random_feature_online.ipynb

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      "source": [
        "<a href=\"https://colab.research.google.com/github/Pehlevan-Group/sgd_structured_features/blob/main/random_feature_online.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "b5lgo97rxmqI"
      },
      "source": [
        "## Random Feature Model Experiments for SGD on Structured Features Paper\n",
        "\n",
        "### Import necessary API's"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "n9CmAw-gUM2B"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import jax.numpy as jnp\n",
        "from jax import grad, vmap, jit\n",
        "from jax.experimental import optimizers \n",
        "from jax import random\n",
        "from google.colab import drive\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6H__-bIwxxCp"
      },
      "source": [
        "### Optional if on google colab, can save files"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "EWJLS2wa1sbD",
        "outputId": "d98f2f7e-6d5d-4684-818f-92b8ef20f5f6"
      },
      "source": [
        "drive.mount('/content/gdrive', force_remount=True)\n",
        "root_dir = \"/content/gdrive/My Drive/\""
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Mounted at /content/gdrive\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f72tReThx2Hj"
      },
      "source": [
        "### Define a Feature Map \n",
        "\n",
        "For data $\\mathbf x \\in \\mathbb{R}^D$, sample a random projection matrix $G_{ij} \\sim \\mathcal{N}(0,1/D)$ and compute the nonlinear feature map.\n",
        "$$\\mathbf{\\psi}(\\mathbf{x}) = \\phi(\\mathbf{G}\\mathbf x)$$\n",
        "\n",
        "The covariance matrix for these features has the form\n",
        "$$ \\mathbf{\\Sigma} = \\left< \\phi( \\mathbf{G} \\mathbf{x}) \\phi(\\mathbf G \\mathbf x)^\\top \\right>_{\\mathbf x}$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "t0yozMWpUcf8"
      },
      "source": [
        "def feature_map(X, N, nonlin):\n",
        "  P,D = X.shape\n",
        "  G = 10/np.sqrt(D) * np.random.standard_normal((N,D))\n",
        "  G = jnp.array(G)\n",
        "  F = nonlin( X @ G.T )\n",
        "  F = F - jnp.mean(F)\n",
        "  return F\n",
        "\n",
        "tanh = lambda x: jnp.tanh(x)\n",
        "linear = lambda x: x\n",
        "relu = lambda x: x * jnp.heaviside(x,0)\n",
        "\n",
        "P = 3000\n",
        "D = 25\n",
        "N = 3200\n",
        "\n",
        "X = np.random.standard_normal((P,D))\n",
        "F_tanh = feature_map(X, N, tanh)\n",
        "F_relu = feature_map(X, N, relu)\n",
        "\n",
        "def spectra(F):\n",
        "  s = jnp.linalg.svd(F, compute_uv=False)\n",
        "  sorted = s.sort()[::-1]\n",
        "  return sorted\n",
        "\n",
        "def sorted_decomp(F, y, square = True):\n",
        "  u, s, _ = jnp.linalg.svd(F)\n",
        "  inds = jnp.argsort(s)[::-1]\n",
        "  s = s[inds]\n",
        "  u = u[:,inds]\n",
        "  vk = (u.T @ y)**2 / np.sum(y**2)\n",
        "  if square == False:\n",
        "    v_non = u.T @ y / np.sqrt(np.sum(y**2))\n",
        "    return s, v_non\n",
        "  return s, vk\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iWluTq4Uyotd"
      },
      "source": [
        "### Compute theoretical learning curves\n",
        "\n",
        "The expected test loss after $t$ steps has the form\n",
        "\n",
        "$$\\left< L_t \\right> = \\mathbf{\\lambda}^\\top \\mathbf{A}^t \\mathbf{v}^2$$ where \n",
        "\n",
        "$$ A_{ij} = \\left(1-2\\eta\\lambda_i + \\eta^2 \\frac{m+1}{m}\\lambda_i \\right)\\delta_{ij} + \\frac{\\eta^2}{m} \\lambda_i \\lambda_j$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gMocA7SCUSEO"
      },
      "source": [
        "def theory(s, teach, eta, T, m = 1, noise = 0):\n",
        "    A = jnp.eye(len(s)) - 2*eta*jnp.diag(s) + 1.0*(m+1)/m *eta**2 * jnp.diag(s**2) + 1.0/m * eta**2 * jnp.outer(s, s)\n",
        "    Inv_mat = jnp.linalg.inv(jnp.eye(A.shape[0]) - A)\n",
        "    x = s.copy()\n",
        "    theory_loss = []\n",
        "    for t in range(T):\n",
        "        losst = 0.5 * jnp.dot(x, teach) + 0.5/m * eta**2 * noise**2 * jnp.dot(s, Inv_mat @ (s-x))\n",
        "        theory_loss += [losst]\n",
        "        x = A @ x\n",
        "    return theory_loss\n",
        "\n",
        "\n",
        "def theory_eig(s, teach, eta, t, m=1, noise = 0):\n",
        "  A = jnp.eye(len(s)) - 2*eta*jnp.diag(s) + 1.0*(m+1)/m *eta**2 * jnp.diag(s**2) + 1.0/m * eta**2 * jnp.outer(s, s)\n",
        "  eigA, VA = jnp.linalg.eigh(A)\n",
        "  Inv_mat = jnp.linalg.inv(jnp.eye(A.shape[0]) - A)\n",
        "  left = VA.T @ s\n",
        "  right = VA.T @ teach\n",
        "\n",
        "  Inv_mat = jnp.linalg.inv(jnp.eye(A.shape[0]) - A)\n",
        "  theory_loss = []\n",
        "  \n",
        "  losst = 0.5 * jnp.dot(left, eigA**t * right) + 0.5/m * eta**2 * noise**2 * jnp.dot(s, Inv_mat @ (s - eigA**t * left))\n",
        "  return losst\n",
        "\n",
        "def theory_white(t, eta, N, m=1):\n",
        "  return (1 - 2*eta + (m+1)/m * eta**2 + 1/m *N*eta**2)**t\n",
        "def theory_pop_white(t, eta):\n",
        "  return (1-eta)**(2*t)\n",
        "\n",
        "def theory_var(s, teach, eta, T, m = 1):\n",
        "  A = jnp.eye(len(s)) - 2*eta*jnp.diag(s) + 1.0*(m+1)/m *eta**2 * jnp.diag(s**2) + 1.0/m * eta**2 * jnp.outer(s, s)\n",
        "  B = jnp.eye(len(s))-eta*jnp.outer(s, jnp.ones(len(s)))-eta*jnp.outer(jnp.ones(len(s)),s)+ eta**2 * 1.0*(m+1)/m * jnp.outer(s,s)\n",
        "  B = B - jnp.diag( jnp.diag(B) )\n",
        "  x = teach.copy()\n",
        "  theory_loss = []\n",
        "  for t in range(T): \n",
        "      losst = jnp.dot(s**2, x**2) + jnp.dot(teach*s, jnp.dot(B**(2*t), s*teach) )\n",
        "      #losst = jnp.dot(s**2, x**2)\n",
        "      theory_loss += [losst]\n",
        "      x = A @ x\n",
        "  return theory_loss"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XGjt7U9hrIYw"
      },
      "source": [
        "def train_fn(F, y, T, eta, m = 1, noise = 0):\n",
        "  loss = jit( lambda w, X, y: 0.5*jnp.mean( (jnp.dot(X, w)-y)**2 ) )\n",
        "  gloss = jit( grad(loss, 0) )\n",
        "  w = jnp.zeros(F.shape[1])\n",
        "\n",
        "  eta_expt = eta*F.shape[0]\n",
        "  opt_init, opt_update, get_params = optimizers.sgd(eta_expt)\n",
        "  opt_state = opt_init(w)\n",
        "\n",
        "  losses = []\n",
        "  for t in range(T):\n",
        "    start = (t * m) % F.shape[0]\n",
        "    opt_state = opt_update(t, gloss(get_params(opt_state),F[start:start+m,:],y[start:start+m]+noise*jnp.array(np.random.standard_normal(m))), opt_state)\n",
        "    losses += [loss(get_params(opt_state), F, y)]\n",
        "  return losses"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-_zjLQsJ3e2L",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 587,
          "referenced_widgets": [
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            "f7ce7854ef9147b2bd7cfba2d26713b2",
            "e3758070ca3e4170ac623e5502db7612",
            "2019697a437745368c493a2bca9efdbd",
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            "d3e7f10631fd452396ee7012f0c85aff",
            "d0e80aff625a46f5b48bc90894cb882b",
            "23a87039c4d349ccb2f9cf68ac816789",
            "4894b9cdd1e044109a49f53e6f95d19e",
            "817c1c81e0484596b94fbd0504d95467",
            "4155993750c143d7aa5f351f8056481a",
            "d0d4ec5620bf49b699d745529fa540ef",
            "cb493d68f7014b07b3568995c886a4b4",
            "ce6c9dc3027546629da1d8ff5e2f81f5",
            "b3a5d2563bef45d6879e4a1520746ac2",
            "61bb99cace4f4a42abff78b013a882f5",
            "00c096b0198748a3b9543309d9fa83a4"
          ]
        },
        "outputId": "96f586a6-5e6a-49df-fa2f-1c53770e3cca"
      },
      "source": [
        "\n",
        "import tensorflow as tf\n",
        "import tensorflow_datasets as tfds\n",
        "\n",
        "num_tot = 50000\n",
        "num_classes = 10\n",
        "size = 32\n",
        "name = 'mnist'\n",
        "ds = tfds.load(name, split=tfds.Split.TRAIN).shuffle(1024).batch(num_tot)\n",
        "\n",
        "plt.rcParams.update({'font.size': 12})\n",
        "\n",
        "for i,ex in enumerate(ds):\n",
        "  Xtf = ex['image']\n",
        "  image = Xtf.numpy() / 255.0\n",
        "  X = np.reshape(image, (image.shape[0], image.shape[1]*image.shape[2]*image.shape[3]))\n",
        "  X = X / np.outer(np.linalg.norm(X, axis = 1), np.ones(X.shape[1]))\n",
        "  y = ex['label'].numpy()\n",
        "  #y_mat = np.eye(num_classes)[y] \n",
        "  break\n",
        "\n",
        "inds_89 = [i for i in range(y.shape[0]) if y[i]==8 or y[i]==9]\n",
        "X89 = X[inds_89,:]\n",
        "y89 = y[inds_89]\n",
        "y89 = 1.0*(y89==8) -1.0*(y89==9)\n",
        "\n",
        "\"\"\"\n",
        "X89 = X\n",
        "y89 = np.zeros(y.shape)\n",
        "for c in range(10):\n",
        "  if c % 2 ==0:\n",
        "    y89 += 1.0 * (y == c)\n",
        "  else:\n",
        "    y89 += -1.0 * (y == c)\n",
        "\"\"\"\n",
        "\n",
        "num_tot = 50000\n",
        "num_classes = 10\n",
        "size = 32\n",
        "name = 'cifar10'\n",
        "ds = tfds.load(name, split=tfds.Split.TRAIN).shuffle(1024).batch(num_tot)\n",
        "\n",
        "plt.rcParams.update({'font.size': 12})\n",
        "\n",
        "for i,ex in enumerate(ds):\n",
        "  Xtf = ex['image']\n",
        "  image = Xtf.numpy() / 255.0\n",
        "  X_C = np.reshape(image, (image.shape[0], image.shape[1]*image.shape[2]*image.shape[3]))\n",
        "  X_C = X_C / np.outer(np.linalg.norm(X_C, axis = 1), np.ones(X_C.shape[1]))\n",
        "  y_C = ex['label'].numpy()\n",
        "  #y_mat = np.eye(num_classes)[y] \n",
        "  break\n",
        "\n",
        "inds_89 = [i for i in range(y_C.shape[0]) if y_C[i]==8 or y_C[i]==9]\n",
        "X89_C = X_C[inds_89,:]\n",
        "y89_C = y_C[inds_89]\n",
        "y89_C = 1.0*(y89_C==8) - 1.0*(y89_C==9)\n",
        "\n",
        "\"\"\"\n",
        "X89_C = X_C\n",
        "y89_C = np.zeros(y_C.shape)\n",
        "for c in range(10):\n",
        "  if c % 2 ==0:\n",
        "    y89_C += 1.0 * (y_C == c)\n",
        "  else:\n",
        "    y89_C += -1.0 * (y_C == c)\n",
        "\"\"\""
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\u001b[1mDownloading and preparing dataset mnist/3.0.1 (download: 11.06 MiB, generated: 21.00 MiB, total: 32.06 MiB) to /root/tensorflow_datasets/mnist/3.0.1...\u001b[0m\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "WARNING:absl:Dataset mnist is hosted on GCS. It will automatically be downloaded to your\n",
            "local data directory. If you'd instead prefer to read directly from our public\n",
            "GCS bucket (recommended if you're running on GCP), you can instead pass\n",
            "`try_gcs=True` to `tfds.load` or set `data_dir=gs://tfds-data/datasets`.\n",
            "\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "8bcd4747c2b048528c0b8c6a9fac9ffa",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, description='Dl Completed...', max=4.0, style=ProgressStyle(descriptio…"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "\n",
            "\u001b[1mDataset mnist downloaded and prepared to /root/tensorflow_datasets/mnist/3.0.1. Subsequent calls will reuse this data.\u001b[0m\n",
            "\u001b[1mDownloading and preparing dataset cifar10/3.0.2 (download: 162.17 MiB, generated: 132.40 MiB, total: 294.58 MiB) to /root/tensorflow_datasets/cifar10/3.0.2...\u001b[0m\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "88f10887b22f4d86b91d9640c07cc62b",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=1.0, bar_style='info', description='Dl Completed...', max=1.0, style=Progre…"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "a1f5945f9f0f4586b808d5d6a4fbe69e",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=1.0, bar_style='info', description='Dl Size...', max=1.0, style=ProgressSty…"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "7ed59b0f45294b1bb7a1dca4981482df",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=1.0, bar_style='info', description='Extraction completed...', max=1.0, styl…"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "\n",
            "\n",
            "\n",
            "\n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "541cbccd1ee4423b873f29295a771e9b",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=1.0, bar_style='info', max=1.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\rShuffling and writing examples to /root/tensorflow_datasets/cifar10/3.0.2.incompleteJ8XAZV/cifar10-train.tfrecord\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "19bcecead3ca4aa585aeba1d6ac7e617",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, max=50000.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\r"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "2019697a437745368c493a2bca9efdbd",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=1.0, bar_style='info', max=1.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\rShuffling and writing examples to /root/tensorflow_datasets/cifar10/3.0.2.incompleteJ8XAZV/cifar10-test.tfrecord\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "817c1c81e0484596b94fbd0504d95467",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, max=10000.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\u001b[1mDataset cifar10 downloaded and prepared to /root/tensorflow_datasets/cifar10/3.0.2. Subsequent calls will reuse this data.\u001b[0m\n",
            "\r"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'\\nX89_C = X_C\\ny89_C = np.zeros(y_C.shape)\\nfor c in range(10):\\n  if c % 2 ==0:\\n    y89_C += 1.0 * (y_C == c)\\n  else:\\n    y89_C += -1.0 * (y_C == c)\\n'"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Kykro7MPEZ3K",
        "outputId": "e08f44d0-6b04-4484-af0c-fbfd550d0121"
      },
      "source": [
        "print(X89_C.shape)\n",
        "print(X89_C)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(50000, 3072)\n",
            "[[0.02005054 0.02005054 0.02005054 ... 0.01809158 0.01809158 0.01809158]\n",
            " [0.03227202 0.03240483 0.03267044 ... 0.00371859 0.0059763  0.01022611]\n",
            " [0.0192574  0.0123348  0.00629327 ... 0.02970422 0.03008182 0.03096287]\n",
            " ...\n",
            " [0.00805227 0.00861734 0.00889988 ... 0.0303726  0.02867739 0.0264171 ]\n",
            " [0.01353016 0.01312016 0.0079951  ... 0.01086513 0.01148014 0.00758509]\n",
            " [0.03162795 0.03179619 0.03095502 ... 0.04289962 0.04273138 0.04289962]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KE68gybX7hO2",
        "outputId": "ab26ac28-f9c6-45d7-f5d6-1122b25a605f"
      },
      "source": [
        "P_sub = 2500\n",
        "N = 4000\n",
        "\n",
        "# MNIST RELU\n",
        "F_MNIST = feature_map(X89[0:P_sub,:], N, relu)\n",
        "s, vk = sorted_decomp(F_MNIST, y89[0:P_sub])\n",
        "\n",
        "F_MNIST = F_MNIST / s[0]\n",
        "s = s/s[0]\n",
        "\n",
        "# MNIST TANH\n",
        "F_MNIST_tanh = feature_map(X89[0:P_sub,:], N, tanh)\n",
        "s_t, vk_t = sorted_decomp(F_MNIST_tanh, y89[0:P_sub])\n",
        "F_MNIST_tanh = F_MNIST_tanh / s_t[0]\n",
        "s_t = s_t/s_t[0]\n",
        "\n",
        "# ISO Features RELU\n",
        "X = np.random.standard_normal((P_sub, 784))\n",
        "\n",
        "F_MNIST_iso = feature_map(X, N, relu)\n",
        "print(F_MNIST_iso.shape)\n",
        "s_iso, vk_iso = sorted_decomp(F_MNIST_iso, y89[0:P_sub])\n",
        "\n",
        "F_MNIST_iso = F_MNIST_iso / s_iso[0]\n",
        "s_iso = s_iso/s_iso[0]\n",
        "\n",
        "# CIFAR-RELU\n",
        "F_CIFAR = feature_map(X89_C[0:P_sub], N, relu)\n",
        "s_c, vk_c = sorted_decomp(F_CIFAR, y89_C[0:P_sub])\n",
        "\n",
        "F_CIFAR = F_CIFAR / s_c[0]\n",
        "s_c = s_c/s_c[0]\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(2500, 4000)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "a-HL7X1QjSm_",
        "outputId": "c4f4a1ea-7258-4118-b094-0a58c1bcc026"
      },
      "source": [
        "C = 100\n",
        "N = 100\n",
        "mvals = jnp.logspace(0, 3, 1000)\n",
        "m = 10\n",
        "scale_eta = [0.1, 0.5,1]\n",
        "all_res = []\n",
        "for scale in scale_eta:\n",
        "  res = []\n",
        "  for m in mvals:\n",
        "    t = C/m\n",
        "    eta = scale*m/(m+N+1)\n",
        "    res += [theory_white(t, eta, N, m)]\n",
        "  all_res += [res]\n",
        "\n",
        "plt.rcParams.update({'font.size': 16})\n",
        "\n",
        "\n",
        "plt.loglog(mvals, jnp.ones(len(mvals)), '--',color = 'black')\n",
        "for i,r in enumerate(all_res):\n",
        "  plt.plot(mvals, r, label = r'$\\eta = %0.1f \\eta^*$' % scale_eta[i])\n",
        "plt.legend()\n",
        "plt.xlabel(r'$m$',fontsize = 20)\n",
        "plt.ylabel(r'$L_{C/m}$',fontsize = 20)\n",
        "plt.tight_layout()\n",
        "plt.savefig(root_dir + 'isotropic_optimal_m.pdf')\n",
        "plt.show()\n",
        "\n",
        "\n",
        "\n",
        "mvals = jnp.logspace(0, 1.5, 30)\n",
        "scale_eta = [0.1, 0.3, 0.5]\n",
        "all_res = []\n",
        "eta = 1\n",
        "for scale in scale_eta:\n",
        "  print(scale)\n",
        "  res = []\n",
        "  for m in mvals:\n",
        "    t = C/m\n",
        "    eta = scale\n",
        "    #eta = scale*m/(m+N+1)\n",
        "    res += [theory_eig(s**2, vk/s**2, eta, t, m)]\n",
        "  all_res += [res]\n",
        "\n",
        "m_expt_vals = [2, 3, 5, 10, 25]\n",
        "all_expt = []\n",
        "all_expt_std = []\n",
        "y_expt = y89[0:P_sub]\n",
        "\n",
        "for scale in scale_eta:\n",
        "  print(scale)\n",
        "  res = []\n",
        "  res_std = []\n",
        "  for m in m_expt_vals:\n",
        "    arr = []\n",
        "    for i in range(30):\n",
        "      random_perm = np.random.permutation(P_sub)\n",
        "      arr += [ train_fn(F_MNIST[random_perm,:], y_expt[random_perm], int(C/m), scale, m = m)[-1] ]\n",
        "    res += [ np.mean(arr )]\n",
        "    res_std += [ np.std(arr) ]\n",
        "  all_expt += [res]\n",
        "  all_expt_std += [res_std]\n",
        "\n",
        "print(all_expt)\n",
        "print(all_expt_std)\n",
        "\n",
        "#plt.loglog(mvals, jnp.dot(power_law_s,teach)*jnp.ones(len(mvals)), '--',color = 'black')\n",
        "for i,r in enumerate(all_res):\n",
        "  plt.loglog(mvals, r, label = r'$\\eta = %0.1f$' % scale_eta[i], color = 'C%d' % i)\n",
        "  plt.errorbar(m_expt_vals, all_expt[i], jnp.array(all_expt_std[i]), fmt='o', color = 'C%d' % i)\n",
        "plt.legend()\n",
        "plt.ylim([1e-1,0.5])\n",
        "plt.xlabel(r'$m$',fontsize = 20)\n",
        "plt.ylabel(r'$L_{C/m}$',fontsize = 20)\n",
        "plt.tight_layout()\n",
        "plt.savefig(root_dir + 'optimal_m_powerlaw.pdf')\n",
        "plt.show()\n",
        "\n",
        "N = 100\n",
        "b = 1\n",
        "a = 2\n",
        "teach = jnp.linspace(1,N,N)**(-a+b)\n",
        "power_law_s = jnp.linspace(1,N, N)**(-b)\n",
        "\n",
        "\n",
        "scale_eta = [0.1, 0.3, 0.5]\n",
        "all_res = []\n",
        "eta = 1\n",
        "for scale in scale_eta:\n",
        "  print(scale)\n",
        "  res = []\n",
        "  for m in mvals:\n",
        "    t = C/m\n",
        "    eta = scale\n",
        "    #eta = scale*m/(m+N+1)\n",
        "    res += [theory_eig(power_law_s, teach, eta, t, m)]\n",
        "  all_res += [res]\n",
        "\n",
        "\n",
        "\n",
        "#plt.loglog(mvals, jnp.dot(power_law_s,teach)*jnp.ones(len(mvals)), '--',color = 'black')\n",
        "for i,r in enumerate(all_res):\n",
        "  plt.loglog(mvals, r, label = r'$\\eta = %0.1f$' % scale_eta[i])\n",
        "plt.legend()\n",
        "plt.ylim([1e-2,1])\n",
        "plt.xlabel(r'$m$',fontsize = 20)\n",
        "plt.ylabel(r'$L_{C/m}$',fontsize = 20)\n",
        "plt.tight_layout()\n",
        "plt.savefig(root_dir + 'optimal_m_powerlaw_synthetic.pdf')\n",
        "plt.show()\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "0.1\n",
            "0.3\n",
            "0.5\n",
            "0.1\n",
            "0.3\n",
            "0.5\n",
            "[[0.25698152, 0.31204265, 0.37143677, 0.43043202, 0.4693448], [0.13713437, 0.17716818, 0.23027563, 0.32362396, 0.41616154], [0.12244478, 0.13714121, 0.17406704, 0.25190836, 0.37055793]]\n",
            "[[0.011615465, 0.008298762, 0.007172362, 0.005092019, 0.0018328739], [0.014714378, 0.016935987, 0.014698934, 0.009648443, 0.0055642137], [0.020385938, 0.017576898, 0.01906778, 0.014050921, 0.0074845534]]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "0.1\n",
            "0.3\n",
            "0.5\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 551
        },
        "id": "AImnQT03FByR",
        "outputId": "846a4094-d313-42d3-f287-d9ad49359658"
      },
      "source": [
        "plt.rcParams.update({'font.size': 16})\n",
        "fs = 20\n",
        "plt.loglog(jnp.linspace(1,len(s), len(s)), s, label = r'ReLU')\n",
        "plt.loglog(jnp.linspace(1,len(s), len(s)), s_t, label = 'Tanh')\n",
        "plt.xlabel(r'$k$',fontsize = fs)\n",
        "plt.ylabel(r'$\\lambda_k$',fontsize=fs)\n",
        "plt.legend()\n",
        "plt.tight_layout()\n",
        "plt.savefig(root_dir + 'spectra_relu_tanh_mnist_random_features.pdf')\n",
        "plt.show()\n",
        "\n",
        "cum_sum = 1-jnp.cumsum(vk)/jnp.sum(vk)\n",
        "cum_sum_tanh = 1- jnp.cumsum(vk_t)/jnp.sum(vk_t)\n",
        "\n",
        "plt.loglog(jnp.linspace(1,len(s), len(s)),cum_sum, label = r'ReLU')\n",
        "plt.loglog(jnp.linspace(1,len(s), len(s)), cum_sum_tanh, label = r'Tanh')\n",
        "plt.xlabel(r'$k$',fontsize = fs)\n",
        "plt.ylabel(r'$\\sum_{n=k}^\\infty \\lambda_n v_n^2$',fontsize=fs)\n",
        "plt.ylim([1e-2, 2])\n",
        "plt.legend()\n",
        "plt.tight_layout()\n",
        "plt.savefig(root_dir + 'task_power_relu_tanh_mnist_random_features.pdf')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tLn9IgZfK1gk",
        "outputId": "049ad295-e184-4b56-9f5f-16122752f61e"
      },
      "source": [
        "eta = 0.6\n",
        "T = 200\n",
        "m = 2\n",
        "\n",
        "all_th = []\n",
        "all_var = []\n",
        "all_mean = []\n",
        "all_std = []\n",
        "\n",
        "eta_vals = [0.1, 0.5]\n",
        "for eta in eta_vals:\n",
        "  print(eta)\n",
        "  th = 2*jnp.array( theory(s**2, vk / s**2, eta, T, m = m) )\n",
        "  #expt = train_fn(F_MNIST, y89[0:P_sub], T, eta, m = m)\n",
        "  all_expt = []\n",
        "  for n in range(40):\n",
        "    perm = np.random.permutation(P_sub)\n",
        "    all_expt += [ train_fn(F_MNIST[perm,:], y89[0:P_sub][perm], T, eta, m = m) ] \n",
        "  all_expt = 2*jnp.array(all_expt)\n",
        "  var = 2*jnp.array( theory_var(s**2, vk / s**2, eta, T, m = m) )\n",
        "  \n",
        "  all_th +=[th]\n",
        "  all_var += [var]\n",
        "  all_mean += [jnp.mean(all_expt, axis =0)]\n",
        "  all_std += [jnp.std(all_expt, axis =0)]\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.1\n",
            "0.5\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 375
        },
        "id": "BcIh7I4NPJiR",
        "outputId": "cf7fd0db-c273-4dc6-f8ce-6bdd06fbfedc"
      },
      "source": [
        "eta = 0.3\n",
        "T = 8000\n",
        "m = 5\n",
        "th = jnp.array( theory(s**2, vk / s**2, eta, T, m = m) )\n",
        "expt = train_fn(F_MNIST, y89[0:P_sub], T, eta, m = m)\n",
        "var = jnp.array( theory_var(s**2, vk / s**2, eta, T, m = m) )\n",
        "\n",
        "\n",
        "th_tanh = jnp.array( theory(s_t**2, vk_t / s_t**2, eta, T, m = m) )\n",
        "expt_tanh = train_fn(F_MNIST_tanh, y89[0:P_sub], T, eta, m=m)\n",
        "\n",
        "th_cifar = jnp.array( theory(s_c**2, vk_c / s_c**2, eta, T, m = m) )\n",
        "expt_cifar = train_fn(F_CIFAR, y89_C[0:P_sub], T, eta, m=m)\n",
        "\n",
        "eta_iso = 0.5/P_sub\n",
        "th_iso = jnp.array( theory(s_iso**2, vk_iso / s_iso**2, eta_iso, T, m = m) )\n",
        "expt_iso = jnp.array( train_fn(F_MNIST_iso, y89[0:P_sub], T, eta_iso, m =  m) )\n",
        "\n",
        "print(expt_cifar)\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "error",
          "ename": "KeyboardInterrupt",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
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            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/_src/numpy/lax_numpy.py\u001b[0m in \u001b[0;36mdeferring_binary_op\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m   5664\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0m_scalar_types\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0m_arraylike_types\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mTracer\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   5665\u001b[0m       \u001b[0;32mreturn\u001b[0m \u001b[0mNotImplemented\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 5666\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mbinary_op\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   5667\u001b[0m   \u001b[0;32mreturn\u001b[0m \u001b[0mdeferring_binary_op\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   5668\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
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            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/_src/numpy/lax_numpy.py\u001b[0m in \u001b[0;36m_promote_args\u001b[0;34m(fun_name, *args)\u001b[0m\n\u001b[1;32m    320\u001b[0m   \u001b[0m_check_arraylike\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun_name\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    321\u001b[0m   \u001b[0m_check_no_float0s\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun_name\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 322\u001b[0;31m   \u001b[0;32mreturn\u001b[0m \u001b[0m_promote_shapes\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun_name\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0m_promote_dtypes\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    323\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    324\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_promote_args_inexact\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun_name\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/_src/numpy/lax_numpy.py\u001b[0m in \u001b[0;36m_promote_dtypes\u001b[0;34m(*args)\u001b[0m\n\u001b[1;32m    266\u001b[0m     \u001b[0mto_dtype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mweak_type\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdtypes\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_lattice_result_type\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    267\u001b[0m     \u001b[0mto_dtype\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdtypes\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcanonicalize_dtype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mto_dtype\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 268\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mlax\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_convert_element_type\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mto_dtype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mweak_type\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32min\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    269\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    270\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_promote_dtypes_inexact\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/_src/numpy/lax_numpy.py\u001b[0m in \u001b[0;36m<listcomp>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m    266\u001b[0m     \u001b[0mto_dtype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mweak_type\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdtypes\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_lattice_result_type\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    267\u001b[0m     \u001b[0mto_dtype\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdtypes\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcanonicalize_dtype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mto_dtype\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 268\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mlax\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_convert_element_type\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mto_dtype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mweak_type\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32min\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    269\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    270\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_promote_dtypes_inexact\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/_src/lax/lax.py\u001b[0m in \u001b[0;36m_convert_element_type\u001b[0;34m(operand, new_dtype, weak_type)\u001b[0m\n\u001b[1;32m    453\u001b[0m   \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    454\u001b[0m     return convert_element_type_p.bind(operand, new_dtype=new_dtype,\n\u001b[0;32m--> 455\u001b[0;31m                                        weak_type=new_weak_type)\n\u001b[0m\u001b[1;32m    456\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    457\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mbitcast_convert_type\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0moperand\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mArray\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnew_dtype\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mDType\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m->\u001b[0m \u001b[0mArray\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/core.py\u001b[0m in \u001b[0;36mbind\u001b[0;34m(self, *args, **params)\u001b[0m\n\u001b[1;32m    262\u001b[0m         args, used_axis_names(self, params) if self._dispatch_on_params else None)\n\u001b[1;32m    263\u001b[0m     \u001b[0mtracers\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtop_trace\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfull_raise\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 264\u001b[0;31m     \u001b[0mout\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtop_trace\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprocess_primitive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtracers\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    265\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mmap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfull_lower\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmultiple_results\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0mfull_lower\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mout\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    266\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/core.py\u001b[0m in \u001b[0;36mprocess_primitive\u001b[0;34m(self, primitive, tracers, params)\u001b[0m\n\u001b[1;32m    604\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    605\u001b[0m   \u001b[0;32mdef\u001b[0m \u001b[0mprocess_primitive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprimitive\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtracers\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 606\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mprimitive\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mimpl\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mtracers\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    607\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    608\u001b[0m   \u001b[0;32mdef\u001b[0m \u001b[0mprocess_call\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprimitive\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtracers\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/interpreters/xla.py\u001b[0m in \u001b[0;36mapply_primitive\u001b[0;34m(prim, *args, **params)\u001b[0m\n\u001b[1;32m    230\u001b[0m   \u001b[0;34m\"\"\"Impl rule that compiles and runs a single primitive 'prim' using XLA.\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    231\u001b[0m   \u001b[0mcompiled_fun\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mxla_primitive_callable\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprim\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0munsafe_map\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marg_spec\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 232\u001b[0;31m   \u001b[0;32mreturn\u001b[0m \u001b[0mcompiled_fun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    233\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    234\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/interpreters/xla.py\u001b[0m in \u001b[0;36m_execute_compiled_primitive\u001b[0;34m(prim, compiled, result_handler, *args)\u001b[0m\n\u001b[1;32m    348\u001b[0m   \u001b[0mdevice\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcompiled\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlocal_devices\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    349\u001b[0m   \u001b[0minput_bufs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mit\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mchain\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfrom_iterable\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdevice_put\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdevice\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32min\u001b[0m \u001b[0margs\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mtoken\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 350\u001b[0;31m   \u001b[0mout_bufs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcompiled\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexecute\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minput_bufs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    351\u001b[0m   \u001b[0mcheck_special\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprim\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout_bufs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    352\u001b[0m   \u001b[0;32mreturn\u001b[0m \u001b[0mresult_handler\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mout_bufs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 284
        },
        "id": "eFH77A3OspMU",
        "outputId": "cf7a8db9-e5ec-4a79-dc64-d7883a8073bc"
      },
      "source": [
        "fs = 20\n",
        "plt.rcParams.update({'font.size': 16})\n",
        "\n",
        "plt.loglog(2*jnp.array(expt), label = r'ReLU')\n",
        "plt.loglog(2*jnp.array(expt_tanh), label = r'Tanh')\n",
        "plt.loglog(2*th, '--', color = 'black', label = r'Gauss. Theory')\n",
        "plt.loglog(2*th_tanh, '--', color = 'black')\n",
        "plt.xlabel(r'$t$',fontsize = fs)\n",
        "plt.ylabel(r'$L_t$',fontsize=fs)\n",
        "plt.legend()\n",
        "plt.tight_layout()\n",
        "plt.savefig(root_dir +'test_err_relu_tanh_mnist_random_features_m_5.pdf')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 321
        },
        "id": "k4YF9tcyWhte",
        "outputId": "6a55b72b-5ae4-40c6-dc8a-ad927eb0bae2"
      },
      "source": [
        "fs = 20\n",
        "print(expt_cifar)\n",
        "\n",
        "plt.rcParams.update({'font.size': 16})\n",
        "#plt.figure(figsize=(6.4,4))\n",
        "plt.loglog(2*jnp.array(expt), label = 'MNIST 8-9')\n",
        "plt.loglog(2*th, '--', color = 'black', label = 'Gauss. Theory')\n",
        "plt.loglog(np.exp( - eta*np.linspace(1,T,T)/4000 ) , label = r'$e^{-t/N}$')\n",
        "plt.xlabel(r'$t$',fontsize = fs)\n",
        "plt.ylabel(r'$L_t$',fontsize=fs)\n",
        "plt.legend()\n",
        "plt.tight_layout()\n",
        "plt.savefig(root_dir +'test_err_mnist_random_power_law_RF.pdf')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 284
        },
        "id": "cGH9cz8Ftftw",
        "outputId": "8843ff39-8686-4615-a0ea-f782b0ca3689"
      },
      "source": [
        "fs = 20\n",
        "plt.rcParams.update({'font.size': 16})\n",
        "\n",
        "plt.loglog(2*jnp.array(expt), label = 'MNIST ReLU' )\n",
        "plt.loglog(2*jnp.array(expt_cifar), label = 'CIFAR ReLU')\n",
        "plt.loglog(2*expt_iso, label = 'Iso. ReLU')\n",
        "plt.loglog(2*th, '--',color = 'black', label ='Gauss. Theory')\n",
        "plt.loglog(2*th_iso, '--',color = 'black')\n",
        "plt.loglog(2*th_cifar, '--', color = 'black')\n",
        "plt.xlabel(r'$t$',fontsize = fs)\n",
        "plt.ylabel(r'$L_t$',fontsize=fs)\n",
        "plt.legend()\n",
        "plt.tight_layout()\n",
        "plt.savefig(root_dir +'structured_data.pdf')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 551
        },
        "id": "g58qcrokeko9",
        "outputId": "1ad229e8-e78c-4b5a-ab60-7c81b196e693"
      },
      "source": [
        "plt.loglog(jnp.linspace(1,1000,1000), s[0:1000], label = r'MNIST ReLU')\n",
        "plt.loglog(jnp.linspace(1,1000,1000), s_c[0:1000], label = 'CIFAR ReLU')\n",
        "plt.loglog(jnp.linspace(1,1000,1000), s_iso[0:1000], label = 'Iso. ReLU')\n",
        "plt.xlabel(r'$k$',fontsize = fs)\n",
        "plt.ylabel(r'$\\lambda_k$',fontsize=fs)\n",
        "plt.legend()\n",
        "plt.tight_layout()\n",
        "plt.savefig(root_dir + 'spectra_relu_mnist_vs_iso.pdf')\n",
        "plt.show()\n",
        "\n",
        "cum_sum = 1- jnp.cumsum(vk) / jnp.sum(vk)\n",
        "cum_sum_iso = 1-jnp.cumsum(vk_iso)/jnp.sum(vk_iso)\n",
        "cum_sum_c = 1-jnp.cumsum(vk_c) / jnp.sum(vk_c)\n",
        "\n",
        "plt.loglog(jnp.linspace(1,1000,1000), cum_sum[0:1000], label = r'MNIST ReLU')\n",
        "plt.loglog(jnp.linspace(1,1000,1000), cum_sum_c[0:1000], label = r'CIFAR ReLU')\n",
        "plt.loglog(jnp.linspace(1,1000,1000), cum_sum_iso[0:1000], label = r'Iso. ReLU')\n",
        "plt.xlabel(r'$k$',fontsize = fs)\n",
        "plt.ylabel(r'$\\sum_{n=k}^\\infty \\lambda_n v_n^2$',fontsize=fs)\n",
        "plt.ylim([1e-2, 2])\n",
        "plt.legend()\n",
        "plt.tight_layout()\n",
        "plt.savefig(root_dir + 'task_power_relu_mnist_vs_iso.pdf')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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VsbRQDV5FMSdSShafWMxnYZ8RWCWQ7zp+RzW7+/8RaggqbAzAqGEDsGYchM/XJul0DSjy2y/Ep7EpIpYNx2PYeyaeGzl6KtlaElrXjY713AgNcMPZ3nzuXFaUim7rha28vu11KttU5vtO31PLpVaZ16DCxgCMHjYpcfBNU6jZGp5YXLJDZWaz41QcG47HsjkilmupN7DQCYJrVs673FarmkOFWnFQUczR0atHeWnjS2TLbL7v+D2NXBuV6flV2BiA0cMGYMdUbWTa4FVQq12pHFKvl/x7MYGNx2PYeDyWiCva5TbfqvZ0rOfOw42q09THRQWPopioC0kXGLZ+GImZiczsPLNMA0eFjQGYRNhkZcC3zcHOGYZt1UarlbKL19PYHBHLhuOx7D59jRs5erwr29EryJNejT2pV91JBY+imJjLKZd5Zt0zJN9IZn63+dSpXKdMzqvCxgBMImwADi+F35+DPjPggScNeqqkjCz+PhrD6oPR7Ii8So5e4u/mSO8gT3oFeaqRbYpiQi4mX2TwX4Ox0Fmwss/KMhmlpsKmFJXpejaFISXM6QRJl2B0uDbTQBm4lpLJn0eusPpgNGFntbuYG3k50zvIk55B1anurJY5UBRjC7scxnN/P8foB0YzrPHdCzCWNhU2BmAyLRuA83thXhcIfQtC3yjz019OTOePQ5dZdTCaQxe1mRUe9K1Cryae9GniSSVbNapNUYxlzKYxhF0JY+0ja3GxNezy8Wo9m/LOJwTq94GdX0PS5TI/fXVnO55/qBarRrVh82uhvNo5gOtpN3h3xRG6Tt3GnjPXyrwmRVE0wxoPIzUrlXlH5hlt8k4VNuVJp4mQkwWb81/Ns6z4VXNgdMc6/P1KW34f2RJbKwsGzd7Dl+tOkKXmZ1OUMtegagN61OrBD0d/YPSm0cSkxpR5DSpsypMqtSBkOPzzE1wx/iJLQgia1azCmtFtGNDMm283RzLgf7s5dy3V2KUpSoUihOCTNp/wWvBr7L28l94rejPr0CwysstuRV/VZ1MCJtVnkyv9Okx/AKoHwdMrwISGJK85FM2byw6j10s+6tuQR5p6G7skRalwLiRd4Mv9X7LpwiaqO1RnRNAIetfujaXOslSOr/psKgq7ytBuApzZAqfWG7ua2/Rs7MlfYx+ivmclxv12kLGL/yFJrSSqKGWqRqUaTOswjXld51HVtirv73qffiv7sTZqrUFnjVYtmxIwyZYNQPYNmNECdJYwchdYlM5fLKUlO0fPjC2nmbbxFNWdbZn2+AM0q1nZ2GUpSoUjpWTzhc188883RCZEUq9KPV5q8hJtvdsW+0Zt1bKpSCytofOHcPUEHJhv7GruYmmhY0zHOvw2vAUAA2fuZsr6k1xNyTRyZYpSsQgh6ODTgaW9lvJxm49JvpHMqE2j+Hjvx6V/LtWyKT6TbdmAdqPn/J4QF6GteWNbydgV5SspI4t3Vxxh5b/RCAHBNSvTub47Xep74KtmI1CUMpWlz2Jl5EpqVqpJc4/mxTqGuqnTAEw6bACi/4FZodDmFW1YtAk7Gp3I30djWH8shmOXkwCo4+ZIlwbudK7vQWMvZ3Q60xnsoChK/lTYGIDJhw3AsuFwdDmM2geVaxq7mkK5EJ/GhuMx/H00hrCoeHL0Eu/Kdozu4M+jTb3V4m6KYsJU2BiAWYRN4kX4phkE9oT+c41dTZElpN1gU0QsC3af4+CFBGpVc+DlzgH0bFRdtXQUxQSpAQKlSAjRSwgxKzEx0dil3J+zN7QaDUeWwsVwY1dTZC721jzS1JsVL7Zi1tPNsLLQMeaXf3h4+nY2HIsx2tQbiqIUjWrZlIBZtGwAMpNhelOwtIEHnoJ6vcCtvknd8FlYOXrJmkPRTF1/kqhraTzg48KQlr609q+Gq5ONsctTlApPXUYzALMJG4Cz22HzJ3B+NyC1qW3q9dYeXk3NLniycvQsDb/I9I2nuJyoTblR192J1v7VaO1flZBaVXG0Ma37ixSlIlBhYwBmFTa5UmIh4g84vgrObgN9NlTy0vp06vWCmq0MstqnoeToJUejE9kZeY2dkVfZFxVPZrYeS50gqIYLrf2r0ca/Gk1quGBtqa4aK4qhqbAxALMMm1ulX4eT6+D4aojcANkZYF8NAh/WWjx+bbVLb2YkIyuHA+eus/P0VXZEXuPwxQT0EuytLXjQrwpd6nvQvaEHlR2sjV2qopRLKmwMwOzD5laZKVrgHF+tBdCNZLCpBAHdtBaPf8cyWwG0NCWmZ7HnzDV2RV5l68k4oq6lYakTtA1wpVdQdToEuuNspxZ2U5TSosLGAMpV2NwqKwPObtUutUX8CenxYGmnBU6DftrDjC615ZJScjQ6idWHollz8DKXEtIBcLazwtPFDi8XO+pVd2JoK1+qOppXi05RTIUKGwMot2Fzq5xsOL8Ljq2CiDWQfFkb0dbrG9CZbx+IXi85cP46+89d59L1dC4lpHPpejqnYpOxt7ZkRLtaPNemFnbW5heqimJMKmwMoEKEza30etjyCWybDM2GQo+pZh04+YmMTebztSdYfywG90o2DGtbm15B1XFzsjV2aYpiFlTYGECFCxvQJvjc+CHsmALNn4eHvzS7YdOFsS8qns/+iiD83HV0Alr7V6NvEy96BXmqUW2Kcg8qbAygQoYNaIGz/l3Y9Q2EjIRun5bLwAE4GZPMqn+jWXnwEhfi0/F0tuXF9v4MCPbGxlJdYlOUO6mwMYAKGzagBc66t2DPDGg5CrpMKreBA9rggm2nrjJtw0kOnE+gurMt3Rp60KJWVVr4VcXZXo1oUxQoOGzULdZK8QgBXT/Rbgrd/S1YWEHH98tt4AghaBfgSts61dgReZVZ287w897z/LAzCp2AJ0J8eLVzXXX/jqIUQIWNUnxCQPcvICcLdkwFnRV0eNvYVRmUEIKH6rjyUB1XMrNz+Pd8AmsOXebnsPOsPniZF0Nr08jbmRqV7fF0scNCzUytKIAKG6WkhIAeU7QWzrYvQGcJoW8Yu6oyYWNpQUgtbR62p1rU5IPVR/n0r4i8112dbOj3gBf9m3kT4O5kxEoVxfhUn00JVOg+mzvp9bDyJTj4M3R4F9q+ZuyKypyUkovX07kQn8a5+DQ2Ho9ly4lYsvWSPk08eaNbIJ4udsYuU1EMSvXZ3IMQ4l3gacAfeERKucLIJZkfnQ76fKu1cDZ9pPXhtB5r7KrKlBCCGlXsqVHFnlbAoAd9uJqSyQ87zzJ7+1nWHb3CY8E1eLqlL/5ujsYuV1HKlAobzXrgJ2CesQsxazoL6Ps9yBxY/552Sa3lS8auyqiqOdrwetdABj3ow5T1J/kl7AILdp+jWc3KdGugjWbzqmxHZXsrRDkdXKEoYIJhI4TwBt4AgoEgwA7wk1JG5bNvDWAq0BkQwAbgZSnl+aKcU0q55+bxSlS7AlhYQr9ZWgtn3VvaoIGQYcauyui8K9szZWAT3nq4Hr/uu8Afhy7z8Z/H8173crGjTxNPnmpRU11qU8olk+uzEUKEAr8C4YAF0IV8wkYIYQ8cBDKBdwAJTALsgcZSytRinHsL8HVhL6OpPpt7yMmCJUO1+dRqtgErW7Cw1lo7FtbaZbZbv7d1hob9wTXA2JWXmfPX0jh2OZFLCRlsPxXH9lNXcbGz4odnmtPY28XY5SlKsZjNTZ1CCJ2UUn/z++eB2eQfNmOBKUBdKWXkzW1+wClgvJRyys1tG4AmBZyuj5Ry5y3H3IIKm9KTfUNr3Vw5DDk3QJ+lhVBO1u3f52TBjRTt8lvtjtBipPa1nM27dj+n41IYMi+M+NQbPN7ch0belejZ2BMri4r130Exb2YTNre6T9hsBGyllK3v2L4VQErZrhjn24IKG+NIiYPw+bBvDqRcgSq1IWQ4NHkCbCrOsOHYpAxeXXKQfVHxZGTp6RDoxndPNFWzTytmo6CwMec/mRoAR/LZfhSob6iTCiGGCSH2CyH2x8XFGeo0FY+jK7R7HV4+DI/OBfsq8Nd4+Koe/DUBYo9rw6vLObdKtvz4XAhHP+jGR30bsvlELP1m7GRx2HmSM7KMXZ6iFJs5t2xuAFOklBPu2D4JmCClLPTgByHEROB5wBVIBjKAFlLKi/d6n2rZGNjFcAibCUeWaZfdrJ3AoxFUbwzVg8CjMbjW1fp8yqm/j17h87URnI5LxdZKR8/Gnrzbo76ai00xWeo+m3uQUk4EJhq5DOVO3s3AexZ0/lBbqvrKIbh8CA4shKw0bR8LG6jVTltfp05XbTRcOdKlgQed67vz74UEloRfZMn+Cxw4f51XOgXg4WxLkxouqk9HMQvm/Jt5Haicz/YqN19TygsnD2g25L/n+hy4FqkFT/QBreWz+Alwqg4PPA1NnwYXH+PVW8qEEDzgU5kHfCrTJ8iTEYvCGf3LPwA42VrSO8iT59r4UctV3SiqmC5zvoy2CbCWUra5Y/sWtM9V5AECRairF9DL39//hVOnThnqNEph5WTDqXXaAINT67VttTtol9wc3cHRTQssp+pQpZbZz0ydkpnNxetpnLuWxrqjV1hz6DJ6veSZ1r4MaeWLd2V7Y5eoVGDlcTTay8CXQICU8szNbb5oQ58nSCm/MnR9qs/GBCWch38WweGlkHhBG3J9q7o9tGl17KsYpz4DiEvOZPK6CH7br3UxtqxVlT5NPOlc352qjjZGrk6paMwqbIQQ/W9+2xEYAbwIxAFxUsqtN/dxQLupM53/bur8CHBCu6kzxdB1qrAxcVJC+nVIiYWUGLgQBls/11o5/edBjQeNXWGpuhCfxvJ/LrHswEWirqVhbaHj0WZevNOjPg425nzFXDEn5hY2BRW1VUoZest+Ptw+Xc1GtOlqogxdI6iwMUuXwmHJM5B4ETq+B63GlLubR6WUHLucxOKwC/wcdp46bo4828aPno2rY2+tQkcxLLMKG1On+mzMXEYirBoNx1aCXzvo9im4NzB2VQax5UQsby47zOXEDKo4WDO5f2M61nM3dllKOabCxgBUy8aMSQnhP8CGiZCRBEGDoP1b4FLD2JWVOikl4eeuM3H1USIuJ/Nuz/o81aKmWkVUMQgVNgagwqYcSIvXlrTeO1N7/uAL2jo8jm7GrcsAkjOyGPXzP2w9GYedlQWjO/rzYqi/sctSyhmDh40QwqeoU/ubOxU25UjiRdj8CRz8RbtRNPhZaD1GG0xQjkgpWXc0hqXhF9lwPIauDdx5rUtd6qhlq5VSUhZhsx9oLaXMzOc1WyllRqmcyASoPpty7GokbP8KDv2qTYPTsD/U6wW1QrVlEsoJvV4yfdMp5u44S/qNHJrVrEywb2VGtKuNk62aCkcpvrIIm8VAppRyyB3bPYGVUsrmpXIiE6JaNuXYtdPa5bWjK+BGMlg5QN1u8PCX5eoenWspmfxv62nCoq5z+GICDb2ceeGhWvRsXF0tJqgUS1mEjT0QBsyUUn5zc1sTYA2wQ0r5eKmcyISosKkAsjMhajtE/KndLFq9MQxeCdYOxq6s1K09cpl3VhzhasoNutR354W2tWjuW36CVSkbZTJAQAhRF9gJ9AWqAouAqVLK90rtJCZEhU0Fc3w1/DZYmwrn8V/A0trYFZU6vV7y9YaTLNxzjpSMbMZ1CeCx4BpqJgKl0AwSNkKIdcC/wD83v54A+gHz0Cb5HCal/LnYJzBxKmwqoPAFsHqM1pfzyCzQlc9FzZIzsnhtyUHWHY3BykIwtmMdhrerrWaYVu7LUEsMHEBbcnkw4A6kAYeBHOA34IQQwia/QQPm7JYBAsYuRSlrzYZA2jXY+AFE7YDGA7R7dMrZTaFOtlb876lmHLqYyKztZ/jy75OsOXSZib0bEOJXRfXnKEVWmn027mjBc+ujDqAHTkkpy9dvI6plU2FJCSdu9uGc+hv02eDdHB4cBvX7gGX5u+S09sgVPlh9lMuJGTT0qsT/nmqmZpdW8mWUmzqFEHZAEBAkpZxpsBMZiQobhdSrcOg32DcH4k+DrQvUbA01W2rBU47W1UnNzGbZP5f4Ym0EOiF4ukVNRnXwx9aqfF5KVIpHzSBgACpslDx6PZzZDEd+h3O74PpZsKkE/WZC4MPGrq5UnY5L4eM/jrMpIpb61Svx7RMPqIXblDwqbJqV5EcAACAASURBVAxAhY1SoGunYemzcPlfeOhVCH1Tu0m0HNlwLIbXlh7kRrae59r4MaJdbbWUgVJmQ59rAo3RLp01klI+VmoHN0EqbJR7ysqAP1+Df34E94bQaxp43/U7aNaiE9J5e/lhtpyMw83JhidDajKiXW2sLdWotYqqVMPm5g2cjfgvWBrffF4pdxdASinL5cVcNV2NUiQRf8Afr0HyZWj4CLQcBV5NjV1VqQo7G8+MLZFsORGHl4sdYzvVoX9Tb3RqZukKp0RhI4ToDLTgv2CphRYo3PI1HTiCtnrmv8BBKeXOkpduulTLRim0jCTY/iXs/wEyk8CrGTR+XBtE4FR+1pfZFBHDtI2RHLyQwAM+Lswb0pzKDuXv5lelYMUOGyHEFGBs7tNbXpJoMwT8hRYuJ6WU+tIp1zyosFGKLCNJGzL9708Qc0Tb5loPmgyClqPLxaqhUkqWHbjEG78fwsHGkkl9G/Jwo+pq/ZwKoiRhE4d28+fnwB7gLPAe8AxwHRgrpVxU6hWbARU2SolcOQKR6+HUBji3A/w7Q7//gUM1Y1dWKv69kMConw9w8Xo6Xi529Ary5Lk2frg6lb/7kJT/lCRs9MBkKeUbd2zvAswGvNEm2xwupbxSeiWbPhU2SqnIXTX0rzcAAfV6QkB37V4dZ29jV1ciGVk5bDgew4p/LrEpIhavynb8Oqwlni52xi5NMZCShM3zwFkp5cZ8XnMEJgPDgARgjJTyp9Ip2fSpsFFKVWwE7J+r3SSakQBCB72/hQeeNHZlpSLsbDyD5+0lK0cy6MEavNwpgGpqgs9yx6BDn4UQ7YE5gC+wGq2VE1PiA5s4FTaKQeRka/05G96Hs9uh/1yo16dc9OdciE9j1rYz/BJ2HjsrCz57tDE9Glc3dllKKSqr9Ww+A17kv1ZOuZzxWQ19VspEZjIs6A3RB8DBVVvaIPfh6Gbs6krkdFwKw38MJzI2hYfqVOOD3g3ULATlRJnNICCEaIO2xEDt8nqfTS7VslEMLjNFW0fn9EY4vRnSrmrbg5+Fh78y69bOjWw9s7efYebW02Rk6xnXOYDn2/hhqZYxMGtlOl2NEMIW+EhK+XqpH9yEqLBRypReD1cOwYGFWt9O0yHQ7g1w9jJ2ZSUSm5TBuyuPsO5oDEE1XJgyMIjaqpVjttTcaAagwkYxCilh/Xuwa7r2vGZrCHoc/Npps0yb4VozUkrWHLrMa0sOkpmtp0fj6rzSqQ7+bk7GLk0pIhU2BqDCRjGq2AiIWA3//KTNMg3aEgfBz0LLl8CuitldZotJymD+rihmbztDtl7yTGtf3nq4nloh1IyosDEAFTaKSZASYo/DuZ3a6qHHVmjbbZwhoCs8PBnsXIxbYxFdTcnk0z8j+P3ARZztrJjQPZDHgmuoudbMgAobA1Bho5ikC/vg0n5t+PTBX6FaALQapY1ic/IwdnVFsuFYDDO3nWZf1HWa+1bm436NCHBXl9ZMmQobA1Bho5i8yI2w4kVIuTm5R73e0OFdcA0wbl1FoNdLloZf5NO/jpOckc0jTb14MqQmQTXMq7VWUaiwMQAVNopZ0Osh5jAcWwV7/wdZaVqfTvu3wcp8po2JT73Bl3+fYOU/l8jI1jO0lS/D2tbCvZKtsUtTbqHCphSpmzoVs5V6FTZ+CAcWgKWdNnrNoRq0fhkCuhi7ukJJysjig1XHWPHvJeysLBjfrS4Dg2tga1Wub+szGypsDKAwLZukpCRiY2PJysoqo6qUisDKygo3NzcqVap0/53zE7UTTvwJiRfgymGIPwtNnoSHxkHV2qVbrIFExqbw5rJD7Iu6jqezLVMea0KLWlWNXVaFp8LGAO4XNklJScTExODl5YWdnR3CDO9/UEyPlJL09HQuXbqEu7t78QMn141U2DQJ9s+DnBvQaAC0HQ/V/EunYAOSUrL5RCwTfj9MbHImD/pW4aUO/rQLcDV2aRWWChsDuF/YREZG4unpib29fRlWpVQUaWlpREdH4+9fSqGQHKPdKLp/Huizoe3r2uU1S9NfaTP9Rg4/7T3HzG1niEvOpKmPC2M7BajQMYKCwkbdKWVAWVlZ2NmZTwesYl7s7OxK9/Kskzt0/RjGHoTAnrD5Y/juQTi8VBtkYMLsrC14/qFa7HijPa93rUtMUiZD5oXx4k/hRMYmG7s8BRU2BqcunSmGYrCfLUc3GPADPLkUrOzh9+fg+5awcxokRRvmnKXExtKCl9r7s2FcO8Z0rMPWE3F0mbqNV387yOGLicYur0JTYaMoSv7qdIYR26HfLLBx0uZj+7oRrH0LMkz7H247awvGdQ5g2/j2PNvajzWHoun17Q6GzAsj/Nx1Y5dXIamwURSlYDoLCHoMnt8Aow9AkydgzwyY0VK7YdTEVXW04Z2e9dnzZkdGtKvN4UuJDJq9hynrT5J2I9vY5VUoKmwURSmcqrWh9zfw/EawdoRFj8C8brBhIlw+aOzq7qmygzUTugfy19iH6FzfnekbTxE6eQuL9pwjR68GSZUFFTZKoc2fPx8hBEIITp48edfrW7duzXt9w4YNedsnTpyIEILatWvf1aEdGRmJEIL58+ffdZ7IyMi8bZmZmUydOpWgoCCcnJyoVKkSgYGBDBkyhFOnThEVFZV37ns9QkNDC/x8uXXmPmxsbKhfvz6TJ09GX4wO8i1bttz13+JW+X3OWwkheOedd4p8XoPzbgbDt2kzEOTcgF3fwMy28MdrcGItZKUbu8ICuVey5bsnmrJ0REtqVrXnnRVHCP1yMwt2RZGRlWPs8so1S2MXoJgfJycnfvzxRz766KPbti9YsAAnJyeSk/Mf/XPmzBnmzp3LiBEjinzOQYMG8ffffzN+/HhatGhBTk4Ox48fZ8mSJRw7doxu3bqxe/fu297TsmVLhg4dyvDhw/O2FeaelB07dmBhYUF8fDzz589n/Pjx6HQ6Xn311SLXXW5Z2UK78dojPQHWvQXhP8C+2eDeCLp8CH6hJrvEQbBvFX4b3pK/j8Uwa9sZ3l91lG82RTKqfW0GNq+BvbX6p7G0qf+iSpE98sgjLFq0iA8//DBvRFR6ejpLly7l0Ucfva2VcqsuXbowadIkhg4diq1t4eezOnPmDMuXL+frr79m7Nixedu7d+/OuHHj0Ov16HQ6WrRocdd7vby88t1+LyEhIVhaar8a3bp149ChQ8yePVuFTUHsXKDvDHj4S21WgjXj4Md+Wui0GgWNBppk6Agh6NrAgy713dl9+hrTNp5i4upjTFl/kjEd6/BUi5pqCpxSZHo/AYrJe/rppzl37hw7duzI27Z8+XL0ej2PPvpoge/7+OOPiY6O5rvvvivS+eLj4wHw8Mh/enydAf8h0+l0BAUFcf78+du2x8XFMWLECLy8vLCxsSEwMJBZs2YZrA6zYG0PjfrDayegz3cgc2D5cJgdCme2GLu6AgkhaOVfjcXDWrB0REse8KnMpD+O0+HLLSzYFUVWjmnfY2QuVMumGG6ZiLPI7/1g9VGORSeVflFFUN+zEu/3alDs99esWZO2bdvy448/8tBDDwGwcOFC+vXrh6NjwWvHN2nShAEDBvDZZ58xbNgwnJwKty5JYGAglSpVYsKECWRlZdG5c2fc3d2LXX9RRUVFUbv2f/OFJSUl0aZNG9LT05k4cSJ+fn6sW7eOkSNHkpmZyejRo8usNpNkZQcPPAVBT8CRpdpUOAv7gH9nbVYCnxBjV5gvIQTBvlWY/0xztpyMY9qGU7y/6ijzdp7l9a516dGourpvrgRUy6YYpJSrpZTDnJ2djV2K0QwePJglS5aQkZHB5cuX2bBhA4MHD77v+z766COuX7/O1KlTC30uR0dHFi1aREpKCk8//TQeHh7Url2bUaNGERERUZKPka+cnByys7OJi4vj008/JTw8/Lb+qWnTpnHu3Dk2btzICy+8QKdOnZg8eTLPPvssH3zwAdnZakgtoF06azwQRu6CdhMg+h+Y1wXmdYeIP0Bvmh3yQgja13Vj+YutmDc0GDsrC0b9/A99v9vJ7tPXjF2e2VItmzJWkhaFKRkwYACjRo1i9erVnDt3Dg8PDzp27Mi2bdvu+b6AgACGDBnCV199xahRowp9vl69ehEVFcXff//N5s2b2blzJzNmzGDu3LmsXr2aTp06lfQj5bmzP+mLL76gb9++ec/Xrl1LSEgIfn5+twVL165dmTNnDseOHaNx48alVo/Zs3GE9m9C6zEQPh/CZsHiJ6CyH3R4Bxo8YrJ9Oh0C3WkX4MayAxeZsv4kg2bvoX1dV97oHkigRwknQK1gTO//sGIWnJyc6Nu3Lz/++CMLFy7kySefLHTfyfvvv09mZiaff/55kc7p4OBAv379mD59OuHh4ezatQsLCwsmTJhQnI9QoD179hAWFsby5ctp2rQpEyZMYMuWLXmvx8bGsm3bNqysrG57DBgwAIBr1wr312/uIIScnLv/ws/dlrtPuWDtoC3a9lKY1qeTOxXOrHYQuQFMdFJgC51gQHANNr8WyoTugew/d53u07bz0k8HOH8tzdjlmY1y9JOslLXBgwfTo0cP9Ho9v/zyS6Hf5+Pjw/Dhw/n222/p1atXsc/fokULunTpwtq1a4t9jPw0a9YMS0tLmjdvTps2bQgMDGT06NEcPHgQnU5H1apVcXNzY9q0afm+v27duoU6j5ubGwDR0dF3vSc6WpuDrCz7psqMpc3NPp1BcOR3rU9n0aPg+xC0fwtqtDDJlo6tlQUj2tXmseAazNx2hgW7olh39AqPNa/B2I51cFMrht6T6f0fVcxG586dGThwICNGjKBBg6JdHnz77bcRQjBp0qT77pucnExqaupd23Nycjh16hTVq1cv0rmLolq1arz33nscOXKE33//HdCGQ0dERODj40NwcPBdj8IOfAgJCcHOzi7vuLfK3Xavm1DNns5C69MZtR+6T4a4CPihO0wJhBUvwfE1JjnbdO5sBFteD+WJEB9+3XeBdpO38OHqY6qlcw+qZaMUm4WFRZFaNLdyc3Nj7NixfPLJJ/fd98SJE3Tr1o1BgwYRGhqKm5sbly9fZs6cORw5coQZM2YUq4bCGj58OJMnT2bSpEn079+fV155hV9//ZWHHnqIV155hbp165KamkpERATbt29n5cqVt71/+/btJCQk3LbN0tKSvn378vbbb/Puu++SmZlJr169sLa2ZsuWLUyZMoWhQ4dSr149g342k2BpDSHDtHnXItbAyXVwfDX8uwiqBUDICGj2jMm1dtwr2fJhn4Y829qPr9af5Mc9Ufy09xyDHvRhWNtaeLqo5UVupcJGMZrXX3+d77//nuvX7z0Lr7+/P2PGjGHDhg0sXbqUq1ev4ujoSJMmTViyZAn9+/c3aJ02Nja8++67DB8+nBUrVtCvXz927drFhx9+yOeff86lS5dwcXGhbt26+d5n9OGHH961zcHBgZSUFN5++228vLz47rvv+Omnn9Dr9fj7+/Pxxx8zbtw4g34uk2PjCEGPaw99jnaJbec0+GMc/PuzFjr1+5jcYm6+1Rz4ZtADXE4MZMrfJ/lp7zl+DjvPkJY1eTHUn8oOplWvsaiVOkvgfit1Hj9+vGL8ZaoYTbn/GZMS9s+F3d9B/BlwDdRmK/BqZuzKCnQpIZ2v15/k9wMXcbC2ZERobZ5p7VthpsBRK3UqimJ+hIDmz8OocHj8Z8hIgtkdYFYohC/QnpsYLxc7Jg8IYu3LbQmpVZXJ604QOnkLv+27gL4CzzCtwkZRFNOn00FgD3hxN3T5GHKyYfUY+DJAu9SWY3o30ga4OzFnSDBLRrTEu7Id438/RN8ZO9kVedXYpRmFChtFUcyHnYs2ueeI7TB4JbgGaCuIzmihtXRMcHmD5r5V+H1kK6YMDOJayg2emLOXx2ftJvxcvLFLK1MqbBRFMT9CQK1QbV2dR+eC0GktnekPwJ7vISfrfkcoU0IIHmnqzcZX2/Fez/pExqby6Pe7eXb+Po5Gm/YS26VFhY2iKOatUX94cQ8MWQ3O3rB2AnxVV1vUzcRCx9bKgmfb+LFtfCjju9Vlf1Q8Pabv4KWfD3A6LsXY5RmUChtFUcyfTgd+beG59TBoMbjVh7/fge9CYP8PJtenY29tyYuh/mx/owOj2vuzOSKWzlO28vqSg1xKML1LgaVBhY2iKOWHEFC3u9bKefwXrY9nzcswrTEc+NHkZpp2trPita512Ta+PUNb+bHy32hCJ2/mq79PkJxhWq2ykqrwYSOEqCyEWCOEOCmEOCiE+FsIUfSFahRFMR1CQODD8PxGGLgQrB1h1Sj4XxvYN8fkBhJUc7ThvV712fx6KN0bVuebTZG0m7yF7zZHkpppWq2y4qrwYQNI4GspZYCUMghYA8wxck2KopQGIbRZB17aC32/B50l/PEqfN3oZuhkGLvC23i52DF90AOsfKk1Db2cmbzuBF2mbuO3/RfINvMVQ00ubIQQ3kKIb4QQu4UQaUIIKYTwLWDfGkKIpUKIRCFEkhBimRDCpyjnk1ImSCk33LJpF5Dv+RRFMVNCaHOvDd8Gg1dpyxv88SrMCIEDCyE709gV3iaohgsLn32Q34a3xMXeivFLD9Fj+g52nDLfe3RMLmwAf2AgcB3YXtBOQgh7YBMQCAwBngbqAJuFEA4lOP/LwMr77lWB7d69m4EDB+Lp6Ym1tTVVq1alc+fOLFiwIG8dli1btiCEYMOG/3J84sSJCCHyfURGRubtl56ejrOzM0IIDh48mG8NoaGht73fycmJ1q1bs2rVqkJ9hjtrsbGxoX79+kyePBl9MWYazu/z3mr+/Pl3fc5bCSF45513inxepYiEgFrttJmmn/gNbCrBqtHaQILDS01uTZ0H/aqwZnQb/vdUU9Kysnlq7l5eWLifqKt3z4Ju6kwxbLZJKd2llA8DS+6x3wtALaCvlHKFlHIl0BuoCQzP3UkIsUEIcbWAR+tbDyiEeP/mMd8s9U9VTnz99de0bt2a+Ph4Pv/8czZs2MC8efMICAhg5MiRrFmz5r7H2LFjB7t3777tUaNGjbzXly9fTlKSNg3JwoULCzxO48aN894/d+5cUlNTeeSRR9i7d2+hP09uLcuXL6dhw4aMHz++SEtWK2bK0hoCumotnSeXgqWttpDbDw9D1E5jV3cbIQTdGlZn/SvtGN+tLrsir9J56lY+/fO4WQ0iMLmZ4aSUhf2zsjewR0qZ96eilPKsEGIn0AeYcnNbodYLFkK8AzwMdJFSqkUp8rFt2zbGjRvHqFGjmD59+m2v9enTh3HjxuW77sydQkJC7rkC5YIFC6hSpQp16tThp59+4vPPP893fycnJ1q0aAFoC6m1atUKHx8ffvjhB0JCQgr1mW6tpVu3bhw6dIjZs2fz6quvFur9ipkTAup0htodYP882PYlzH9Yu2G0/TtQo7mxK8xja2XBi6H+9G/qzeR1J5i1/Qy/H7jIa13qMiC4BhY6YewS78kUWzaF1QA4ks/2o0D9ohzoZoumF1rQ3PN2XiHEMCHEfiHE/ri4uKKcxux9/vnnVKlShS+++CLf12vXrk3jxo1LdI5Lly6xYcMGHn/8cZ5//nliYmJYt25dod7r7e2Nq6sr58+fL9a5dTodQUFBd70/Li6OESNG4OXlhY2NDYGBgcyaNatY51BMlM4CHnwBxv6rzb125QjM7QQ/DYTof41d3W3cKtkyeUAQK19qjW9VByYsO0zvb3ew90zhliM3FpNr2RRBFbR+nTvFA5ULexAhRANgInAa2CqEAMjOb4psACnlLGAWaEsMFK1k4K8JcOVwkd9WqjwaQffPivSWnJwcNm/eTN++fbG1Ldnyt7n9Orl0Oh26mwtjLVq0CL1ez+DBg/OWY164cCE9evS473GTk5O5du0atWvXLnZtUVFRt70/KSmJNm3akJ6ezsSJE/Hz82PdunWMHDmSzMxMRo8eXexzKSbIyk6be63ZUAibCTunw6x2UK8XhL4F7kX6O9agGnu7sGRES1Yfusxnfx7nsVl76NGoOhO6B1Kjir2xy7uLOYdNqZBSHgVMu/1pAq5evUp6ejo1a9Ys8bHuDKsnn3ySRYsWAdoltLp16+ZdBuvbty8rVqwgISEBFxeXu46Vna3dg3DhwgXGjx9PlSpVeOWVVwpdS27wXb9+nTlz5hAeHs7SpUvzXp82bRrnzp3j8OHD1KlTB4BOnTqRkJDABx98wMiRI+95SVAxUzaO8NCr2vIGu2fAnhnaMtUPPAUd3gEnD2NXCGj9Ob2DPOlcz51Z287w/dZI1h+PYdhDtRgZWhsHG9P52TSdSoruOvm3YApq8ZiGIrYoyqM9e/ZgYWGR97xq1aoA7Nu3j+PHjzNp0qS814YMGcLixYv59ddfGT58+G3H2blzJ1ZWVnnPbWxsWL9+PbVq1Sp0LXcG3xdffEHfvn3znq9du5aQkBD8/Pzygg2ga9euzJkzh2PHjpX40qFiwmydof2bEDIctk2GsFlwZBm0GAmtRmszFJgAO2sLxnaqw4Bgbz5fG8G3myNZEn6BN7vXo3eQJzoT6M8x5z6bo2j9NneqDxwz5ImFEL2EELMSEyvGbK2gBYKdnR3nzp0r8bGaNWtGcHBw3sPPzw/QWjUAvXr1IiEhgYSEBJo3b46rq2u+o9KCgoLYt28fe/bsYe7cuTg5OTFgwACK0pe2Z88ewsLCWL58OU2bNmXChAls2bIl7/XY2Fi2bduGlZXVbY8BAwYAcO1a4a6T57Z+7ryEeOs21UIyYfZVoNunMGInBHSB7V9qU+Bs+xIyTWcCTU8XO6Y9/gC/j2yFq5MNL//6LwNn7ub4ZeMvMmfOP92rgC+FELWklGcAbt782RqYYMgTSylXA6uDg4NfMOR5TImlpSWhoaGsX7+ezMxMbGxsSvX4N27c4JdffgG0ELlTXFwcp06dyruUBeDo6EhwsNa1ltv66NChAxMnTuS7774r1HmbNWuGpaUlzZs3p02bNnn9RAcPHkSn01G1alXc3NyYNm1avu+vW7duoc7j5uYGQHR09F3viY6OBsDd3b1Qx1KMyC0QBsyHNuNg88ew6SNtSYOHxkHTIdrlNxPQrGZlVr3UhqXhF/n0r+P0mL6dp1rU5PWudXGytbr/AQzAJFs2Qoj+Qoj+QO5C491vbmt3y26zgShgpRCijxCiN9rNmBeAmWVacAUxYcIErl27xvjx4/N9/ezZsxw6dKhYx16zZg3x8fG8//77bN68+bbH4sWLgXvfcwPQvn17+vXrx5w5c7h48WKRa6hWrRrvvfceR44c4ffffwe04dARERH4+Pjc1hrLfTg5ORXq2CEhIdjZ2eUd91a520JDQ4tcs2Ik1RvDE7/CcxvAvQGse0tr6YTPN5nJPnU6wcDmNdj8WihPhtRk0Z5zdJ26jXVHrxinICmlyT3Q5ivL77Hljv18gN+BJCAZWAH4lkF9vYBZ/v7+8l6OHTt2z9fN0dSpU6UQQnbq1EkuWrRIbtu2Ta5cuVKOGTNG2tvbyxUrVkgppdy8ebME5Pr16/Pe+/7770tAZmVl3XXc3r17S0dHR5mcnJzveUNCQqSvr6/U6/VSSinbtWsnW7dufdd+hw4dkkIIOWrUqHt+joJqycjIkN7e3rJx48ZSr9fLhIQEGRgYKAMCAuT3338vN23aJFevXi0nT54se/funfe+3M/73nvvySVLltz2WL58uZRSykmTJkkhhHz++eflypUr5V9//SXfeOMNaWVlJYcOHXrPegtSHn/GzNK5PVLO7Srl+5WknNFKytNbjF3RXcLPxcuuU7fKmm+skS/+FC6vJmcY5DzAfpnfv5v5bVSPwj2aNWt2z//o5fUfgp07d8r+/ftLDw8PaWlpKStXriw7d+4sf/zxR5mTkyOlLFrYxMbGSisrK/nss88WeM5Zs2ZJQG7evFlKWXDYSCnloEGDpK2trYyOji7wePcKvpkzZ0pALlu2TEopZXx8vHz55Zelr6+vtLKykq6urrJNmzZy6tSpee/J/bz5PRwcHPL2++GHH2RwcLC0s7OTNjY2skGDBvKLL76Q2dnZBdZ6L+X1Z8ws6fVSHlkm5dSGWuj8OljK2AhjV3WbG9k58puNJ6X/W3/IZh/9Lf86XPDvSHEVFDZCe00pjuDgYLl///4CXz9+/Dj16tUrw4qUikb9jJmgrAzY/hXsmg45N6DpYGj/Nji6GbuyPMcvJzHut4Mcv5xE94YefNinIa5OpdMPK4QIl/ncp2iSfTaKoihmy8oWOrwNrxyFB4fDP4tg+gPa0GkTWUenXvVKrB7Vmte71mVjRCxdv97G2iOG7ctRYaMoimIIDtW0++peCtPmWts0Cb5pBgcXQzFmFi9tlhY6Xmrvzx+j2+DpYsuIReGM+/VfEtMNM7mnCptiqIj32SiKUkxVa8PjP8HQP8HBFZYPhzkd4HzhZyc3pDruTix/sTVjOtZh5cFoun29zSDr5qiwKQYp5Wop5TBnZ2djl6IoirnwbQ0vbIZ+syDhPMzrAr8+rX1vZFYWOsZ1DmDZyFbYWVsQdrb0J/U055s6FUVRzItOB0GPQb2e2pxr27+CU+uhzSvQeow2EagRBdVw4c8xD6ETpT+9jWrZKIqilDVrB2j3Oozapy3ituUT+PZBOPK70VcLtbWywNqy9KNBhU0xqD4bRVFKhUsNGLgAhqzRJv1c+izM6Whya+iUBhU2xaD6bBRFKVV+D8HwrdD7G4g/o62hs/Q5SLps7MpKjQobRVEUU6Cz0G4AHXtQW0snYg18F6It4JaVYezqSkyFjaIoiimxdYaO78HIXeAdDOvfhRkhcG6XsSsrERU2SqHNnz8fIQSRkZFGq2Ho0KEIIfIe9vb2NG3alHnz5hXrePf7TBMnTkQIcdvCabmioqIQQjBnzpxinVtR7qlqbXh6GTy9Qhs08EN3WPEipJb+PTBlQYWNYnZcXV3ZvXs34n2quAAADXVJREFUu3fv5pdffsHFxYXnnnsu3+n7FcXs1W4PL+7Whkcf+hW+DYa9s0xmKYPCUmFTDGo0mnFZW1vTokULWrRoQZ8+fVi1ahUuLi7Mnj3b2KUpimFYO0CniTBiB3g0gr9eh3ldIfa4sSsrNBU2xaBGo/1n3bp1tGrVCmdnZxwdHalbty4ffvjhbfusXbuWli1bYmdnh7OzM3379uXEiROlVoOjoyMBAQGcP3/7ndj/b+/+g6uq0zuOvx/LJSA1ETAxgiK4CLpklZoMhJUiBBEKmjqS3cWllhbZ7lZta9cBxckCg7NlnVGxP2akKTOuOOowQP2BQmSp3eCWooHouop0ccPSNJaJSJCFZFYCT/+4N9mEJOT25p577uV+XjNnknzPOfc8N8+9efI959zv99ChQyxcuJD8/HxycnKYOHEiL7/8ctKOK5JyBdfDn74Gd62Hzz+BdVNh27K0mpq6NxpBIMUef/dxDhw7EGoM1w27jocnPdzvx6mvr6e8vJyKigpWrFjBwIEDOXjwIPX19R3bVFdXM2/ePMrKyti4cSMnT55kxYoVTJ06lffff5+RI0f2O44zZ87Q0NBAcXFxR1tDQwOTJ0+moKCAtWvXkp+fz8aNG5k/fz6vvPIK5eXl/T6uSCjM4IZvwFfKotNSv1sF/7Udbn8Krp0VdnS9UrGRhNXV1fHll1/yzDPPkJubC0BZWVmXbSorK7nmmmvYvn07AwZEX25Tpkxh3LhxPPnkkzz11FMJHbv9gn1TUxNr1qzhiy++oLKysmP9qlWrcHdqamoYPnw4ALNnz6ahoYEVK1ao2EjmGzIc7ngablwAr/01vFABRfNhzuPw+/lhR9eNik2KJaNHkS4mTpxIJBJhwYIFLF68mGnTplFQ8LsJok6dOkVdXR2PPvpoR6EBGDNmDDfffDM1NTUJHbexsZFIJNLxs5nx0ksvMXny5I626upq5s6dS15eXpc7yWbPns3SpUs5ceJER4EUyWijSuF7b8PP1kbHWvvVWzDnR3DDt6K9oDShazaSsLFjx/Lmm29y9uxZ7rnnHgoLCyktLe0oIs3Nzbg7V1xxRbd9CwsLOXbsWELHLSgooLa2lnfeeYcXX3yRMWPGsHjxYg4c+N3pyaamJjZs2EAkEumyLF26FIDPP49vVNv2InnmTPc7f9rbOhdSkVAMyIHpj0RvIBg+NjqNwUt3Q0ti77EgqNhIv8yYMYPq6mqOHz/Ozp07GTBgAPPmzePo0aMMHToUM+PIke4zAB45coRhw4YldMxIJEJJSQmTJk3i7rvvZtu2bbS1tfHQQw91bDN8+HAqKiqora3tcRkxYkRcx2rvqX366afd1rW3XX755Qk9D5Gkyx8Pi3fAbT+ET3ZGJ2v7xeawowJUbBKiW5+7y8nJoaysjGXLlnHq1CkOHTrEkCFDKC4uZtOmTV16BocPH2b37t1Mnz49KcceP348999/P9u2baO2thaAOXPm8MEHHzBhwgRKSkq6LTk58c233h5jT5/h2bJlC4MGDaK0tDQpz0MkKS66CL7+APzFT6MfDN1yb3SAz5B7Oer/J8DdtwJbS0pKvhN2LGFat24du3btYu7cuVx11VUcPXqUNWvWMGLECIqKigB47LHHmDdvHrfffjv33XcfJ0+eZOXKleTl5XXpicycOZPDhw8nPDrBI488QlVVFatXr2br1q2sXr2aSZMmMW3aNB544AFGjx5Nc3MzH374IfX19d1GHKiurqawsLBLW15eHrNmzWLJkiUsX76cpqYmZsyYQVtbG2+88QZVVVWsXLmSoUOHJhSzSKAKi+DPq6PXcmp+FB3uZv56GD01nHjcXUuCS3FxsZ/P/v37z7s+0zz77LMO+MGDB93dfffu3V5eXu5XXnmlDxw40AsLC72iosIPHDjQZb/t27d7aWmpDxo0yHNzc728vLzbNrfccotfffXVfcawaNEiHzlyZI/rli9f7oDX1dW5u3tDQ4Pfe++9PmLECI9EIl5YWOi33nqrP//8892eU0/LhAkT3N29ra3Nn3jiCS8qKvKcnBwfPHiwFxcX+/r16+P+3QXlQnuNSUAa69z/4Sb3VZe67/iB+5etgR0K2Os9/L00D3minkxWUlLie/fu7XX9xx9/zPXXX5/CiCTb6DUmcfvtb2BHJez7MVxeBN/cED3NlmRmts/dS85t1zUbEZFskHMJ3PH3sHAznPgU/vkW+OiVlB1exUZEJJtcOys6UVv+ONi0KDqS9OnWwA+rYiMikm0uHQWL34RpS+H9F2D9rdB8ONBDqtiIiGSj34tAWSV8exMcb4B/mQGHdgV2OBWbgOkGDAmKXluSFONug++8BRdfBhvuhD3ropO1JZmKTYAikQitrcGfC5Xs1Nra2mWMOJGEXTYWluyEcbOh+uHoXWtJpmKTgHhHECgoKKCxsZGWlhb9FypJ4+60tLTQ2NjYZeBTkX4ZlAvfegFm/x2M/sOkP7w+Z9MPfX3OBuDEiRM0NTVx+vTpFEUl2SASiVBQUKCRqyXt9PY5Gw1XE7Dc3Fz9QRCRrKfTaCIiEjgVGxERCZyKjYiIBE7FRkREAqdiIyIigVOxERGRwOlzNv1gZp8B545elwec+2nPc9suA44GGFpveootFY8Rzz59bXO+9b2tUy4S2yfZuYi3LZtyEe/2mZiLq909v1trTzOqaUl8Aar6aqOXmezCiC0VjxHPPn1tc771va1TLtIjF/+PtqzJRbzbX0i50Gm05NsaZ1sYkhFHIo8Rzz59bXO+9b2tUy4S2yfZuUjnPEA4uYh3+wsmFzqNFgIz2+s9DOcgqadcpA/lIn0EkQv1bMJRFXYA0kG5SB/KRfpIei7UsxERkcCpZyMiIoFTsRERkcCp2IiISOBUbNKQmX3FzH5mZr80s/fMTHfohMTMfhDLw1kzuzPseLKVmQ01s9djufi5me0ws7Fhx5WNzGyjmX0Q+9v0rpnNjGc/FZv0tA54zt3HAcuAF8zMQo4pW/0EmAPsCjuQLOfA0+4+zt1vBF4H1occU7b6rrvf4O5/AHwX2GRmfdYSFZskMLMrzewfzew/zazFzNzMRvey7VVmttnMvjCzE2b2r2Y2qtP6fKAU+DGAu/8EMKA48CdyAUhmLgDcfY+716ci9gtNMnPh7sfdfWenXXYDPT6WdBXAe+J4px/z4o1DxSY5xgLfBJqBt3vbyMwuBt4CrgMWAfcA1wL/bmZDYpuNAv7X3U932vXXsXbpWzJzIf0TZC4eBF5NarQXrqTnwczWmlk9sAWY7+5n+4wi1eMQXYgLcFGn75cQ7fKP7mG7vwHOAGM7tY0B2oDvx34uBn55zn47gLvCfp6ZsCQzF+ds/1PgzrCfXyYtAeZiJdGezcVhP8dMWILKQ2z9HKAWGNhXHOrZJIHHU9WjyoE97v5Jp30PAf8B/HGs6b+BK8ws0mm/0bF26UOScyH9EEQuzKwSmAv8kbu3JCvWC1mQ7wl3rwaGAl/r68FVbFJrAvBhD+0fAV8FcPfPgHeBPwMws1lEr9nsS02IWaPPXEjKxJULM1sJ3AHc5u79nRJAuuszD2Y22MzGtK8wsynAcKDP65oDkhSkxGcY0fOm5zpG9L+Ddt8DnjOzpUALsNBjfVZJmrhyYWariJ56yAeKzOyfgFJ3/59UBJkl+syFmU0AVgG/AmpiN2e2uQbuTKZ43hODgRfN7BKip9dOEb1m09N+XajYpCF3Pwh8Pew4BNx9FdE/chIid/+IaA9fQuTux4Apieyr02ip1UzXHky73v6jkOAoF+lDuUgPgeZBxSa1PiJ6XvRcXwX2pziWbKdcpA/lIj0EmgcVm9R6DSg1s2vaG2Ifrro5tk5SR7lIH8pFegg0D5rPJknMrCL27UyiF/jvAz4DPnP3mtg2Q4CfA61AJdH73R8DLgFucPeTqY77QqRcpA/lIj2kQx5UbJLEzHr7Rda4+/RO240C1gLttzT/G/Cgu/866BizhXKRPpSL9JAOeVCxERGRwOmajYiIBE7FRkREAqdiIyIigVOxERGRwKnYiIhI4FRsREQkcCo2IiISOBUbkQxkZn8bm0v+22HHIhIPFRuRzFQc+7o31ChE4qQRBEQykJntB0YCl2piPckE6tmIZJjYgInjgfdUaCRTqNiIZJ6JRN+7+zo3mtlQM3s1di3naTOLhBOeSHeaFlok89wU+9pRbMxsMrCR6EyL33D3zWEEJtIb9WxEMk/7zQH7AMzs+8DbwAmgRIVG0pF6NiKZ5ybgN8BRM3sVKAeeA/7S3VtDjUykF7obTSSDmNkgooWmCWgDCoC/cvf1oQYm0gedRhPJLDcSPSORA4wCNqvQSCZQsRHJLO03BzwEvA78iZk9GGI8InFRsRHJLJ1HDlhA9CaBJ83srvBCEumbrtmIZBAzqwOuAy5x9zNmVgjsIXrtpszd94QaoEgv1LMRyRBmNhAoAn7h7mcA3P0IMBf4LbDVzMaGGKJIr1RsRDLH14AI8F7nRnffD9wF5AHbzeyyEGITOS+dRhMRkcCpZyMiIoFTsRERkcCp2IiISOBUbEREJHAqNiIiEjgVGxERCZyKjYiIBE7FRkREAqdiIyIigfs/xPWnUr4K5KgAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iPQcC7rX0Vg3"
      },
      "source": [
        "eta_vals = [0.05, 0.1, 0.2]\n",
        "#eta_vals = [0.05, 0.1, 0.2]\n",
        "\n",
        "T = 1000\n",
        "\n",
        "all_theory = []\n",
        "all_expt = []\n",
        "for i, eta in enumerate(eta_vals):\n",
        "  all_theory += [jnp.array( theory(s**2, vk / s**2, eta, T) )]\n",
        "  all_expt += [jnp.array( train_fn(F_MNIST, y89[0:P_sub], T, eta) )]\n",
        "\n",
        "\n",
        "eta = 0.25\n",
        "m_vals = [1, 5, 10]\n",
        "all_theory_m = []\n",
        "all_expt_m = []\n",
        "\n",
        "for i, m in enumerate(m_vals):\n",
        "  all_theory_m += [jnp.array( theory(s**2, vk / s**2, eta, T, m=m) )]\n",
        "  all_expt_m += [jnp.array( train_fn(F_MNIST, y89[0:P_sub], T, eta, m=m) )]\n",
        "\n",
        "all_theory_noise = []\n",
        "all_expt_noise = []\n",
        "all_noise = [0, 0.5, 1]\n",
        "num_rep = 10\n",
        "for i, noise in enumerate(all_noise):\n",
        "  all_theory_noise += [jnp.array( theory(s**2, vk / s**2, eta, T, m = 1, noise = noise) )]\n",
        "  mean = jnp.zeros(T)\n",
        "  for n in range(num_rep):\n",
        "    mean += 1/num_rep * jnp.array( train_fn(F_MNIST, y89[0:P_sub], T, eta, m = 1, noise=noise) )\n",
        "  all_expt_noise += [mean]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 818
        },
        "id": "nTMKpzax005O",
        "outputId": "171d33e8-5485-4c43-d308-3d757d97ad08"
      },
      "source": [
        "fs = 20\n",
        "plt.rcParams.update({'font.size': 16})\n",
        "\n",
        "for i, eta in enumerate(eta_vals):\n",
        "  plt.loglog(2*all_expt[i], label = r'$\\eta=%0.2f$' % eta)\n",
        "  if i == len(eta_vals)-1:\n",
        "    plt.loglog(2*all_theory[i], '--', color = 'black', label = 'Gauss. Theory')\n",
        "  else:\n",
        "    plt.loglog(2*all_theory[i], '--', color = 'black')\n",
        "\n",
        "plt.legend()\n",
        "plt.xlabel(r'$t$',fontsize = fs)\n",
        "plt.ylabel(r'$L_t$',fontsize = fs)\n",
        "plt.tight_layout()\n",
        "plt.savefig(root_dir + 'mnist_random_feature_vary_lr.pdf')\n",
        "plt.show()\n",
        "\n",
        "\n",
        "for i, m in enumerate(m_vals):\n",
        "  plt.loglog(2*all_expt_m[i], label = r'$m=%d$' % m)\n",
        "  plt.loglog(2*all_theory_m[i], '--', color = 'black')\n",
        "  plt.loglog(2*all_theory_m[i], '--', color = 'black')\n",
        "\n",
        "plt.legend()\n",
        "plt.xlabel(r'$t$',fontsize = fs)\n",
        "plt.ylabel(r'$L_t$',fontsize = fs)\n",
        "plt.tight_layout()\n",
        "plt.savefig(root_dir + 'mnist_random_feature_vary_batch.pdf')\n",
        "plt.show()\n",
        "\n",
        "\n",
        "for i, noise in enumerate(all_noise):\n",
        "  plt.loglog(2*all_expt_noise[i], label = r'$\\sigma=%0.2f$' % noise)\n",
        "for i, noise in enumerate(all_noise):\n",
        "  plt.loglog(2*all_theory_noise[i], '--', color = 'black')\n",
        "\n",
        "plt.legend()\n",
        "plt.xlabel(r'$t$',fontsize = fs)\n",
        "plt.ylabel(r'$L_t$',fontsize = fs)\n",
        "plt.tight_layout()\n",
        "plt.savefig(root_dir + 'mnist_random_feature_vary_noise.pdf')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZRSKy7rcC6SI"
      },
      "source": [
        "# compute variance example ... \n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "VSI0O_DSLqQ-",
        "outputId": "a99b3226-104f-4da8-a326-eff197328e36"
      },
      "source": [
        "# compute fourth moment stuff\n",
        "\n",
        "print(F_MNIST.shape)\n",
        "N = 20\n",
        "F100 = F_MNIST[:,0:N]\n",
        "\n",
        "Sigma = 1/F100.shape[0] * F100.T @ F100\n",
        "K = F100 @ F100.T\n",
        "D = jnp.diag( jnp.diag(K) )\n",
        "\n",
        "K4 =  1/F100.shape[0] * F100.T @ D @ F100\n",
        "print(jnp.amin(K4))\n",
        "print(jnp.amax(K4))\n",
        "\n",
        "\n",
        "K_gauss = 2 * Sigma.T @ Sigma + Sigma * jnp.trace(Sigma)\n",
        "print(jnp.amin(K_gauss))\n",
        "print(jnp.amax(K_gauss))\n",
        "\n",
        "\n",
        "plt.imshow(Sigma, cmap = 'rainbow')\n",
        "plt.show()\n",
        "\n",
        "#print(np.amax(K_gauss-K4) / np.amax(K_gauss))\n",
        "#print(np.amin(K_gauss-K4)/ np.amax(K_gauss))\n",
        "\n",
        "#plt.imshow(K_gauss - K4 , cmap = 'rainbow')\n",
        "#plt.show()\n",
        "\n",
        "eigs,vecs = jnp.linalg.eigh(Sigma)\n",
        "indsort = jnp.argsort(eigs)[::-1]\n",
        "eigs = eigs[indsort[1:]]\n",
        "vecs = vecs[:,indsort[1:]]\n",
        "\n",
        "\n",
        "kappa_gauss = 2 * jnp.diag(eigs**2) + jnp.sum(eigs) * jnp.diag(eigs)\n",
        "kappa_4 = vecs.T @ K4 @ vecs\n",
        "\n",
        "kappa_4 = kappa_4 / jnp.amax(kappa_4)\n",
        "kappa_gauss = kappa_gauss/jnp.amax(kappa_gauss)\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "plt.figure(figsize=(10.5,3.2))\n",
        "\n",
        "plt.subplot(1,3,1)\n",
        "plt.imshow(kappa_gauss,cmap = 'rainbow', vmin = 0, vmax = 1)\n",
        "plt.colorbar(fraction=0.046)\n",
        "plt.title(r'$\\kappa_{Gauss}$',fontsize = 20)\n",
        "plt.xticks([])\n",
        "plt.yticks([])\n",
        "\n",
        "plt.subplot(1,3,2)\n",
        "plt.imshow(kappa_4, cmap = 'rainbow', vmin = 0, vmax = 1)\n",
        "plt.colorbar(fraction=0.046)\n",
        "plt.title(r'$\\kappa_4$',fontsize = 20)\n",
        "plt.xticks([])\n",
        "plt.yticks([])\n",
        "\n",
        "plt.subplot(1,3,3)\n",
        "plt.imshow(jnp.abs(kappa_4-kappa_gauss), cmap='rainbow')\n",
        "plt.colorbar(fraction=0.046)\n",
        "plt.title(r'$|\\kappa_4 - \\kappa_{Gauss}|$',fontsize = 20)\n",
        "plt.xticks([])\n",
        "plt.yticks([])\n",
        "plt.savefig(root_dir + 'non_gauss_diff_effect_mnist.pdf')\n",
        "plt.show()\n",
        "\n",
        "N = 20\n",
        "F100 = F_CIFAR[:,0:N]\n",
        "\n",
        "Sigma = 1/F100.shape[0] * F100.T @ F100\n",
        "K = F100 @ F100.T\n",
        "D = jnp.diag( jnp.diag(K) )\n",
        "\n",
        "K4 =  1/F100.shape[0] * F100.T @ D @ F100\n",
        "print(jnp.amin(K4))\n",
        "print(jnp.amax(K4))\n",
        "\n",
        "\n",
        "K_gauss = 2 * Sigma.T @ Sigma + Sigma * jnp.trace(Sigma)\n",
        "print(jnp.amin(K_gauss))\n",
        "print(jnp.amax(K_gauss))\n",
        "\n",
        "\n",
        "plt.imshow(Sigma, cmap = 'rainbow')\n",
        "plt.show()\n",
        "\n",
        "\n",
        "\n",
        "#print(np.amax(K_gauss-K4) / np.amax(K_gauss))\n",
        "#print(np.amin(K_gauss-K4)/ np.amax(K_gauss))\n",
        "\n",
        "#plt.imshow(K_gauss - K4 , cmap = 'rainbow')\n",
        "#plt.show()\n",
        "\n",
        "eigs,vecs = jnp.linalg.eigh(Sigma)\n",
        "indsort = jnp.argsort(eigs)[::-1]\n",
        "eigs = eigs[indsort[1:]]\n",
        "vecs = vecs[:,indsort[1:]]\n",
        "\n",
        "kappa_gauss = 2 * jnp.diag(eigs**2) + jnp.sum(eigs) * jnp.diag(eigs)\n",
        "kappa_4 = vecs.T @ K4 @ vecs\n",
        "\n",
        "kappa_4 = kappa_4 / jnp.amax(kappa_4)\n",
        "kappa_gauss = kappa_gauss/jnp.amax(kappa_gauss)\n",
        "\n",
        "\n",
        "\n",
        "plt.figure(figsize=(10.5,3.2))\n",
        "\n",
        "plt.subplot(1,3,1)\n",
        "plt.imshow(kappa_gauss,cmap = 'rainbow', vmin = 0, vmax = 1)\n",
        "plt.colorbar(fraction=0.046)\n",
        "plt.title(r'$\\kappa_{Gauss}$',fontsize = 20)\n",
        "plt.xticks([])\n",
        "plt.yticks([])\n",
        "\n",
        "#plt.show()\n",
        "\n",
        "plt.subplot(1,3,2)\n",
        "plt.imshow(kappa_4, cmap = 'rainbow', vmin = 0, vmax = 1)\n",
        "plt.colorbar(fraction=0.046)\n",
        "plt.title(r'$\\kappa_4$',fontsize = 20)\n",
        "plt.xticks([])\n",
        "plt.yticks([])\n",
        "#plt.tight_layout()\n",
        "\n",
        "plt.subplot(1,3,3)\n",
        "plt.imshow(jnp.abs(kappa_4-kappa_gauss), cmap='rainbow')\n",
        "plt.colorbar(fraction=0.046)\n",
        "plt.title(r'$|\\kappa_4 - \\kappa_{Gauss}|$',fontsize = 20)\n",
        "plt.xticks([])\n",
        "plt.yticks([])\n",
        "#plt.tight_layout()\n",
        "plt.savefig(root_dir + 'non_gauss_diff_effect_cifar.pdf')\n",
        "plt.show()\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(2500, 4000)\n",
            "-1.5127896e-12\n",
            "6.184941e-12\n",
            "-2.9141355e-12\n",
            "1.0285776e-11\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 792x230.4 with 6 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "-6.750334e-14\n",
            "1.5952143e-13\n",
            "-1.4639695e-13\n",
            "2.2353102e-13\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 792x230.4 with 6 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}