CIFAR_scalings_feature_space_SGD.ipynb

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      "metadata": {
        "id": "view-in-github",
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      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Pehlevan-Group/sgd_structured_features/blob/main/CIFAR_scalings_feature_space_SGD.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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        },
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        "outputId": "a9f9b6f1-3017-4bad-d48c-321e3473b3da"
      },
      "source": [
        "!pip install -q git+https://www.github.com/google/neural-tangents\n",
        "\n",
        "import numpy as np\n",
        "import math\n",
        "import matplotlib.pyplot as plt\n",
        "import jax.numpy as jnp\n",
        "\n",
        "from jax import random\n",
        "from jax.experimental import optimizers\n",
        "from jax.api import jit, grad, vmap\n",
        "import functools\n",
        "import neural_tangents as nt\n",
        "from neural_tangents import stax\n",
        "import sys\n",
        "\n",
        "from jax.config import config\n",
        "config.update(\"jax_debug_nans\", True)\n",
        "\n",
        "\n",
        "import tensorflow as tf\n",
        "import tensorflow_datasets as tfds\n",
        "import matplotlib.pyplot as plt\n",
        "from mpl_toolkits.mplot3d import Axes3D\n",
        "from google.colab import drive\n",
        "import scipy as sp\n",
        "import scipy.optimize\n",
        "import pandas as pd\n",
        "from jax.config import config\n",
        "config.update(\"jax_enable_x64\", True)\n",
        "\n",
        "from jax.experimental.ode import odeint\n",
        "\n",
        "#drive.mount('/content/gdrive', force_remount=True)\n",
        "#root_dir = \"/content/gdrive/My Drive/\""
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "  Building wheel for neural-tangents (setup.py) ... \u001b[?25l\u001b[?25hdone\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZtyhhVNePXJP",
        "outputId": "26681a0a-c154-4435-ee62-c6f614c47fe0"
      },
      "source": [
        "!pip install wandb\n",
        "import wandb\n",
        "!wandb login"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Collecting wandb\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/98/5f/45439b4767334b868e1c8c35b1b0ba3747d8c21be77b79f09eed7aa3c72b/wandb-0.10.30-py2.py3-none-any.whl (1.8MB)\n",
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            "\u001b[?25hCollecting configparser>=3.8.1\n",
            "  Downloading https://files.pythonhosted.org/packages/fd/01/ff260a18caaf4457eb028c96eeb405c4a230ca06c8ec9c1379f813caa52e/configparser-5.0.2-py3-none-any.whl\n",
            "Collecting subprocess32>=3.5.3\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/32/c8/564be4d12629b912ea431f1a50eb8b3b9d00f1a0b1ceff17f266be190007/subprocess32-3.5.4.tar.gz (97kB)\n",
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            "Collecting shortuuid>=0.5.0\n",
            "  Downloading https://files.pythonhosted.org/packages/25/a6/2ecc1daa6a304e7f1b216f0896b26156b78e7c38e1211e9b798b4716c53d/shortuuid-1.0.1-py3-none-any.whl\n",
            "Requirement already satisfied: protobuf>=3.12.0 in /usr/local/lib/python3.7/dist-packages (from wandb) (3.12.4)\n",
            "Collecting sentry-sdk>=0.4.0\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/1c/4a/a54b254f67d8f4052338d54ebe90126f200693440a93ef76d254d581e3ec/sentry_sdk-1.1.0-py2.py3-none-any.whl (131kB)\n",
            "\u001b[K     |████████████████████████████████| 133kB 48.9MB/s \n",
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            "Requirement already satisfied: PyYAML in /usr/local/lib/python3.7/dist-packages (from wandb) (3.13)\n",
            "Collecting GitPython>=1.0.0\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/a6/99/98019716955ba243657daedd1de8f3a88ca1f5b75057c38e959db22fb87b/GitPython-3.1.14-py3-none-any.whl (159kB)\n",
            "\u001b[K     |████████████████████████████████| 163kB 49.9MB/s \n",
            "\u001b[?25hCollecting pathtools\n",
            "  Downloading https://files.pythonhosted.org/packages/e7/7f/470d6fcdf23f9f3518f6b0b76be9df16dcc8630ad409947f8be2eb0ed13a/pathtools-0.1.2.tar.gz\n",
            "Collecting docker-pycreds>=0.4.0\n",
            "  Downloading https://files.pythonhosted.org/packages/f5/e8/f6bd1eee09314e7e6dee49cbe2c5e22314ccdb38db16c9fc72d2fa80d054/docker_pycreds-0.4.0-py2.py3-none-any.whl\n",
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            "Collecting gitdb<5,>=4.0.1\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/ea/e8/f414d1a4f0bbc668ed441f74f44c116d9816833a48bf81d22b697090dba8/gitdb-4.0.7-py3-none-any.whl (63kB)\n",
            "\u001b[K     |████████████████████████████████| 71kB 10.1MB/s \n",
            "\u001b[?25hCollecting smmap<5,>=3.0.1\n",
            "  Downloading https://files.pythonhosted.org/packages/68/ee/d540eb5e5996eb81c26ceffac6ee49041d473bc5125f2aa995cf51ec1cf1/smmap-4.0.0-py2.py3-none-any.whl\n",
            "Building wheels for collected packages: subprocess32, pathtools\n",
            "  Building wheel for subprocess32 (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for subprocess32: filename=subprocess32-3.5.4-cp37-none-any.whl size=6489 sha256=2d1fd2d883dd151705c8971a0ddaae064de62280ff2204b33bbdabfbe1c44619\n",
            "  Stored in directory: /root/.cache/pip/wheels/68/39/1a/5e402bdfdf004af1786c8b853fd92f8c4a04f22aad179654d1\n",
            "  Building wheel for pathtools (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for pathtools: filename=pathtools-0.1.2-cp37-none-any.whl size=8786 sha256=9f448c185f51f3e4615f5b36c6091738648aa11f954bc22f51bc966e0d256443\n",
            "  Stored in directory: /root/.cache/pip/wheels/0b/04/79/c3b0c3a0266a3cb4376da31e5bfe8bba0c489246968a68e843\n",
            "Successfully built subprocess32 pathtools\n",
            "Installing collected packages: configparser, subprocess32, shortuuid, sentry-sdk, smmap, gitdb, GitPython, pathtools, docker-pycreds, wandb\n",
            "Successfully installed GitPython-3.1.14 configparser-5.0.2 docker-pycreds-0.4.0 gitdb-4.0.7 pathtools-0.1.2 sentry-sdk-1.1.0 shortuuid-1.0.1 smmap-4.0.0 subprocess32-3.5.4 wandb-0.10.30\n",
            "\u001b[34m\u001b[1mwandb\u001b[0m: You can find your API key in your browser here: https://wandb.ai/authorize\n",
            "\u001b[34m\u001b[1mwandb\u001b[0m: Paste an API key from your profile and hit enter: \n",
            "\u001b[34m\u001b[1mwandb\u001b[0m: Appending key for api.wandb.ai to your netrc file: /root/.netrc\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RZ9uKyAflrI0",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0b303f0a-d8bf-4abb-e1bb-466fd1cee10f"
      },
      "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": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 384,
          "referenced_widgets": [
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            "871d165cfcf5468485d3af35e70f98ed",
            "d97c0e5c8ace411cbcdc0a123f0a8ad1"
          ]
        },
        "id": "b4FAFZEN9FSZ",
        "outputId": "a5799307-9d77-4529-9f8d-d2ca850b925e"
      },
      "source": [
        "# Download CIFAR-10\n",
        "num_tot = 50000\n",
        "num_classes = 10\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 = np.reshape(image, (image.shape[0], image.shape[1]*image.shape[2]*image.shape[3]))\n",
        "  image = jnp.array( image.transpose((0,3,1,2)) )\n",
        "  y = ex['label'].numpy()\n",
        "  y_mat = np.eye(10)[y]\n",
        "  break\n",
        "\n",
        "ds = tfds.load(name, split=tfds.Split.TEST).shuffle(1024).batch(num_tot)\n",
        "\n",
        "for i,ex in enumerate(ds):\n",
        "  Xtf_te = ex['image']\n",
        "  image_test = Xtf_te.numpy() / 255.0\n",
        "  print(image_test.shape)\n",
        "  Xte = np.reshape(image_test, (image_test.shape[0], image_test.shape[1]*image_test.shape[2]*image_test.shape[3]))\n",
        "  image_test = image_test.transpose((0,3,1,2))\n",
        "  yte = ex['label'].numpy()\n",
        "  y_mat_te = np.eye(10)[yte]\n",
        "  break"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\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": "b836cb02433e4d5e83f1f340c5398d5f",
              "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": "76c161ca329c4a52b254512e367222bf",
              "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": "851a253c91684b59bd28f4981d69c70a",
              "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": "16ce4a8b3bca4959a9fefc27d648944c",
              "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.incompletePPA0LI/cifar10-train.tfrecord\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "25aa5994ad974aa4b6f8f6c49cb0ceeb",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, max=50000.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "638dee6c11a34fabbf83c4b9ec54f277",
              "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": [
            "Shuffling and writing examples to /root/tensorflow_datasets/cifar10/3.0.2.incompletePPA0LI/cifar10-test.tfrecord\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "f1014b853ad74574a1292742a9b3eaaa",
              "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",
            "(10000, 32, 32, 3)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "w0S6KEuD9Vd8"
      },
      "source": [
        "def convnet(k, depth, pool = True):\n",
        "  layers = []\n",
        "  for l in range(depth):\n",
        "    #layers += [stax.Conv(k, (3, 3), (1,1)), stax.Relu()]\n",
        "    layers += [stax.Conv(k, (3,3), padding='SAME'), stax.Relu()]\n",
        "    if pool == True:\n",
        "      layers += [stax.AvgPool((2,2), strides = (2,2))]\n",
        "  layers += [stax.Flatten(), stax.Dense(10)]\n",
        "  return stax.serial(*layers)\n",
        "\n",
        "#init_fn, apply_fn, kernel_fn=convnet(200,2)\n",
        "#kernel_fn_batched = nt.batch(kernel_fn, batch_size=250)\n",
        "\n",
        "#_, _, kernel_fn_non = convnet(200,2, pool=False)\n",
        "#kernel_fn_batched_non = nt.batch(kernel_fn, batch_size=250)\n",
        "\n",
        "\n",
        "def fully_connected(width, depth):\n",
        "  layers = []\n",
        "  for l in range(depth):\n",
        "    layers += [stax.Dense(width), stax.Relu()]\n",
        "  layers += [stax.Dense(10)]\n",
        "  return stax.serial(*layers)\n",
        "\n",
        "\n",
        "\n",
        "def WideResnetBlock(channels, strides=(1, 1), channel_mismatch=False):\n",
        "  Main = stax.serial(\n",
        "      stax.Relu(), stax.Conv(channels, (3, 3), strides, padding='SAME'),\n",
        "      stax.Relu(), stax.Conv(channels, (3, 3), padding='SAME'))\n",
        "  Shortcut = stax.Identity() if not channel_mismatch else stax.Conv(\n",
        "      channels, (3, 3), strides, padding='SAME')\n",
        "  return stax.serial(stax.FanOut(2),\n",
        "                     stax.parallel(Main, Shortcut),\n",
        "                     stax.FanInSum())\n",
        "\n",
        "def WideResnetGroup(n, channels, strides=(1, 1)):\n",
        "  blocks = []\n",
        "  blocks += [WideResnetBlock(channels, strides, channel_mismatch=True)]\n",
        "  for _ in range(n - 1):\n",
        "    blocks += [WideResnetBlock(channels, (1, 1))]\n",
        "  return stax.serial(*blocks)\n",
        "\n",
        "def WideResnet(block_size, k, num_classes):\n",
        "  return stax.serial(\n",
        "      stax.Conv(16, (3, 3), padding='SAME'),\n",
        "      WideResnetGroup(block_size, int(16 * k)),\n",
        "      WideResnetGroup(block_size, int(32 * k), (2, 2)),\n",
        "      WideResnetGroup(block_size, int(64 * k), (2, 2)),\n",
        "      stax.AvgPool((8, 8)),\n",
        "      stax.Flatten(),\n",
        "      stax.Dense(num_classes, 1., 0.))\n",
        "\n",
        "\n",
        "def MyrtleNetwork(width, depth, W_std=np.sqrt(2.0), b_std=0.):\n",
        "  layer_factor = {5: [2, 1, 1], 7: [2, 2, 2], 10: [3, 3, 3]}\n",
        "  activation_fn = stax.Relu()\n",
        "  layers = []\n",
        "  conv = functools.partial(stax.Conv, W_std=W_std, b_std=b_std, padding='SAME')\n",
        "  \n",
        "  layers += [conv(width, (3, 3)), activation_fn] * layer_factor[depth][0]\n",
        "  layers += [stax.AvgPool((2, 2), strides=(2, 2))]\n",
        "  layers += [conv(width, (3, 3)), activation_fn] * layer_factor[depth][1]\n",
        "  layers += [stax.AvgPool((2, 2), strides=(2, 2))]\n",
        "  layers += [conv(width, (3, 3)), activation_fn] * layer_factor[depth][2]\n",
        "  layers += [stax.AvgPool((2, 2), strides=(2, 2))] * 3\n",
        "  layers += [stax.Flatten(), stax.Dense(10, W_std, 0.0)]\n",
        "\n",
        "  return stax.serial(*layers)\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iw4bF4lb5Vow"
      },
      "source": [
        "#### Reshape image data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gY463z_G9foH",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f991cd44-96e9-4369-f7b5-28e3179b9331"
      },
      "source": [
        "\n",
        "image = jnp.array(image, dtype = jnp.float64).transpose((0,2,3,1))\n",
        "image_test = jnp.array(image_test, dtype = jnp.float64).transpose((0,2,3,1))\n",
        "print(image.shape)\n",
        "print(image_test.shape)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(50000, 32, 32, 3)\n",
            "(10000, 32, 32, 3)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wbNbUNwKmMKZ"
      },
      "source": [
        "width = 5000\n",
        "depth = 2\n",
        "\n",
        "all_eigs = []\n",
        "all_v = []\n",
        "all_K = []\n",
        "\n",
        "\n",
        "N_pt = 6000\n",
        "\n",
        "#_, _, kernel_fn = MyrtleNetwork(width, depth)\n",
        "_, _, kernel_fn = convnet(width, depth, pool = False)\n",
        "\n",
        "kbatch =  nt.batch(kernel_fn, batch_size=100)\n",
        "#kbatch = jit(kbatch, static_argnums=2)\n",
        "K = kbatch(image[0:N_pt,:,:,:], None, 'ntk')\n",
        "\n",
        "\n",
        "all_K += [K]\n",
        "eigs, vec = jnp.linalg.eigh(K)\n",
        "\n",
        "v = jnp.sum( ( 1/vec.shape[0] * vec.T @ y_mat[0:N_pt,:])**2 , axis = 1)\n",
        "indsort = jnp.argsort(eigs)[::-1]\n",
        "\n",
        "all_eigs += [ eigs[indsort] ]\n",
        "all_v += [ v[indsort] ]\n",
        "\n",
        "_, _, kernel_mlp = fully_connected(width, depth)\n",
        "Data = image[0:N_pt,:,:,:].reshape((N_pt, image.shape[1]*image.shape[2]*image.shape[3]))\n",
        "kbatch_mlp = nt.batch(kernel_mlp, batch_size=200)\n",
        "K_mlp = kernel_mlp(Data, None, 'ntk')\n",
        "eig_mlp, vec_mlp= jnp.linalg.eigh(K_mlp)\n",
        "indsort = jnp.argsort(eig_mlp)[::-1]\n",
        "\n",
        "v = jnp.sum( ( 1/vec.shape[0] * vec_mlp.T @ y_mat[0:N_pt,:])**2 , axis = 1)\n",
        "all_eigs += [ eig_mlp[indsort] ]\n",
        "all_v += [ v[indsort] ] "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 879
        },
        "id": "RRa2-I8AmYw7",
        "outputId": "a702e061-281e-4a2a-c855-9e51a534723c"
      },
      "source": [
        "def extract_power_law(spec, start=0, end=None, xarr = []):\n",
        "  if end == None:\n",
        "    end = len(spec)\n",
        "  inds= np.linspace(start, end, end - start) \n",
        "  if len(xarr) > 0:\n",
        "    inds = xarr[start:end]\n",
        "  beta = - np.cov(np.log(inds), np.log(spec[start:end]))[0,1] / np.var(np.log(inds))\n",
        "  return beta\n",
        "\n",
        "labels = ['CONV', 'MLP']\n",
        "all_b = []\n",
        "start = 50\n",
        "end = 2500\n",
        "\n",
        "for i,eigs in enumerate(all_eigs):\n",
        "  b_i = extract_power_law( eigs, start,end)\n",
        "  eig_i = eigs/eigs[0]\n",
        "  \n",
        "  pred =  np.linspace(start,end, end-start)**(-b_i)\n",
        "  pred = pred * np.mean(eig_i[start:end]) /  np.mean(pred)\n",
        "  plt.loglog( np.linspace(1,len(all_eigs[i]), len(all_eigs[i])), eig_i , label = labels[i])\n",
        "  plt.loglog( np.linspace(start, end, end-start), pred  , '--', color = 'black')\n",
        "  if i == len(all_v)-1:\n",
        "    plt.loglog( np.linspace(start,end, end-start), pred, '--', color = 'black', label = 'Fit' )\n",
        "  else:\n",
        "    plt.loglog( np.linspace(start,end, end-start), pred, '--', color = 'black' )\n",
        "\n",
        "  all_b += [b_i]\n",
        "plt.xlabel(r'$k$',fontsize = 20)\n",
        "plt.ylabel(r'$\\lambda_k$',fontsize =20)\n",
        "#plt.title('Kernel Eigenvalues', fontsize = 20)\n",
        "plt.legend()\n",
        "plt.tight_layout()\n",
        "plt.savefig(root_dir + 'cifar_conv_vs_MLP_spectra_scaling_exponents.pdf')\n",
        "plt.show()\n",
        "print(all_b)\n",
        "\n",
        "all_a = []\n",
        "\n",
        "for i, v in enumerate(all_v): \n",
        "  plt.loglog(v, label = labels[i])\n",
        "  a_i = extract_power_law( v, start,end)\n",
        "  all_a += [a_i]\n",
        "  pred = np.linspace(start,end, end-start)**(-a_i)\n",
        "  pred = pred/np.mean(pred) * np.mean(v[start:end])\n",
        "  if i == len(all_v)-1:\n",
        "    plt.loglog( np.linspace(start,end, end-start), pred, '--', color = 'black', label = 'Fit' )\n",
        "  else:\n",
        "    plt.loglog( np.linspace(start,end, end-start), pred, '--', color = 'black' )\n",
        "\n",
        "plt.xlabel(r'$k$',fontsize = 20)\n",
        "plt.ylabel(r'$v_k^2$',fontsize =20)\n",
        "#plt.title('Task Power Spectrum', fontsize= 20)\n",
        "plt.legend()\n",
        "plt.tight_layout()\n",
        "plt.savefig(root_dir + 'cifar_conv_vs_MLP_task_scaling_exponents.pdf')\n",
        "plt.show()\n",
        "\n",
        "\n",
        "all_a2 = []\n",
        "for i, v in enumerate(all_v): \n",
        "  cum_v = np.cumsum(v) / np.sum(v)\n",
        "  acumv = ( 1-cum_v ) * len(cum_v) / (10+len(cum_v) - np.linspace(1,len(cum_v), len(cum_v)))\n",
        "  a_i = extract_power_law( acumv, start,end)\n",
        "  all_a2 += [a_i]\n",
        "  pred = np.linspace(start,end, end-start)**(-a_i)\n",
        "  pred = pred/np.mean(pred) * np.mean(1-cum_v[start:end])\n",
        "  pred = pred * acumv[end] / pred[-1]\n",
        "  plt.loglog(acumv, label = labels[i])\n",
        "\n",
        "  if i == len(all_v)-1:\n",
        "    plt.loglog( np.linspace(start,end, end-start), pred, '--', color = 'black', label = 'Fit' )\n",
        "  else:\n",
        "    plt.loglog( np.linspace(start,end, end-start), pred, '--', color = 'black' )\n",
        "\n",
        "\n",
        "plt.xlabel(r'$k$',fontsize = 20)\n",
        "plt.ylabel(r'$\\sum_{n=k}^\\infty \\lambda_n v_n^2 $',fontsize =20)\n",
        "plt.ylim([0.5,0.9])\n",
        "#plt.title('Task Power Spectrum', fontsize= 20)\n",
        "plt.legend()\n",
        "plt.tight_layout()\n",
        "plt.savefig(root_dir + 'cifar_conv_vs_MLP_task_scaling_exponents_tailsum_better_title.pdf')\n",
        "plt.show()\n",
        "print(all_a2)\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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hZbt50JMcMZWR5S9gi/pZKyWl1FV5UnLShJSLO/ayy6li2dJsafoS9vQUvOfcxfn32pO54xuwZVodmlLKDVWqVMlj3knShOSBBt81jB13reX9oKeIv3ARnwUPkfR2c2yb/gPpyVaHp5RyI6NHj2bv3r0e8XxJ3Gn6WnfSpk0bExERYXUYV2WMYeXeM2xcOps7Er6mrVcUab5l8Gn/MN7tH4ag8laHqJTHi4yMpHHjxlaH4XGudN1EZJsxpk1e+2iFlIu7P0PKSUTo0aQKL/7tGRKH/cizoVP5NbUu3mvfJPOdG7D9+AycP2J1mEoplS+akHJx92dIeRERujeqxBvjHsJ3+FyeLPcfvktvjz1iBvYPbsT2zSg4vcPqMJVS6qq023cxIiJ0bViRLg3uZW10Dx5bvpHWZ75mxN4lBO2dj612V7w7jYM6XcGDet4opUoGTUjFkIhwS4MKdK7flw0Hb+ax5b/T6OQ8xhxeSoXDA7DVvQ3vQZ/qMyallFvRW3bFmIjQsV4YMx69lS4PTmFc5S94LWM4toOrSfygHXF711gdolIewW63Wx2CRylsZzlNSCWAiHBz3TBmP9KFOx56janhHxGf5kWZrwfyw0fj2X403uoQlXJbQUFBnDx5kvT09EL/R1uSGGOIj48nICCgwPtqt+9cRKQv0LdevXoPRUdHWx2Oy5w4fZaEbx+jybmf+cXWnOkVJzKoc0t6N6uCr7f+nqJUNrvdTlxcHAkJCWRm6gvo+REQEEB4eDi+vr6Xrbtat29NSFfgCe8hXTdjSNv8OT7Ln+O8CeLx1Cc4WvpGRnSoybCbalA2yM/qCJVSxYy+h6TyJoJ/+zF4j11F+XLlmRvwD8YHLOSdZZG0f30lk3/YQ0q6/kaolCoaJSIhichNIrJRRH4Vka9E5PI6siSr3AwZuwZpOpjBF2eyq+5/GN40kC82HuHOf61j90n3f0lYKeX5SkRCAo4D3Y0xtwBHgP7WhuOG/EvDoGnQ718EnY1g0vGHWHxHCimpmQz8ZD3Tfj2I3a63d5VSrlMiEpIx5rQx5lLW13RA+3DmRQRa3Q8PrYbAsjRePYb1wRP4Z+Vf+GTxVu6fvoWzF1OtjlIpVUy5XUISkSdEJEJE0kRkRq515URkgYgki8hRERlWwLZrArcDi5wYcvFT6QZ4+FcY8B+8g8O4O/4/bCv1JEOOvcbE9z5lxZ4zVkeolCqG3K6XnYgMwlHB9AQCjTEjc6z7CkcSHQ20BH4CbjbG7BGRysDcPJq81xhzRkRCgB+Bh4wx+68VR4noZZdfZ/dAxP+w7ZiLd3oi++3hRIUPpse9/0dgSDmro1NKeRCP7PYtIlOA8OyEJCJBwHmgqTEmKmvZLOCkMWbiNdryAX4A3jHGrMzP8TUh5SE9mYwd3xK75lOqJu8lDT/OVr2Val0exLv+reDlbXWESik3V1y6fTcAMrOTUZYdQJN87DsUaAdMEpE1InJPXhuJyNis24URsbGx1x9xceMXhG/bkVT9+0Z29Pqe5f63UfrkWry/uptLbzXCvmwSxOyzOkqllIfypAqpM/CtMaZyjm0eAu4zxnR19vG1Qro2Ywwrd59g87LZ3JSwjG7ev+ODHVO1FdKoD9TtDlVaaOWklPrD1SokTxrtOwkIybUsBEh05kFyDB3kzGaLJRGhR7Pq3Nr0WX6OHMXIFZtpGLOMIac30PDUa7DqNWz+ZfCq2w2p2w3qdoMyNawOWynlpjypQsp+htTEGBOdtWwmcOpaz5AKQyukgjPGsDIyhmlrD3H8+FHa2nfS2WsXt3jvopKcByCzbF186nV3VE+1OkFA7t8xlFLFmUd1asjqgOADvAyEAw/heHaUKSJzAQOMwdHLbjFZveycePwSMbiqq2XY7ESfTWL3yQR2njjPhaO7qRS3gc5eu7nZOxI/kwriDfVuhU5/g5odrA5ZKVUEPC0hTcaRjHJ6xRgzWUTKAdOB24B4YKIxZo4r4tAKyfmOxifz+brDLIg4RBPbfkaERdMjdQX+6eewV++A1y3jHQlKZ7NVqtjyqIRkNa2QXO98cjqzNh3liw1HSE5O5F7v1Yz1+ZGqco4jpZpR/dH5eJeuaHWYSikX0IRUCFohuV56pp2DsUkcjE3iyNkLhOz/lrtjPyI9qAqhDy+G0HCrQ1RKOZkmpALQCsk6xhhe+2Q6T8e8QKmQ8niP/AHK17U6LKWUExWXF2OLhDFmkTFmbGhoqNWhlDgiwoh77mW47SUupSTC9DvgzC6rw1JKFRFNSLmISF8RmZaQoHMAWaF2WBDduvagf8qLpNkF/tsDNv0H7DpAu1LFnSakXLRCst6jXetiyjdgKK9jq9kZlj4Ls/rDheNWh6aUciFNSMrt+Pt489qApmw/H8A47+c53OGfmJPb4ZP28NN4OLPb6hCVUi6gCUm5pY71whjTqTaLd5+h2+pa9E57nU2+7ciM+AL+05Gkj7tgTu+0OkyllBNpL7tctJede7mYmsGGA3H8EhXH5sPxXIw/S19Zy8M+P1LG6xLc9TkBTe+0OkylVD5pt+9C0PeQ3FOmzc7JC5dYtXUnrTc8RlOvw1y8+TnK3DwKgvVlWqXcnSakQtCE5P5+3XOU1G/HcjubALjgVY6TZVoT2u0pwpvdYnF0Sqm8aEIqBE1InuFwbCLLly6k9Lk9VE6Jok3qRkIkhX1+TThToy++TfrQrHFjQgJ8rQ5VKYUmpALRZ0ieLTY+jn2LP6HWoa+obk4BsMh+M4tqPMug9o24o2nla7SglHIlTUiFoBWShzOGpJN7uLBxFlX3TOOoVOOJ1Ee4qUNXnu9zA77e2sFUKStoQioETUjFyKE1mG9HIZfOcc4EsyugDWV7TqR5K52DSamipgmpEDQhFTNJMRC1lKO/ryLs2BICTRqR/s0oVb0F4V1G4VujtdURKlUiaEIqBE1IxdelC7FELnyDgKNrqGU/jrcYUvp/Ttkb+1kdmlLFniakQtCEVPzZ7IafI/ZQ7acRNJIjnKvek4o3DYYmg8BLnzEp5QpFMv2EiNRwVltW0tG+Sw5vL6HnTU3xG72Yn3x6Yo5thO9Gc+ydW1j76yoybTrCuFJFyWkVkohEAB2NMWl5rAswxqQ65UBFRCukkiUt08YX6w9zftOXPJzyGWUkifVebah8z3vUbdjc6vCUKjaK5JadiMwF0owxD+RaXhX43hjT1ikHKiKakEouW/J5Di95n8q7p+GNjbN17iIgvDmV6rZEwtuCt4/VISrlsYoqIZUCtgCfGmP+lbWsJfAjsM4Yc69TDlS42CoBC4AMwAbcZ4w5fbV9NCGpo4ejODTzCdradxAsjgI/KbAapW55Eq/W94NfkMURKuV5iqxTg4g0BNYDA4DywJfAe8aYl5x2kMLF5Q0YY4xdREYC4caYKVfbRxOSAkhKy+RQTCKHDu5n/7bVdE+YT1uvKFK9SuHbuDfevd6A4ApWh6mUx3BZQhKRZcDvwG9Zf+4HBgLTAR9grDFmTqEP4AIi8iRwwhiz4GrbaUJSuRljWLbnDLs3raDakfnc5bsBn7LheA39Cio0tDo8pTyCK3vZbQeaA+8Be4FE4O84bovNAfaLiH9BGhSRJ0QkQkTSRGRGrnXlRGSBiCSLyFERGVaAdluKyGbgiay4lSoQEeGOplUYP+Z+km5/l6GpE0k8H4Ptk5tJm94Xts8CfY1CqUJz5jOkSkDLXJ/6gB2INsY0yWc7g7L26QkEGmNG5lj3FY4kOjqr/Z+Am40xe0SkMjA3jybvNcacydHGEKC7MeaRq8WhFZK6ltX7Y/j3j5u488Isuvrtp4btKNw4HPp9BCJWh6eUW7paheS07kLGmLPAsqxP9oEDgRZZn/y2Mz9r3zZAeI62goC7gKbGmCRgnYj8AIwAJmYlna55tSkifsaY9KyvCUBK/s9Mqbx1a1iRbg378d22VnT59jc+qrSYPr99SVrSOfxbDIa63SGwrNVhKuUxXNp/1RhzCdiU9bleDYBMY0xUjmU7gC752LeliLyN41ZiKvBgXhuJyFhgLECNGsXiPV9VBAa1qsbWI+eYsv8uDmcmMyLqZ/yjF2O8/ZC2Y+C217SruFL54En/SoKBi7mWJQClr7WjMWYLcM0pRI0x04Bp4LhlV4gYVQkkIrxxl+Pl2eiz7fhw82F+37ya+1jDoE2fYKKWIX3edlRMSqkrcmpCEpGaODo5tACaGWPucWLzSUBIrmUhODpSOE2OCfqc2awqIepXKs2kfs3Z26YWby+/mWVRzXn+/DyqzLmPtE7PUrp6M6jRXt9hUioPherUkPUSbDP+TD7Ns75nJwzB8d6Pd6EDE5mC432hkVnfg4DzQBNjTHTWspnAKWPMxMIe50q0U4O6XsYYFu86ww9rtzLu7As09joGQJpPCKm3vEDoTUMhINTiKJUqWtf9HpKI3Aa058/kUwdH0iHHn5eA3Tie6/wO7DDGrC9EsD44KreXcXRqeAjHs6PMrOGJDDAGRy+7xWT1sivoca5yfJ3CXDndwdgk5q3ZxoFdmxjLPNp6RWHHi4PV+lOlz0SCqzayOkSlisR1JSQReRf4v+yvOVYZHCMxLMGRgKKMMdc9PLKITMaRjHJ6xRgzWUTK4Xjp9jYgHkfvOpe8eKsVknIFYwwHY5KY+9031I1ZziDzM3bxYnv1UdzQ53HKVq5pdYhKudT1JqRYHBXLmzh6yx0GXgJG4biF9n/GmC+dGrGFtEJSRSly/34yv3+SZimbsSGcrtCZSl3G4Nu4N3j7Wh2eUk53vQnJDkw1xjyba/ntwGc4bqv9CDyc8wVUT6cVkipKh/bvZPv3H9E5eRmV5ALJvmWRlsMo1W4UhNW3OjylnOZ6E9IY4LAxZmUe64KBqTje3bkAPGWMmX39IVtHKyRlFWMMv+4/w47V82h0agHdvX7DR+ycC2tD2Y4PIk0HgW+g1WEqdV1cPtq3iHQD/gvUAhbhqJbOXnfDFtIKSRWVmJgYRo8ezVtvvUXjxo0B2HvqItv27CV92xy6pyylttdZbAFl8W7QE256CMLz/PeslNtz+RTmxpjVOLp9fwzcCewpyMCn7kSnMFdF7f333+fHH3/khhtuoFatWnzwwQc0qhzMiNva88Df32f1bUsZZV5mSUpjknf/CP+9FfvsIXB8q9WhK+VUTp0PCUBEOuHoCVf3et5DsppWSKqo7Ny5kx49emCMIS4uDgA/Pz/27t1L3bp1ATh7MZUPVkbze9QR7kicx0ifnylNMrY63fFpMxJqdYJS5Sw8C6Xyp0gGV81mjFknIs2B15zdtlLF0erVq4mLiyP7l8OAgAB8fX3x93fM3PLAAw/Qrl07pjzyCCJNWRPVjqdW7aTlydkMPbSGSodWOsbNazoYWj/gGAlCKQ/k9AqpuNAKSRWl9PR0Pv30U2bMmMHOnTvJzMxk06ZNNGnShNKlHcM1+vv706dPH95++21q167N9mPn+WB5JPZDv3Bf8DZ62NbhbU9DGtwBbcdA7Vu067hyO0U2hXlxoL3slNXsdjvLli2jV69eAFSsWJHY2Ni/bPPII4/w73//O2sW27O89P1u0hPjmBCwkLsCt+F/KQYCy8Etf4c2D4JvgBWnotRlNCEVglZIyl38+uuvvPfee6xevZrszjYhISEkJCTw+eefs2TJEt555x32Jfnz9rL9HIs5x4gyu3jAeynVk/eAX2noNM6RmPQ5k7KYJqRC0ISk3FFkZCRvvfUWpUuX5sMPP6R169Zs374dgLJly/LCpJco17Yfq6Pi2HAglh4B+3ih3Cqqx60Db39oOgg6j4cwHc1eWUMTUiFoQlKeILuHXs5beiLC7NmzuaFTL/7xUyRbjpzjRv9T/LPGVhqe+RGvjGSo0gJaj4QbR+hzJlWkXP4eUnGi7yEpT9K8eXNiYmJITk7mueeeIzQ0FGMMGRkZNKwQwJY3hlJqySQuphp6Rfeny6WpbAofhd2WAT8+Df++GTZPg4xLVp+KUlohXYlWSMpT2e2OQffnzZvHPff8OUemt7c35es0xd60Dy07dGNinUN0OzUNr/hoqNISbn4SGvbSyQOVS2mFpFQJ4uXlhZeXF0OGDOHIkSN07NgREcFmsxETvYP4ha8T4OvD6K3VaPKLfjQAAB0VSURBVL57BEsbv4Ht4hn4bjR81Ba2z4JUvUOgip4mJKWKsZo1a7Ju3ToyMzP55JNPqF+/Pu+88w6LxnWl/p7P2TNtHL3ufZzAN1Pos70LsakCPzwBn3SA376ElHNWn4IqQfSW3RXoLTtV3IWEhJCYmHjZ8mat27LhPkNwQhT4BkGXv0OLoVC6sgVRquJGb9kppS5z4cIFPvzwQ2rW/HOWWl//AC5UaEmzsy/RO/puwl6P475HJ7BzQgOYPQT2LITMNAujVsWZVki56EgNqiTav38/48ePZ9CgQdw34gFeeG86H7z2LBlJF8A4OkkE+wudq3sxbUh1wm9/zDENRmAZiyNXnkYrpAIwxiwyxowNDQ21OhSlikzDhg1ZtGgRo0aNws/Hi/jIDWQkngNjR3z88Q4uT7LNlyUHbJjKjWH1FN4fXJOZT9+O/ehm0F9slRNoQlJKXWb69Ons3r2bXr164Y0NW1I82G1UHv0xt8c8xedNZvLiyhQeeH8FfrXb07xGCFOfuZ+UixesDl15sBJ1y05EhgIfGmMqXGtb7dSglENmZiZvv/02u3bt4vmpn/DRymj+O24gpas3on6YP8d+W8uZcxcBqBbqzYn5r0CrEVwghDJl9Jae+isdOggQEW/gW6CWMabVtbbXhKRU3vbs2UOLFi2w2WyAEFC1Pnc98CgVzm6gZloU4+od4ffTGdw4LYVK5UPp3Xcgz06cSMOGDa0OXbkBfYbkMBRHQrJbHYhSnqxJkyakpqby2muvUaFiRVJPRTH79af58mAASffOIW7MFjJaPUiLqv7EnUvgfzNm0KhRI8qEhjBv3jyrw1duzO0Skog8ISIRIpImIjNyrSsnIgtEJFlEjorIsHy26Q0MAb52QchKlTg+Pj68+OKLxJw9w9atW+nYpRt33/8g/9twhLq9H2Pgu2uZPO170vcu4ctH29K5hjdpKYnUiv4cDvzMC88/T7du3Zg3b94fQx0p5Xa37ERkEI4qpicQaIwZmWPdVziS6GigJfATcLMxZo+IVAbm5tHkvVlt2YwxX4pIxJXKxZz0lp1SBXckLpl2bVsRcyQKgFIhZRj94GjenPAQgbtmwe9zICWem/6XwdZjjgFdfXx8aNGiBQ8++CCPPfaYleGrIuCRz5BEZAoQnp2QRCQIOA80NcZEZS2bBZw0xky8RltvAjfiSHQdgC+MMU9dbR9NSEoV3g8rfuGx/3uGk/t+A2MnpHxl9h88TOUggchFsPVzdm/9lbc22lh6WIi9mEpgYCApKSkAzJw5k379+mmniGKouCSkG4H1xphSObYZD3QxxvQtQLtXrJBEZCwwFqBGjRqtjx49eh1noJTafSyW0eOe42CyH+Xa9qV7+WS+e/1xxj40hpceGYz/rjmwYy6nYi+w/VIV7hw6lrjwO6hQtxkA1apVo1+/fjz77LN/GVFCea7ikpA6A98aYyrn2OYh4D5jTFdnH18rJKWc5/i5FD5cGc30Tz/m3Kr/gjF4eXvTuVMn3nn9VVr7HYIdX8OxDaRmwjtRNZizPYF9h0/+8Yxp1KhRTJ8+3eIzUderuPSySwJCci0LAS4fHfI66AR9Sjlf9XKlmHp3CyLmvsej09cR0u4u8Avil19+oc3NXThYpjM8uASe+o2Abs/wwk3p7BmeQNqUWnz29J20a9WCvn0dN0JeffVVgoOD6dmzJ4sXL7b4zJQzeVJCigJ8RKR+jmUtgD3OPIgOHaSU69QOC+KTkTez7Yf/8dycdYSPeJPgFj3559pzbD4UT8MOvejx+q9s7/olDP0an1rtGBO6nk19DzPw4nTY8TUmwzG46/Lly+nTpw/+/v506NCBuLg4i89OXS+3u2UnIj6AD/AyEA48BGQaYzJFZC5ggDE4etktJquXnROPr4OrKlVEziWnM3PjEWZuPErc+Quc+XQMGSmOUR+qVKnC448/zrOPj8Rn9zewdTokHAPfUtCwN1tpwdSv17Jy1SoSEhJITU3Fx8eHp556iipVqvDkk08SHBxs7Qmqy3jUMyQRmYwjGeX0ijFmsoiUA6YDtwHxwERjzBxXxKHPkJQqOpfSbXy3/QT/XXuIyG0bSNv4JReP78cYw+DBg/n222/Bbofjm2HXN7BnAVw6D4Hl4Ib+JNW5k+DG3cHLCz8/PzIyMgDHBIWDBg1iwoQJVK6s8zm5A49KSFbTCkkp62Ta7MzffpJ//3KQgydisUXM5eGHH2bCvbcy4ZmnmT9/Pk888QTjn34KnyO/wK5vYf8SyEiBkGrQYijnqnbjvdlL+fqbbzhw4ADGGBo1akRkZCR2u539+/fTuHFjq0+1xNKEVAhaISllHZvdsHzPGf63/ghbjpyjXJAfrP6A39csxhiDj48Pt912G1OnTqVJvZqOpLTjKzi02jF/U7k6cEN/0uvewaeLtlCjZk369+/Pl19+yYgRIwgJCaFr1648/fTTdO3a1erTLVE0IRWAVkhKuZfNh+L59NdDrNoXQ6BJJWT3PCLXLiYx8SKlSpUiOTn5z42TYmDfj7D3Bzj8KxgblKkBDXtD435sPePF3yc+x+bNm0lNTQUgICCA+fPn06tXL4vOsGTRhFQIWiEp5V6izibywcpolu4+g90YGqVH0bxMBm9OmsCpU6eoX78+3bt35+2333aMLJ5yDvYvdowMcXA12NKgVBg06AkN7mDNCV/e/+RT1q5dy/79+wkLC+Pee+9l3759jBw5kkceeYSAgACrT7vY0YRUAFohKeXeTidcYsaGI3y1+RgXUzPpWK88rbyO88q40SQmOl5LrFmzJs888wyPP/44Xl5ekJYI0Stg309wYAWkJoC3H9TqDA17Qb0eUK42bdq0Ydu2bQCICHXr1mX48OG8/HLuflaqsDQhFYJWSEq5t+S0TGZvPspnaw8Tm5hGw0qlaZIeyYrZH7N71y4AFi5cSP/+/bHb7Y7EBGDLgGObHM+dopbAuUOO5eXrQf3bOVOmNe98s57vFn7PkSNHqFChAmfPngVg0qRJjBw5krp161pxysWCJqRC0ISklGdIzbCxaMcpPl93mH1nEikf5Ef/hsHEbZrPh+9OBaBx48akp6czfvx4Hn744T+TkzEQf9BRNUWvgCPrHLf2vP2hRntSqt7MAVs4zXsMIeL3nbRt2xaAsmXLcuuttzJ+/HjatWtn1al7JE1IhaAJSSnPYoxh48F4Pl93mJX7YvDz9qJfy6qM7lSb4Xd2Y/v27QD4+/vTt29f3n777csHbE1PcSSlQ2scPfZi9jqW+wRir9qKWftLMe3nfUTsjiY9PR2AcePG8d5775Geno6Pj8+fyU7lSRNSAegzJKU838HYJP63/jDzt58kJd1G65plGdCwFMtnvMv8774jJSWFtm3bsmXLlj8Gb80zkSTHwbGNcHQDHF0PZ3Y5upV7+bAkPpwPNyTx5ot/o/ltQxk+9im++eYbWrZsyejRoxk9ejQ+Pj5FfObuTxNSIWiFpJTnS0jJ4OuIY8zefIyj8SlUCvHnnjbV8Tu6gXYtm9K2bVtef/11Xn31VQYMGMDUqVMJDw+/coOpF+H4Fji2wZGkTm4Dm6NSemVrCP9aF0f8RUd3ci8vLxo2bMjvv/+On59fUZyuR9CEVAiakJQqPmx2w5r9MXy56ShromIRoFvDigxrV4NN8z/nH/+YwqVLjhlsGzZsyPPPP8/9999/7YYzUh1JKTtBHd/C0ZiLvL0hjYXRkJQhnF87HWp24M77n6JOnTpMmDDh6kmvmNOEVAiakJQqno6fS+Hrrcf5OuI4sYlpVA0NYEibcIhewyfvv0N0dDReXl4kJycTEBBAZmZm/m+92TLhzE5Hcjq2EfvhdXilXSA9006p15OwOe4OElauLLf3vINnJ06kefPmrjtZN6QJqQD0GZJSJUOGzc7Pe88yZ8sx1kbH4e0l3NqoIj1q+pB4YDujRz9ISkoKZcuWpW7dukyaNImhQ4cW7CB2O8RFwdH1pB9cy+fzlvL5hlh2nLWTaYcuDcuz5t/PcCH0BraeNtzWZ4BrTtaNaEIqBK2QlCo5jsQl89XWY8yLOEF8cjrhZQMZ0LIarcqmMXbYIA4ePAhAUFAQgwcP5q233qJixYoFP5AxcOEY9sPr+P7bOVQ3J2gTeIxJK1OYsjYdfx+hTf3KjB06gOGPPI1XWD0QcfLZWksTUiFoQlKq5EnLtLF8z1m+iTjO+gNx2A20rlmWzpUMq2a+zfKlS0hLS+P1119n4sSJpKamXv/wQmmJ7Fz5Da+8+T6rIvZzIcUxdYa3wMbHqtK24y1Q/Sao3g6q3gi+gU44U+toQioETUhKlWwxiaks2H6SedtOEB2ThJ+3F10alCfw0C/8c+JTBAf606ZNG/bv388999zDG2+8QVhY2HUfN3r/ft567UXW/Por+98fiNfJrbR/83dikw13NfFn/MDWVGzS2ZGkwm+C0GpOONuiowmpEDQhKaXA8cLtrpMJLPjtJIt2nCYuKY3SAT70alqZXbP/yarFC0lPT0dEaNasGa+++ir9+/d3agxtW9/Itt9+J/u/6ym3BvFCJ2/Hl5BwqNEOanZ0jM0XVt+tb/NpQioETUhKqdwybXY2Hopn4W+nWLbnDElpmVQI9qXC0dX8tmQ2Z04ep06dOn88c7p48SIhISFOOXZqaiqffPIJX3zxBbNnzqBpmHG8E3V8k2NsvsTTjg2DK0PtzlC7C9TpCmWqO+X4zqIJqQC0l51SKj9SM2z8HHmWhb+d4teoWNJtdsqmxXBTNX8eHtKLqA3LGDZsGC1btmTKlCn07t3bdcEY4xgk9shaxzxQh3+F5FjHurAGUPdWx6jmtTqBl7fr4sgHTUiFoBWSUiq/Ei5lsDLyLIt2nGL9gXjSbXb8T/7G6SUfkxh/BoDQ0FDuu+8+3nzzTYKDg10bkDEQE+kYj+/Ayj8HjS1dBZreBc3vgcrNLLm1pwmpEDQhKaUKIzE1g+V7zrJi71l+jY7lwsmDXFzzP1KO/I6x29gVfZim9WoRFxfnlE4Q+ZKeAtHLYOe3EL0c7BlQoTE0vxua3e2YVbeIlPiEJCK1gK3AnqxFdxtjYq+2jyYkpdT1Ss2wselQPCsjY1ix6ySHdm6kVN22NKsWwtJnelCqVClGjXyAKVOmuL5qypZyDvYsgJ3fOJ4/gaNDRPMhjsrJxd3KNSE5EtLbxpjB+d1HE5JSypmMMUSeTmTVvrMs3XGMlR+OJ/XoTsfo4SI0bn4j/3rvXW7t1qXogjp/BHZ9Czu+hvhoR4eIW8ZDqwfAxzUDwmpCciSkjcABYC3wgrnGiWtCUkq5UmxiGit2nuDdd97i9+XfYks+T5nWfRjyf5NpW8WX25vXoEbFskUTjDGO6TVW/cMxUGyZGtDrLUdHCCe7WkJyu5mkROQJEYkQkTQRmZFrXTkRWSAiySJyVESG5bPZ00A94BagIjDIuVErpVTBVCjtz7COdYmY/ylJ52P597xljB73HDtPJPDkw6OpWbk85es24+kP57LvzEVcWjyIOHrgjVoMw78Dv9Lw1b2waBxkprnuuLnDcLcKSUQGAXagJxBojBmZY91XOJLoaKAl8BNwszFmj4hUBubm0eS9xpgzOdroDbQ3xrx0tTi0QlJKWcEYw7OT/8m/P3yPpAvxAHgFhlCl3Z2MHvcctzauRLs65fD3cWH37cw0WDUFNnwINW6GoV9BYBmnNO2Rt+xEZAoQnp2QRCQIOA80NcZEZS2bBZw0xky8RluljTGJWT+/DkQaY2ZebR9NSEopq23cuJG/jZ/A5k0b8CsVQq1xc0jNsOOTEke3Nk3o2rAC3RtVpEqoizoi7JoHCx6Bqi3hgUVO6fBwtYTkSfPrNgAys5NRlh1Afp4AdspKcCnAYWBSXhuJyFhgLECNGkXXDVIppfLSoUMHNq5fS2pqKlFRUTRo3ITP5y9j/pId7D1VnRV7zwJwQ5UQbm1cke6NKtIivAxeXk56v6jZYPD2g2/uh8Xjof/Hzmn3CjypQuoMfGuMqZxjm4eA+4wxXZ19fK2QlFLuKDIykvr16+Pt7c2BmCRW7YthZWQMEUfPYTcQFuxH14YVubVRRTrVD6N0gO/1H3T5JMftuzErITzP4ibfikuFlATkHhQqBEh05kFyDB3kzGaVUsopGjdu/MfP9SuVpn6l0jzcpS4XUtL5JSqWlZExLN9zhnnbTuDrLbSrXZ4ejStyW5PKVCtTyFtuXSbAzq9hybMw5meXjfDgSRVS9jOkJsaY6KxlM4FT13qGVBhaISmlPFWmzc62o+dZtS+GnyPPcjA2GYC2tcoy4MZq9GlWhTKlCvie0eZPYckEeGIbhBX+F3aP6tQgIj44KreXgXDgIRzPjjJFZC5ggDE4etktJquXnROPr4OrKqWKlUOxSSzZfYYFv53kQEwSvt5Ct4YVGXhjNbo1qkiAbz567MVFw0dt4M73oc2oQsfiaQlpMo5klNMrxpjJIlIOmA7cBsQDE40xc1wRh1ZISqnixhjDnlMXWfjbSb7fcYrYRMfcTn2aVWFQq3Da1iqLXOl2nDHwdgOo0wXu+m+hY/CohGQ1rZCUUiWBzW7YcDCOBb+dZOnuM6Sk27ihSggPd6nDnc2r4p1XT71vRznmXnomstDH1YRUCFohKaVKipT0TH74/RSfrT3Ewdhk6lcM5vnejenWqOJfN1zzJqz5J0yKA+/C9d7zqKGDrCYifUVkWkJCgtWhKKVUkSjl58O9N9VgxdNd+HhYKzLthlEztjJh3g4updv+3DCovOPPlHiXxKEJKRdjzCJjzNjQ0FCrQ1FKqSLl5SX0aV6FZeNu4fFudfkm4gQDP1nPodgkxwalsuZv0oRUNLRCUkqVdH4+Xvy9ZyP+N6otZy+mct9/NxObmAZ+WXM2pSe75LiakHLRCkkppRy6NazIrNHtOJ+SzqNfbiPdK+vdpcxUlxxPE5JSSqkralotlKmDWxBx9DyztjrGziNDE5JSSikL9G1RlaE3VWfBrjjHgsxLLjmOJqRc9BmSUkpdbnSn2iTZs7p6a4VUNPQZklJKXa5uhWD8/AMcX2zpLjmGJiSllFLXJCLUr5Q94YJrBlTQhKSUUipfGmQlJJvNdo0tC0cTUi76DEkppfIWXt7xHlJSaoZL2teElIs+Q1JKqbwF+TvmdE3L0ISklFLKQgGlSjM781YuBtd1SfuakJRSSuVLQHAZXsgcTUy5PAfrvm6akJRSSuVLcNYtu8S0TJe0rwlJKaVUvmRPdZ6aob3sioT2slNKqbxlTyLrqnldNSHlor3slFIqb9nTmttdlJE0ISmllMoXL8lOSC5q3zXNuh8R6SoiK0VktYgMtDoepZTyNFn5yGUVko9LWnUzIhIIPAP0Msa4ZlRApZQq5v6okFxUIpWUCqkDcAlYJCILRKSy1QEppZSnKXG37ETkCRGJEJE0EZmRa125rISSLCJHRWRYPputBNQD+gKfAZOdGrRSSpUAXlkZoyTdsjsFTAF6AoG51n0MpONIMC2Bn0RkhzFmT1bVMzeP9u4FLgDrjTHpIrISeM5l0SulVDGVXSGZkpKQjDHzAUSkDRCevVxEgoC7gKbGmCRgnYj8AIwAJhpjzgBd82pTRLYCz4iI4Ehkh1x6EkopVQyVCfRl5TNdCAv2d0n7bpeQrqIBkGmMicqxbAfQ5Vo7GmPiRGQB8AuOmaUezGs7ERkLjAWoUaPGdQeslFLFiY+3F3UrBLusfbd7hnQVwcDFXMsSgNL52dkY87Ex5hZjTBdjzMErbDPNGNPGGNOmQoUK1xmuUkqpgvCkhJQEhORaFgIkOvMgOnSQUkpZw5MSUhTgIyL1cyxrAexx5kF06CCllLKG2yUkEfERkQDAG/AWkQAR8THGJAPzgVdFJEhEOgL9gVlOPr5WSEopZQG3S0jAizheYp0IDM/6+cWsdY/h6AoeA3wFPGqM0QpJKaWKAXFVf3JPJSJ9gb716tV7KDo62upwlFKqWBGRbcaYPKecdccKyVJaISmllDU86T2kIpFdIQEXRSS7RArF0cWcK3zPvSwMiHNlnFeIwdn7Xmu7q62/1jW60rLc3935WhZkv8Jey4IsLwnX0tl/J/Narv++r73+ev5917ziEY0x+rnGB5h2te+5lwERRR2TK/a91nZXW3+ta5Tfa+vO17Ig+xX2WhZkeUm4ls7+O5mf65Z7mTtfRyuvZWH+Tub+6C27/Fl0je9XWuZK13O8/O57re2utj6/1yg/19bVCnvMguxX2GtZkOUl4Vo6++9kXsv13/e117vk37d2anABEYkwV3hopwpGr6Xz6LV0Dr2OrqMVkmtMszqAYkSvpfPotXQOvY4uohWSUkopt6AVklJKKbegCUkppZRb0IRUhETkTRFZKyKzRMTX6ng8lYiEisgWEUkSkaZWx+PJROQmEdkoIr+KyFf697JwRKSSiGwQkV9EZJWIVLE6Jk+kCamIiEgLoJoxpjOwDxhscUieLAXoA8yzOpBi4DjQ3RhzC3AEx4DFquDigE7GmC7ATGC0xfF4JE1IRedmYHnWz0uBjhbG4tGMMRnGmFir4ygOjDGnjTGXsr6mA3Yr4/FUxhibMSb72pXGydPilBSakApIRJ4QkQgRSRORGbnWlRORBSKSLCJHRWRYjtVl+XPG2wSgXBGF7Lau41qqXK73WopITeB2rHmZ1m1cz3UUkZYishl4AthehGEXGzqWXcGdAqYAPXFMhZHTxzh+y6wEtAR+EpEdxjFFxgX+nPE2FDhXNOG6tcJeS3W5Ql9LEQnBMa/YSGNMRtGF7JYKfR2NMb8D7URkCPAc8EiRRV1MaIVUQMaY+caYhUB8zuUiEgTcBUwyxiQZY9YBPwAjsjbZAPTI+rknsL6IQnZb13EtVS6FvZYi4gPMBV4xxuwv4rDdznVcR78cmyfgeM6pCkgTkvM0ADKNMVE5lu0AmsAfvz2dFZG1Wcu+K/oQPcZVryWAiCzGcYvpMxEZWbTheZRrXcuhQDtgkoisEZF7ijpAD3Gt69gyq6fiamAcMLWoAywO9Jad8wTz5zOibAk4HnACYIz5e5FG5Lnycy17F2lEnuuq19IYMwvH7Tp1dde6jluAW4o6qOJGKyTnSeLPZ0TZQoBEC2LxdHotnUevpXPodSwCmpCcJwrwEZH6OZa1QLt/FoZeS+fRa+kceh2LgCakAhIRHxEJALwBbxEJEBEfY0wyMB94VUSCRKQjjpcM9XbIFei1dB69ls6h19Firpz1sDh+gMmAyfWZnLWuHLAQSAaOAcOsjtedP3ot9Vq620evo7UfnX5CKaWUW9BbdkoppdyCJiSllFJuQROSUkopt6AJSSmllFvQhKSUUsotaEJSSinlFjQhKaWUcguakJTyQCLytIgYnbhQFSeakJTyTK2z/oywNAqlnEhHalDKA4nIXqAaUMboP2JVTGiFpJSHyZq9tCHwmyYjVZxoQlLK87TE8W93W86FIlJWRL7Perb0voj4WhOeUoWjM8Yq5XlaZf35R0ISkXbA10BZ4G5jzDwrAlPqemiFpJTnye7QsA1ARP4GrMUxxXYbTUbKU2mFpJTnaYVj6uw4Efke6Ad8ATxqjLlkaWRKXQftZaeUB8mazTQRiAEygYrAk8aY/1oamFJOoLfslPIsLXDc2fAHagDzNBmp4kITklKeJbtDwzPAj8BwERlnYTxKOY0mJKU8S84RGu7F0bHhHREZZF1ISjmHPkNSyoOIyHagEVDaGGMTkcrAJhzPkrobYzZZGqBS10ErJKU8hIj4AU2BXcYYG4Ax5gzQG0gDFolIPQtDVOq6aEJSynM0A3yB33IuNMbsBQYBocASEQmzIDalrpveslNKKeUWtEJSSinlFjQhKaWUcguakJRSSrkFTUhKKaXcgiYkpZRSbkETklJKKbegCUkppZRb0ISklFLKLWhCUkop5RY0ISmllHIL/w9D1uJKt8+c0wAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "[1.008635010215918, 0.7868183179574973]\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 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "[0.07671703648705944, 0.0482533345423585]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "99uuERbs5Kxy"
      },
      "source": [
        "import timeit\n",
        "def train_model(params, apply_fn, learning_rate=0.001, batch_size = 25, num_step = 2500, conv=True):\n",
        "\n",
        "  \n",
        "  loss = jit( lambda params, Xtr, ytr: 10*jnp.mean(  ( apply_fn(params, Xtr) - ytr)**2  ) )\n",
        "  test_loss = jit( lambda params: 10*jnp.mean( ( apply_fn(params, image_test[0:500,:,:,:]) - y_mat_te[0:500,:])**2  ) )\n",
        "  if conv == False:\n",
        "    test_loss = jit( lambda params: 10*jnp.mean( ( apply_fn(params, Xte[0:500,:]) - y_mat_te[0:500,:])**2  ) )\n",
        "\n",
        "  grad_fn  = jit(grad(loss, 0))\n",
        "  \n",
        "  opt_init, opt_update, get_params = optimizers.adam(learning_rate)\n",
        "  opt_state = opt_init(params)\n",
        "  train = []\n",
        "  test = []\n",
        "  start = timeit.default_timer()\n",
        "  for t in range(num_step):\n",
        "    start = (batch_size * t) % 50000\n",
        "    if conv == True:\n",
        "      D_t = image[start:start+batch_size,:,:,:]\n",
        "    else:\n",
        "      D_t = X[start:start+batch_size,:]\n",
        "    y_t = y_mat[start:start+batch_size,:]\n",
        "    opt_state = opt_update(t, grad_fn(get_params(opt_state), D_t, y_t) , opt_state)\n",
        "    #train_loss = loss(get_params(opt_state),  D_t, y_t )\n",
        "    #train += [train_loss]\n",
        "\n",
        "    #wandb.log({'train-loss': np.array(train_loss), 'test-loss': np.array(test_loss(get_params(opt_state))) })\n",
        "    if t % 100 == 0:\n",
        "      test  += [test_loss(get_params(opt_state))]\n",
        "      sys.stdout.write('\\r t = %d | train: %0.4f | test = %0.4f' % (t, loss(get_params(opt_state),  D_t, y_t ), test[-1]))\n",
        "      \n",
        "  return train, test"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tSUE7ARpB426"
      },
      "source": [
        "### Train MLP and Conv net to compare"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qOGMhFuk6TKB",
        "outputId": "0fe52a56-9bf2-4acc-cdc3-d89840410f67"
      },
      "source": [
        "width = 512\n",
        "num_step = 12000\n",
        "init_fn, apply_fn, _ = fully_connected(width, depth)\n",
        "_, params= init_fn(random.PRNGKey(0), (-1, 3*32**2))\n",
        "train_mlp, test_mlp = train_model(params, apply_fn, num_step = num_step, conv=False)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            " t = 11900 | train: 0.6793 | test = 0.7022"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 272
        },
        "id": "0fsfSO-lH7RM",
        "outputId": "6eeb4e99-1694-48c2-d2ff-e4f194fa5411"
      },
      "source": [
        "plt.loglog(test_mlp)\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/"
        },
        "id": "t0AfZCaDCpWV",
        "outputId": "a6c85a65-68e5-450d-d09b-d8d4c6968244"
      },
      "source": [
        "width = 50\n",
        "num_step = 12000\n",
        "print(image_test.shape)\n",
        "print(image.shape)\n",
        "init_fn, apply_fn, _ = convnet(width, depth)\n",
        "_, params= init_fn(random.PRNGKey(0), (-1, 32,32,3))\n",
        "train_conv, test_conv = train_model(params, apply_fn, learning_rate = 0.01, num_step = num_step, conv=True)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(10000, 32, 32, 3)\n",
            "(50000, 32, 32, 3)\n",
            " t = 11900 | train: 0.6083 | test = 0.5745"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 293
        },
        "id": "kg_zcaTjEBng",
        "outputId": "7c65aeda-be99-4eb8-9b78-21ab0f26ad60"
      },
      "source": [
        "start = 1\n",
        "end = 12000\n",
        "arr = np.linspace(start, end, len(test_conv))\n",
        "\n",
        "plt.loglog(arr, test_conv, label = labels[0])\n",
        "plt.loglog(arr, test_mlp, label = labels[1])\n",
        "\n",
        "scale_1 = arr**(-all_a2[0])\n",
        "scale_1 = scale_1 / scale_1[-1] * test_conv[-1]\n",
        "\n",
        "scale_2 = arr**(-all_a2[1])\n",
        "scale_2 = scale_2 / scale_2[-1] * test_mlp[-1]\n",
        "plt.loglog(arr[1:], scale_1[1:], '--',color = 'black', label = 'Theory')\n",
        "plt.loglog(arr[1:], scale_2[1:], '--', color = 'black')\n",
        "plt.xlabel(r'$t$',fontsize=20)\n",
        "plt.ylabel(r'$L_t$',fontsize=20)\n",
        "plt.ylim([5e-1,1.1])\n",
        "plt.xlim([10,np.amax(arr)])\n",
        "#plt.title('CIFAR Online Scalings',fontsize=20)\n",
        "plt.legend()\n",
        "plt.tight_layout()\n",
        "plt.savefig(root_dir + 'wide_conv_vs_mlp_cifar_longer.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"
          }
        }
      ]
    }
  ]
}