\n",
    "#plt.legend()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_name = 'vgg11'\n",
    "x = np.multiply(alphas[model_name], np.log10(lmaxs[model_name]) )\n",
    "y =  2.0*np.log10(norms[model_name]) \n",
    "plt.scatter(x,y,label=model_name, color='blue' , s=marker_size)\n",
    "\n",
    "\n",
    "plt.title(r\"$\\alpha\\;\\log_{10}\\lambda^{max}$ vs $\\log_{10}\\Vert W\\Vert^{2}_{F}$\"+\"\\nVGG11 BN  Conv2D Layers\")\n",
    "plt.legend(prop=legend_prop)\n",
    "plt.xlabel(r\"$\\alpha\\;\\log_{10}\\lambda^{max}$\")\n",
    "plt.ylabel(r\"$\\log_{10}\\Vert W\\Vert^{2}_{F}$\")\n",
    "\n",
    "plt.savefig(\"img/relation-vgg11.png\")"
   ]
  },
  {
   "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"
  },
  "widgets": {
   "state": {
    "52ecdae62c394a67868cd3ee83e19861": {
     "views": [
      {
       "cell_index": 14
      }
     ]
    },
    "e232317699e24554b5ed09fa6c78c662": {
     "views": [
      {
       "cell_index": 8
      }
     ]
    }
   },
   "version": "1.2.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}