picture_of_tasks_tutorial.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "view-in-github"
   },
   "source": [
    "<a href=\"https://colab.research.google.com/github/grasp-lyrl/picture_of_space_of_tasks/blob/main/picture_of_tasks_tutorial.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "VNucC_Sueuo4"
   },
   "source": [
    "# Overview\n",
    "\n",
    "This notebook is a short tutorial to understand the techniques used in the paper titled [A picture of the space of typical learnable tasks](https://arxiv.org/abs/2210.17011) by [Rahul Ramesh](https://rahulramesh.info), [Jialin Mao](https://www.linkedin.com/in/jialin-mao-339346182), [Itay Griniasty](https://scholar.google.co.il/citations?user=a3Uhp58AAAAJ&hl=en), [Rubing Yang](https://www.amcs.upenn.edu/people/rubing-yang), [Han Kheng Teoh](https://www.linkedin.com/in/han-kheng-teoh-09392a70), [Mark K. Transtrum](https://physics.byu.edu/faculty/transtrum/index), [James P. Sethna](https://sethna.lassp.cornell.edu) and [Pratik Chaudhari](https://pratikac.github.io/).\n",
    "\n",
    "Numerous algorithms---for transfer, few-shot, multi-task or continual learning---are able to successfully leverage data from multiple tasks. But why is this possible? What is the structure in data that allows us to learn from different tasks? We find that typical trajectories of neural networks seem to lie on a low-dimensional manifold; we speculate that this is because typical tasks lie on a low-dimensional manifold.\n",
    "\n",
    "Central to these results are the tools developed in our work titled [The Training Process of Many Deep Networks Explores the Same Low-Dimensional Manifold](https://arxiv.org/abs/2305.01604) by [Jialin Mao](https://www.linkedin.com/in/jialin-mao-339346182), [Itay Griniasty](https://scholar.google.co.il/citations?user=a3Uhp58AAAAJ&hl=en), [Han Kheng Teoh](https://www.linkedin.com/in/han-kheng-teoh-09392a70), [Rahul Ramesh](https://rahulramesh.info) [Rubing Yang](https://www.amcs.upenn.edu/people/rubing-yang), [Mark K. Transtrum](https://physics.byu.edu/faculty/transtrum/index), [James P. Sethna](https://sethna.lassp.cornell.edu) and [Pratik Chaudhari](https://pratikac.github.io/). We will first start by understanding some of these tools.\n",
    "\n",
    "We will then martial these tools to analyze the geometry of the representations learned by neural networks. More results on supervised, self-supervised, meta- and transfer learning are presented in our paper.\n",
    "\n",
    "Let's start by importing libraries and defining some helper functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "cellView": "form",
    "id": "Br4GADBIejOx"
   },
   "outputs": [],
   "source": [
    "#@title Imports\n",
    "import torch\n",
    "import pickle\n",
    "import random\n",
    "import numpy as np\n",
    "import torchvision\n",
    "import pandas as pd\n",
    "\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "import torchvision.transforms as transforms\n",
    "import plotly.graph_objects as go\n",
    "\n",
    "from scipy import optimize\n",
    "from functools import partial\n",
    "from sklearn.decomposition import PCA\n",
    "\n",
    "from torch.utils.data import Dataset, DataLoader\n",
    "from typing import List\n",
    "from torch import Tensor\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from matplotlib.colors import to_rgb, to_hex\n",
    "\n",
    "\n",
    "plt.style.use('seaborn-v0_8-whitegrid')\n",
    "\n",
    "sns.set(context='poster',\n",
    "        style='ticks',\n",
    "        font_scale=0.65,\n",
    "        rc={'axes.grid':True,\n",
    "            'grid.color':'.9',\n",
    "            'grid.linewidth':0.75})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "9N8CQMsbFv-q",
    "outputId": "7871577c-6b4a-43ba-baa7-06adff34a071"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Files already downloaded and verified\n",
      "taskA_preds.npy.1   100%[===================>] 211.72M  97.9MB/s    in 2.2s    \n",
      "taskB_preds.npy.1   100%[===================>] 211.72M  91.5MB/s    in 2.3s    \n",
      "dataset_S.pkl.1     100%[===================>]   6.51K  --.-KB/s    in 0s      \n"
     ]
    }
   ],
   "source": [
    "#@title Data\n",
    "def cifar_transform():\n",
    "    mean = (0.4914, 0.4822, 0.4465)\n",
    "    std = (0.2471, 0.2435, 0.2616)\n",
    "\n",
    "    transform = transforms.Compose([\n",
    "        transforms.ToTensor(),\n",
    "        transforms.Normalize(mean, std),\n",
    "    ])\n",
    "    return transform\n",
    "\n",
    "\n",
    "def get_task_dataloader(task):\n",
    "    \"\"\"\n",
    "    Get the dataloaders of all even classes and all odd classes\n",
    "    \"\"\"\n",
    "    dataset = torchvision.datasets.CIFAR100(\n",
    "        root='./data', train=True, download=False, transform=cifar_transform())\n",
    "    \n",
    "    idx = np.where(np.array(dataset.targets) % 2 == task)[0]\n",
    "    dataset.data = dataset.data[idx]\n",
    "    dataset.targets = [int(x) for x in (np.array(dataset.targets)[idx] / 2)]\n",
    "\n",
    "    loader = torch.utils.data.DataLoader(\n",
    "        dataset, batch_size=64, shuffle=True, num_workers=2)\n",
    "        \n",
    "    return loader\n",
    "    \n",
    "        \n",
    "def get_cifar_dataloader():\n",
    "    dataset = torchvision.datasets.CIFAR100(\n",
    "        root='./data', train=True,\n",
    "        download=False, transform=cifar_transform())\n",
    "\n",
    "    dataset.data = dataset.data[:5000]\n",
    "    dataset.targets = [int(x) for x in (np.array(dataset.targets)[:5000])]\n",
    "    \n",
    "    loader = torch.utils.data.DataLoader(\n",
    "        dataset, batch_size=128, shuffle=False, num_workers=2)     \n",
    "\n",
    "    return loader\n",
    "\n",
    "def load_synthetic_data():\n",
    "    # Lets load the dataset and plot it\n",
    "    with open(\"dataset_S.pkl\", \"rb\") as fp:\n",
    "        dataset_S = pickle.load(fp)\n",
    "\n",
    "    plt.figure(figsize=(4, 4))\n",
    "    for lab in range(3):\n",
    "        ind = np.where(dataset_S['Y'] == lab)[0]\n",
    "        plt.scatter(dataset_S['X'][ind, 0], dataset_S['X'][ind, 1], s=40)\n",
    "    plt.legend([\"Class 0\", \"Class 1\", \"Class 2\"],\n",
    "               bbox_to_anchor=(1.1, 1.05))\n",
    "    \n",
    "    plt.show()\n",
    "    return dataset_S\n",
    "\n",
    "def cifar100_start_end():\n",
    "    loader = get_cifar_dataloader()\n",
    "    labels = []\n",
    "    for _, targets in loader:\n",
    "        labels.append(targets.numpy())\n",
    "    labels = np.concatenate(labels)\n",
    "\n",
    "    p_0 = np.sqrt(np.zeros((5000, 100)) + 0.01)\n",
    "    p_star = np.sqrt(np.eye(100)[labels])\n",
    "\n",
    "    return p_0, p_star\n",
    "\n",
    "\n",
    "def set_seed(seed=0):\n",
    "    rng = np.random.default_rng(seed)\n",
    "    true_seed = int(rng.integers(2**30))\n",
    "    random.seed(true_seed)\n",
    "    np.random.seed(true_seed)\n",
    "    torch.backends.cudnn.deterministic = True\n",
    "    torch.backends.cudnn.benchmark = False\n",
    "    torch.manual_seed(true_seed)\n",
    "\n",
    "\n",
    "# Download dataset\n",
    "dataset = torchvision.datasets.CIFAR100(root='./data', download=True)\n",
    "\n",
    "# Download predictions and sample dataset\n",
    "!wget -q --show-progress https://huggingface.co/rahul13ramesh/picture_of_space_of_tasks/resolve/main/taskA_preds.npy\n",
    "!wget -q --show-progress https://huggingface.co/rahul13ramesh/picture_of_space_of_tasks/resolve/main/taskB_preds.npy\n",
    "!wget -q --show-progress https://huggingface.co/rahul13ramesh/picture_of_space_of_tasks/resolve/main/dataset_S.pkl\n",
    "\n",
    "\n",
    "# Colorscheme\n",
    "col = {\n",
    "    'taskA': '#0C7BDC',\n",
    "    'taskB': '#FF950A'\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "cellView": "form",
    "id": "YiSilXL6GlDR"
   },
   "outputs": [],
   "source": [
    "#@title Networks\n",
    "class MLP(nn.Module):\n",
    "    def __init__(self, input_size, hidden=[500,500], num_classes=2):\n",
    "        super(MLP, self).__init__()\n",
    "        sizes = [input_size] + list(hidden)\n",
    "\n",
    "        self.hidden = nn.ModuleList()\n",
    "\n",
    "        for i in range(len(sizes) - 1):\n",
    "            self.hidden.append(nn.Linear(sizes[i], sizes[i+1], bias=False))\n",
    "            self.hidden.append(nn.ReLU())\n",
    "        self.fc = nn.Linear(sizes[-1], num_classes, bias=False)\n",
    "\n",
    "    def forward(self, x):\n",
    "        for layer in self.hidden:\n",
    "            x = layer(x)\n",
    "        out = self.fc(x)\n",
    "        return out\n",
    "\n",
    "def update_mlp_params(x, y, net, optimizer, criterion):\n",
    "    optimizer.zero_grad(set_to_none=True)\n",
    "    x = x.to(DEV)\n",
    "    y = y.to(DEV)\n",
    "    out = net(x)\n",
    "    loss = criterion(out, y)\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "\n",
    "\n",
    "class BasicBlock(nn.Module):\n",
    "    def __init__(self,\n",
    "                 in_planes: int,\n",
    "                 out_planes: int,\n",
    "                 stride: int,\n",
    "                 drop_rate: float = 0.0 ) -> None:\n",
    "        nn.Module.__init__(self)\n",
    "\n",
    "\n",
    "        self.bn1 = nn.BatchNorm2d(in_planes)\n",
    "        self.bn2 = nn.BatchNorm2d(out_planes)\n",
    "\n",
    "        self.relu1 = nn.ReLU(inplace=True)\n",
    "        self.conv1 = nn.Conv2d(in_planes, out_planes, kernel_size=3,\n",
    "                               stride=stride, padding=1, bias=False)\n",
    "        self.relu2 = nn.ReLU(inplace=True)\n",
    "        self.conv2 = nn.Conv2d(out_planes, out_planes, kernel_size=3,\n",
    "                               stride=1, padding=1, bias=False)\n",
    "        self.droprate = drop_rate\n",
    "        self.equalInOut = (in_planes == out_planes)\n",
    "        self.convShortcut = nn.Conv2d(in_planes, out_planes,\n",
    "                                      kernel_size=1, stride=stride,\n",
    "                                      padding=0, bias=False)\n",
    "\n",
    "    def forward(self, x: Tensor) -> Tensor:\n",
    "        if not self.equalInOut:\n",
    "            x = self.relu1(self.bn1(x))\n",
    "        else:\n",
    "            out = self.relu1(self.bn1(x))\n",
    "        out = self.relu2(self.bn2(self.conv1(out if self.equalInOut else x)))\n",
    "        if self.droprate > 0:\n",
    "            out = F.dropout(out, p=self.droprate, training=self.training)\n",
    "        out = self.conv2(out)\n",
    "        return torch.add(x if self.equalInOut else self.convShortcut(x), out)\n",
    "\n",
    "\n",
    "class NetworkBlock(nn.Module):\n",
    "    def __init__(self,\n",
    "                 nb_layers: int,\n",
    "                 in_planes: int,\n",
    "                 out_planes: int,\n",
    "                 block: BasicBlock,\n",
    "                 stride: int,\n",
    "                 drop_rate: float = 0.0) -> None:\n",
    "        nn.Module.__init__(self)\n",
    "        self.layer = self._make_layer(block, in_planes, out_planes, nb_layers,\n",
    "                                      stride, drop_rate)\n",
    "\n",
    "    def _make_layer(self,\n",
    "                    block: BasicBlock,\n",
    "                    in_planes: int,\n",
    "                    out_planes: int,\n",
    "                    nb_layers: int,\n",
    "                    stride: int,\n",
    "                    drop_rate: float = 0) -> nn.Sequential:\n",
    "        layers = []\n",
    "        for i in range(int(nb_layers)):\n",
    "            layers.append(block(i == 0 and in_planes or out_planes, out_planes,\n",
    "                                i == 0 and stride or 1, drop_rate))\n",
    "        return nn.Sequential(*layers)\n",
    "\n",
    "    def forward(self, x: Tensor) -> Tensor:\n",
    "        return self.layer(x)\n",
    "\n",
    "\n",
    "class WideResnet(nn.Module):\n",
    "    \"\"\"\n",
    "    Wide-Resnet (https://arxiv.org/abs/1605.07146) for multiple tasks.\n",
    "    This implementation assumes all tasks have the same number of classes.\n",
    "    \"\"\"\n",
    "    def __init__(self,\n",
    "                 num_cls: int,\n",
    "                 depth = 28, \n",
    "                 width = 10) -> None:\n",
    "        \"\"\"\n",
    "        Args:\n",
    "            - num_cls: Number of classes\n",
    "            - cls_per_task: Nuber of classes per task (only needed \n",
    "        \"\"\"\n",
    "        super(WideResnet, self).__init__()\n",
    "        assert((depth - 4) % 6 == 0)\n",
    "\n",
    "        inp_channels = 3\n",
    "        nChannels = [16, 16*width, 32*width, 64*width]\n",
    "\n",
    "        n = (depth - 4) // 6\n",
    "        block = BasicBlock\n",
    "\n",
    "        self.conv1 = nn.Conv2d(inp_channels, nChannels[0], kernel_size=3,\n",
    "                               stride=1, padding=1, bias=False)\n",
    "\n",
    "        self.block1 = NetworkBlock(n, nChannels[0], nChannels[1], block, 1)\n",
    "        self.block2 = NetworkBlock(n, nChannels[1], nChannels[2], block, 2)\n",
    "        self.block3 = NetworkBlock(n, nChannels[2], nChannels[3], block, 2)\n",
    "\n",
    "        self.bn1 = nn.BatchNorm2d(nChannels[3])\n",
    "\n",
    "        self.relu = nn.ReLU(inplace=True)\n",
    "        self.pool = nn.AdaptiveAvgPool2d(1)\n",
    "        self.softmax = nn.Softmax(dim=1)\n",
    "        self.fc = nn.Linear(nChannels[3], num_cls, bias=False)\n",
    "\n",
    "        self.nChannels = nChannels[3]\n",
    "\n",
    "        for m in self.modules():\n",
    "            if isinstance(m, nn.Conv2d):\n",
    "                nn.init.kaiming_normal_(m.weight, mode='fan_out',\n",
    "                                        nonlinearity='relu')\n",
    "            elif isinstance(m, nn.BatchNorm2d):\n",
    "                m.weight.data.fill_(1)\n",
    "                m.bias.data.zero_()\n",
    "\n",
    "    def forward(self,\n",
    "                x: Tensor) -> Tensor:\n",
    "        out = self.conv1(x)\n",
    "        out = self.block1(out)\n",
    "        out = self.block2(out)\n",
    "        out = self.block3(out)\n",
    "        out = self.relu(self.bn1(out))\n",
    "        out = self.pool(out)\n",
    "        out = out.view(-1, self.nChannels)\n",
    "        self.rep = out\n",
    "        logits = self.fc(out)\n",
    "        \n",
    "        return logits\n",
    "\n",
    "    def euclid_dist(self, proto, rep):\n",
    "        n = rep.shape[0]\n",
    "        k = proto.shape[0]\n",
    "        rep = rep.unsqueeze(1).expand(n, k, -1)\n",
    "        proto = proto.unsqueeze(0).expand(n, k, -1)\n",
    "        logits = -((rep - proto)**2).sum(dim=2)\n",
    "        return logits\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "cellView": "form",
    "id": "m8nXvAZdH7Cc"
   },
   "outputs": [],
   "source": [
    "#@title CIFAR100 training\n",
    "\n",
    "def imprint(net, loader):\n",
    "    num_cls = len(set(loader.dataset.targets))\n",
    "    hid_dim = net.fc.weight.shape[1]\n",
    "    prototypes = torch.zeros(num_cls, hid_dim)\n",
    "    lab_count = torch.zeros(num_cls)\n",
    "    if GPU:\n",
    "        prototypes = prototypes.cuda()\n",
    "        lab_count = lab_count.cuda()\n",
    "\n",
    "    with torch.no_grad():\n",
    "        for dat, labels in loader:\n",
    "            if GPU:\n",
    "                dat, labels = dat.cuda(), labels.cuda()\n",
    "\n",
    "            _ = net(dat)\n",
    "            rep = net.rep\n",
    "            prototypes.index_add_(0, labels, rep)\n",
    "            lab_count += torch.bincount(labels, minlength=num_cls)\n",
    "\n",
    "    prototypes = prototypes / lab_count.reshape(-1, 1)\n",
    "    return prototypes\n",
    "\n",
    "def update_grad_descent(net, data, optimizer, criterion, scaler):\n",
    "    inputs, labels = data\n",
    "    if GPU:\n",
    "        inputs, labels = inputs.cuda(), labels.cuda()\n",
    "\n",
    "    optimizer.zero_grad()\n",
    "\n",
    "    with torch.cuda.amp.autocast(enabled=GPU):\n",
    "        outputs = net(inputs)\n",
    "        loss = criterion(outputs, labels)\n",
    "    scaler.scale(loss).backward()\n",
    "    scaler.step(optimizer)\n",
    "    scaler.update()\n",
    "\n",
    "\n",
    "def evaluate(net, dataloader, imprinted_wts):\n",
    "    loss, acc, count = 0.0, 0.0, 0.0\n",
    "    criterion = nn.CrossEntropyLoss()\n",
    "    net.eval()\n",
    "    preds = []\n",
    "    with torch.no_grad():\n",
    "        for dat, labels in dataloader:\n",
    "            if GPU:\n",
    "                dat, labels = dat.cuda(), labels.cuda()\n",
    "\n",
    "            batch_size = int(labels.size()[0])\n",
    "            _ = net(dat)\n",
    "            rep = net.rep\n",
    "            out = net.euclid_dist(imprinted_wts, rep)\n",
    "\n",
    "            probs = F.softmax(out, dim=1).detach()\n",
    "            if GPU:\n",
    "                probs = probs.cpu()\n",
    "\n",
    "            preds.append(probs.numpy())\n",
    "\n",
    "    preds = np.concatenate(preds, axis=0)\n",
    "    return preds\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "cellView": "form",
    "id": "X7ujetSaXqJx"
   },
   "outputs": [],
   "source": [
    "#@title Plotting functions\n",
    "\n",
    "def plot_explained_variance(expl_variance_ratio):\n",
    "    exp_var = np.cumsum(expl_variance_ratio) * 100\n",
    "\n",
    "    plt.figure(figsize=(3, 3))\n",
    "    plt.plot(range(1, len(exp_var)+1), exp_var)\n",
    "    plt.ylim([0, 105])\n",
    "    plt.xlabel(\"Eigen-vectors\")\n",
    "    plt.ylabel(\"Explained variance\")\n",
    "    plt.show()\n",
    "\n",
    "def plot_sphere(xs, ys, zs):\n",
    "    line = np.arange(0, 1.0001, 0.1)\n",
    "    lines = [line, 0*line, 0*line]\n",
    "\n",
    "\n",
    "    theta = np.arange(0, np.pi/2+0.02, 0.05)\n",
    "    xcirc, ycirc = np.cos(theta), np.sin(theta)\n",
    "    arcs = [xcirc, ycirc, xcirc*0]\n",
    "\n",
    "\n",
    "    all_plots = []\n",
    "\n",
    "    for i in range(3):\n",
    "        xline = lines[i%3]\n",
    "        yline = lines[(i+1)%3]\n",
    "        zline = lines[(i+2)%3]\n",
    "        \n",
    "        xarc = arcs[i%3]\n",
    "        yarc = arcs[(i+1)%3]\n",
    "        zarc = arcs[(i+2)%3]\n",
    "        \n",
    "        all_plots.append(go.Scatter3d(\n",
    "            x=xline, y=yline, z=zline,\n",
    "            marker=dict(size=0.01),\n",
    "            line=dict(\n",
    "                color='black',\n",
    "                width=3),\n",
    "            showlegend=False\n",
    "        ))\n",
    "        \n",
    "        all_plots.append(go.Scatter3d(\n",
    "            x=xarc, y=yarc, z=zarc,\n",
    "            marker=dict(size=0.01),\n",
    "            line=dict(\n",
    "                color='black',\n",
    "                width=3),\n",
    "            showlegend=False\n",
    "        ))\n",
    "        \n",
    "    all_plots.append(go.Scatter3d(\n",
    "        x=xs,\n",
    "        y=ys,\n",
    "        z=zs,\n",
    "        mode='markers',\n",
    "        marker=dict(\n",
    "            size=3.5,\n",
    "            color='steelblue',\n",
    "            opacity=0.7),\n",
    "        showlegend=False))\n",
    "        \n",
    "    fig = go.Figure(data=all_plots)\n",
    "\n",
    "    fig.update_layout(\n",
    "        scene_camera=dict(eye=dict(x=1.1, y=1.2, z=1.)),\n",
    "        template='plotly_white',\n",
    "    )\n",
    "\n",
    "    fig.show()\n",
    "\n",
    "\n",
    "def col_dark(rgb):\n",
    "    rgb = to_rgb(rgb)\n",
    "    rgb = 0.4 + 0.5 * np.array(rgb) \n",
    "    return to_hex(rgb)\n",
    "\n",
    "\n",
    "def plot_explained_stress(expl_stress):\n",
    "    plt.figure(figsize=(4, 4))\n",
    "    plt.plot(range(1, len(expl_stress)), expl_stress[1:,], c='black', alpha=1.0, linewidth=2)\n",
    "    plt.ylim([0, 105])\n",
    "    plt.xlabel(\"Number of eigen-vectors\")\n",
    "    plt.ylabel(\"Explained stress (%)\")\n",
    "    plt.show()\n",
    "\n",
    "def plot_inpca(embed):\n",
    "\n",
    "    mod_name = ['CIFAR100-A', 'CIFAR100-B']\n",
    "    col_name = [col['taskA'], col['taskB']]\n",
    "\n",
    "    tab = []\n",
    "\n",
    "    for i in range(len(embed)):\n",
    "        for s in range(embed[i].shape[0]):\n",
    "            for t in range(embed[i].shape[1]):\n",
    "                x = list(embed[i][s, t, :3])\n",
    "                x = x + [t, mod_name[i], s]\n",
    "                tab.append(x)\n",
    "\n",
    "    tab = pd.DataFrame(tab)\n",
    "    tab.columns = ['PC 1', 'PC 2', 'PC 3', 'Epoch', \"Model\", \"seed\"]\n",
    "    tab.head()\n",
    "\n",
    "    all_plots = []\n",
    "\n",
    "    for i in range(2):\n",
    "        mt = tab[tab['Model'] == mod_name[i]]\n",
    "        plot1 = go.Scatter3d(\n",
    "            x=mt['PC 1'], y=mt['PC 2'], z=mt['PC 3'],\n",
    "            name=mod_name[i],\n",
    "            mode='markers',\n",
    "            marker=dict(\n",
    "                size=3,\n",
    "                color=col_name[i],\n",
    "                opacity=0.7),\n",
    "            line=dict(\n",
    "                color='black',\n",
    "                width=10),\n",
    "            showlegend=True\n",
    "        )\n",
    "        all_plots.append(plot1)\n",
    "    \n",
    "        mt_avg = mt.groupby('Epoch').mean(numeric_only=True)\n",
    "        plot1 = go.Scatter3d(\n",
    "            x=mt_avg['PC 1'], y=mt_avg['PC 2'], z=mt_avg['PC 3'],\n",
    "            marker=dict(\n",
    "                size=0.01,\n",
    "                color=col_dark(col_name[i]),\n",
    "                opacity=0.4),\n",
    "            line=dict(\n",
    "                color=col_dark(col_name[i]),\n",
    "                width=7),\n",
    "            showlegend=False\n",
    "        )\n",
    "        \n",
    "        all_plots.append(plot1)\n",
    "\n",
    "    fig = go.Figure(data=all_plots)\n",
    "    fig.update_layout(\n",
    "        template='plotly_white',\n",
    "        scene = dict(\n",
    "            xaxis_title='PC 1',\n",
    "            yaxis_title='PC 2',\n",
    "            zaxis_title='PC 3'),\n",
    "        width=700,\n",
    "        margin=dict(r=20, b=10, l=10, t=10), \n",
    "        scene_camera=dict(\n",
    "            eye=dict(x=1.65, y=1.2, z=1.9)),\n",
    "        legend= {'itemsizing': 'constant'},\n",
    "        scene_aspectmode='cube'\n",
    "    )\n",
    "\n",
    "    fig.show()\n",
    "\n",
    "\n",
    "def plot_progress(progress):\n",
    "    plt.figure(figsize=(4, 4))\n",
    "    epochs = list(np.arange(0, 4, 1/4)) + list(np.arange(4, 25))\n",
    "    for task in progress:\n",
    "        prog_mean = progress[task].mean(0)\n",
    "        prog_var = progress[task].std(0)\n",
    "        plt.plot(epochs, prog_mean, c=col[task])\n",
    "        plt.fill_between(epochs, prog_mean - prog_var, prog_mean + prog_var,\n",
    "                        color=col[task], alpha=0.2, label='_nolegend_')\n",
    "\n",
    "    plt.xlabel(\"Epochs\")\n",
    "    plt.ylabel(\"Progress\")\n",
    "    plt.title(\"Geometric progress of two tasks\")\n",
    "    plt.legend(['CIFAR100-A', 'CIFAR100-B'], loc='lower right')\n",
    "    plt.show()\n",
    "\n",
    "def plot_trajectory_distance(prog_sample, dist):\n",
    "    plt.plot(prog_sample, dist, c='black')\n",
    "    plt.fill_between(prog_sample, 0, dist,\n",
    "                    color='black', alpha=0.1)\n",
    "\n",
    "    plt.xlabel(\"Progress\")\n",
    "    plt.ylabel(\"Bhattacharyya distance\")\n",
    "    plt.title(\"Bhat. distance between trajectories\")\n",
    "    plt.show()\n",
    "\n",
    "def plot_reimann_length(lenA, lenB):\n",
    "    plt.bar(['CIFAR100-A', 'CIFAR100-B'], \n",
    "            [lenA[0], lenB[0]], alpha=0.8,\n",
    "            yerr=[lenA[1], lenB[1]])\n",
    "    plt.ylim([160, 180])\n",
    "    plt.ylabel(\"Reimann length\")\n",
    "    plt.xlabel(\"Task\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "vVi0KQAfHpAd",
    "outputId": "ab8b0a05-1bd9-4b73-c3ea-30db7b47216a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running on device: cpu\n"
     ]
    }
   ],
   "source": [
    "GPU = torch.cuda.is_available()\n",
    "DEV = 'cuda' if GPU else 'cpu'\n",
    "\n",
    "print(\"Running on device: %s\" % DEV)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "wxpw3qZPYtP9"
   },
   "source": [
    "# Prediction Space\n",
    "\n",
    "With the setup behind us, we are ready to get started! One of the key ideas is to view neural nets as points in prediction space. We will introduce this space using a synthetic dataset with 3 classes. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 390
    },
    "id": "5jtaIo6daDI3",
    "outputId": "032fc439-7346-49b2-cda3-f1450a4c302e"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dataset_S = load_synthetic_data()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "LAW3yhFJHusZ"
   },
   "outputs": [],
   "source": [
    "# Define dataloader for the synthetic dataset\n",
    "xdat = torch.from_numpy(dataset_S['X']).float()\n",
    "ydat = torch.from_numpy(dataset_S['Y']).long()\n",
    "\n",
    "data = torch.utils.data.TensorDataset(xdat, ydat)\n",
    "loader = torch.utils.data.DataLoader(data, batch_size=4, shuffle=True)\n",
    "\n",
    "if GPU:\n",
    "    xdat = xdat.cuda()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dhLDil0HNRx6"
   },
   "source": [
    "We would like to understand the training trajectory of a 2-layer fully-connected network on this synthetic dataset. To study the training trajectory, we could record the weights of the network periodically with the trajectory denoted by $(w_1, w_2, \\cdots, w_T)$. This problem is non-convex in the weights making it hard to analyze the trajectories in weight space. \n",
    "\n",
    "We instead think of each model in terms of its outputs on a fixed set of inputs $\\{x_i\\}_{i=1}^N$. We represent each network with weights $w$ as a point $P_w$ in *prediction space* where\n",
    "$$P_w = \\begin{bmatrix}\n",
    "    p_w(y=1 \\mid x_1) & p_w(y=2 \\mid x_1) & \\cdots \\cdots & p_w(y=C \\mid x_1) \\\\\n",
    "    p_w(y=1 \\mid x_2) & p_w(y=2 \\mid x_2) & \\cdots \\cdots & p_w(y=C \\mid x_2) \\\\\n",
    "    \\vdots & \\vdots & & \\vdots \\\\\n",
    "    p_w(y=1 \\mid x_N) & p_w(y=2 \\mid x_N) & \\cdots \\cdots & p_w(y=C \\mid x_N)\n",
    "\\end{bmatrix}.$$\n",
    "\n",
    "The prediction vector $P_w$ is an object of size $N \\times C$; It contains the predicted output probabilities over the $C$ classes, on each of the $N$ samples.Instead of looking at the sequence $(w_1, \\cdots w_T)$, we will instead study the sequence $(P_{w_1}, P_{w_2}, \\cdots P_{w_T})$. \n",
    "\n",
    "\n",
    "We record the sequence of $P_w$ at T=62 points during training on the synthetic dataset. We train 10 fully-connected networks from different random initializations (seeds) which gives us 10 trajectories in total. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "s3mQXJi0H7B9"
   },
   "outputs": [],
   "source": [
    "def get_synthetic_data_predictions(seed):\n",
    "    \"\"\"\n",
    "    Train a neural network on synthetic data and record the predictions \n",
    "    at periodic intervals\n",
    "    \"\"\"\n",
    "    set_seed(seed)\n",
    "    net = MLP(input_size=2, \n",
    "              hidden=[500, 500],\n",
    "              num_classes=3).to(DEV)\n",
    "    optimizer = torch.optim.SGD(net.parameters(), lr=0.01,\n",
    "                                momentum=0.9, nesterov=True)\n",
    "    criterion = nn.CrossEntropyLoss()\n",
    "\n",
    "    preds_list = []\n",
    "    for ep in range(5):\n",
    "        for idx, (x, y) in enumerate(loader):\n",
    "            \n",
    "            # Log predictions on entire dataset\n",
    "            if (ep == 0) or (idx % 20 == 0):\n",
    "                probs = F.softmax(net(xdat), dim=1)\n",
    "                if GPU:\n",
    "                    probs = probs.cpu()\n",
    "                preds_list.append(probs.detach().numpy())\n",
    "\n",
    "            # Update parameters with gradient descent\n",
    "            update_mlp_params(x, y, net, optimizer, criterion)\n",
    "\n",
    "    return np.array(preds_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "nlv5FKcSI0Pw",
    "outputId": "81254667-3ea5-4414-d989-44f9b13da1a5"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10, 62, 200, 3)\n"
     ]
    }
   ],
   "source": [
    "# Record predictions for 10 trajectories\n",
    "all_preds = []\n",
    "for sd in range(10):\n",
    "    all_preds.append(get_synthetic_data_predictions(sd))\n",
    "all_preds = np.array(all_preds)\n",
    "print(all_preds.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "rXUjzQlZKIJS"
   },
   "source": [
    "`all_preds` is a np.array of size `[seeds x T x N x C]` and contains the prediction vectors ($P_w$) of 620 models, where each model is represented by a prediction vector of size 600 ($N \\times C$). \n",
    "\n",
    "But do we really need 600 dimensions to represent each model? Principal component analysis (PCA) reveals that the sequence of prediction vectors are effectively low-dimensional. Just 5 dimensions preserve 94% of the explained variance! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 353
    },
    "id": "WJu9wWtXKEi2",
    "outputId": "5c09dfc4-9710-4c6a-beea-0023407fa97b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Explained variance of the first 5 dimensions is 93.63%\n"
     ]
    },
    {
     "data": {
      "image/png": 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EzczMsGDBApk2JycnXLx4Ebdu3cKrV6/Qq1evZr9GtKysDMePHwefz4efn5/Cda5fv47r16/LtHl4eGD9+vUwNDRUuu2cnBzk5OSwqis1NbVe61GfKCHcp9Jtn7Vpa2vj/fffV+cmVXLmzBkUFRVh6NChMDU1lVmmra2NRYsWwdPTE+bm5hCLxUhOTsamTZtw+fJlzJ8/H+Hh4dBQMr3m4cOHERISorZaFZ26i6ur5dp4PMXrEnYk+5L2aeNp7ftYrSHKNb/99huAfwaW3mRkZISlS5fKtA0cOBAODg7w8fHB7du3cfHiRYwYMaLR6ywoKMCzZ8/k2p8Xlsq15eXlQpNPz41Rt9zc3OYuodVrKfu4oKCgQevXK0SPHTsGoGaCug4dOkhf15ePj0+D1leHBw8eIDExESYmJhgyZEi936erq4tx48Zhx44diI+Pb5IQNTIygomJiVx7Je+1XJupqSldcK9GDMMgNzcXXbt2pWtwG0lL28fZ2dkNWr9eIfrpp5+Cx+PBwcEBHTp0kL6ur+YIUclRqLIBpbpIrnuVDJwp4uvriwEDBrCqLTU1FUFBQTJtivanorMfvgavRfwgtjQ8Hu3XxtZa93G9QtTHxwc8Hk8617zkNVeVl5dLB5QmT57c4PffuXMHANC9e3el65iZmcHMzIx1jfVR+zpRHo/uWCKEa+oVot98802dr7nmzJkzePXqFTw8POQGlCSSk5Nha2srF0onT57EqVOnIBAIMGbMmKYoVymaX4kQ7mM1sHTx4kVoamo2qK+xKUmuDVV0h5LEhg0b8OTJEzg6OsLExARisRh3795FYmIi+Hw+Vq9eDXNz86YqWSGaX4kQ7mMVoosXL8bAgQM5GaIPHz5EfHz8WweUvL29cf78edy5cwdXr16FWCyGsbExvL29MWvWLPTr168Jq1ZMbn4lClFCOIdViHbq1AkdO3ZUcynqYWVlVa+L2f38/JRegM8V8qfzzVQIIUQpVhccOjo6Ijk5Wd21kFpq3/ZJfaKEcA+rEF28eDGysrKwY8cOdddD3kB9ooRwH6vT+bS0NEyYMAE//vgjTp06hWHDhsHMzAzt27dXuH5zXCfaGtS+TY4ubyKEe1iFqORie4Zh8Pfff+Phw4d1rk8hyo5cnygdiRLCOaxClOsX27cWtZ8/Qn2ihHAPqxDl+sX2rYVcnyhlKCGcQ48D4jAaWCKE+yhEOYz6RAnhPpWfJ/rw4UOkp6fXOasnDSyxU3t0nvpECeEe1iF669YtrFmzBo8ePVK6DsMw4PF4FKIs1R5YosE8QriHVYg+ePAAH330EcrKyvDuu+8iPz8fWVlZGDt2LJ48eYKUlBSIxWJ4enpKH59HGo5O5wnhPlZ9ort370Z5eTnWrl2LsLAwODs7AwA2btyIQ4cOISoqCvb29nj06BFWrVql1oLbEnGt03l6oj0h3MMqRG/evAlLS0ulDzy2srLCjh07kJubi23btqlUYFsmf8dSMxVCCFGKVYgWFBSgT58+0teS6TcqKiqkbYaGhnB1dcX58+dVLLHtotN5QriPVYjq6elBLBbLvAYgN2OlQCDA8+fPVSivbaMn2xPCfaxC1MTEBDk5OdLXVlZWAIArV65I20QiEeLj49G5c2fVKmzDqumhzIRwHqsQdXV1xYMHD1BYWAgAGDZsGLS0tBAcHIzg4GCEhoZixowZKCwsZD0jJlF02yeFKCFcwypEx44dCxcXF+mDmQ0NDfHxxx+jqqoKe/fuxfr163Hv3j107doVy5cvV2vBbQn1iRLCfayuE7W3t8fPP/8s0zZt2jTY29vj3LlzePXqFXr16oVJkyZBX19fLYW2RdQnSgj3qXzb55veeecdvPPOO+rcZJtGlzgRwn2sTudPnz4tczkTaRz0FCdCuI/VkeiKFStgYGCAUaNGwcfHB/3791d3XQTUJ0pIS8DqSNTd3R3FxcWIiIjAtGnTMGrUKGzfvh3Z2dnqrq9Nk7vEic7nCeEcViH63//+F1evXsXHH38MoVCIjIwMbN26FSNGjMDMmTNx5MgRlJSUqLvWNocGlgjhPtYPZe7cuTPmzJmDqKgoHD9+HIGBgTAyMkJcXBxWrVoFd3d3fPzxx7h+/bo6621T5PtEm6kQQohSavm1FAqF+OSTT3D16lXs2bMHY8eOBQAcP34cc+fOVcdHtEkM9YkSwnlqvcRJQ0MD77//PgwNDdG+fXscPnxY7jIdUn+1H4VHD2UmhHvUFqJ5eXk4fvw4oqKi8PfffwOoCVW67ZO92n2ifApRQjhHpRAtKyvDuXPnEBUVhRs3bqC6uhoMw6BXr17w8fHBhAkT0LVrV3XV2ubQJU6EcB+rEL1x4waioqJw7tw5iEQiMAwDAwMDjBs3Dj4+PrC3t1d3nW1S7Z4QOhAlhHtYhWhgYGDNmzU14eHhgYkTJ2Lo0KEQCATqrK3NozuWCOE+ViHat29fTJw4EV5eXujUqZO6ayL/U3tOJS0Bv5kqIYQowypEjxw5ou46iAL9bbrg8OW/pa+dbah/mRCuUeslTkS97Hsb44vZrohOfAzXdyzgamfS3CURQmqhEOU4VzsTWBjVTMlCCOEeupGQEEJUQCFKCCEqoBAlhBAVUIgSQogKKEQJIUQFrWp0ftiwYUqfru/g4ICIiAiZNoZhEBkZibCwMDx69AgCgQD29vaYP38+XFxcmqJkQkgLV68QDQkJYf0BPB4PixYtYv3+htLT08OsWbPk2hVdIrRu3TqEhoaiW7du8Pf3R0lJCU6dOoWZM2fihx9+wKhRo5qiZEJIC1bvEOXxeAqm8K37Xm6GYZo8RPX19bFkyZK3rnfr1i2EhobC0tISkZGR0NPTAwAEBARgypQpWL16NQYNGoQOHTo0dsmEkBasXiG6ePFiubbMzExERUWhffv2GDRoELp16wYAyM7ORkxMDMrKyuDj44Pu3burt2I1CQ8PBwAsWLBAGqAAYGtrCy8vLxw5cgRnzpyBn59fc5VICGkBWIVoZmYmJk+ejFGjRmHNmjUwNDSUWV5YWIigoCBcvnwZkZGR6qu2HioqKnDs2DE8e/YMurq6sLW1hZOTk9xRc2xsLABg0KBBcttwd3fHkSNHEBcXRyFKCKkTq4GlH374Adra2ggODoaWlpbcckNDQ3z33XcYOXIkNm/ejE2bNqlcaH09f/4cn3zyiUxb7969ERwcjL59+wIARCIR8vLyoKOjA2NjY7lt9OjRAwDw+PFjpZ+Tk5ODnJwcVjWmpqayeh8hhHtYP5TZzc1NYYBKaGlpoX///rhx4wbr4hpq0qRJcHFxQe/evaGtrY3Hjx/jp59+wsmTJzF79mwcO3YMpqameP36NQDInMa/SdIPWlRUpPSzDh8+rNKAW23K5qKStNNcVY2D9m/ja+37mFWIFhcX1xkwEkVFRU06/3ztboe+ffti48aNqK6uxunTp/HTTz/hiy++aLJ66qugoADPnj2rc53c3NwmqqZtov3b+FrKPi4oKGjQ+qxC1MLCArGxsXjw4AH69OmjcJ0HDx4gNjYWPXv2ZPMRajVlyhScPn0aCQkJAP45ApUckdZWXFwMoGakvykYGRkpfUoTwzDIzc1F165dabbPRkD7t/G1tH2s7FpzZViF6AcffICgoCDMmDED8+bNg5eXF7p06QKgpk/y5MmT2LNnD6qqquDv78/mI9RK8vR9kUgEANDR0UGXLl2Ql5eH58+fy/WLZmRkAAAsLS2VbtPX15f1TKapqakICgqSaXvbDxePx2sRP4AtFe3fxtda9zGrEA0ICEBycjIiIyMRHByM4OBg6fxKlZWVAGr++vj6+iIgIEB91bJ0+/ZtAJC53MrNzQ0nTpzA9evX4ePjI7N+dHQ0AMDV1VXpNs3MzGBmZqb+YgkhLQrre+fXrl2LkJAQuLi4QCAQoKKiAhUVFRAIBHBxccHWrVuxbt06ddZap4cPH6K0tFSuPS0tDZs3bwYAjB8/XtouOULesWOHzGl9SkoKTp48iY4dO2L06NGNXDUhpKVT6d55T09PeHp6QiwW48WLFwBqTp35/KafUO306dP4+eef4eLiAjMzM7Rv3x7p6em4du0aqqqqMHHiRHh7e0vXd3Z2xowZMxAaGooJEyZg5MiR0ts+q6qqEBQUpHT0nhBCJNTyABI+n4/OnTurY1Osubm5IT09Hffu3UN8fDxKS0thYGCAgQMHSm8MqG3VqlWwtrbGwYMHERYWBk1NTTg6OmLBggX0ABJCSL2oHKJpaWm4ffs2CgsL0bt3bwwfPhwAUF1djaqqqjqvJVUnV1fXOvswFeHxePDz86O7kgghrLHuE83KysKMGTMwYcIErF69Gj/88AMuXLggXX7o0CE4ODggJiZGLYUSQggXsQrRgoICTJs2DTdv3oS1tTUCAgLk7kYYO3Ys+Hy+TLASQkhrw+p0fufOncjNzcX8+fOxbNky8Hg8/PrrrzLr6OnpQSgUSi9wJ4SQ1ojVkejly5dhYWGBf/3rX3VePGtubo68vDzWxRFCCNexCtHc3FzY2Ni8feMaGkpvrSSEkNaAVYjq6Ojg1atXb10vOzsbBgYGbD6CEEJaBFYham1tjbt379b5tJPMzEwkJyfjnXfeYV0cIYRwHasQ9fX1RUlJCT7++GOFj8QrLS3FmjVrIBaL4evrq3KRhBDCVaxG5729vXH27FlcunQJI0aMwHvvvQcAuHv3Lj755BNcu3YNhYWFGDlyJDw9PdVaMCGEcAmrI1Eej4cff/wRc+bMQVlZGc6ePQug5hmiUVFRKCoqwowZM7Bx40a1FksIIVzD+rZPTU1NfPzxx5g3bx7i4uKQmZkJsVgMU1NTDBgwoNnvpSeEkKag8r3zHTt2xMiRI9VRCyGEtDis750nhBCi4pFoWVkZ7t69i7y8PFRUVChdr/aT4wkhpLVgHaK7d+/Grl27pPMW1YVClBDSWrEK0V9//RWbNm0CAPTp0wc9e/aErq6uWgsjhJCWgFWIHjx4EHw+H5s3b6ZBJUJIm8ZqYCkzMxNOTk4UoISQNo9ViOrr68vN1U4IIW0RqxB9//33cfv2bbmn2RNCSFvDKkSXL1+OsrIyrF+/HpWVlequiRBCWgxWA0sREREYPHgwfvnlF1y6dAlubm4wNTVV+JR7Ho+HRYsWqVwoIYRwEasQDQkJAY/HA8MwyM7OxpEjR+TWkSynECWEtGasQnTRokV1zq1ECCFtBasQXbJkibrrIISQFokeQEIIISqgECWEEBXU63Q+JCQEADB9+nR07NhR+ro+aGCJENKa1TtEeTwexo0bJw1Ryei7MjQ6TwhpC+oVopLR+E6dOsm8JoSQtq5eIVp7NJ5G5wkhpAYNLBFCiAooRAkhRAUqzbFUXl6OGzdu4PHjxyguLlY40EQDS4SQ1ox1iJ4+fRpfffUVioqKlK5Do/OEkNaOVYgmJCTgP//5j/SypwcPHiAtLQ3z5s1DRkYGYmJi8Pr1a/j6+sLU1FTdNRNCCGewCtG9e/eiuroau3btwuDBg/HZZ58hLS0Ny5cvBwC8ePECq1atwtWrVxU+4YkQQloLVgNLSUlJsLa2xuDBgxUu79SpE77//nuIxWJs3bpVpQIJIYTLWIXoy5cvYWlpKX2tqVlzQFtWViZt09HRgYuLC65du6ZahYQQwmGsQrRjx44ygamvrw8AyM7OllmvqqoKL168UKE8QgjhNlZ9ot27d5cJTBsbGzAMg1OnTmHp0qUAgIKCAsTFxcHExEQ9lb7FixcvcOHCBVy5cgVpaWnIzc2FQCCAUCjEpEmT4OvrCw2Nf/5mZGVlYfjw4Uq3N3fuXKxcubIpSieEtGCsQvS9997D7t278fTpU5iamsLDwwP6+vrYsWMHHj16BBMTE5w7dw4lJSXw8/NTd80K/f777/jyyy9hbGwMNzc3mJmZIT8/H+fPn8cXX3yBa9euYcuWLXL3/NvY2MDT01Nue05OTk1SNyGkZWMVol5eXsjPz0d2djZMTU3RoUMHrFu3DitXrsTvv/8uXc/GxgaLFy9WW7F1sbS0xPbt2zF06FDw+Xxp+4oVK+Dn54ezZ8/i3LlzGDVqlMz7bG1t6VkAhBDWWIVo7969sXbtWpm2ESNG4OzZs7hy5QpevXqFXr16wcPDQzro1NgGDBigsN3Y2Bj+/v7YvHkz4uLi5EKUEEJUodaEMzExgb+/vzo3qRaSIH/zCFUiLy8PYWFhePXqFQwNDeHk5AQrK6umLpEQ0kI1zWFiM6qqqkJUVBQA4P3335dbfv36dVy/fl2mzcPDA+vXr4ehoaHS7ebk5CAnJ4dVTampqazeRwjhnnqF6M2bN1X6EBcXF5Xer4qNGzciLS0NgwcPlglRbW1tLFq0CJ6enjA3N4dYLEZycjI2bdqEy5cvY/78+QgPD5cZ0X/T4cOHGzRNytsomyVA0l7XLAKEPdq/ja+17+N6heiMGTNYP8mex+MhOTmZ1XtVdeDAAezduxc9e/bEt99+K7PMyMhIejmWxMCBA+Hg4AAfHx/cvn0bFy9exIgRIxq9zoKCAjx79qzOdXJzcxu9jraM9m/jayn7uKCgoEHr1ytEm/NIkq1ffvkF69atg5WVFfbv31/nqfmbdHV1MW7cOOzYsQPx8fFNEqJGRkZKr6dlGAa5ubno2rUrTcnSCGj/Nr6Wto9r3zT0NvUK0dDQUFbFNJd9+/Zhw4YNEAqF2LdvH4yMjBr0fslcUiKRSOk6vr6+Sq8IeJvU1FQEBQXJtL3th4vH47WIH8CWivZv42ut+7jVDSzt3r0bGzduhK2tLfbu3VvvI9A33blzB0DNnVnKmJmZwczMjHWdhJDWQS3Tg1RXV6OwsBCFhYWorq5WxyZZ2bZtGzZu3Ag7Ozvs27evzgBNTk5W2NF98uRJnDp1CgKBAGPGjGnMcgkhrYBKR6KXL1/GgQMHkJiYiPLycgCAlpYW+vfvj+nTp9d5b7q6HT16FD/++CP4fD6cnZ0VdkF069YNkyZNAgBs2LABT548gaOjI0xMTCAWi3H37l0kJiaCz+dj9erVMDc3b7L6CSEtE+sQXb16NQ4dOiQ9mhMIBABq5l36888/cePGDUyePBlff/21eip9i6ysLACAWCzG/v37Fa7j6uoqDVFvb2+cP38ed+7cwdWrVyEWi2FsbAxvb2/MmjUL/fr1a5K6CSEtG6sQDQ8PR0REBAwMDPDRRx/B29sbXbt2BVBzGcOJEyfw3//+F5GRkejbty8++OADtRatyJIlSxp0D7yfn1+TPRyFENJ6seoTDQsLg0AgQGhoKObOnSsNUADo2rUrPvroIxw4cACampr47bff1FYsIYRwDasQTU9Ph5ubG4RCodJ1hEIh3NzckJ6ezro4QgjhOlYh2qFDBxgYGLx1PX19fejq6rL5CEIIaRFYheh7772HhIQEVFZWKl2nsrISiYmJcHNzY10cIYRwHasQXb58OUQiET799FO8fPlSbvmrV6/w2WefQSQSYcWKFarWSAghnMVqdD4qKgpDhw5FVFQULl26BHd3d3Tr1g1AzSPioqOjUVpaigkTJkgfQyfB4/GwaNEi1SsnhBAOYBWiISEh0ntgS0tLcf78eYXrRUVFSa8j5fF4YBiGQpQQ0qqwCtFFixa1ygcJEEJIQ7EKUZrYjRBCaqjlASSEENJWsQrRP//8s97r7t69m81HEEJIi8AqRD/66CP88MMPdT72Lj8/H7Nnz8bmzZtZF0cIIVzH+o6lXbt2Yfr06QrnBrp27RomTJiAP//8E3Z2dioXSQghXMUqRI8fP47+/fsjISEBEyZMkF7iVFVVhW+//Rb/93//h8LCQsyePRvh4eFqLZgQQriE1eh8165dERoaiq1bt2LXrl1YunQpJk+ejJSUFNy9exdGRkb45ptvFM7zTgghrQnr0XkNDQ0sW7YM+/btg66uLiIjI3Hv3j0MGDAAx48fpwAlhLQJKl3iVF5ejuPHj6O4uBgMw4BhGGRkZCAzM1Nd9RFCCKexDtHU1FRMmjQJkZGR6N69Ow4cOAA/Pz/k5ORg+vTp2LlzpzrrJIQQTmIVor/++iumTJmChw8fYsyYMTh27BhcXV3x9ddfY9OmTWjfvj22bNmCWbNmITc3V901E0IIZ7AK0a+//ho8Hg9BQUHYvHkzOnToIF02duxYHDt2DPb29oiNjYWPj4+6aiWEEM5hFaJ9+vTB4cOHMWXKFIXLu3fvjoMHD2Lu3LkKnzdKCCGtBatLnCIjI9GuXbs61+Hz+fj3v/+NgQMHsiqMEEJaAlZHom8L0DcNGDCAzUcQQkiLUK8QLS4uRnl5eYM3npKSgosXLzb4fYQQ0lLUK0RdXFzw1VdfKVw2c+ZM7NmzR+GyAwcOYPHixeyrI4QQjqtXn6jkQnpF4uLipPMrEUJIW0MPZSaEEBVQiBJCiAooRAkhRAUUooQQogIKUUIIUUG971jKz8/HzZs3G7Ts+fPn7CsjhJAWoN4hGh0djejoaLl2Ho+ndBkhhLR29QpRMzOzxq6DEEJapHqF6KVLlxq7DkIIaZFoYIkQQlRAIUoIISqgECWEEBVQiBJCiAooRAkhRAWspgdpTe7fv4+QkBDcvHkTpaWlMDc3x8SJExEYGAhNzTa/ewghb9GmUyIhIQGzZ8+GWCzGmDFj0KVLF1y9ehXBwcFITExESEgIeDxec5dJCOGwNhuiYrEYn3/+OcrKyrB7924MGTIEALBs2TLMnj0bFy5cwIkTJ+Dt7d3MlRJCuKzN9onGxsYiPT0dbm5u0gAFAC0tLSxbtgwAEB4e3lzlEUJaiDYdogDg7u4ut8zJyQk6OjpISkpCRUVFU5dGCGlB2uzpfHp6OgCgR48ecsv4fD66d++OtLQ0ZGZmwsrKSm6dnJwc5OTksPrs27dvy7xOTU2tc/2CggJkZ2ez+izydrR/G19L2se1fx9FIlGd67fZEC0uLgYA6OnpKVyuq6sLACgqKlK4/PDhwwgJCVFLLUFBQWrZDiFE/TIzM+tc3mZP5wkhRB3abIh26NABAPD69WuFy0tKSgAA+vr6TVYTIaTlabOn8z179gQAZGRkyC0Ti8XIysoCn8+Hubm5wvf7+vpiwIABrD47Pz8fiYmJMDAwgIGBASwsLKCtrS23Xmpqqsyp/urVq2Ftbc3qM4k82r+NryXu49LSUjx58kT6etiwYXWu32ZD1M3NDTt37kR0dDTmzZsnsyw+Ph4ikQhOTk7Q0tJS+H4zMzOVHlY9evToBr/H2toazs7OrD+T1I32b+Nrjfu4zZ7Ou7m5wdLSErGxsbh69aq0vaKiAlu2bAEA+Pv7N1d5hJAWos0eifL5fGzYsAGBgYFYtGgRxo4dC2NjY1y9ehUPHjyAp6cnxo8f39xlEkI4rs2GKAD0798fERER2Lp1K65evQqRSARzc3P85z//QWBgIN03Twh5qzYdogBgY2ODbdu2NXcZhJAWqs32iRJCiDpQiBJCiAooRAkhRAUUooQQogIKUUIIUQGFKCGEqIBClBBCVEAhSgghKqAQJYQQFbT5O5a4zMzMDIsXL5Z5TdSH9m/jawv7mMcwDNPcRRBCSEtFp/OEEKICClFCCFEBhSghhKiAQpQQQlRAo/Mcdf/+fYSEhODmzZsoLS2Fubk5Jk6ciMDAQGhq0j+bxIsXL3DhwgVcuXIFaWlpyM3NhUAggFAoxKRJk+Dr6wsNjX+OFbKysjB8+HCl25s7dy5Wrlwp1y4SibBr1y6cPn0aT58+hYGBAQYNGoRly5ahW7dujfLduGLYsGHIzs5WuMzBwQEREREybQzDIDIyEmFhYXj06BEEAgHs7e0xf/58uLi4KNxOYWEhQkJCcOnSJeTn56Nz584YNmwYlixZgk6dOqn9O6kTjc5zUEJCAmbPng2xWIwxY8agS5cuMtOWhISE0FP3/ycsLAxffvkljI2N4ebmBjMzM+Tn5+P8+fN4/fo1Ro0ahS1btkj3lyREbWxs4OnpKbc9JycnDBw4UKatrKwMM2fOxO3bt+Ho6AgXFxdkZGTg/Pnz6NixI8LDw2FpadkUX7dZDBs2DEVFRZg1a5bcMhMTE/j5+cm0rV27FqGhoejWrRtGjhyJkpISnDp1CqWlpfjhhx8watQomfULCwsxdepUPHnyBO7u7rC1tUVKSgqio6PRo0cPhIeHw9DQsFG/o0oYwilVVVXMqFGjGKFQyFy5ckXaXl5ezgQEBDBCoZCJiopqxgq5JSYmhrlw4QJTVVUl056Xl8cMGTKEEQqFzO+//y5tz8zMZIRCIfPJJ5/U+zO2bdvGCIVCZsWKFUx1dbW0/eDBg4xQKGQCAwNV/yIc5uHhwXh4eNRr3Zs3bzJCoZAZOXIkU1RUJG1PTk5m+vXrx7i6ujKvX7+Wec/nn3/OCIVCJjg4WKY9ODiYEQqFzKpVq1T/Eo2I+kQ5JjY2Funp6XBzc8OQIUOk7VpaWli2bBkAIDw8vLnK45wBAwZg+PDh4PP5Mu3GxsbS2Vrj4uJYb59hGOnp6ooVK2TOAPz9/WFubo6YmBiZecrbMsnP5oIFC6Cnpydtt7W1hZeXF16+fIkzZ85I20tKSnDixAno6Ohg4cKFMttauHAhdHR0cOLECZSUlDTNF2CBQpRjYmNjAQDu7u5yy5ycnKCjo4OkpCRUVFQ0dWktjqTvuHbAAkBeXh7CwsKwc+dORERE4OHDhwq3kZGRgadPn6Jnz55yfZ88Hk966i/5d2utKioqcOzYMezcuROhoaG4desWGAU9gZL9MGjQILllkp/pN/+oJSUloby8HP3794eOjo7M+jo6Oujfvz/Kyspw584ddX4dtaIRCo5JT08HAPTo0UNuGZ/PR/fu3ZGWlobMzExYWVk1dXktRlVVFaKiogAA77//vtzy69ev4/r16zJtHh4eWL9+vUz/2+PHjwFAaZ+npF2yXmv1/PlzfPLJJzJtvXv3RnBwMPr27QugZvAtLy8POjo6MDY2ltuG5Gf6zX1Vn/0bHR2N9PR0DBgwQPUv0gjoSJRjiouLAUDmVOhNurq6AICioqImq6kl2rhxI9LS0jB48GCZENXW1saiRYtw9OhR3Lp1C7Gxsfj555/xzjvv4PLly5g/fz6qq6ul679+/RoA0KFDB4WfI2mXrNcaTZo0CQcOHEBMTAwSExNx9OhReHl54e+//8bs2bPx9OlTAP/sA2U/u5J99ebPbmvYvxSipNU5cOAA9u7di549e+Lbb7+VWWZkZISlS5eib9++0NPTQ8eOHTFw4EDs378fFhYWuH37Ni5evNhMlXPT4sWL4ebmBiMjI+jo6KBv377YuHEjxo4di5cvX+Knn35q7hKbFYUox7ztL6+kg11fX7/JampJfvnlF6xbtw5WVlYIDQ2t96Uxurq6GDduHAAgPj5e2i45qpKcIdT2tjOH1mzKlCkAai7JA/7ZB8p+diX76s2f3dawfylEOaZnz54AagY0ahOLxcjKygKfz4e5uXlTl8Z5+/btw9dffw2hUIjQ0FCF/XJ1kVzULRKJpG1v6/N8W59ea1Z7f+no6KBLly4QiUR4/vy53PqSn+k391V996/k94KLKEQ5xs3NDQAQHR0ttyw+Ph4ikQiOjo7Q0tJq6tI4bffu3diwYQNsbW2xf/9+GBkZNXgbkhHg7t27S9t69OgBExMTpKeny921wzAMYmJiAPzz79aW3L59G4Ds/pLsh9qDdsA/P9Ourq7SNkdHR7Rr1w4JCQkyf7yAmnBOSEhA+/btYW9vr/b61YVClGPc3NxgaWmJ2NhYXL16VdpeUVGBLVu2AID0+kdSY9u2bdi4cSPs7Oywb9++Ok/hk5OTFV6ac/LkSZw6dQoCgQBjxoyRtvN4PEydOhUAsGnTJpn3hoeHIzMzEwMHDoSFhYUavxF3PHz4EKWlpXLtaWlp2Lx5MwBg/Pjx0nbJz+aOHTtkTutTUlJw8uRJdOzYEaNHj5a26+rqYvz48RCJRNi+fbvMZ2zfvh0ikQjjx4+XDqhyEd32yUEJCQkIDAxEdXU1xo4dC2NjY7rtU4mjR4/i008/BZ/Px/Tp0xX2nXXr1g2TJk0CAMyYMQNPnjyBo6MjTExMIBaLcffuXSQmJoLP5+PLL7+U9vVJKLrt88mTJzh37lyrv+1z69at+Pnnn+Hi4gIzMzO0b98e6enpuHbtGqqqqjBx4kRs2LBB5udR1ds++/bti+TkZERHR8PCwgK//fYbp2/7pBDlqPv372Pr1q24desWRCIRzM3NMWnSJHoASS1bt25FSEhIneu4uroiNDQUAHDo0CGcP38eDx48wIsXLyAWi2FsbAwnJyfMmjUL/fr1U7gNkUiEnTt34vTp03j27Bn09fXh7u7e6h9AEhcXh/DwcNy7dw8FBQUoLS2FgYEB7OzsMHnyZLlABP55AMnBgwfx6NEjaGpqwsHBAQsWLKjzASRbt27FpUuXUFBQACMjI+kDSLgcoACFKCGEqIT6RAkhRAUUooQQogIKUUIIUQGFKCGEqIBClBBCVEAhSgghKqAQJYQQFVCIEkKICujWF1JvdU2d+6abN29CX18fsbGxmDlzpswdQ4S0NhSipMHc3d3rfMycQCBowmrIm6ytrQEAqampzVxJ20EhShps3rx59Xr0m729PU6fPg1tbe0mqIqQ5kEhShqNtrY2TaZHWj0aWCKNJjY2FtbW1pgxY4bC5SdPnsTkyZPh4OAANzc3LFy4EPfv38eRI0dgbW2NTz/9VOH70tLS8Omnn2Lo0KHo168f3NzcMG/ePKXTFltbW0tPc48dO4ZJkybBwcEBrq6uWLp0aYPmjL906RKsra0REBCgdJ3bt2/D2tpa5rmZbGsHaqbI2LVrF3x9feHk5AQHBweMGDECH3/8sXRqDsk+q/2d3/zuEtXV1Thy5AgCAgLg7OyMd955B6NGjcK3336LwsJCuc9/89+xpKQEwcHBGDFiBPr16yczV3xcXBwWLFiAYcOGSb/buHHjsGbNmgbt45aGjkRJswgJCcHWrVuhoaEBZ2dnGBsb4969e5gyZQp8fX2Vvi8qKgqrVq1CZWUlbGxsYG9vj7y8PERHR+OPP/7AmjVr8MEHHyh876ZNm7B37144OztjyJAhSEpKwtmzZ5GQkIATJ05Ip7uoy+DBg2FkZISEhARkZmYqnKbl2LFjAICJEyeqXHtmZiY+/PBDZGRkQE9PD87OztDW1kZOTg5Onz4NDQ0N9O/fHxYWFpg4cSKOHj2q8LMlGIbBihUrcObMGWhpacHNzQ0dOnRAQkIC9u7dizNnzmD//v0Kp+wuKyvDjBkzkJGRARcXF9ja2qJjx44AgMjISKxatQoaGhpwcHCAo6MjiouLkZ2djfDwcLi6urbaB1eDIaSePDw8GKFQyNy4caNe69+4cYMRCoXM9OnTZdpv377N2NjYMPb29kxcXJy0XSwWM99++y0jFAoZoVDIfPLJJzLvS05OZuzs7BgnJycmJiZGZlliYiLj7OzM2NnZMQ8fPpRZJtnee++9x6Smpkrbi4uLGT8/P0YoFDJbt26t13diGIZZt26d0veUl5czrq6ujI2NDZOTk6NS7WKxmPH29maEQiGzYsUK5vXr1zLvKygoYG7evKnwuyoTGhrKCIVCZsiQIczjx49l6l6xYgUjFAqZyZMny7xH8u8oFAqZiRMnMgUFBXLblfxsJCYmyi17/Pgx8+TJE6U1tXR0Ok8abObMmXKni5L/KTt1f1NYWBiqq6vh5+cn85BeDQ0NLF++HCYmJgrft3PnTlRWVuKzzz7DgAEDZJY5Ojpi4cKFqKysxG+//abw/UuXLoVQKJS+1tXVxZw5cwCgztPp2nx8fADUHFnW9scff+Dly5dwc3ODqampSrVfvHgR9+/fR8+ePfHNN9/Izc1uaGgIZ2fnetcNAD///DMAYMWKFTJHm1paWlizZg309PRw584d3Lp1S+H7V69erfAhyYWFhdDX14ejo6Pcsh49erTqiRXpdJ40WF2XOPXq1eut77958yYAYOzYsXLLBAIBRo0ahf3798u0V1dXIzo6Gnw+HyNHjlS4XUmgSCZQq23w4MFybZJZJPPy8t5at0Tfvn0hFAqRlpaG+Ph4ODk5SZdJTuUlQatK7deuXQMATJgwQS2XjT179gxZWVkQCATS6aHfpK+vjxEjRuDIkSO4efOmXEB37txZYUgCQL9+/XDz5k18+umnCAwMhLW1dZuZwoZClDRYfS9xUiY3NxcAlE6rYWZmJtf28uVL6Rzkbzv6UjQ4AkDmyFBCMgFaZWWltO3hw4fYs2eP3Lqenp7w9PQEUNPn+O233yIqKkoaoi9fvsSVK1ego6MjE5Zsa8/JyQGgvumCJfvdzMwMfD5f4TqSI0bJum9S9O8i8eWXX2Lx4sU4evQojh49CgMDAzg4OMDd3R0+Pj4wMDBQwzfgJgpRwjkaGvK9TGKxGEDNkaqXl1ed71c2QKRou4rk5+dLB2je1K1bN2mIjh8/Ht9//z3OnDmDL774AlpaWjh9+jQqKyvh5eUFHR0dlWvn2pFc+/btlS7r3bs3Tpw4gT///BPXrl1DfHy8dMBs+/bt+Omnn5TOX9XSUYiSJtelSxdkZWXh6dOn6Nq1q9xyRbeWdurUCe3atUNVVRWCgoKgpaXVaPW5ubm99Y4fY2NjDBo0CH/88QcuXryIMWPGSPtI3zyVB9jXLjlyfvz4cYO/gyKSfZ2TkwOxWKzwaDQzM1Nm3YYQCAQYPHiwtNukoKAAwcHBOHr0KL7++mulfdUtHQ0skSYnOaU9ffq03LLKykqcO3dOrl1TUxMDBw6EWCzGhQsXGr3G+pBcRhQVFYXHjx8jKSkJZmZmcl0dbGt3d3eXbv/N7oa6SPpOq6qq5JaZmJige/fuqKysxKlTp+SWv379Wlqfslk5G8LIyAjLly8H0LpvQ6UQJU0uICAAPB4PERERiI+Pl7YzDIMtW7ZI+wJrW7hwITQ1NfHVV18pDCOxWIwbN24gKSmpsUqXMXz4cOjp6eHatWvYu3cvAMDb21vhaTib2ocPHw5ra2s8evQIn3/+OUpKSmTeU1hYKDeK3qVLFwA1/bqKBAYGAqi5ZvbNC+ArKioQFBSEoqIi2NvbN2jUv7S0FPv27VPYF33lyhUAivujWws6nScNtnv3boV9hhIzZsyAnZ2d0uWSOci3b9+O6dOnw8XFRXqxfXZ2Nvz9/REeHi43Im1vb48NGzZg1apVWLRoESwsLNCrVy906NAB+fn5SElJwatXr/Dll18qHUVWp3bt2mHMmDGIiIiQnqrWPpVXpXY+n4+QkBDMnj0bx48fx5UrV+Dk5ARtbW1kZ2cjOTkZXl5eMoE3YsQI7Nu3D4GBgXjvvfekfbPr1q0DAEybNg23bt3C77//Di8vL5mL7Z89ewYTExN8//33DdoPlZWV2LBhA7777jvY2NjAwsICPB4P6enpSElJgaamJlauXNnAvdtyUIiSBouOjq5zuaenZ50hCgDLli1Dz549sW/fPiQlJaF9+/bo378/Nm3aJD16UTRA5O3tDXt7e+zfvx8xMTG4ceMGNDQ0YGxsjP79+2PYsGFKLyNqDD4+PoiIiABQc71nXSPpbGq3sLDAsWPHsH//fpw7dw43btwAUHPE6eXlBX9/f5n1ly9fDh6Ph/Pnz+P8+fPSbgBJiGpoaGDz5s0YPHgwIiMjER8fj4qKCpiZmWHOnDmYO3euwutA66Kjo4M1a9YgLi4OKSkp+OOPP8AwDLp27QpfX18EBgbKXJ/b2vAYhmGauwhC3jR79mzExMRgy5YtCu8/J4RLqE+UNItHjx5Jr52UqKqqwu7duxETE4NOnTph6NChzVMcIQ1Ap/OkWRw6dAi//PIL7OzsYGJigpKSEqSlpeHZs2cQCARYv359ndclEsIVFKKkWXh4eCAnJwd//fUXUlNTUVlZic6dO8Pb2xsffvghbGxsmrtEQuqF+kQJIUQF1CdKCCEqoBAlhBAVUIgSQogKKEQJIUQFFKKEEKICClFCCFEBhSghhKiAQpQQQlRAIUoIISr4f4HWo67dF1zFAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 300x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_predictions = all_preds.reshape(620, 600)\n",
    "\n",
    "pca = PCA()\n",
    "pca.fit(model_predictions)\n",
    "\n",
    "top5 = np.sum(pca.explained_variance_ratio_[0:5]) * 100\n",
    "print(\"Explained variance of the first 5 dimensions is %.2f%%\" % top5)\n",
    "\n",
    "plot_explained_variance(pca.explained_variance_ratio_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "eVJpBmThXAL8"
   },
   "source": [
    "We will see that the prediction vectors of trajectories are effectively low-dimensional even if we change hyper-parameters, architecture, optimizer. But it doesn't end there! It is also low-dimensional if we change the training dataset or train using just unlabeled data. 🤯\n",
    "\n",
    "We do not have theory to explain why the trajectories are low-dimensional. But understanding this phenomenon may be integral to understanding why neural networks generalize well despite being seemingly high-dimensional objects.\n",
    "\n",
    "We would like to study the prediction space formally and the next section explains some of the tools that we develop for this purpose. We employ some neat constructions based on Information geometry to study the trajectories of representations. For example, the square root of the predictions $\\sqrt{P_w(. \\mid x_i)}$ lies on the surface of the sphere. This may seem like a peculiar coordinate transformation but it turns out that the shortest path (geodesic) on the surface of the sphere is exactly the shortest path in another manifold (the latter can be hard to compute). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 542
    },
    "id": "Znse574KNWwA",
    "outputId": "8a3b9a62-b343-4b33-aa51-45c6488006c1"
   },
   "outputs": [
    {
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   ],
   "source": [
    "sqrt_pred_sample = np.sqrt(all_preds[:, :, 0]).reshape(-1, 3)\n",
    "\n",
    "xs = sqrt_pred_sample[:, 0]\n",
    "ys = sqrt_pred_sample[:, 1]\n",
    "zs = sqrt_pred_sample[:, 2]\n",
    "\n",
    "plot_sphere(xs, ys, zs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "V4RvrPDZY0E3"
   },
   "source": [
    "# Building a picture of the space of tasks\n",
    "\n",
    "In this work:\n",
    "\n",
    "> we build techniques to study the training trajectories of networks when trained using different tasks (say ImageNet vs. iNaturalist) and using different methods (constrastive learning vs. supervised learning).\n",
    "\n",
    "We introduce the techniques by studying trajectories taken by networks on two tasks--- CIFAR100-A and CIFAR100-B --- which are subsets of the CIFAR100 dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "eHr0SkI_xuhp"
   },
   "source": [
    "## Imprinting helps us compare models trained on different tasks\n",
    "\n",
    "\n",
    "The first step is to train a network on each task and record the predictions made by the network during training. But we already have a problem. We would like to understand the networks by studying the object $P_w$ but CIFAR100-A and CIFAR100-B are trained on different sets of classes and hence the predictions are defined on completely different spaces. Our solution to this problem is imprinting. \n",
    "\n",
    "\n",
    "Consider a neural network with weights $w = [u, v]$ where\n",
    "$$P_w(. \\mid x) = \\psi_v \\circ \\phi_u(x).$$\n",
    "The network consists of a function $\\phi$ which is the internal representation which is followed by a linear layer $\\psi$. **Imprinting replaces the linear layer $\\psi_v$ with a different one that makes the model predict on some shared output space.**\n",
    "\n",
    "In order to embed $w_a$ trained on CIFAR100-A and $w_b$ trained on CIFAR100-B in the same prediction space, we retrain $\\psi_{v_a}$ and $\\psi_{v_b}$ and force the modified networks to predict on the entirety of CIFAR100. This allows us to study how similar the internal representations of two networks are regardless of which dataset they are trained on. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "cellView": "form",
    "id": "Hcokkv6XJqV6"
   },
   "outputs": [],
   "source": [
    "#@title Get imprinted predictions\n",
    "def train(task=0, seed=0):\n",
    "    print(\"Training on task%s with seed %d\" % (chr(65+task), seed))\n",
    "    set_seed(seed)\n",
    "    arch = WideResnet(50, 16, 4)\n",
    "    net = torch.compile(arch)\n",
    "    if GPU:\n",
    "        net.cuda()\n",
    "\n",
    "    optimizer = torch.optim.SGD(net.parameters(), lr=0.01,\n",
    "                                momentum=0.9, nesterov=True)\n",
    "\n",
    "    criterion = nn.CrossEntropyLoss()\n",
    "    scaler = torch.cuda.amp.GradScaler()\n",
    "    dataloader = get_task_dataloader(task)\n",
    "    test_cifar_loader = get_cifar_dataloader()\n",
    "\n",
    "    # Train network with mixed precision\n",
    "    all_preds = []\n",
    "    for ep in tqdm(range(25)):\n",
    "        for i, data in enumerate(dataloader):\n",
    "            if i == 0 or (i % 40 == 0 and ep < 2):\n",
    "                imprinted_wts = imprint(net, test_cifar_loader)\n",
    "                all_preds.append(evaluate(net, test_cifar_loader, imprinted_wts))\n",
    "\n",
    "            update_grad_descent(net, data, optimizer, criterion, scaler)\n",
    "    all_preds = np.array(all_preds)\n",
    "\n",
    "    return all_preds\n",
    "\n",
    "def get_cifar100_preds():\n",
    "    task_preds = []\n",
    "    for i in range(2):\n",
    "        all_preds = []\n",
    "        for seed in range(3):\n",
    "            preds = train(i, seed)\n",
    "            all_preds.append(preds)\n",
    "\n",
    "        task_preds.append(np.array(all_preds))\n",
    "    \n",
    "    return task_preds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "kz-jbOADsjjT"
   },
   "source": [
    "We train the networks on CIFAR100-A and CIFAR100-B respectively and record the imprinted predictions on the entire CIFAR100 test dataset. Training these networks take about 15 minutes so we will load the pre-computed predictions from a file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "QHlkAev1iLSI"
   },
   "outputs": [],
   "source": [
    "preds = {}\n",
    "preds['taskA'] = np.load(\"taskA_preds.npy\")\n",
    "preds['taskB'] = np.load(\"taskB_preds.npy\")\n",
    "\n",
    "# This takes around 20 mins with a GPU, Instead we will load the predictions from a file\n",
    "# ret_preds = get_cifar100_preds()\n",
    "# preds['taskA'] = ret_preds[0]\n",
    "# preds['taskB'] = ret_preds[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "7yeIo8Jhu4a-"
   },
   "source": [
    "## InPCA embedding\n",
    "\n",
    "We use InPCA to build a qualitative picture of the prediction space. These techniques reveal that the trajectories span a low-dimensional manifold in prediction space.\n",
    "\n",
    "Each prediction vector $P_w$ defines a probabilistic model over the $N$ samples. Hence, the KL-divergence or the Bhattacharyya divergence ($d_B$) define natural ways to measure the distance between two probabilistic models. \n",
    "$$ d_B(P_{w_1}, P_{w_2}) = -\\frac{1}{N} \\sum_{i=1}^N \\log \\left(\\sum_{c} \\sqrt{P_{w_1}(y=c \\mid x_i) P_{w_2}(y=c \\mid x_i)} \\right)$$. \n",
    "\n",
    "\n",
    "In order to find a low-dimensional embedding for a collection of trajectories we use Intensive-PCA (InPCA). This dimensionality reduction method finds an embedding that preserves the pairwise Bhattacharyya distance between all pairs of models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "wrtnVpudXcTV"
   },
   "outputs": [],
   "source": [
    "def bhattacharyya_distance_matrix(mat):\n",
    "    \"\"\"\n",
    "    Takes a collection of models and computes the pairwise \n",
    "    Bhattacharyya distance between all pairs of models.\n",
    "    \"\"\"\n",
    "    mat = np.sqrt(mat) + 1e-9\n",
    "    mat1 = np.transpose(mat, axes=[1, 0, 2])\n",
    "    mat2 = np.transpose(mat, axes=[1, 2, 0])\n",
    "\n",
    "    Dmat = 0.0\n",
    "    dim = len(mat1)\n",
    "    batch = 500\n",
    "\n",
    "    # Compute distance in batches to avoid OOM \n",
    "    for i in range(0, dim, batch):\n",
    "        Dmat += (np.log(mat1[i:i+batch] @ mat2[i:i+batch])).sum(0)\n",
    "    Dmat = Dmat / dim\n",
    "    return Dmat\n",
    "\n",
    "\n",
    "def compute_inpca(Dmat):\n",
    "    \"\"\"\n",
    "    Compute the InPCA embedding from a pairwise distance matrix\n",
    "    \"\"\"\n",
    "    # Double center matrix\n",
    "    ldim = Dmat.shape[0]\n",
    "    Pmat = np.eye(ldim) - 1.0/ ldim\n",
    "    Wmat = (Pmat @ Dmat @ Pmat) / 2\n",
    "\n",
    "    eigenval, eigenvec = np.linalg.eigh(Wmat)\n",
    "\n",
    "    #Sort eigen-values by magnitude\n",
    "    sort_ind = np.argsort(-np.abs(eigenval))\n",
    "    eigenval = eigenval[sort_ind]\n",
    "    eigenvec = eigenvec[:, sort_ind]\n",
    "    sqrt_eigenval = np.sqrt(np.abs(eigenval))\n",
    "\n",
    "    # Find projections\n",
    "    projection = eigenvec * sqrt_eigenval.reshape(1, -1)\n",
    "\n",
    "    return eigenval, projection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "TMlqkP38XeEF",
    "outputId": "2a7350b4-a241-45fa-f317-0945a199ed23"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(222, 5000, 100)\n"
     ]
    }
   ],
   "source": [
    "# Concatenate all the predictions\n",
    "predictions = np.concatenate([preds['taskA'].reshape(-1, 5000, 100),\n",
    "                              preds['taskB'].reshape(-1, 5000, 100)], axis=0)\n",
    "\n",
    "# Compute InPCA embedding of all models\n",
    "distance_matrix = bhattacharyya_distance_matrix(predictions)\n",
    "eigenval, embed = compute_inpca(distance_matrix)\n",
    "embed = embed.reshape([2, 3, 37, -1])\n",
    "\n",
    "print(predictions.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "VtlSwME1xCoJ"
   },
   "source": [
    "The explained stress measures what fraction of distances that are preserved by the first $k$ dimensions of the embedding. Like we saw in the synthetic dataset, the manifold of predictions is effectively low-dimensional and very few dimensions capture most of the stress. \n",
    "\n",
    "Nearly 5 dimensions capture 85% of the stress even though the predicton vector is of size $5 \\times 10^5$ (size is $N \\times C$). We see that the trajectories continue to be effectively low-dimensional even if we consider a dataset as larger as ImageNet."
   ]
  },
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   "cell_type": "code",
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    "id": "7HC5jPc2XhtW",
    "outputId": "0ad3a54f-fc58-4ce4-fe1e-33c6bf2441ed"
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   "outputs": [
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\n",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Explained stress\n",
    "eig_sq = (eigenval)**2\n",
    "eig_sq = eig_sq / np.sum(eig_sq)\n",
    "expl_stress = np.concatenate([[0], np.cumsum(eig_sq)])\n",
    "expl_stress = 1 - np.sqrt(1 - np.clip(expl_stress, 0,1)) \n",
    "expl_stress *= 100\n",
    "\n",
    "plot_explained_stress(expl_stress)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2wyEN4yZyYxZ"
   },
   "source": [
    "We next plot the first 3 dimensions of the InPCA embedding. Both models start at the same point $P_0$ (for all samples, $p(y) = 1/C$) probability for each class) and share the initial parts of the trajectory. This is surprising considering that they are trained on a completely disjoint set of classes. We do not expect this to occur unless different tasks share some underlying structure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 542
    },
    "id": "xd722kZdXi40",
    "outputId": "7aaa364c-743a-4d4c-b0ff-9f04ea10f236"
   },
   "outputs": [
    {
     "data": {
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   "source": [
    "plot_inpca(embed)"
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   "cell_type": "markdown",
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    "id": "vJjltxns2qHa"
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   "source": [
    "## Computational Information Geometry\n",
    "\n",
    "We next, build some tools to quantitatively understand the training trajectories in the prediction space."
   ]
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   "cell_type": "markdown",
   "metadata": {
    "id": "AAkGszOUy7Dh"
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   "source": [
    "### Geometric Progress\n",
    "\n",
    "Most randomly initialized models start at ignorance $P_0$--which predicts a probability of $\\frac{1}{C}$ for all classes on every sample. We would like to train these models to $P_*$ (probability 1 for true label) which is a model that minimizes the test loss.\n",
    "\n",
    "We compute the geometric progress for each point in the trajectory with respect to the geodesic joining $P_0$ and $P_*$. The progress increases monotonically which means that training on a subset of CIFAR100 makes progress on the entire CIFAR100 task."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "OqodvhGuYECf"
   },
   "outputs": [],
   "source": [
    "def interpolate(start, end, t):\n",
    "    \"\"\"\n",
    "    - Get a point on the geodesic joining \"start\" and \"end\". \n",
    "    - The geodesic is the same as the geodesic on the surface of a sphere\n",
    "      which is the great cirlce equation\n",
    "    \"\"\"\n",
    "    cospq = (start * end).sum(-1, keepdims=True)\n",
    "    dg = np.arccos(np.clip(cospq, 0, 1))\n",
    "\n",
    "    # Use masks, incase, start and end are identical\n",
    "    mask = (dg <= 1e-6).reshape(-1)\n",
    "    gamma = np.array(start)\n",
    "    gamma[~mask] = np.sin((1-t)* dg[~mask]) * start[~mask] + \\\n",
    "                   np.sin(t    * dg[~mask]) * end[~mask]\n",
    "    gamma[~mask] = gamma[~mask] / np.sin(dg[~mask])\n",
    "\n",
    "    return gamma\n",
    "\n",
    "\n",
    "def project(traj, start, end):\n",
    "    \"\"\"\n",
    "    - Computes the progress (λ) for each model in the trajectory.\n",
    "    - Progress is a scalar that belongs to the set [0, 1].\n",
    "    - It measures how far the model is along the geodesic\n",
    "      joining 'start' and 'end'.\n",
    "    \"\"\"\n",
    "    def dB(t, n=0):\n",
    "        vec = interpolate(start, end, t)\n",
    "        dist = (-np.log((vec * traj[n]).sum(-1))).sum()\n",
    "        return dist\n",
    "\n",
    "    lam = []\n",
    "    for ep in range(len(traj)):\n",
    "        dn = partial(dB, n=ep)\n",
    "        # Find the point on the geodesic with smallest distance\n",
    "        # to the model. This corresponds to the geometric progress. \n",
    "        l = optimize.minimize_scalar(dn, bounds=(0, 1), method='bounded').x\n",
    "        lam.append(float(l))\n",
    "\n",
    "    return lam"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "CS9CSH3YYIdz"
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   "outputs": [],
   "source": [
    "def get_progress(trajectory, p_0, p_star):\n",
    "    targets = np.argmax(p_star, axis=1)\n",
    "    prog_list = []\n",
    "    acc_list = []\n",
    "    for ep in range(len(trajectory)):\n",
    "        preds = np.argmax(trajectory[ep], axis=1)\n",
    "        prog = project([np.sqrt(trajectory[ep])], p_0, p_star)[0]\n",
    "\n",
    "        acc = np.sum(preds == targets) / len(targets)\n",
    "        \n",
    "        prog_list.append(prog)\n",
    "        acc_list.append(acc)\n",
    "        \n",
    "    return prog_list"
   ]
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   "execution_count": null,
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    "id": "vpI9_C8RYJ-h",
    "outputId": "9e5b55b9-1f5d-4b0b-8c53-ecc152c978b9"
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   "outputs": [
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\n",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "progress = {}\n",
    "p_0, p_star = cifar100_start_end()\n",
    "\n",
    "for i, task_pred in enumerate([preds['taskA'], preds['taskB']]):\n",
    "    prog_mat = []\n",
    "    for seed in range(task_pred.shape[0]):\n",
    "        prog = get_progress(task_pred[seed], p_0, p_star)\n",
    "        prog_mat.append(prog)\n",
    "        \n",
    "    progress['task{}'.format(chr(65+i))] = np.array(prog_mat)\n",
    "\n",
    "plot_progress(progress)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "XAtuq2fB3AAd"
   },
   "source": [
    "### Reindexing trajectories with progress\n",
    "\n",
    "Let two trajectories be denoted by $(P_{w_1}, \\cdots, P_{w_T})$ and $(P_{u_1}, \\cdots, P_{u_T})$. We could compare the two trajectories with a pairwise comparison of the models at different time-steps. However, this comparison is flawed, since \"epoch\" does not serve as a reliable notion of time (see paper for more details).\n",
    "\n",
    "We hence use geometric progress to index trajectories and it serves as our notion of time. Given any value of $s \\in [0, 1]$, `sample_trajectory` will return a model that corresponds to a progress of $s$ along the geodesic joining $P_0$ and $P_*$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "e_-YnU0-YMan"
   },
   "outputs": [],
   "source": [
    "def sample_trajectory(traj, λ_true, λ_sample):\n",
    "    \"\"\"\n",
    "    Sample from the parameterized trajectory\n",
    "    \"\"\"\n",
    "    ind = 0\n",
    "    max_ind = len(λ_true)\n",
    "\n",
    "    samples = []\n",
    "\n",
    "    for λ in λ_sample:\n",
    "\n",
    "        # Find first λ_true (from left) bigger than λ\n",
    "        while ind < max_ind:\n",
    "            if λ_true[ind] > λ:\n",
    "                break;\n",
    "            ind += 1\n",
    "\n",
    "        # Draw sample\n",
    "        if ind == max_ind:\n",
    "            sample = traj[-1]\n",
    "        elif ind == 0:\n",
    "            sample = traj[0]\n",
    "        else:\n",
    "            seg_start = traj[ind - 1]\n",
    "            seg_end = traj[ind]\n",
    "\n",
    "            λ_start = λ_true[ind-1]\n",
    "            λ_end = λ_true[ind]\n",
    "            assert(λ_start <= λ and λ_end >= λ)\n",
    "\n",
    "            λ_segment = (λ - λ_start) / (λ_end - λ_start)\n",
    "            λ_segment = np.clip(λ_segment, 0, 1)\n",
    "            sample = interpolate(seg_start, seg_end, λ_segment)\n",
    "\n",
    "        samples.append(sample)\n",
    "\n",
    "    samples = np.array(samples)\n",
    "    return samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "h-MRq3TvYOZP"
   },
   "outputs": [],
   "source": [
    "pmin = np.min(progress['taskA'])\n",
    "pmax = np.max(progress['taskB'])\n",
    "\n",
    "prog_sample = np.arange(pmin, pmax, 0.01)\n",
    "\n",
    "preds_reindexed = {}\n",
    "\n",
    "for task in progress:\n",
    "    preds_new = []\n",
    "    for seed, prog_true in enumerate(progress[task]):\n",
    "        pnew = sample_trajectory(preds[task][seed], prog_true, prog_sample)\n",
    "        preds_new.append(pnew)\n",
    "        \n",
    "    preds_reindexed[task] = np.array(preds_new)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "n1YNJ8zh40iR"
   },
   "source": [
    "### Comparing trajectories\n",
    "\n",
    "After reindexing the trajectories using progress, we can reliably compare two trajectories at different values of progress. We can us ethis to quantify how similar two trajectories are in prediction space. The plot indicates that that the trajectories of CIFAR100-A and CIFAR100-B are different both initially and towards the end of training."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "fPD8u7BVYPrM"
   },
   "outputs": [],
   "source": [
    "avg_predsA = preds_reindexed['taskA'].mean(0)\n",
    "avg_predsB = preds_reindexed['taskB'].mean(0)\n",
    "dist = (-np.log(1e-9 + (avg_predsA * avg_predsB).sum(-1)).mean(-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 497
    },
    "id": "mn5pvpYSYQ21",
    "outputId": "910bdbed-c1fc-4d9f-be78-e55953afa259"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_trajectory_distance(prog_sample, dist)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "gaEnSOsH5aZu"
   },
   "source": [
    "### Computing the Reimann Length of a trajectory\n",
    "\n",
    "Finally, we can compute the Reimann lengths of the trajectory. In our work, we use this to show that episodic meta-learning trajectories are 10-40x longer than supervised learning but they eventually end at the same point in prediction space. The Reimann length could be used as a measure of inefficiency of the training process."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "qbjiqRNMYRrt"
   },
   "outputs": [],
   "source": [
    "def reimann_length(trajectory):\n",
    "    dist = (-np.log(1e-9 + (trajectory[:-1] * trajectory[1:]).sum(-1)).mean(-1))\n",
    "    length = (2 * np.sqrt(dist).sum(-1))\n",
    "    return length.mean(), length.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 480
    },
    "id": "-ZGUgjy3YS4m",
    "outputId": "af4cc0fc-eda3-441e-8a63-105848fa8499"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lenA = reimann_length(preds['taskA'])\n",
    "lenB = reimann_length(preds['taskB'])\n",
    "plot_reimann_length(lenA, lenB)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "GiEEfUxYX0x7"
   },
   "source": [
    "This concludes this mini-tutorial that introduces all the tools developed in our work. These tools are very general: they allow us to compare very different methods and trajectories of models trained on different datasets. We point these tools towards understanding phenomena relating to pre-training, episodic meta-learning, contrastive learning and fine-tuning. By shedding light on some interesting phenomena, we hope to improve our understanding of the geometric structure of the space of tasks. 😃"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "QeFxC92mZOnw"
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "colab": {
   "authorship_tag": "ABX9TyPsaIfh+0zTWRdgyX0zzxnq",
   "include_colab_link": true,
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}