knot_theory.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "n-vSyzB-qmir"
   },
   "source": [
    "\n",
    "Copyright 2021 DeepMind Technologies Limited\n",
    "\n",
    "Licensed under the Apache License, Version 2.0 (the \"License\"); you may not use this file except in compliance with the License. You may obtain a copy of the License at\n",
    "\n",
    "https://www.apache.org/licenses/LICENSE-2.0\n",
    "Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an \"AS IS\" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reimplimitation/Validation of DeepMind Colab\n",
    "- [Original Notebook](https://colab.research.google.com/github/deepmind/mathematics_conjectures/blob/main/knot_theory.ipynb)\n",
    "- [Original Repo](https://github.com/google-deepmind/mathematics_conjectures)\n",
    "- [Nature Paper](https://www.nature.com/articles/s41586-021-04086-x)\n",
    "\n",
    "The code is nearly identical to the original notebook which you can compare with the link above. We've only made some minor changes (the rest is unmodified)\n",
    "- We [rewrote the network](#Network-Definition-\\(modified\\)) to be defined with a loop so you can use the array on the next line to define the architecture\n",
    "- We noticed an off-by-one error on the last layer. Original has an output of 13 and it should be 14 (even). In most cases this seems not to make a big difference.\n",
    "\n",
    "We noticed that we could shrink DeepMind's Network and still get >80% accuracy. We find that you can reliably get netowrks with <200 parameters to classify with >80% accuracy. We've included some of our results [here](#Our-Results). If you find better results, let us know! :)\n",
    "  \n",
    "# How To Use?\n",
    "1) First, make sure that you install the requirements (if you haven't, create a new cell and run `!pip install -r requirements.txt`)\n",
    "2) Download [gsutils](https://cloud.google.com/storage/docs/gsutil_install) (This is called [in this cell](Run me first to get data)). Make sure that `gsutils` is within your path (the installation should handle this. You may need to close jupyter and reopen in a new terminal). We will download the file for you if we don't find it.\n",
    "\n",
    "For quick validation you can just hit run and you will get an output from a 4 layer network (2 hidden layers) where each hidden layer has 5 neurons. Your result should match the shown outputs of this notebook (within small variance)\n",
    "\n",
    "To define a different MLP structure edit `hidden_layers` on the cell below. The numbers represent the hidden neurons per hidden layer. This is arbitrary so `[4,5,6]` would define a 5 layer network (3 hidden layers) where there are 4 neurons in the first hidden layer, 5 in the second hidden layer, and 6 in the third hidden layer. The input layer is always 17 neurons and the output is 14 (when using `use_fix`). You can see the summary of your network in the output just above [this cell](#Network-Setup)\n",
    "\n",
    "When using smaller networks you may want to edit some of the user defined parameters, specifically `num_training_steps` (suggest use the commented `50_000`). This defines the *maximum* number of training steps that will be used. Network will early stop if validation loss increases. \n",
    "\n",
    "We also suggest trying different random seeds. There is some variance to the results so this may be good to check. You can find the user defined variables [here](#User-Defined-Parameters)\n",
    "\n",
    "### What We Don't Do\n",
    "We didn't want to stray from DeepMind's code much so we don't implement any different training techniques or anything else. It is likely that results could be improved with changes such as different optimizers, learning rates (learning schedulers), or any number of modern DL training techniques. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Length of array = number of hidden layers\n",
    "# Array entries = number of hidden neurons per hidden layer\n",
    "# e.g. [5,5] = 4 layer network with [17, 5, 5, 14] (17 input neurons, 2 hidden layers w/ 5 hidden neurons, 14 output neurons)\n",
    "hidden_layers = [5,5]\n",
    "# Set True to use the off-by-one error fix\n",
    "use_fix = True"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Our Results\n",
    "Numbers may vary. With smaller networks the network will likely stop training at the max number of training steps (10k in original)\n",
    "All results in this table are with identical settings except changing the hidden layer.\n",
    "(Your numbers may vary slightly, especially in smaller networks. See tips below)\n",
    "| Network | Number of Parameters | Accuracy Pre Salient | Accuracy Post Salient |\n",
    "|:--------|---------------------:|---------------------:|----------------------:|\n",
    "|[300,300,300] | 190,214 | 0.8137779 | 0.8013719 |\n",
    "|[100,100,100] | 23,414 | 0.82789063 | 0.8204076 |\n",
    "|[50,50,50] | 6,714 | 0.8512915 | 0.8164692 |\n",
    "|[10,10,10] | 554 | 0.8444977 | 0.82296765 |\n",
    "|[5,5,5] | 234 | 0.83061475 | 0.80422723 |\n",
    "|[4,4,4] | 182 | 0.7673045 | 0.6519413 |\n",
    "|[3,3,3] | 134 | 0.66332996 | 0.74925333 | \n",
    "| - | - | - | - |\n",
    "|[50,50] | 4,164 | 0.87154156 | 0.8265122 |\n",
    "|[10,10] | 444 | 0.8302209 | 0.8149923 |\n",
    "|[5,5] | 204 | 0.82191736 | 0.8132528 |\n",
    "|[4,4] | 162 | 0.81886506 | 0.810299 |\n",
    "|[3,3] | 122 | 0.77718335 | 0.76238143 |\n",
    "\n",
    "Here are some results where we have changed the random seed and training length. We set `num_training_steps` to 50k for an arbitrarially long run and report how many steps before the network early stopped (`Steps`)\n",
    "| Network | Number of Parameters | seed | Accuarcy Pre Salient | Steps | Accuracy Post Salient | Steps |\n",
    "|:--------|---------------------:|:----:|---------------------:|:-----:|----------------------:|:-----:|\n",
    "| [3,3] | 122 | 552 | 0.8160097 | 20700 | 0.81686306 | 22100 |\n",
    "| [2,2] | 84 | 8110 | 0.81328565  | 22700 | 0.8043914 | 23300 |\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# User Defined Parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We've moved user defined parameters here to make this easier to run\n",
    "#### Tips\n",
    "- Change random seed\n",
    "- Increase `num_training_steps`\n",
    "\n",
    "Most runs smaller than `[50,50,50]` will likely run the full `num_training_steps` so it is a good idea to change this value to see that actual potential of the network. Larger networks will likely early stop. This can also result in a small network getting a very different result when the random seed is different.\n",
    "\n",
    "Defaults\n",
    "| Variable | Value | Description |\n",
    "|:---------|-------:|-----------:|\n",
    "| `random_seed` | 2 | Random seed for notebook |\n",
    "| `num_training_steps` | 10_000 | Maximum number of training steps (will early stop) |\n",
    "| `network_weight_rng` | 1 | [Seed for generating network's initial random weights](#Network-Setup) |\n",
    "| `batch_size` | 64 | Training Batch size |\n",
    "| `learning_rate` | 0.001 | Training Learning Rate |\n",
    "| `validation_interval` | 100 | Frequency to check against validation split |\n",
    "\n",
    "`network_weight_rng` is used [here](#Network-Setup)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This run was performed with random_seed=2\n"
     ]
    }
   ],
   "source": [
    "# These are default values provided by the original colab\n",
    "import random\n",
    "#random_seed = random.randint(0,10000)\n",
    "random_seed = 2 # @param {type: \"integer\"}\n",
    "print(f\"This run was performed with {random_seed=}\")\n",
    "#\n",
    "# *maximum* number of training steps (will early stop!)\n",
    "num_training_steps = 10_000 # @param {type: \"integer\"}\n",
    "### Suggest using this, especially if smaller network\n",
    "#num_training_steps = 50_000 # @param {type: \"integer\"}\n",
    "#\n",
    "# Random number for initializing the network weights\n",
    "network_weight_rng = 1 # @param {type: \"integer\"}\n",
    "#\n",
    "#\n",
    "batch_size = 64 # @param {type: \"integer\"}\n",
    "learning_rate = 0.001 # @param {type: \"float\"}\n",
    "validation_interval = 100 # @param {type: \"integer\"}\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Run me first to get data\n",
    "\n",
    "You may need to download [gsutil](https://cloud.google.com/storage/docs/gsutil_install)\n",
    "\n",
    "After doing so, close jupyter and open it back up in a new terminal. Making sure you have the binary in your path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# @title Download data\n",
    "import pandas as pd\n",
    "\n",
    "#_, input_filename = tempfile.mkstemp()\n",
    "input_filename = \"./knot_theory_invariants.csv\"\n",
    "# USE YOUR OWN gsutil cp COMMAND HERE\n",
    "!(if [[ ! -a {input_filename} ]]; then \\\n",
    "    gsutil cp \"gs://maths_conjectures/knot_theory/knot_theory_invariants.csv\" {input_filename}; \\\n",
    "fi)\n",
    "\n",
    "full_df = pd.read_csv(input_filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Run (Mostly Unmodified Deep Mind Code)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pip installs\n",
    "Uncomment me if first time!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "cellView": "form",
    "id": "xQnp1V1cvdxy"
   },
   "outputs": [],
   "source": [
    "# @title Install required modules\n",
    "from IPython.display import clear_output\n",
    "\n",
    "#!pip install dm-haiku\n",
    "#!pip install optax\n",
    "clear_output()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "cellView": "form",
    "id": "3NFhPsG4u1L1"
   },
   "outputs": [],
   "source": [
    "# @title Imports\n",
    "import tempfile\n",
    "\n",
    "import haiku as hk\n",
    "import jax\n",
    "import jax.numpy as jnp\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import optax\n",
    "import seaborn as sns\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load and Preprocess Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "cellView": "form",
    "id": "C-kZ_rW-h8Nk"
   },
   "outputs": [],
   "source": [
    "# @title Load and preprocess data\n",
    "\n",
    "#@markdown The columns of the dataset which will make up the inputs to the network.\n",
    "#@markdown In other words, for a knot k, X(k) will be a vector consisting of these quantities. In this case, these are the geometric invariants of each knot.\n",
    "#@markdown For descriptions of these invariants see https://knotinfo.math.indiana.edu/\n",
    "display_name_from_short_name = {\n",
    "    'chern_simons': 'Chern-Simons',\n",
    "    'cusp_volume': 'Cusp volume',\n",
    "    'hyperbolic_adjoint_torsion_degree': 'Adjoint Torsion Degree',\n",
    "    'hyperbolic_torsion_degree': 'Torsion Degree',\n",
    "    'injectivity_radius': 'Injectivity radius',\n",
    "    'longitudinal_translation': 'Longitudinal translation',\n",
    "    'meridinal_translation_imag': 'Re(Meridional translation)',\n",
    "    'meridinal_translation_real': 'Im(Meridional translation)',\n",
    "    'short_geodesic_imag_part': 'Im(Short geodesic)',\n",
    "    'short_geodesic_real_part': 'Re(Short geodesic)',\n",
    "    'Symmetry_0': 'Symmetry: $0$',\n",
    "    'Symmetry_D3': 'Symmetry: $D_3$',\n",
    "    'Symmetry_D4': 'Symmetry: $D_4$',\n",
    "    'Symmetry_D6': 'Symmetry: $D_6$',\n",
    "    'Symmetry_D8': 'Symmetry: $D_8$',\n",
    "    'Symmetry_Z/2 + Z/2': 'Symmetry: $\\\\frac{Z}{2} + \\\\frac{Z}{2}$',\n",
    "    'volume': 'Volume',\n",
    "}\n",
    "column_names = list(display_name_from_short_name)\n",
    "target = 'signature'\n",
    "\n",
    "#@markdown Split the data into a training, a validation and a holdout test set. To check\n",
    "#@markdown the robustness of the model and any proposed relationship, the training\n",
    "#@markdown process can be repeated with multiple different train/validation/test splits.\n",
    "\n",
    "random_state = np.random.RandomState(random_seed)\n",
    "train_df, validation_and_test_df = train_test_split(\n",
    "    full_df, random_state=random_state)\n",
    "validation_df, test_df = train_test_split(\n",
    "    validation_and_test_df, test_size=.5, random_state=random_state)\n",
    "\n",
    "# Find bounds for the signature in the training dataset.\n",
    "max_signature = train_df[target].max()\n",
    "min_signature = train_df[target].min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>pre { white-space: pre !important; }</style>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# I'm here because Haiku's display is wide. I'll add horizontal scrolling support to output cells\n",
    "from IPython.display import display, HTML\n",
    "display(HTML(\"<style>pre { white-space: pre !important; }</style>\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Network Definition (modified)\n",
    "Modification in `net_forward` to allow user to modify based on `hidden_layers` from above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "cellView": "form",
    "id": "jmBkFuYGu_j5"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+----------------------------+------------------------------------------------------------------+-----------------+-----------+-----------+---------------+---------------+\n",
      "| Module                     | Config                                                           | Module params   | Input     | Output    |   Param count |   Param bytes |\n",
      "+============================+==================================================================+=================+===========+===========+===============+===============+\n",
      "| sequential (Sequential)    | Sequential(                                                      |                 | f32[1,17] | f32[1,14] |           204 |      816.00 B |\n",
      "|                            |     layers=[Linear(output_size=5),                               |                 |           |           |               |               |\n",
      "|                            |             <PjitFunction of <function sigmoid at 0x15cba5120>>, |                 |           |           |               |               |\n",
      "|                            |             Linear(output_size=5),                               |                 |           |           |               |               |\n",
      "|                            |             <PjitFunction of <function sigmoid at 0x15cba5120>>, |                 |           |           |               |               |\n",
      "|                            |             Linear(output_size=14)],                             |                 |           |           |               |               |\n",
      "|                            | )                                                                |                 |           |           |               |               |\n",
      "+----------------------------+------------------------------------------------------------------+-----------------+-----------+-----------+---------------+---------------+\n",
      "| linear (Linear)            | Linear(output_size=5)                                            | w: f32[17,5]    | f32[1,17] | f32[1,5]  |            90 |      360.00 B |\n",
      "|  └ sequential (Sequential) |                                                                  | b: f32[5]       |           |           |               |               |\n",
      "+----------------------------+------------------------------------------------------------------+-----------------+-----------+-----------+---------------+---------------+\n",
      "| linear_1 (Linear)          | Linear(output_size=5)                                            | w: f32[5,5]     | f32[1,5]  | f32[1,5]  |            30 |      120.00 B |\n",
      "|  └ sequential (Sequential) |                                                                  | b: f32[5]       |           |           |               |               |\n",
      "+----------------------------+------------------------------------------------------------------+-----------------+-----------+-----------+---------------+---------------+\n",
      "| linear_2 (Linear)          | Linear(output_size=14)                                           | w: f32[5,14]    | f32[1,5]  | f32[1,14] |            84 |      336.00 B |\n",
      "|  └ sequential (Sequential) |                                                                  | b: f32[14]      |           |           |               |               |\n",
      "+----------------------------+------------------------------------------------------------------+-----------------+-----------+-----------+---------------+---------------+\n"
     ]
    }
   ],
   "source": [
    "# @title Network Definition\n",
    "\n",
    "#@markdown Create a simple feedforward network, using the DM Haiku library\n",
    "#@markdown (https://github.com/deepmind/dm-haiku).\n",
    "\n",
    "#@markdown The output of the network is a predicted categorical distribution, represented\n",
    "#@markdown by a vector q, where softmax(q)[i] is the predicted probability that the\n",
    "#@markdown signature of the knot is equal to 2*i + min_signature. Note that signature is\n",
    "#@markdown always an even integer.\n",
    "\n",
    "#@markdown We take the cross entropy between this distribution and the true distribution\n",
    "#@markdown (i.e. 1 at the true value of the signature, 0 everywhere else) as the loss\n",
    "#@markdown function.\n",
    "def net_forward(inp, use_fix=True):\n",
    "    net = []\n",
    "    for layer in hidden_layers:\n",
    "        net.append(hk.Linear(layer))\n",
    "        net.append(jax.nn.sigmoid)\n",
    "    net.append(hk.Linear(int((max_signature - min_signature) / 2) + (1 if use_fix else 0)))\n",
    "    return hk.Sequential(net)(inp)\n",
    "\n",
    "# Print out network and parameter info\n",
    "x = jnp.zeros((1, 17))\n",
    "print(hk.experimental.tabulate(net_forward)(x))\n",
    "# Uncomment if you want line by line\n",
    "#for method_invocation in hk.experimental.eval_summary(net_forward)(x):\n",
    "#  print(method_invocation)\n",
    "\n",
    "def softmax_cross_entropy(logits, labels):\n",
    "  # Labels are the true values of the signature\n",
    "  one_hot = jax.nn.one_hot((labels - min_signature) / 2, logits.shape[-1])\n",
    "  return -jnp.sum(jax.nn.log_softmax(logits) * one_hot, axis=-1)\n",
    "\n",
    "\n",
    "# The cross-entropy loss is composed with the network predictions, to define\n",
    "# `loss_fn` as a function on X and y.\n",
    "def loss_fn(inputs, labels):\n",
    "  return jnp.mean(softmax_cross_entropy(net_forward(inputs), labels))\n",
    "\n",
    "\n",
    "# Haiku network transformation steps.\n",
    "loss_fn_t = hk.without_apply_rng(hk.transform(loss_fn))\n",
    "net_forward_t = hk.without_apply_rng(hk.transform(net_forward))\n",
    "\n",
    "\n",
    "@jax.jit\n",
    "def predict(params, data_X):\n",
    "  return (np.argmax(net_forward_t.apply(params, data_X), axis=1) * 2 +\n",
    "          min_signature)\n",
    "\n",
    "\n",
    "#@markdown Calculate the mean and standard deviation over each column in the training\n",
    "#@markdown dataset. We use this to normalize each feature, this is best practice for\n",
    "#@markdown inputting features into a network, but is also very important in this case\n",
    "#@markdown to ensure the gradients used for saliency are meaningfully comparable.\n",
    "def normalize_features(df, cols, add_target=True):\n",
    "  features = df[cols]\n",
    "  sigma = features.std()\n",
    "  if any(sigma == 0):\n",
    "    print(sigma)\n",
    "    raise RuntimeError(\n",
    "        \"A poor data stratification has led to no variation in one of the data \"\n",
    "        \"splits for at least one feature (ie std=0). Restratify and try again.\")\n",
    "  mu = features.mean()\n",
    "  normed_df = (features - mu) / sigma\n",
    "  if add_target:\n",
    "    normed_df[target] = df[target]\n",
    "  return normed_df\n",
    "\n",
    "\n",
    "def get_batch(df, cols, size=None):\n",
    "  batch_df = df if size is None else df.sample(size)\n",
    "  X = batch_df[cols].to_numpy()\n",
    "  y = batch_df[target].to_numpy()\n",
    "  return X, y\n",
    "\n",
    "\n",
    "normed_train_df = normalize_features(train_df, column_names)\n",
    "# Sometimes this line will cause a RuntimeError when running smaller networks. Just restart the kernel and try again.\n",
    "normed_validation_df = normalize_features(validation_df, column_names)\n",
    "normed_test_df = normalize_features(test_df, column_names)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Network Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "cellView": "form",
    "id": "_ZyvOA1g_08D"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/homebrew/anaconda3/lib/python3.11/site-packages/haiku/_src/initializers.py:127: UserWarning: Explicitly requested dtype float64  is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  unscaled = jax.random.truncated_normal(\n",
      "/opt/homebrew/anaconda3/lib/python3.11/site-packages/haiku/_src/base.py:658: UserWarning: Explicitly requested dtype float64 requested in zeros is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  param = init(shape, dtype)\n"
     ]
    }
   ],
   "source": [
    "# @title Network Setup (re-run before re-training)\n",
    "\n",
    "train_X, train_y = get_batch(normed_train_df, column_names, batch_size)\n",
    "\n",
    "# Pick a random seed for the network weights. To check the robustness of the\n",
    "# model, the training process can be repeated with multiple different random\n",
    "# seeds.\n",
    "rng = jax.random.PRNGKey(network_weight_rng)\n",
    "init_params = loss_fn_t.init(rng, train_X, train_y)\n",
    "\n",
    "opt_init, opt_update = optax.adam(learning_rate)\n",
    "opt_state = opt_init(init_params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Network Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "cellView": "form",
    "id": "sofhcPK4vZWl"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Step count: 0\n",
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      "Train loss: 0.45500627160072327\n",
      "Validation loss: 0.4625166654586792\n",
      "(5, 5)\n",
      "Test Accuracy:  0.819423\n"
     ]
    }
   ],
   "source": [
    "# @title Network Training\n",
    "\n",
    "# We train until the validation loss stops decreasing, checking every <validation_interval> steps,\n",
    "# up to a maximum of 10k steps.\n",
    "\n",
    "\n",
    "@jax.jit\n",
    "def update(params, opt_state, batch_X, batch_y):\n",
    "  grads = jax.grad(loss_fn_t.apply)(params, batch_X, batch_y)\n",
    "  upds, new_opt_state = opt_update(grads, opt_state)\n",
    "  new_params = optax.apply_updates(params, upds)\n",
    "  return new_params, new_opt_state\n",
    "\n",
    "\n",
    "def train(columns_to_train_on, params, opt_state, update_fn):\n",
    "  best_validation_loss = np.inf\n",
    "  for i in range(num_training_steps):\n",
    "    train_X, train_y = get_batch(normed_train_df, columns_to_train_on,\n",
    "                                 batch_size)\n",
    "    params, opt_state = update_fn(params, opt_state, train_X, train_y)\n",
    "\n",
    "    if i % validation_interval == 0:\n",
    "      # Run validation on the full validation dataset.\n",
    "      validation_X, validation_y = get_batch(normed_validation_df,\n",
    "                                             columns_to_train_on)\n",
    "      train_loss = loss_fn_t.apply(params, train_X, train_y)\n",
    "      validation_loss = loss_fn_t.apply(params, validation_X, validation_y)\n",
    "      print(f\"Step count: {i}\")\n",
    "      print(f\"Train loss: {train_loss}\")\n",
    "      print(f\"Validation loss: {validation_loss}\")\n",
    "\n",
    "      if validation_loss > best_validation_loss:\n",
    "        print(\"Validation loss increased. Stopping!\")\n",
    "        return params\n",
    "      else:\n",
    "        best_validation_loss = validation_loss\n",
    "  return params\n",
    "\n",
    "\n",
    "trained_params = train(column_names, init_params, opt_state, update)\n",
    "# Print the test accuracy, i.e. the proportion of the knots for which the\n",
    "# network predicts the correct signature.\n",
    "test_X, test_y = get_batch(normed_test_df, column_names)\n",
    "print(trained_params[\"linear_1\"][\"w\"].shape)\n",
    "# The final below accuracy should be in the low 80%s.\n",
    "print(\"Test Accuracy: \",\n",
    "      np.mean((predict(trained_params, test_X) - test_y) == 0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "qj0TjRTnAmGW"
   },
   "source": [
    "The below cell replicates Figure 2a from the paper, though for simplicity omitting the error bars.\n",
    "\n",
    "To compute the saliency, we take the gradient of the loss function, with respect to each of the the components of the X input to the network (i.e. the geometric invariants of each knot), and average over the dataset.\n",
    "\n",
    "We plot the feature saliencies in decreasing order. The plot (should!) show that the overall loss is influenced far more by the longitudinal translation and the real and imaginary parts of the meridional translation than any of the other invariants."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Saliency Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "cellView": "form",
    "id": "j1CEbkUgxtGZ",
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# @title Saliency Analysis\n",
    "train_X = normalize_features(train_df, column_names, add_target=False).to_numpy()\n",
    "train_y = train_df[target].to_numpy()\n",
    "\n",
    "\n",
    "saliencies = np.mean(\n",
    "    np.abs(jax.grad(loss_fn_t.apply, 1)(trained_params, train_X, train_y)), axis=0)\n",
    "\n",
    "\n",
    "decreasing_saliency = reversed(sorted(zip(saliencies, display_name_from_short_name.values())))\n",
    "sorted_saliencies, sorted_columns = zip(*decreasing_saliency)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(6,8))\n",
    "sns.barplot(y=np.array(sorted_columns),\n",
    "            x=np.array(sorted_saliencies) / max(sorted_saliencies),\n",
    "            color=\"#0077c6\");\n",
    "\n",
    "ax.tick_params(labelsize=15);\n",
    "ax.set_ylabel('Geometric invariants X(z)', fontsize=20);\n",
    "plt.xlabel('Normalized attribution score', fontsize=20);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Confirming The Feature Saliency"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "cellView": "form",
    "id": "EsDbwItnlNUY"
   },
   "outputs": [],
   "source": [
    "# @title Confirming the Feature Saliency\n",
    "\n",
    "#@markdown To confirm the results of the saliency analysis, we re-train the network with\n",
    "#@markdown only these three features as input to the network.\n",
    "salient_column_names = ['longitudinal_translation',\n",
    "                        'meridinal_translation_imag',\n",
    "                        'meridinal_translation_real']\n",
    "target = 'signature'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Confirming the Feature Saliency: Network Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "cellView": "form",
    "id": "SKY75X_sEsy2"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/homebrew/anaconda3/lib/python3.11/site-packages/haiku/_src/initializers.py:127: UserWarning: Explicitly requested dtype float64  is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  unscaled = jax.random.truncated_normal(\n",
      "/opt/homebrew/anaconda3/lib/python3.11/site-packages/haiku/_src/base.py:658: UserWarning: Explicitly requested dtype float64 requested in zeros is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n",
      "  param = init(shape, dtype)\n"
     ]
    }
   ],
   "source": [
    "# @title Confirming the Feature Saliency: Network Setup (re-run before re-training)\n",
    "\n",
    "train_X, train_y = get_batch(normed_train_df, salient_column_names, batch_size)\n",
    "\n",
    "init_params_salient = loss_fn_t.init(rng, train_X, train_y)\n",
    "\n",
    "opt_init_salient, opt_update_salient = optax.adam(learning_rate)\n",
    "opt_state_salient = opt_init(init_params_salient)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Confirming the Feature Saliency: Network Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "cellView": "form",
    "id": "lGOfm424lXtR"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Step count: 0\n",
      "Train loss: 2.7614235877990723\n",
      "Validation loss: 2.805657386779785\n",
      "Step count: 100\n",
      "Train loss: 2.388213872909546\n",
      "Validation loss: 2.419311285018921\n",
      "Step count: 200\n",
      "Train loss: 2.1496756076812744\n",
      "Validation loss: 2.161698579788208\n",
      "Step count: 300\n",
      "Train loss: 1.9615678787231445\n",
      "Validation loss: 1.9971750974655151\n",
      "Step count: 400\n",
      "Train loss: 1.9326486587524414\n",
      "Validation loss: 1.896746039390564\n",
      "Step count: 500\n",
      "Train loss: 1.7300117015838623\n",
      "Validation loss: 1.826549768447876\n",
      "Step count: 600\n",
      "Train loss: 1.8089721202850342\n",
      "Validation loss: 1.7697826623916626\n",
      "Step count: 700\n",
      "Train loss: 1.8630174398422241\n",
      "Validation loss: 1.7183831930160522\n",
      "Step count: 800\n",
      "Train loss: 1.7237074375152588\n",
      "Validation loss: 1.6680281162261963\n",
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      "Validation loss: 0.4812586009502411\n",
      "Test Accuracy:  0.81358105\n"
     ]
    }
   ],
   "source": [
    "# @title Confirming the Feature Saliency: Network Training\n",
    "\n",
    "\n",
    "#@markdown Re-train the network using only the most salient features.\n",
    "@jax.jit\n",
    "def update_salient(params, opt_state, batch_X, batch_y):\n",
    "  grads = jax.grad(loss_fn_t.apply)(params, batch_X, batch_y)\n",
    "  upds, new_opt_state = opt_update_salient(grads, opt_state)\n",
    "  new_params = optax.apply_updates(params, upds)\n",
    "  return new_params, new_opt_state\n",
    "\n",
    "\n",
    "trained_params_salient = train(salient_column_names, init_params_salient,\n",
    "                               opt_state_salient, update_salient)\n",
    "\n",
    "#@markdown Print the test accuracy. This should be very similar to the test accuracy in\n",
    "#@markdown the case that all columns / invariants are included, demonstrating that most\n",
    "#@markdown of the predictve information about the signature is contained in the three\n",
    "#@markdown selected invariants.\n",
    "test_X, test_y = get_batch(normed_test_df, salient_column_names)\n",
    "\n",
    "#@markdown The final below accuracy should be in the low 80%s, probably 0.8 -> 0.85\n",
    "print(\"Test Accuracy: \",\n",
    "      np.mean((predict(trained_params_salient, test_X) - test_y) == 0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Slope vs. Signature: Proposed Linear Relationship"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "cellView": "form",
    "id": "ZIqvjO_O8Zti"
   },
   "outputs": [],
   "source": [
    "# @title Slope vs. Signature: Proposed Linear Relationship\n",
    "\n",
    "#@markdown The quantity we proposed was the \"natural slope\", given by\n",
    "#@markdown real(longitudinal_translation / meridinal_translation). We show that\n",
    "#@markdown this is approximately twice the signature (up to a correction term based on\n",
    "#@markdown other hyperbolic invariants) which we can check by comparing the predictions\n",
    "#@markdown made by this rule to those made by the previously trained models.\n",
    "\n",
    "\n",
    "def predict_signature_from_slope(data_X, min_signature, max_signature):\n",
    "  meridinal_translation = (\n",
    "      data_X['meridinal_translation_real'] +\n",
    "      1j * data_X['meridinal_translation_imag'])\n",
    "  slope = data_X['longitudinal_translation'] / meridinal_translation\n",
    "  return slope.real / 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Proposed Linear Relationship: Scatter plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "cellView": "form",
    "id": "KAwLtNFxTwCc"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Signature')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# @title Proposed Linear Relationship: Scatter plot\n",
    "\n",
    "#@markdown Scatter plot of the slope against predicted signature.\n",
    "predictions = [\n",
    "    predict_signature_from_slope(x, min_signature, max_signature)\n",
    "    for _, x in test_df.iterrows()\n",
    "]\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 8))\n",
    "sns.scatterplot(\n",
    "    x=predictions, y=test_df[target], alpha=0.2)\n",
    "ax.set_xlabel('Predicted Signature')\n",
    "ax.set_ylabel('Signature')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Proposed Linear Relationship: Test Accuracy\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "cellView": "form",
    "id": "HkoLDdYV_Idv"
   },
   "outputs": [],
   "source": [
    "# @title Proposed Linear Relationship: Test Accuracy\n",
    "\n",
    "\n",
    "#@markdown In order to compute the \"test accuracy\" in the same way as before, we quantize\n",
    "#@markdown the predicted signature values to even integers, between min_signature and\n",
    "#@markdown max_signature.\n",
    "def quantize(x, min_signature, max_signature):\n",
    "  return min(max(2 * round(x / 2), min_signature), max_signature)\n",
    "\n",
    "\n",
    "quantized_predictions = [\n",
    "    quantize(x, min_signature, max_signature) for x in predictions\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ZhJAExt6739Y"
   },
   "source": [
    "Now we can compute the \"test accuracy\" of this prediction.\n",
    "\n",
    "The value is slightly lower than for the trained network predictors (although still far higher than chance), but this is not unexpected.\n",
    "\n",
    "Indeed, the proposed rule gives a provable bound on the signature over all knots, instead of maximizing prediction performance over a given finite dataset, as the networks are doing. Although we do use separate training, validation and test datasets for the networks, these are all drawn from approximately the same distribution, whereas the proposed rule could be considered (in some imprecise sense) to have been \"trained\" on the set of all knots, a very different distribution.\n",
    "\n",
    "The correction term may also have some bias, for example tending to be positive more often than it is negative, information which the network predictors would be able to use to increase their prediction performance relative to that of the proposed rule."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Network output here is fixed (unmodified)\n",
    "We did not modify this part but the result is always `0.738192917391447` if you are using a seed of 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "id": "2m-RE-PQ74GC"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test Accuracy:  0.738192917391447\n"
     ]
    }
   ],
   "source": [
    "#@markdown The below accuracy will probably be lower than the previous ~80%, but not by much, likely still >70%\n",
    "print(\"Test Accuracy: \", np.mean(test_df[target] - quantized_predictions == 0))"
   ]
  }
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