Confusion-Scheme-CNN-PyTorch.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "0797e054",
   "metadata": {},
   "source": [
    "# Confusion Scheme Learning\n",
    "### Training a CNN in PyTorch to find a phase transition critical temperature using data generated from Quantum Monte Carlo simulations "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a02cea20",
   "metadata": {},
   "source": [
    "Here we illustrate how the <b>\"learning by confusion''</b> (LBC) technique can be used to find the transition temperature $\\beta_c$ in the square lattice Holstein model, below which a long-range ordered charge density wave (CDW) phase occurs. Our Hybrid Quantum Monte Carlo (HMC) simulations give us many different kinds of measurements. Some of this data is imaginary-time resolved (e.g. density-density correlations), and we can also store \"snapshots\" of local quantities (e.g. electron density per site) taken periodically throughout the measurement phase of a simulation. \n",
    "\n",
    "In this notebook, we will specifically look at snapshots of the phonon field (i.e. the set of phonon dispacement variables in the lattice) for a $12 \\times 12$ lattice with $144$ sites. Saving snapshots every $n_s$ measurement sweeps, we store $n_{\\textrm{snap}} = n_{\\textrm{meas}}/n_s$ configurations per inverse temperature $\\beta$, and perform HMC simulations at $45$ fixed temperatures in the range $\\beta \\in [1.0, 12.0]$. After processing this data into a single csv file, our training data has dimension $(9000, 144)$ (for $n_\\textrm{snap}=200$, $n_s=50$, $n_\\textrm{meas}=10000$). Each row contains data from a single snapshot, which we can reshape into a (greyscale) $12 \\times 12$ image to use as input for our CNN. \n",
    "\n",
    "More traditional techniques for determining $\\beta_c$ (e.g. performing simulations for a range of lattice sizes followed by finite-size scaling of a chosen order parameter) yield a value of $\\beta_c = 6.0 \\pm 0.1$ (for the Holstein model parameters we study here, i.e. $\\omega_0/t=1$ and $\\lambda_D=0.25$). Please refer to the reference <i>Phonon Dispersion and the Competition between Pairing and Charge Order</i>, Costa <i>et. al.</i> [Phys. Rev. Lett 120, 187003 (2018)](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.120.187003) for further details.\n",
    "\n",
    "Below we will find that the LBC method can discover this critical temperature ($\\beta_c \\approx 6$) without having to perform a finite-size scaling, or even needing to know in advance any information about the order parameter!\n",
    "\n",
    "However, snapshots of the phonon field are just one set of measurements we can take during a Quantum Monte Carlo simulation of the Holstein model. What kind of measurements work best for discovering the critical point? In another notebook, [<b>Methodology_and_Results.ipynb</b>](https://github.com/owenpb/Confusion-Scheme-Learning/blob/main/Methodology_and_Results.ipynb), we explore the efficacy of various sets of training data in locating the phase transition with confusion scheme learning."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3096c39f",
   "metadata": {},
   "source": [
    "### 1. Import Libraries:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "65fb8aa1",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "import torch\n",
    "import torchvision\n",
    "import torch.nn as nn\n",
    "from torch.utils.data import DataLoader, TensorDataset"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ebb3148b",
   "metadata": {},
   "source": [
    "### 2. Read in data (phonon snapshots). Display some samples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "fd1779d0",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = np.loadtxt('data/L12_phonon_position_snapshots_ns50.csv', delimiter=',')\n",
    "X = data[:, :-1]\n",
    "T = data[:, -1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "549a4c4d",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1200x700 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(2, 4, figsize=(12, 7))\n",
    "index = 0\n",
    "\n",
    "for i in range(2):\n",
    "    for j in range(4):\n",
    "\n",
    "        axs[i, j].imshow(X[index*1285].reshape(12, 12), cmap=\"binary\", origin='lower')\n",
    "\n",
    "        axs[i, j].set_xticks([])\n",
    "        axs[i, j].set_yticks([])\n",
    "        axs[i, j].set_title(r'$\\beta = $' + str(T[index*1285]))\n",
    "\n",
    "        index += 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1bfcea87",
   "metadata": {},
   "source": [
    "### 3. Test/train split:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "f1686080",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train_array, X_test_array, T_train_array, T_test_array = train_test_split(X, T, test_size=0.2, random_state=1, shuffle=True)\n",
    "X_train_array, X_val_array, T_train_array, T_val_array = train_test_split(X_train_array, T_train_array, test_size=0.25, random_state=1, shuffle=True)\n",
    "\n",
    "X_train_array = np.reshape(X_train_array, (X_train_array.shape[0], 1, 12, 12))\n",
    "X_val_array = np.reshape(X_val_array, (X_val_array.shape[0], 1, 12, 12))\n",
    "X_test_array = np.reshape(X_test_array, (X_test_array.shape[0], 1, 12, 12))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70e1e784",
   "metadata": {},
   "source": [
    "### 4. Training step:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "53ce435d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def train(model, num_epochs, train_dl, valid_dl):\n",
    "\n",
    "    loss_hist_train = [0] * num_epochs\n",
    "    accuracy_hist_train = [0] * num_epochs\n",
    "    loss_hist_valid = [0] * num_epochs\n",
    "    accuracy_hist_valid = [0] * num_epochs\n",
    "    \n",
    "    best_val_loss = np.inf\n",
    "    patience = 10\n",
    "    \n",
    "    for epoch in range(num_epochs):\n",
    "\n",
    "        for x_batch, y_batch in train_dl:\n",
    "            \n",
    "            pred = model(x_batch)[:, 0]\n",
    "                        \n",
    "            loss = loss_fn(pred, y_batch)\n",
    "            loss.backward()\n",
    "            optimizer.step()\n",
    "            optimizer.zero_grad()\n",
    "\n",
    "            loss_hist_train[epoch] += loss.item()*y_batch.size(0)\n",
    "            is_correct = ((pred >= 0.5).float() == y_batch).float()\n",
    "\n",
    "            accuracy_hist_train[epoch] += is_correct.sum()\n",
    "\n",
    "        loss_hist_train[epoch] /= len(train_dl.dataset)\n",
    "        accuracy_hist_train[epoch] /= len(train_dl.dataset)\n",
    "        \n",
    "        model.eval()\n",
    "        with torch.no_grad():\n",
    "            for x_batch, y_batch in valid_dl:\n",
    "\n",
    "                pred = model(x_batch)[:, 0]\n",
    "                loss = loss_fn(pred, y_batch)\n",
    "                loss_hist_valid[epoch] += loss.item()*y_batch.size(0)\n",
    "                is_correct = ((pred >= 0.5).float() == y_batch).float()\n",
    "                accuracy_hist_valid[epoch] += is_correct.sum()\n",
    "                \n",
    "        loss_hist_valid[epoch] /= len(valid_dl.dataset)\n",
    "        accuracy_hist_valid[epoch] /= len(valid_dl.dataset)\n",
    "        \n",
    "        print(f'Epoch {epoch + 1}    Train Accuracy: {accuracy_hist_train[epoch]:.4f}   Train Loss: {loss_hist_train[epoch]:.4f}     Valid Accuracy: {accuracy_hist_valid[epoch]:.4f}   Valid Loss: {loss_hist_valid[epoch]:.4f}')\n",
    "        \n",
    "        if loss_hist_valid[epoch] < best_val_loss:\n",
    "            \n",
    "            best_val_loss = loss_hist_valid[epoch]\n",
    "            early_stop_counter = patience\n",
    "            best_model = model\n",
    "        \n",
    "        else:    \n",
    "            early_stop_counter -= 1\n",
    "            \n",
    "        if early_stop_counter == 0:\n",
    "            break\n",
    "            \n",
    "    print(f'\\n Best validation accuracy = {np.max(accuracy_hist_valid)} \\n\\n')\n",
    "            \n",
    "    return loss_hist_train[:epoch+1], accuracy_hist_train[:epoch+1], loss_hist_valid[:epoch+1], accuracy_hist_valid[:epoch+1], best_model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "578ab5bc",
   "metadata": {},
   "source": [
    "### 5. Confusion scheme:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5308d0c",
   "metadata": {},
   "source": [
    "Let us choose $23$ candidate critical (inverse) temperatures in the range $[1.0, 12.0]$ to sweep through. For each guess for $\\beta_c$, we will assign target labels $y=1$ to snapshot configurations with $\\beta < \\beta_c$ (disordered phase), and target labels $y=0$ to configurations with $\\beta_c \\geq \\beta_c$ (ordered phase)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "21c3da36",
   "metadata": {},
   "outputs": [],
   "source": [
    "T_min = 1\n",
    "T_max = 12\n",
    "Tc_values = np.linspace(T_min, T_max, 23)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fcc909d8",
   "metadata": {},
   "source": [
    "After assigning target labels and preparing DataLoaders (with batch_size = $32$), we feed our snapshots to a Convolutional Neural Network (CNN) implemented in PyTorch using nn.Sequential.\n",
    "\n",
    "<b>Architecture of ConvNet:</b> 2 convolution layers followed by 2 fully connected layers.\n",
    "\n",
    "Input dimensions in [N, C, H, W] format: [batch_size, 1, 12, 12].\n",
    "\n",
    "Note: images have one channel only.\n",
    "\n",
    "1. **Conv2d:** $32$ filters with $\\textrm{kernel_size}=3$; \"same\" padding. Output dimensions: $[\\textrm{batch_size}, 32, 12, 12]$.\n",
    "2. **ReLU** activation.\n",
    "3. **MaxPool2d** with $\\textrm{kernel_size}=2$: Output dimensions: $[\\textrm{batch_size}, 32, 6, 6]$.\n",
    "4. **Conv2d:** $64$ filters with $\\textrm{kernel_size}=3$; \"same\" padding. Output dimensions: $[\\textrm{batch_size}, 64, 6, 6]$.\n",
    "5. **ReLU** activation.\n",
    "6. **MaxPool2d** with $\\textrm{kernel_size}=2$: Output dimensions: $[\\textrm{batch_size}, 64, 3, 3]$.\n",
    "7. **nn.Flatten**. Output dimensions: $[\\textrm{batch_size}, 64\\times3\\times3]$ = $[\\textrm{batch_size}, 576]$.\n",
    "8. **nn.Linear** with $\\textrm{out_features}=256$. Output dimensions = $[\\textrm{batch_size}, 256]$.\n",
    "9. **ReLU** activation.\n",
    "10. **Dropout** (probability $p=0.1$).\n",
    "11. **nn.Linear** with $\\textrm{out_features}=1$. Output dimensions = $[\\textrm{batch_size}, 1]$.\n",
    "12. **nn.Sigmoid**. Output dimensions = $[\\textrm{batch_size}, 1]$ (Tensor of class probabilities for each sample in batch).\n",
    "\n",
    "<b>Loss function:</b> Binary cross-entropy (nn.BCEloss)\n",
    "\n",
    "<b>Optimizer:</b> Adam with weight decay ($L2$ regularization)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "74eeb82a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1    Train Accuracy: 0.9941   Train Loss: 0.0085     Valid Accuracy: 1.0000   Valid Loss: 0.0000\n",
      "Epoch 2    Train Accuracy: 1.0000   Train Loss: 0.0000     Valid Accuracy: 1.0000   Valid Loss: 0.0001\n",
      "Epoch 3    Train Accuracy: 1.0000   Train Loss: 0.0001     Valid Accuracy: 1.0000   Valid Loss: 0.0001\n",
      "Epoch 4    Train Accuracy: 1.0000   Train Loss: 0.0001     Valid Accuracy: 1.0000   Valid Loss: 0.0001\n",
      "Epoch 5    Train Accuracy: 1.0000   Train Loss: 0.0001     Valid Accuracy: 1.0000   Valid Loss: 0.0001\n",
      "Epoch 6    Train Accuracy: 1.0000   Train Loss: 0.0001     Valid Accuracy: 1.0000   Valid Loss: 0.0001\n",
      "Epoch 7    Train Accuracy: 1.0000   Train Loss: 0.0001     Valid Accuracy: 1.0000   Valid Loss: 0.0001\n",
      "Epoch 8    Train Accuracy: 1.0000   Train Loss: 0.0001     Valid Accuracy: 1.0000   Valid Loss: 0.0001\n",
      "Epoch 9    Train Accuracy: 1.0000   Train Loss: 0.0001     Valid Accuracy: 1.0000   Valid Loss: 0.0001\n",
      "Epoch 10    Train Accuracy: 1.0000   Train Loss: 0.0001     Valid Accuracy: 1.0000   Valid Loss: 0.0001\n",
      "Epoch 11    Train Accuracy: 1.0000   Train Loss: 0.0001     Valid Accuracy: 1.0000   Valid Loss: 0.0001\n",
      "\n",
      " Best validation accuracy = 1.0 \n",
      "\n",
      "\n",
      "Tc guess = 1.0, Test set accuracy = 1.0 \n",
      "\n",
      "\n",
      "\n",
      "Epoch 1    Train Accuracy: 0.9550   Train Loss: 0.1478     Valid Accuracy: 0.9544   Valid Loss: 0.1090\n",
      "Epoch 2    Train Accuracy: 0.9613   Train Loss: 0.0842     Valid Accuracy: 0.9767   Valid Loss: 0.0598\n",
      "Epoch 3    Train Accuracy: 0.9743   Train Loss: 0.0623     Valid Accuracy: 0.9789   Valid Loss: 0.0458\n",
      "Epoch 4    Train Accuracy: 0.9746   Train Loss: 0.0597     Valid Accuracy: 0.9756   Valid Loss: 0.0573\n",
      "Epoch 5    Train Accuracy: 0.9761   Train Loss: 0.0525     Valid Accuracy: 0.9783   Valid Loss: 0.0438\n",
      "Epoch 6    Train Accuracy: 0.9787   Train Loss: 0.0487     Valid Accuracy: 0.9739   Valid Loss: 0.0535\n",
      "Epoch 7    Train Accuracy: 0.9793   Train Loss: 0.0491     Valid Accuracy: 0.9789   Valid Loss: 0.0532\n",
      "Epoch 8    Train Accuracy: 0.9854   Train Loss: 0.0365     Valid Accuracy: 0.9794   Valid Loss: 0.0425\n",
      "Epoch 9    Train Accuracy: 0.9891   Train Loss: 0.0295     Valid Accuracy: 0.9728   Valid Loss: 0.0650\n",
      "Epoch 10    Train Accuracy: 0.9852   Train Loss: 0.0362     Valid Accuracy: 0.9817   Valid Loss: 0.0435\n",
      "Epoch 11    Train Accuracy: 0.9900   Train Loss: 0.0252     Valid Accuracy: 0.9733   Valid Loss: 0.0652\n",
      "Epoch 12    Train Accuracy: 0.9917   Train Loss: 0.0222     Valid Accuracy: 0.9783   Valid Loss: 0.0506\n",
      "Epoch 13    Train Accuracy: 0.9954   Train Loss: 0.0134     Valid Accuracy: 0.9811   Valid Loss: 0.0500\n",
      "Epoch 14    Train Accuracy: 0.9941   Train Loss: 0.0150     Valid Accuracy: 0.9767   Valid Loss: 0.0549\n",
      "Epoch 15    Train Accuracy: 0.9980   Train Loss: 0.0084     Valid Accuracy: 0.9772   Valid Loss: 0.0561\n",
      "Epoch 16    Train Accuracy: 0.9987   Train Loss: 0.0068     Valid Accuracy: 0.9794   Valid Loss: 0.0540\n",
      "Epoch 17    Train Accuracy: 0.9983   Train Loss: 0.0080     Valid Accuracy: 0.9767   Valid Loss: 0.0614\n",
      "Epoch 18    Train Accuracy: 0.9994   Train Loss: 0.0050     Valid Accuracy: 0.9744   Valid Loss: 0.0689\n",
      "\n",
      " Best validation accuracy = 0.9816666841506958 \n",
      "\n",
      "\n",
      "Tc guess = 1.5, Test set accuracy = 0.972777783870697 \n",
      "\n",
      "\n",
      "\n",
      "Epoch 1    Train Accuracy: 0.9231   Train Loss: 0.1941     Valid Accuracy: 0.9400   Valid Loss: 0.1420\n",
      "Epoch 2    Train Accuracy: 0.9481   Train Loss: 0.1178     Valid Accuracy: 0.9506   Valid Loss: 0.1141\n",
      "Epoch 3    Train Accuracy: 0.9639   Train Loss: 0.0889     Valid Accuracy: 0.9683   Valid Loss: 0.0814\n",
      "Epoch 4    Train Accuracy: 0.9657   Train Loss: 0.0797     Valid Accuracy: 0.9617   Valid Loss: 0.0816\n",
      "Epoch 5    Train Accuracy: 0.9685   Train Loss: 0.0704     Valid Accuracy: 0.9711   Valid Loss: 0.0669\n",
      "Epoch 6    Train Accuracy: 0.9730   Train Loss: 0.0658     Valid Accuracy: 0.9578   Valid Loss: 0.0944\n",
      "Epoch 7    Train Accuracy: 0.9713   Train Loss: 0.0653     Valid Accuracy: 0.9706   Valid Loss: 0.0658\n",
      "Epoch 8    Train Accuracy: 0.9735   Train Loss: 0.0600     Valid Accuracy: 0.9683   Valid Loss: 0.0705\n",
      "Epoch 9    Train Accuracy: 0.9798   Train Loss: 0.0505     Valid Accuracy: 0.9733   Valid Loss: 0.0663\n",
      "Epoch 10    Train Accuracy: 0.9796   Train Loss: 0.0478     Valid Accuracy: 0.9706   Valid Loss: 0.0790\n",
      "Epoch 11    Train Accuracy: 0.9796   Train Loss: 0.0474     Valid Accuracy: 0.9683   Valid Loss: 0.0703\n",
      "Epoch 12    Train Accuracy: 0.9870   Train Loss: 0.0331     Valid Accuracy: 0.9711   Valid Loss: 0.0697\n",
      "Epoch 13    Train Accuracy: 0.9865   Train Loss: 0.0329     Valid Accuracy: 0.9683   Valid Loss: 0.0731\n",
      "Epoch 14    Train Accuracy: 0.9893   Train Loss: 0.0261     Valid Accuracy: 0.9689   Valid Loss: 0.0704\n",
      "Epoch 15    Train Accuracy: 0.9941   Train Loss: 0.0200     Valid Accuracy: 0.9694   Valid Loss: 0.0747\n",
      "Epoch 16    Train Accuracy: 0.9937   Train Loss: 0.0198     Valid Accuracy: 0.9689   Valid Loss: 0.0762\n",
      "Epoch 17    Train Accuracy: 0.9974   Train Loss: 0.0118     Valid Accuracy: 0.9728   Valid Loss: 0.0911\n",
      "\n",
      " Best validation accuracy = 0.9733333587646484 \n",
      "\n",
      "\n",
      "Tc guess = 2.0, Test set accuracy = 0.971666693687439 \n",
      "\n",
      "\n",
      "\n",
      "Epoch 1    Train Accuracy: 0.9059   Train Loss: 0.2093     Valid Accuracy: 0.9100   Valid Loss: 0.1889\n",
      "Epoch 2    Train Accuracy: 0.9489   Train Loss: 0.1192     Valid Accuracy: 0.9600   Valid Loss: 0.0968\n",
      "Epoch 3    Train Accuracy: 0.9494   Train Loss: 0.1206     Valid Accuracy: 0.9572   Valid Loss: 0.0976\n",
      "Epoch 4    Train Accuracy: 0.9593   Train Loss: 0.0943     Valid Accuracy: 0.9606   Valid Loss: 0.0896\n",
      "Epoch 5    Train Accuracy: 0.9652   Train Loss: 0.0841     Valid Accuracy: 0.9672   Valid Loss: 0.0759\n",
      "Epoch 6    Train Accuracy: 0.9704   Train Loss: 0.0717     Valid Accuracy: 0.9706   Valid Loss: 0.0710\n",
      "Epoch 7    Train Accuracy: 0.9744   Train Loss: 0.0588     Valid Accuracy: 0.9556   Valid Loss: 0.1011\n",
      "Epoch 8    Train Accuracy: 0.9748   Train Loss: 0.0586     Valid Accuracy: 0.9728   Valid Loss: 0.0699\n",
      "Epoch 9    Train Accuracy: 0.9802   Train Loss: 0.0478     Valid Accuracy: 0.9683   Valid Loss: 0.0819\n",
      "Epoch 10    Train Accuracy: 0.9804   Train Loss: 0.0493     Valid Accuracy: 0.9689   Valid Loss: 0.0718\n",
      "Epoch 11    Train Accuracy: 0.9854   Train Loss: 0.0390     Valid Accuracy: 0.9717   Valid Loss: 0.0716\n",
      "Epoch 12    Train Accuracy: 0.9811   Train Loss: 0.0463     Valid Accuracy: 0.9739   Valid Loss: 0.0734\n",
      "Epoch 13    Train Accuracy: 0.9839   Train Loss: 0.0401     Valid Accuracy: 0.9656   Valid Loss: 0.0904\n",
      "Epoch 14    Train Accuracy: 0.9850   Train Loss: 0.0374     Valid Accuracy: 0.9706   Valid Loss: 0.0788\n",
      "Epoch 15    Train Accuracy: 0.9944   Train Loss: 0.0201     Valid Accuracy: 0.9694   Valid Loss: 0.0890\n",
      "Epoch 16    Train Accuracy: 0.9919   Train Loss: 0.0225     Valid Accuracy: 0.9706   Valid Loss: 0.0863\n",
      "Epoch 17    Train Accuracy: 0.9967   Train Loss: 0.0144     Valid Accuracy: 0.9622   Valid Loss: 0.1250\n",
      "Epoch 18    Train Accuracy: 0.9987   Train Loss: 0.0096     Valid Accuracy: 0.9700   Valid Loss: 0.0931\n",
      "\n",
      " Best validation accuracy = 0.9738888740539551 \n",
      "\n",
      "\n",
      "Tc guess = 2.5, Test set accuracy = 0.9627777934074402 \n",
      "\n",
      "\n",
      "\n",
      "Epoch 1    Train Accuracy: 0.9104   Train Loss: 0.2020     Valid Accuracy: 0.9433   Valid Loss: 0.1316\n",
      "Epoch 2    Train Accuracy: 0.9409   Train Loss: 0.1370     Valid Accuracy: 0.9533   Valid Loss: 0.1051\n",
      "Epoch 3    Train Accuracy: 0.9441   Train Loss: 0.1242     Valid Accuracy: 0.9533   Valid Loss: 0.0991\n",
      "Epoch 4    Train Accuracy: 0.9576   Train Loss: 0.0986     Valid Accuracy: 0.9600   Valid Loss: 0.0948\n",
      "Epoch 5    Train Accuracy: 0.9524   Train Loss: 0.1062     Valid Accuracy: 0.9550   Valid Loss: 0.1021\n",
      "Epoch 6    Train Accuracy: 0.9643   Train Loss: 0.0831     Valid Accuracy: 0.9622   Valid Loss: 0.0869\n",
      "Epoch 7    Train Accuracy: 0.9657   Train Loss: 0.0801     Valid Accuracy: 0.9644   Valid Loss: 0.0818\n",
      "Epoch 8    Train Accuracy: 0.9674   Train Loss: 0.0796     Valid Accuracy: 0.9500   Valid Loss: 0.1029\n",
      "Epoch 9    Train Accuracy: 0.9685   Train Loss: 0.0729     Valid Accuracy: 0.9656   Valid Loss: 0.0817\n",
      "Epoch 10    Train Accuracy: 0.9731   Train Loss: 0.0656     Valid Accuracy: 0.9650   Valid Loss: 0.0861\n",
      "Epoch 11    Train Accuracy: 0.9811   Train Loss: 0.0486     Valid Accuracy: 0.9561   Valid Loss: 0.1063\n",
      "Epoch 12    Train Accuracy: 0.9819   Train Loss: 0.0458     Valid Accuracy: 0.9661   Valid Loss: 0.0873\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 13    Train Accuracy: 0.9880   Train Loss: 0.0338     Valid Accuracy: 0.9611   Valid Loss: 0.0924\n",
      "Epoch 14    Train Accuracy: 0.9891   Train Loss: 0.0306     Valid Accuracy: 0.9578   Valid Loss: 0.1177\n",
      "Epoch 15    Train Accuracy: 0.9817   Train Loss: 0.0425     Valid Accuracy: 0.9528   Valid Loss: 0.1232\n",
      "Epoch 16    Train Accuracy: 0.9898   Train Loss: 0.0297     Valid Accuracy: 0.9561   Valid Loss: 0.1226\n",
      "Epoch 17    Train Accuracy: 0.9928   Train Loss: 0.0216     Valid Accuracy: 0.9589   Valid Loss: 0.1024\n",
      "Epoch 18    Train Accuracy: 0.9970   Train Loss: 0.0141     Valid Accuracy: 0.9594   Valid Loss: 0.1171\n",
      "Epoch 19    Train Accuracy: 0.9972   Train Loss: 0.0105     Valid Accuracy: 0.9556   Valid Loss: 0.1389\n",
      "\n",
      " Best validation accuracy = 0.9661111235618591 \n",
      "\n",
      "\n",
      "Tc guess = 3.0, Test set accuracy = 0.9544444680213928 \n",
      "\n",
      "\n",
      "\n",
      "Epoch 1    Train Accuracy: 0.8874   Train Loss: 0.2208     Valid Accuracy: 0.9367   Valid Loss: 0.1441\n",
      "Epoch 2    Train Accuracy: 0.9391   Train Loss: 0.1317     Valid Accuracy: 0.9239   Valid Loss: 0.1671\n",
      "Epoch 3    Train Accuracy: 0.9441   Train Loss: 0.1253     Valid Accuracy: 0.9350   Valid Loss: 0.1337\n",
      "Epoch 4    Train Accuracy: 0.9452   Train Loss: 0.1190     Valid Accuracy: 0.9228   Valid Loss: 0.1822\n",
      "Epoch 5    Train Accuracy: 0.9572   Train Loss: 0.0967     Valid Accuracy: 0.9483   Valid Loss: 0.1090\n",
      "Epoch 6    Train Accuracy: 0.9593   Train Loss: 0.0894     Valid Accuracy: 0.9572   Valid Loss: 0.0935\n",
      "Epoch 7    Train Accuracy: 0.9654   Train Loss: 0.0813     Valid Accuracy: 0.9506   Valid Loss: 0.1069\n",
      "Epoch 8    Train Accuracy: 0.9724   Train Loss: 0.0685     Valid Accuracy: 0.9583   Valid Loss: 0.0901\n",
      "Epoch 9    Train Accuracy: 0.9730   Train Loss: 0.0669     Valid Accuracy: 0.9550   Valid Loss: 0.0967\n",
      "Epoch 10    Train Accuracy: 0.9778   Train Loss: 0.0587     Valid Accuracy: 0.9522   Valid Loss: 0.1061\n",
      "Epoch 11    Train Accuracy: 0.9824   Train Loss: 0.0459     Valid Accuracy: 0.9494   Valid Loss: 0.1123\n",
      "Epoch 12    Train Accuracy: 0.9820   Train Loss: 0.0458     Valid Accuracy: 0.9544   Valid Loss: 0.1023\n",
      "Epoch 13    Train Accuracy: 0.9906   Train Loss: 0.0275     Valid Accuracy: 0.9528   Valid Loss: 0.1097\n",
      "Epoch 14    Train Accuracy: 0.9937   Train Loss: 0.0227     Valid Accuracy: 0.9439   Valid Loss: 0.1625\n",
      "Epoch 15    Train Accuracy: 0.9946   Train Loss: 0.0171     Valid Accuracy: 0.9494   Valid Loss: 0.1238\n",
      "Epoch 16    Train Accuracy: 0.9950   Train Loss: 0.0185     Valid Accuracy: 0.9517   Valid Loss: 0.1302\n",
      "Epoch 17    Train Accuracy: 0.9965   Train Loss: 0.0141     Valid Accuracy: 0.9494   Valid Loss: 0.1338\n",
      "Epoch 18    Train Accuracy: 0.9993   Train Loss: 0.0087     Valid Accuracy: 0.9544   Valid Loss: 0.1332\n",
      "\n",
      " Best validation accuracy = 0.9583333134651184 \n",
      "\n",
      "\n",
      "Tc guess = 3.5, Test set accuracy = 0.9522222280502319 \n",
      "\n",
      "\n",
      "\n",
      "Epoch 1    Train Accuracy: 0.9033   Train Loss: 0.2062     Valid Accuracy: 0.9389   Valid Loss: 0.1266\n",
      "Epoch 2    Train Accuracy: 0.9315   Train Loss: 0.1456     Valid Accuracy: 0.9344   Valid Loss: 0.1401\n",
      "Epoch 3    Train Accuracy: 0.9331   Train Loss: 0.1436     Valid Accuracy: 0.9472   Valid Loss: 0.1121\n",
      "Epoch 4    Train Accuracy: 0.9456   Train Loss: 0.1159     Valid Accuracy: 0.9589   Valid Loss: 0.0962\n",
      "Epoch 5    Train Accuracy: 0.9476   Train Loss: 0.1149     Valid Accuracy: 0.9172   Valid Loss: 0.1558\n",
      "Epoch 6    Train Accuracy: 0.9509   Train Loss: 0.1076     Valid Accuracy: 0.9478   Valid Loss: 0.1085\n",
      "Epoch 7    Train Accuracy: 0.9570   Train Loss: 0.0959     Valid Accuracy: 0.9522   Valid Loss: 0.1041\n",
      "Epoch 8    Train Accuracy: 0.9557   Train Loss: 0.0959     Valid Accuracy: 0.9561   Valid Loss: 0.1043\n",
      "Epoch 9    Train Accuracy: 0.9587   Train Loss: 0.0936     Valid Accuracy: 0.9450   Valid Loss: 0.1252\n",
      "Epoch 10    Train Accuracy: 0.9639   Train Loss: 0.0827     Valid Accuracy: 0.9561   Valid Loss: 0.0920\n",
      "Epoch 11    Train Accuracy: 0.9672   Train Loss: 0.0746     Valid Accuracy: 0.9550   Valid Loss: 0.0946\n",
      "Epoch 12    Train Accuracy: 0.9774   Train Loss: 0.0586     Valid Accuracy: 0.9539   Valid Loss: 0.0991\n",
      "Epoch 13    Train Accuracy: 0.9806   Train Loss: 0.0492     Valid Accuracy: 0.9494   Valid Loss: 0.1295\n",
      "Epoch 14    Train Accuracy: 0.9857   Train Loss: 0.0403     Valid Accuracy: 0.9522   Valid Loss: 0.1086\n",
      "Epoch 15    Train Accuracy: 0.9850   Train Loss: 0.0404     Valid Accuracy: 0.9372   Valid Loss: 0.1650\n",
      "Epoch 16    Train Accuracy: 0.9783   Train Loss: 0.0525     Valid Accuracy: 0.9411   Valid Loss: 0.1432\n",
      "Epoch 17    Train Accuracy: 0.9911   Train Loss: 0.0270     Valid Accuracy: 0.9494   Valid Loss: 0.1233\n",
      "Epoch 18    Train Accuracy: 0.9987   Train Loss: 0.0119     Valid Accuracy: 0.9522   Valid Loss: 0.1331\n",
      "Epoch 19    Train Accuracy: 0.9989   Train Loss: 0.0095     Valid Accuracy: 0.9472   Valid Loss: 0.1348\n",
      "Epoch 20    Train Accuracy: 0.9998   Train Loss: 0.0073     Valid Accuracy: 0.9517   Valid Loss: 0.1313\n",
      "\n",
      " Best validation accuracy = 0.9588888883590698 \n",
      "\n",
      "\n",
      "Tc guess = 4.0, Test set accuracy = 0.9477777481079102 \n",
      "\n",
      "\n",
      "\n",
      "Epoch 1    Train Accuracy: 0.9144   Train Loss: 0.1892     Valid Accuracy: 0.9417   Valid Loss: 0.1306\n",
      "Epoch 2    Train Accuracy: 0.9385   Train Loss: 0.1308     Valid Accuracy: 0.9450   Valid Loss: 0.1056\n",
      "Epoch 3    Train Accuracy: 0.9474   Train Loss: 0.1195     Valid Accuracy: 0.9461   Valid Loss: 0.1073\n",
      "Epoch 4    Train Accuracy: 0.9509   Train Loss: 0.1071     Valid Accuracy: 0.9544   Valid Loss: 0.0957\n",
      "Epoch 5    Train Accuracy: 0.9500   Train Loss: 0.1072     Valid Accuracy: 0.9500   Valid Loss: 0.0970\n",
      "Epoch 6    Train Accuracy: 0.9581   Train Loss: 0.1009     Valid Accuracy: 0.9506   Valid Loss: 0.1094\n",
      "Epoch 7    Train Accuracy: 0.9565   Train Loss: 0.0975     Valid Accuracy: 0.9528   Valid Loss: 0.0975\n",
      "Epoch 8    Train Accuracy: 0.9613   Train Loss: 0.0912     Valid Accuracy: 0.9300   Valid Loss: 0.1548\n",
      "Epoch 9    Train Accuracy: 0.9641   Train Loss: 0.0859     Valid Accuracy: 0.9494   Valid Loss: 0.0972\n",
      "Epoch 10    Train Accuracy: 0.9654   Train Loss: 0.0783     Valid Accuracy: 0.9478   Valid Loss: 0.1005\n",
      "Epoch 11    Train Accuracy: 0.9720   Train Loss: 0.0710     Valid Accuracy: 0.9500   Valid Loss: 0.1004\n",
      "Epoch 12    Train Accuracy: 0.9806   Train Loss: 0.0513     Valid Accuracy: 0.9489   Valid Loss: 0.1120\n",
      "Epoch 13    Train Accuracy: 0.9781   Train Loss: 0.0521     Valid Accuracy: 0.9494   Valid Loss: 0.1020\n",
      "Epoch 14    Train Accuracy: 0.9809   Train Loss: 0.0450     Valid Accuracy: 0.9528   Valid Loss: 0.1049\n",
      "\n",
      " Best validation accuracy = 0.9544444680213928 \n",
      "\n",
      "\n",
      "Tc guess = 4.5, Test set accuracy = 0.9477777481079102 \n",
      "\n",
      "\n",
      "\n",
      "Epoch 1    Train Accuracy: 0.9317   Train Loss: 0.1577     Valid Accuracy: 0.9622   Valid Loss: 0.0971\n",
      "Epoch 2    Train Accuracy: 0.9569   Train Loss: 0.1016     Valid Accuracy: 0.9500   Valid Loss: 0.1113\n",
      "Epoch 3    Train Accuracy: 0.9561   Train Loss: 0.1034     Valid Accuracy: 0.9689   Valid Loss: 0.0864\n",
      "Epoch 4    Train Accuracy: 0.9572   Train Loss: 0.0986     Valid Accuracy: 0.9644   Valid Loss: 0.0883\n",
      "Epoch 5    Train Accuracy: 0.9581   Train Loss: 0.0915     Valid Accuracy: 0.9672   Valid Loss: 0.0847\n",
      "Epoch 6    Train Accuracy: 0.9619   Train Loss: 0.0867     Valid Accuracy: 0.9628   Valid Loss: 0.0902\n",
      "Epoch 7    Train Accuracy: 0.9624   Train Loss: 0.0828     Valid Accuracy: 0.9589   Valid Loss: 0.0993\n",
      "Epoch 8    Train Accuracy: 0.9669   Train Loss: 0.0752     Valid Accuracy: 0.9517   Valid Loss: 0.1136\n",
      "Epoch 9    Train Accuracy: 0.9694   Train Loss: 0.0732     Valid Accuracy: 0.9672   Valid Loss: 0.0851\n",
      "Epoch 10    Train Accuracy: 0.9743   Train Loss: 0.0626     Valid Accuracy: 0.9667   Valid Loss: 0.0841\n",
      "Epoch 11    Train Accuracy: 0.9780   Train Loss: 0.0578     Valid Accuracy: 0.9667   Valid Loss: 0.0901\n",
      "Epoch 12    Train Accuracy: 0.9776   Train Loss: 0.0552     Valid Accuracy: 0.9483   Valid Loss: 0.1214\n",
      "Epoch 13    Train Accuracy: 0.9781   Train Loss: 0.0509     Valid Accuracy: 0.9644   Valid Loss: 0.0961\n",
      "Epoch 14    Train Accuracy: 0.9843   Train Loss: 0.0395     Valid Accuracy: 0.9650   Valid Loss: 0.1065\n",
      "Epoch 15    Train Accuracy: 0.9922   Train Loss: 0.0239     Valid Accuracy: 0.9594   Valid Loss: 0.1104\n",
      "Epoch 16    Train Accuracy: 0.9915   Train Loss: 0.0246     Valid Accuracy: 0.9650   Valid Loss: 0.0952\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 17    Train Accuracy: 0.9931   Train Loss: 0.0214     Valid Accuracy: 0.9600   Valid Loss: 0.1281\n",
      "Epoch 18    Train Accuracy: 0.9983   Train Loss: 0.0103     Valid Accuracy: 0.9500   Valid Loss: 0.1341\n",
      "Epoch 19    Train Accuracy: 0.9980   Train Loss: 0.0098     Valid Accuracy: 0.9639   Valid Loss: 0.1119\n",
      "Epoch 20    Train Accuracy: 0.9994   Train Loss: 0.0086     Valid Accuracy: 0.9628   Valid Loss: 0.1169\n",
      "\n",
      " Best validation accuracy = 0.9688888788223267 \n",
      "\n",
      "\n",
      "Tc guess = 5.0, Test set accuracy = 0.9561111330986023 \n",
      "\n",
      "\n",
      "\n",
      "Epoch 1    Train Accuracy: 0.9472   Train Loss: 0.1335     Valid Accuracy: 0.9628   Valid Loss: 0.0920\n",
      "Epoch 2    Train Accuracy: 0.9706   Train Loss: 0.0778     Valid Accuracy: 0.9578   Valid Loss: 0.1060\n",
      "Epoch 3    Train Accuracy: 0.9707   Train Loss: 0.0754     Valid Accuracy: 0.9661   Valid Loss: 0.0932\n",
      "Epoch 4    Train Accuracy: 0.9720   Train Loss: 0.0717     Valid Accuracy: 0.9628   Valid Loss: 0.0904\n",
      "Epoch 5    Train Accuracy: 0.9709   Train Loss: 0.0756     Valid Accuracy: 0.9611   Valid Loss: 0.0993\n",
      "Epoch 6    Train Accuracy: 0.9704   Train Loss: 0.0770     Valid Accuracy: 0.9628   Valid Loss: 0.0897\n",
      "Epoch 7    Train Accuracy: 0.9717   Train Loss: 0.0726     Valid Accuracy: 0.9639   Valid Loss: 0.0905\n",
      "Epoch 8    Train Accuracy: 0.9730   Train Loss: 0.0635     Valid Accuracy: 0.9639   Valid Loss: 0.0897\n",
      "Epoch 9    Train Accuracy: 0.9743   Train Loss: 0.0655     Valid Accuracy: 0.9661   Valid Loss: 0.0980\n",
      "Epoch 10    Train Accuracy: 0.9778   Train Loss: 0.0541     Valid Accuracy: 0.9650   Valid Loss: 0.0982\n",
      "Epoch 11    Train Accuracy: 0.9789   Train Loss: 0.0550     Valid Accuracy: 0.9633   Valid Loss: 0.0933\n",
      "Epoch 12    Train Accuracy: 0.9822   Train Loss: 0.0430     Valid Accuracy: 0.9611   Valid Loss: 0.1051\n",
      "Epoch 13    Train Accuracy: 0.9848   Train Loss: 0.0378     Valid Accuracy: 0.9628   Valid Loss: 0.1061\n",
      "Epoch 14    Train Accuracy: 0.9896   Train Loss: 0.0296     Valid Accuracy: 0.9589   Valid Loss: 0.1211\n",
      "Epoch 15    Train Accuracy: 0.9941   Train Loss: 0.0208     Valid Accuracy: 0.9594   Valid Loss: 0.1198\n",
      "Epoch 16    Train Accuracy: 0.9944   Train Loss: 0.0166     Valid Accuracy: 0.9594   Valid Loss: 0.1302\n",
      "Epoch 17    Train Accuracy: 0.9974   Train Loss: 0.0136     Valid Accuracy: 0.9583   Valid Loss: 0.1464\n",
      "Epoch 18    Train Accuracy: 0.9954   Train Loss: 0.0138     Valid Accuracy: 0.9589   Valid Loss: 0.1282\n",
      "\n",
      " Best validation accuracy = 0.9661111235618591 \n",
      "\n",
      "\n",
      "Tc guess = 5.5, Test set accuracy = 0.9666666388511658 \n",
      "\n",
      "\n",
      "\n",
      "Epoch 1    Train Accuracy: 0.9485   Train Loss: 0.1374     Valid Accuracy: 0.9722   Valid Loss: 0.0737\n",
      "Epoch 2    Train Accuracy: 0.9691   Train Loss: 0.0840     Valid Accuracy: 0.9700   Valid Loss: 0.0768\n",
      "Epoch 3    Train Accuracy: 0.9689   Train Loss: 0.0831     Valid Accuracy: 0.9722   Valid Loss: 0.0687\n",
      "Epoch 4    Train Accuracy: 0.9709   Train Loss: 0.0785     Valid Accuracy: 0.9722   Valid Loss: 0.0697\n",
      "Epoch 5    Train Accuracy: 0.9700   Train Loss: 0.0793     Valid Accuracy: 0.9611   Valid Loss: 0.0953\n",
      "Epoch 6    Train Accuracy: 0.9709   Train Loss: 0.0754     Valid Accuracy: 0.9672   Valid Loss: 0.0838\n",
      "Epoch 7    Train Accuracy: 0.9719   Train Loss: 0.0771     Valid Accuracy: 0.9694   Valid Loss: 0.0772\n",
      "Epoch 8    Train Accuracy: 0.9752   Train Loss: 0.0699     Valid Accuracy: 0.9717   Valid Loss: 0.0727\n",
      "Epoch 9    Train Accuracy: 0.9743   Train Loss: 0.0657     Valid Accuracy: 0.9728   Valid Loss: 0.0725\n",
      "Epoch 10    Train Accuracy: 0.9778   Train Loss: 0.0614     Valid Accuracy: 0.9739   Valid Loss: 0.0723\n",
      "Epoch 11    Train Accuracy: 0.9743   Train Loss: 0.0670     Valid Accuracy: 0.9717   Valid Loss: 0.0707\n",
      "Epoch 12    Train Accuracy: 0.9800   Train Loss: 0.0527     Valid Accuracy: 0.9694   Valid Loss: 0.0790\n",
      "Epoch 13    Train Accuracy: 0.9835   Train Loss: 0.0494     Valid Accuracy: 0.9717   Valid Loss: 0.0812\n",
      "\n",
      " Best validation accuracy = 0.9738888740539551 \n",
      "\n",
      "\n",
      "Tc guess = 6.0, Test set accuracy = 0.972777783870697 \n",
      "\n",
      "\n",
      "\n",
      "Epoch 1    Train Accuracy: 0.9398   Train Loss: 0.1643     Valid Accuracy: 0.9544   Valid Loss: 0.1071\n",
      "Epoch 2    Train Accuracy: 0.9535   Train Loss: 0.1127     Valid Accuracy: 0.9572   Valid Loss: 0.1004\n",
      "Epoch 3    Train Accuracy: 0.9557   Train Loss: 0.1114     Valid Accuracy: 0.9561   Valid Loss: 0.1209\n",
      "Epoch 4    Train Accuracy: 0.9611   Train Loss: 0.0992     Valid Accuracy: 0.9500   Valid Loss: 0.1334\n",
      "Epoch 5    Train Accuracy: 0.9606   Train Loss: 0.0965     Valid Accuracy: 0.9578   Valid Loss: 0.0934\n",
      "Epoch 6    Train Accuracy: 0.9622   Train Loss: 0.0928     Valid Accuracy: 0.9561   Valid Loss: 0.0959\n",
      "Epoch 7    Train Accuracy: 0.9631   Train Loss: 0.0911     Valid Accuracy: 0.9533   Valid Loss: 0.0976\n",
      "Epoch 8    Train Accuracy: 0.9654   Train Loss: 0.0823     Valid Accuracy: 0.9544   Valid Loss: 0.0947\n",
      "Epoch 9    Train Accuracy: 0.9652   Train Loss: 0.0825     Valid Accuracy: 0.9550   Valid Loss: 0.1085\n",
      "Epoch 10    Train Accuracy: 0.9669   Train Loss: 0.0815     Valid Accuracy: 0.9533   Valid Loss: 0.1069\n",
      "Epoch 11    Train Accuracy: 0.9672   Train Loss: 0.0807     Valid Accuracy: 0.9517   Valid Loss: 0.1050\n",
      "Epoch 12    Train Accuracy: 0.9750   Train Loss: 0.0656     Valid Accuracy: 0.9472   Valid Loss: 0.1294\n",
      "Epoch 13    Train Accuracy: 0.9785   Train Loss: 0.0611     Valid Accuracy: 0.9522   Valid Loss: 0.1401\n",
      "Epoch 14    Train Accuracy: 0.9767   Train Loss: 0.0607     Valid Accuracy: 0.9528   Valid Loss: 0.1059\n",
      "Epoch 15    Train Accuracy: 0.9843   Train Loss: 0.0436     Valid Accuracy: 0.9533   Valid Loss: 0.1472\n",
      "\n",
      " Best validation accuracy = 0.9577777981758118 \n",
      "\n",
      "\n",
      "Tc guess = 6.5, Test set accuracy = 0.9594444632530212 \n",
      "\n",
      "\n",
      "\n",
      "Epoch 1    Train Accuracy: 0.9228   Train Loss: 0.1842     Valid Accuracy: 0.9478   Valid Loss: 0.1262\n",
      "Epoch 2    Train Accuracy: 0.9461   Train Loss: 0.1380     Valid Accuracy: 0.9417   Valid Loss: 0.1473\n",
      "Epoch 3    Train Accuracy: 0.9456   Train Loss: 0.1266     Valid Accuracy: 0.9478   Valid Loss: 0.1376\n",
      "Epoch 4    Train Accuracy: 0.9483   Train Loss: 0.1258     Valid Accuracy: 0.9456   Valid Loss: 0.1429\n",
      "Epoch 5    Train Accuracy: 0.9541   Train Loss: 0.1089     Valid Accuracy: 0.9494   Valid Loss: 0.1108\n",
      "Epoch 6    Train Accuracy: 0.9563   Train Loss: 0.1052     Valid Accuracy: 0.9511   Valid Loss: 0.1105\n",
      "Epoch 7    Train Accuracy: 0.9581   Train Loss: 0.1018     Valid Accuracy: 0.9444   Valid Loss: 0.1330\n",
      "Epoch 8    Train Accuracy: 0.9630   Train Loss: 0.0953     Valid Accuracy: 0.9417   Valid Loss: 0.1360\n",
      "Epoch 9    Train Accuracy: 0.9617   Train Loss: 0.0941     Valid Accuracy: 0.9511   Valid Loss: 0.1148\n",
      "Epoch 10    Train Accuracy: 0.9596   Train Loss: 0.0962     Valid Accuracy: 0.9472   Valid Loss: 0.1362\n",
      "Epoch 11    Train Accuracy: 0.9637   Train Loss: 0.0887     Valid Accuracy: 0.9489   Valid Loss: 0.1205\n",
      "Epoch 12    Train Accuracy: 0.9685   Train Loss: 0.0813     Valid Accuracy: 0.9494   Valid Loss: 0.1325\n",
      "Epoch 13    Train Accuracy: 0.9681   Train Loss: 0.0785     Valid Accuracy: 0.9517   Valid Loss: 0.1178\n",
      "Epoch 14    Train Accuracy: 0.9693   Train Loss: 0.0749     Valid Accuracy: 0.9506   Valid Loss: 0.1214\n",
      "Epoch 15    Train Accuracy: 0.9772   Train Loss: 0.0596     Valid Accuracy: 0.9411   Valid Loss: 0.1582\n",
      "Epoch 16    Train Accuracy: 0.9793   Train Loss: 0.0542     Valid Accuracy: 0.9456   Valid Loss: 0.1555\n",
      "\n",
      " Best validation accuracy = 0.9516666531562805 \n",
      "\n",
      "\n",
      "Tc guess = 7.0, Test set accuracy = 0.9427777528762817 \n",
      "\n",
      "\n",
      "\n",
      "Epoch 1    Train Accuracy: 0.9006   Train Loss: 0.2202     Valid Accuracy: 0.9222   Valid Loss: 0.2010\n",
      "Epoch 2    Train Accuracy: 0.9330   Train Loss: 0.1625     Valid Accuracy: 0.9361   Valid Loss: 0.1563\n",
      "Epoch 3    Train Accuracy: 0.9339   Train Loss: 0.1644     Valid Accuracy: 0.9372   Valid Loss: 0.1437\n",
      "Epoch 4    Train Accuracy: 0.9370   Train Loss: 0.1533     Valid Accuracy: 0.9333   Valid Loss: 0.1581\n",
      "Epoch 5    Train Accuracy: 0.9409   Train Loss: 0.1471     Valid Accuracy: 0.9472   Valid Loss: 0.1248\n",
      "Epoch 6    Train Accuracy: 0.9456   Train Loss: 0.1352     Valid Accuracy: 0.9456   Valid Loss: 0.1277\n",
      "Epoch 7    Train Accuracy: 0.9452   Train Loss: 0.1352     Valid Accuracy: 0.9322   Valid Loss: 0.1697\n",
      "Epoch 8    Train Accuracy: 0.9491   Train Loss: 0.1263     Valid Accuracy: 0.9383   Valid Loss: 0.1553\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 9    Train Accuracy: 0.9476   Train Loss: 0.1272     Valid Accuracy: 0.9461   Valid Loss: 0.1308\n",
      "Epoch 10    Train Accuracy: 0.9520   Train Loss: 0.1173     Valid Accuracy: 0.9411   Valid Loss: 0.1436\n",
      "Epoch 11    Train Accuracy: 0.9548   Train Loss: 0.1131     Valid Accuracy: 0.9461   Valid Loss: 0.1286\n",
      "Epoch 12    Train Accuracy: 0.9578   Train Loss: 0.1101     Valid Accuracy: 0.9433   Valid Loss: 0.1429\n",
      "Epoch 13    Train Accuracy: 0.9589   Train Loss: 0.1028     Valid Accuracy: 0.9456   Valid Loss: 0.1307\n",
      "Epoch 14    Train Accuracy: 0.9607   Train Loss: 0.0980     Valid Accuracy: 0.9461   Valid Loss: 0.1289\n",
      "Epoch 15    Train Accuracy: 0.9650   Train Loss: 0.0920     Valid Accuracy: 0.9417   Valid Loss: 0.1343\n",
      "\n",
      " Best validation accuracy = 0.9472222328186035 \n",
      "\n",
      "\n",
      "Tc guess = 7.5, Test set accuracy = 0.9405555725097656 \n",
      "\n",
      "\n",
      "\n",
      "Epoch 1    Train Accuracy: 0.8881   Train Loss: 0.2440     Valid Accuracy: 0.9239   Valid Loss: 0.1752\n",
      "Epoch 2    Train Accuracy: 0.9252   Train Loss: 0.1787     Valid Accuracy: 0.9250   Valid Loss: 0.1776\n",
      "Epoch 3    Train Accuracy: 0.9241   Train Loss: 0.1759     Valid Accuracy: 0.9339   Valid Loss: 0.1537\n",
      "Epoch 4    Train Accuracy: 0.9391   Train Loss: 0.1531     Valid Accuracy: 0.9378   Valid Loss: 0.1466\n",
      "Epoch 5    Train Accuracy: 0.9337   Train Loss: 0.1628     Valid Accuracy: 0.9289   Valid Loss: 0.1774\n",
      "Epoch 6    Train Accuracy: 0.9378   Train Loss: 0.1495     Valid Accuracy: 0.9400   Valid Loss: 0.1486\n",
      "Epoch 7    Train Accuracy: 0.9374   Train Loss: 0.1471     Valid Accuracy: 0.9394   Valid Loss: 0.1441\n",
      "Epoch 8    Train Accuracy: 0.9452   Train Loss: 0.1351     Valid Accuracy: 0.9128   Valid Loss: 0.2206\n",
      "Epoch 9    Train Accuracy: 0.9424   Train Loss: 0.1363     Valid Accuracy: 0.9383   Valid Loss: 0.1429\n",
      "Epoch 10    Train Accuracy: 0.9504   Train Loss: 0.1206     Valid Accuracy: 0.9333   Valid Loss: 0.1660\n",
      "Epoch 11    Train Accuracy: 0.9481   Train Loss: 0.1197     Valid Accuracy: 0.9372   Valid Loss: 0.1512\n",
      "Epoch 12    Train Accuracy: 0.9481   Train Loss: 0.1180     Valid Accuracy: 0.9272   Valid Loss: 0.1707\n",
      "Epoch 13    Train Accuracy: 0.9519   Train Loss: 0.1125     Valid Accuracy: 0.9356   Valid Loss: 0.1422\n",
      "Epoch 14    Train Accuracy: 0.9606   Train Loss: 0.0964     Valid Accuracy: 0.9361   Valid Loss: 0.1600\n",
      "Epoch 15    Train Accuracy: 0.9644   Train Loss: 0.0926     Valid Accuracy: 0.9383   Valid Loss: 0.1580\n",
      "Epoch 16    Train Accuracy: 0.9620   Train Loss: 0.0951     Valid Accuracy: 0.9306   Valid Loss: 0.1769\n",
      "Epoch 17    Train Accuracy: 0.9681   Train Loss: 0.0815     Valid Accuracy: 0.9356   Valid Loss: 0.1679\n",
      "Epoch 18    Train Accuracy: 0.9709   Train Loss: 0.0758     Valid Accuracy: 0.9289   Valid Loss: 0.1650\n",
      "Epoch 19    Train Accuracy: 0.9759   Train Loss: 0.0652     Valid Accuracy: 0.9200   Valid Loss: 0.2069\n",
      "Epoch 20    Train Accuracy: 0.9780   Train Loss: 0.0586     Valid Accuracy: 0.9311   Valid Loss: 0.2039\n",
      "\n",
      " Best validation accuracy = 0.9399999976158142 \n",
      "\n",
      "\n",
      "Tc guess = 8.0, Test set accuracy = 0.9377777576446533 \n",
      "\n",
      "\n",
      "\n",
      "Epoch 1    Train Accuracy: 0.8665   Train Loss: 0.2709     Valid Accuracy: 0.9100   Valid Loss: 0.1955\n",
      "Epoch 2    Train Accuracy: 0.9191   Train Loss: 0.1892     Valid Accuracy: 0.9306   Valid Loss: 0.1648\n",
      "Epoch 3    Train Accuracy: 0.9278   Train Loss: 0.1768     Valid Accuracy: 0.9233   Valid Loss: 0.1634\n",
      "Epoch 4    Train Accuracy: 0.9276   Train Loss: 0.1744     Valid Accuracy: 0.9339   Valid Loss: 0.1573\n",
      "Epoch 5    Train Accuracy: 0.9293   Train Loss: 0.1670     Valid Accuracy: 0.9239   Valid Loss: 0.1625\n",
      "Epoch 6    Train Accuracy: 0.9265   Train Loss: 0.1697     Valid Accuracy: 0.9200   Valid Loss: 0.1943\n",
      "Epoch 7    Train Accuracy: 0.9365   Train Loss: 0.1541     Valid Accuracy: 0.9289   Valid Loss: 0.1632\n",
      "Epoch 8    Train Accuracy: 0.9309   Train Loss: 0.1586     Valid Accuracy: 0.9106   Valid Loss: 0.1964\n",
      "Epoch 9    Train Accuracy: 0.9409   Train Loss: 0.1450     Valid Accuracy: 0.9139   Valid Loss: 0.1971\n",
      "Epoch 10    Train Accuracy: 0.9391   Train Loss: 0.1440     Valid Accuracy: 0.9178   Valid Loss: 0.1814\n",
      "Epoch 11    Train Accuracy: 0.9439   Train Loss: 0.1350     Valid Accuracy: 0.8961   Valid Loss: 0.2600\n",
      "Epoch 12    Train Accuracy: 0.9374   Train Loss: 0.1512     Valid Accuracy: 0.9394   Valid Loss: 0.1522\n",
      "Epoch 13    Train Accuracy: 0.9472   Train Loss: 0.1260     Valid Accuracy: 0.9150   Valid Loss: 0.2067\n",
      "Epoch 14    Train Accuracy: 0.9517   Train Loss: 0.1205     Valid Accuracy: 0.9317   Valid Loss: 0.1607\n",
      "Epoch 15    Train Accuracy: 0.9511   Train Loss: 0.1205     Valid Accuracy: 0.9217   Valid Loss: 0.1825\n",
      "Epoch 16    Train Accuracy: 0.9574   Train Loss: 0.1120     Valid Accuracy: 0.9267   Valid Loss: 0.1644\n",
      "Epoch 17    Train Accuracy: 0.9567   Train Loss: 0.1060     Valid Accuracy: 0.9233   Valid Loss: 0.1797\n",
      "Epoch 18    Train Accuracy: 0.9630   Train Loss: 0.0987     Valid Accuracy: 0.9256   Valid Loss: 0.1745\n",
      "Epoch 19    Train Accuracy: 0.9700   Train Loss: 0.0810     Valid Accuracy: 0.9144   Valid Loss: 0.2001\n",
      "Epoch 20    Train Accuracy: 0.9737   Train Loss: 0.0735     Valid Accuracy: 0.9211   Valid Loss: 0.2143\n",
      "\n",
      " Best validation accuracy = 0.9394444227218628 \n",
      "\n",
      "\n",
      "Tc guess = 8.5, Test set accuracy = 0.92166668176651 \n",
      "\n",
      "\n",
      "\n",
      "Epoch 1    Train Accuracy: 0.8559   Train Loss: 0.2802     Valid Accuracy: 0.9106   Valid Loss: 0.2049\n",
      "Epoch 2    Train Accuracy: 0.9015   Train Loss: 0.2169     Valid Accuracy: 0.9167   Valid Loss: 0.2043\n",
      "Epoch 3    Train Accuracy: 0.9085   Train Loss: 0.2089     Valid Accuracy: 0.9006   Valid Loss: 0.2143\n",
      "Epoch 4    Train Accuracy: 0.9081   Train Loss: 0.1998     Valid Accuracy: 0.9156   Valid Loss: 0.1901\n",
      "Epoch 5    Train Accuracy: 0.9157   Train Loss: 0.1928     Valid Accuracy: 0.8972   Valid Loss: 0.2147\n",
      "Epoch 6    Train Accuracy: 0.9041   Train Loss: 0.2068     Valid Accuracy: 0.9122   Valid Loss: 0.2051\n",
      "Epoch 7    Train Accuracy: 0.9183   Train Loss: 0.1857     Valid Accuracy: 0.9039   Valid Loss: 0.2068\n",
      "Epoch 8    Train Accuracy: 0.9228   Train Loss: 0.1811     Valid Accuracy: 0.9167   Valid Loss: 0.1865\n",
      "Epoch 9    Train Accuracy: 0.9211   Train Loss: 0.1752     Valid Accuracy: 0.9206   Valid Loss: 0.1773\n",
      "Epoch 10    Train Accuracy: 0.9315   Train Loss: 0.1586     Valid Accuracy: 0.9128   Valid Loss: 0.1865\n",
      "Epoch 11    Train Accuracy: 0.9294   Train Loss: 0.1601     Valid Accuracy: 0.9106   Valid Loss: 0.1918\n",
      "Epoch 12    Train Accuracy: 0.9350   Train Loss: 0.1546     Valid Accuracy: 0.9233   Valid Loss: 0.1781\n",
      "Epoch 13    Train Accuracy: 0.9391   Train Loss: 0.1446     Valid Accuracy: 0.9178   Valid Loss: 0.1851\n",
      "Epoch 14    Train Accuracy: 0.9404   Train Loss: 0.1418     Valid Accuracy: 0.9183   Valid Loss: 0.1819\n",
      "Epoch 15    Train Accuracy: 0.9394   Train Loss: 0.1355     Valid Accuracy: 0.9156   Valid Loss: 0.1839\n",
      "Epoch 16    Train Accuracy: 0.9454   Train Loss: 0.1315     Valid Accuracy: 0.9106   Valid Loss: 0.1881\n",
      "Epoch 17    Train Accuracy: 0.9474   Train Loss: 0.1276     Valid Accuracy: 0.9000   Valid Loss: 0.2251\n",
      "Epoch 18    Train Accuracy: 0.9507   Train Loss: 0.1199     Valid Accuracy: 0.9089   Valid Loss: 0.2104\n",
      "Epoch 19    Train Accuracy: 0.9650   Train Loss: 0.0918     Valid Accuracy: 0.9100   Valid Loss: 0.2027\n",
      "\n",
      " Best validation accuracy = 0.9233333468437195 \n",
      "\n",
      "\n",
      "Tc guess = 9.0, Test set accuracy = 0.9055555462837219 \n",
      "\n",
      "\n",
      "\n",
      "Epoch 1    Train Accuracy: 0.8467   Train Loss: 0.2966     Valid Accuracy: 0.8950   Valid Loss: 0.2207\n",
      "Epoch 2    Train Accuracy: 0.8843   Train Loss: 0.2387     Valid Accuracy: 0.8811   Valid Loss: 0.2368\n",
      "Epoch 3    Train Accuracy: 0.8969   Train Loss: 0.2204     Valid Accuracy: 0.9189   Valid Loss: 0.1891\n",
      "Epoch 4    Train Accuracy: 0.9080   Train Loss: 0.1976     Valid Accuracy: 0.9178   Valid Loss: 0.1843\n",
      "Epoch 5    Train Accuracy: 0.9126   Train Loss: 0.1947     Valid Accuracy: 0.9194   Valid Loss: 0.1864\n",
      "Epoch 6    Train Accuracy: 0.9100   Train Loss: 0.1974     Valid Accuracy: 0.8472   Valid Loss: 0.2938\n",
      "Epoch 7    Train Accuracy: 0.9219   Train Loss: 0.1745     Valid Accuracy: 0.9222   Valid Loss: 0.1757\n",
      "Epoch 8    Train Accuracy: 0.9237   Train Loss: 0.1730     Valid Accuracy: 0.9144   Valid Loss: 0.1879\n",
      "Epoch 9    Train Accuracy: 0.9235   Train Loss: 0.1715     Valid Accuracy: 0.9211   Valid Loss: 0.1780\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 10    Train Accuracy: 0.9298   Train Loss: 0.1610     Valid Accuracy: 0.9072   Valid Loss: 0.2029\n",
      "Epoch 11    Train Accuracy: 0.9363   Train Loss: 0.1490     Valid Accuracy: 0.9206   Valid Loss: 0.1747\n",
      "Epoch 12    Train Accuracy: 0.9433   Train Loss: 0.1362     Valid Accuracy: 0.9194   Valid Loss: 0.1813\n",
      "Epoch 13    Train Accuracy: 0.9407   Train Loss: 0.1339     Valid Accuracy: 0.9094   Valid Loss: 0.2036\n",
      "Epoch 14    Train Accuracy: 0.9450   Train Loss: 0.1280     Valid Accuracy: 0.9144   Valid Loss: 0.1877\n",
      "Epoch 15    Train Accuracy: 0.9524   Train Loss: 0.1157     Valid Accuracy: 0.9111   Valid Loss: 0.1950\n",
      "Epoch 16    Train Accuracy: 0.9583   Train Loss: 0.1042     Valid Accuracy: 0.9128   Valid Loss: 0.1928\n",
      "Epoch 17    Train Accuracy: 0.9431   Train Loss: 0.1277     Valid Accuracy: 0.8867   Valid Loss: 0.2346\n",
      "Epoch 18    Train Accuracy: 0.9574   Train Loss: 0.1000     Valid Accuracy: 0.8994   Valid Loss: 0.2417\n",
      "Epoch 19    Train Accuracy: 0.9680   Train Loss: 0.0836     Valid Accuracy: 0.9028   Valid Loss: 0.2310\n",
      "Epoch 20    Train Accuracy: 0.9735   Train Loss: 0.0689     Valid Accuracy: 0.9133   Valid Loss: 0.2209\n",
      "\n",
      " Best validation accuracy = 0.9222221970558167 \n",
      "\n",
      "\n",
      "Tc guess = 9.5, Test set accuracy = 0.9100000262260437 \n",
      "\n",
      "\n",
      "\n",
      "Epoch 1    Train Accuracy: 0.8461   Train Loss: 0.2847     Valid Accuracy: 0.8906   Valid Loss: 0.2314\n",
      "Epoch 2    Train Accuracy: 0.8822   Train Loss: 0.2323     Valid Accuracy: 0.8989   Valid Loss: 0.2093\n",
      "Epoch 3    Train Accuracy: 0.8863   Train Loss: 0.2228     Valid Accuracy: 0.8867   Valid Loss: 0.2300\n",
      "Epoch 4    Train Accuracy: 0.8991   Train Loss: 0.2078     Valid Accuracy: 0.9022   Valid Loss: 0.1962\n",
      "Epoch 5    Train Accuracy: 0.8946   Train Loss: 0.2158     Valid Accuracy: 0.9050   Valid Loss: 0.1953\n",
      "Epoch 6    Train Accuracy: 0.9039   Train Loss: 0.2022     Valid Accuracy: 0.8744   Valid Loss: 0.2362\n",
      "Epoch 7    Train Accuracy: 0.9022   Train Loss: 0.1989     Valid Accuracy: 0.9017   Valid Loss: 0.1963\n",
      "Epoch 8    Train Accuracy: 0.9048   Train Loss: 0.1932     Valid Accuracy: 0.8944   Valid Loss: 0.2130\n",
      "Epoch 9    Train Accuracy: 0.9087   Train Loss: 0.1940     Valid Accuracy: 0.9078   Valid Loss: 0.1964\n",
      "Epoch 10    Train Accuracy: 0.9093   Train Loss: 0.1842     Valid Accuracy: 0.8889   Valid Loss: 0.2221\n",
      "Epoch 11    Train Accuracy: 0.9174   Train Loss: 0.1815     Valid Accuracy: 0.9072   Valid Loss: 0.1907\n",
      "Epoch 12    Train Accuracy: 0.9167   Train Loss: 0.1772     Valid Accuracy: 0.9094   Valid Loss: 0.1922\n",
      "Epoch 13    Train Accuracy: 0.9217   Train Loss: 0.1662     Valid Accuracy: 0.9033   Valid Loss: 0.2051\n",
      "Epoch 14    Train Accuracy: 0.9254   Train Loss: 0.1615     Valid Accuracy: 0.9078   Valid Loss: 0.1976\n",
      "Epoch 15    Train Accuracy: 0.9165   Train Loss: 0.1749     Valid Accuracy: 0.9067   Valid Loss: 0.1987\n",
      "Epoch 16    Train Accuracy: 0.9352   Train Loss: 0.1493     Valid Accuracy: 0.9011   Valid Loss: 0.2046\n",
      "Epoch 17    Train Accuracy: 0.9278   Train Loss: 0.1562     Valid Accuracy: 0.8883   Valid Loss: 0.2300\n",
      "Epoch 18    Train Accuracy: 0.9404   Train Loss: 0.1375     Valid Accuracy: 0.8944   Valid Loss: 0.2228\n",
      "Epoch 19    Train Accuracy: 0.9483   Train Loss: 0.1267     Valid Accuracy: 0.8900   Valid Loss: 0.2212\n",
      "Epoch 20    Train Accuracy: 0.9539   Train Loss: 0.1133     Valid Accuracy: 0.8911   Valid Loss: 0.2276\n",
      "\n",
      " Best validation accuracy = 0.9094444513320923 \n",
      "\n",
      "\n",
      "Tc guess = 10.0, Test set accuracy = 0.8999999761581421 \n",
      "\n",
      "\n",
      "\n",
      "Epoch 1    Train Accuracy: 0.8581   Train Loss: 0.2643     Valid Accuracy: 0.8744   Valid Loss: 0.2257\n",
      "Epoch 2    Train Accuracy: 0.8874   Train Loss: 0.2268     Valid Accuracy: 0.8944   Valid Loss: 0.2074\n",
      "Epoch 3    Train Accuracy: 0.8913   Train Loss: 0.2118     Valid Accuracy: 0.8900   Valid Loss: 0.2048\n",
      "Epoch 4    Train Accuracy: 0.9020   Train Loss: 0.1966     Valid Accuracy: 0.9111   Valid Loss: 0.1868\n",
      "Epoch 5    Train Accuracy: 0.9044   Train Loss: 0.2014     Valid Accuracy: 0.9089   Valid Loss: 0.1868\n",
      "Epoch 6    Train Accuracy: 0.9044   Train Loss: 0.1917     Valid Accuracy: 0.9022   Valid Loss: 0.1957\n",
      "Epoch 7    Train Accuracy: 0.9072   Train Loss: 0.1878     Valid Accuracy: 0.9017   Valid Loss: 0.1953\n",
      "Epoch 8    Train Accuracy: 0.9107   Train Loss: 0.1813     Valid Accuracy: 0.9006   Valid Loss: 0.2027\n",
      "Epoch 9    Train Accuracy: 0.9156   Train Loss: 0.1767     Valid Accuracy: 0.9006   Valid Loss: 0.1951\n",
      "Epoch 10    Train Accuracy: 0.9220   Train Loss: 0.1697     Valid Accuracy: 0.9083   Valid Loss: 0.1923\n",
      "Epoch 11    Train Accuracy: 0.9257   Train Loss: 0.1619     Valid Accuracy: 0.9089   Valid Loss: 0.1890\n",
      "Epoch 12    Train Accuracy: 0.9278   Train Loss: 0.1547     Valid Accuracy: 0.9100   Valid Loss: 0.1916\n",
      "Epoch 13    Train Accuracy: 0.9319   Train Loss: 0.1521     Valid Accuracy: 0.9011   Valid Loss: 0.2067\n",
      "Epoch 14    Train Accuracy: 0.9252   Train Loss: 0.1598     Valid Accuracy: 0.8972   Valid Loss: 0.2039\n",
      "Epoch 15    Train Accuracy: 0.9348   Train Loss: 0.1461     Valid Accuracy: 0.9033   Valid Loss: 0.2028\n",
      "\n",
      " Best validation accuracy = 0.9111111164093018 \n",
      "\n",
      "\n",
      "Tc guess = 10.5, Test set accuracy = 0.8994444608688354 \n",
      "\n",
      "\n",
      "\n",
      "Epoch 1    Train Accuracy: 0.8856   Train Loss: 0.2413     Valid Accuracy: 0.8933   Valid Loss: 0.2008\n",
      "Epoch 2    Train Accuracy: 0.8954   Train Loss: 0.2071     Valid Accuracy: 0.9072   Valid Loss: 0.1896\n",
      "Epoch 3    Train Accuracy: 0.9037   Train Loss: 0.1913     Valid Accuracy: 0.9072   Valid Loss: 0.1914\n",
      "Epoch 4    Train Accuracy: 0.9115   Train Loss: 0.1839     Valid Accuracy: 0.9150   Valid Loss: 0.1769\n",
      "Epoch 5    Train Accuracy: 0.9144   Train Loss: 0.1793     Valid Accuracy: 0.9150   Valid Loss: 0.1787\n",
      "Epoch 6    Train Accuracy: 0.9161   Train Loss: 0.1771     Valid Accuracy: 0.9078   Valid Loss: 0.2018\n",
      "Epoch 7    Train Accuracy: 0.9174   Train Loss: 0.1742     Valid Accuracy: 0.9144   Valid Loss: 0.1817\n",
      "Epoch 8    Train Accuracy: 0.9215   Train Loss: 0.1679     Valid Accuracy: 0.8911   Valid Loss: 0.2041\n",
      "Epoch 9    Train Accuracy: 0.9272   Train Loss: 0.1586     Valid Accuracy: 0.8906   Valid Loss: 0.2074\n",
      "Epoch 10    Train Accuracy: 0.9257   Train Loss: 0.1576     Valid Accuracy: 0.9056   Valid Loss: 0.1891\n",
      "Epoch 11    Train Accuracy: 0.9322   Train Loss: 0.1444     Valid Accuracy: 0.9144   Valid Loss: 0.1849\n",
      "Epoch 12    Train Accuracy: 0.9372   Train Loss: 0.1387     Valid Accuracy: 0.9039   Valid Loss: 0.1923\n",
      "Epoch 13    Train Accuracy: 0.9376   Train Loss: 0.1365     Valid Accuracy: 0.9156   Valid Loss: 0.1899\n",
      "Epoch 14    Train Accuracy: 0.9361   Train Loss: 0.1380     Valid Accuracy: 0.9094   Valid Loss: 0.1912\n",
      "\n",
      " Best validation accuracy = 0.9155555367469788 \n",
      "\n",
      "\n",
      "Tc guess = 11.0, Test set accuracy = 0.9061111211776733 \n",
      "\n",
      "\n",
      "\n",
      "Epoch 1    Train Accuracy: 0.9272   Train Loss: 0.1928     Valid Accuracy: 0.9367   Valid Loss: 0.1554\n",
      "Epoch 2    Train Accuracy: 0.9326   Train Loss: 0.1608     Valid Accuracy: 0.9400   Valid Loss: 0.1927\n",
      "Epoch 3    Train Accuracy: 0.9328   Train Loss: 0.1528     Valid Accuracy: 0.9367   Valid Loss: 0.1520\n",
      "Epoch 4    Train Accuracy: 0.9330   Train Loss: 0.1494     Valid Accuracy: 0.9372   Valid Loss: 0.1446\n",
      "Epoch 5    Train Accuracy: 0.9359   Train Loss: 0.1423     Valid Accuracy: 0.9361   Valid Loss: 0.1470\n",
      "Epoch 6    Train Accuracy: 0.9393   Train Loss: 0.1373     Valid Accuracy: 0.9367   Valid Loss: 0.1491\n",
      "Epoch 7    Train Accuracy: 0.9376   Train Loss: 0.1410     Valid Accuracy: 0.9367   Valid Loss: 0.1732\n",
      "Epoch 8    Train Accuracy: 0.9404   Train Loss: 0.1318     Valid Accuracy: 0.9367   Valid Loss: 0.1465\n",
      "Epoch 9    Train Accuracy: 0.9435   Train Loss: 0.1274     Valid Accuracy: 0.9383   Valid Loss: 0.1461\n",
      "Epoch 10    Train Accuracy: 0.9404   Train Loss: 0.1307     Valid Accuracy: 0.9417   Valid Loss: 0.1518\n",
      "Epoch 11    Train Accuracy: 0.9469   Train Loss: 0.1209     Valid Accuracy: 0.9411   Valid Loss: 0.1465\n",
      "Epoch 12    Train Accuracy: 0.9504   Train Loss: 0.1161     Valid Accuracy: 0.9322   Valid Loss: 0.1529\n",
      "Epoch 13    Train Accuracy: 0.9500   Train Loss: 0.1187     Valid Accuracy: 0.9411   Valid Loss: 0.1497\n",
      "Epoch 14    Train Accuracy: 0.9502   Train Loss: 0.1136     Valid Accuracy: 0.9389   Valid Loss: 0.1525\n",
      "\n",
      " Best validation accuracy = 0.9416666626930237 \n",
      "\n",
      "\n",
      "Tc guess = 11.5, Test set accuracy = 0.945555567741394 \n",
      "\n",
      "\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1    Train Accuracy: 0.9941   Train Loss: 0.0096     Valid Accuracy: 1.0000   Valid Loss: 0.0000\n",
      "Epoch 2    Train Accuracy: 1.0000   Train Loss: 0.0000     Valid Accuracy: 1.0000   Valid Loss: 0.0000\n",
      "Epoch 3    Train Accuracy: 1.0000   Train Loss: 0.0001     Valid Accuracy: 1.0000   Valid Loss: 0.0001\n",
      "Epoch 4    Train Accuracy: 1.0000   Train Loss: 0.0001     Valid Accuracy: 1.0000   Valid Loss: 0.0001\n",
      "Epoch 5    Train Accuracy: 1.0000   Train Loss: 0.0001     Valid Accuracy: 1.0000   Valid Loss: 0.0001\n",
      "Epoch 6    Train Accuracy: 1.0000   Train Loss: 0.0001     Valid Accuracy: 1.0000   Valid Loss: 0.0001\n",
      "Epoch 7    Train Accuracy: 1.0000   Train Loss: 0.0001     Valid Accuracy: 1.0000   Valid Loss: 0.0001\n",
      "Epoch 8    Train Accuracy: 1.0000   Train Loss: 0.0001     Valid Accuracy: 1.0000   Valid Loss: 0.0001\n",
      "Epoch 9    Train Accuracy: 1.0000   Train Loss: 0.0001     Valid Accuracy: 1.0000   Valid Loss: 0.0001\n",
      "Epoch 10    Train Accuracy: 1.0000   Train Loss: 0.0001     Valid Accuracy: 1.0000   Valid Loss: 0.0001\n",
      "Epoch 11    Train Accuracy: 1.0000   Train Loss: 0.0001     Valid Accuracy: 1.0000   Valid Loss: 0.0001\n",
      "\n",
      " Best validation accuracy = 1.0 \n",
      "\n",
      "\n",
      "Tc guess = 12.0, Test set accuracy = 1.0 \n",
      "\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "test_accuracies = []\n",
    "\n",
    "for Tc in Tc_values:\n",
    "    \n",
    "    if Tc == T_max:\n",
    "        y_train_array = (T_train_array <= Tc).astype(int)\n",
    "        y_test_array = (T_test_array <= Tc).astype(int)\n",
    "        y_val_array = (T_val_array <= Tc).astype(int)\n",
    "    else:\n",
    "        y_train_array = (T_train_array < Tc).astype(int)\n",
    "        y_test_array = (T_test_array < Tc).astype(int)\n",
    "        y_val_array = (T_val_array < Tc).astype(int)\n",
    "    \n",
    "    \n",
    "    X_train = torch.tensor(X_train_array, dtype=torch.float32)\n",
    "    X_test = torch.tensor(X_test_array, dtype=torch.float32)\n",
    "    X_val = torch.tensor(X_val_array, dtype=torch.float32)\n",
    "    y_train = torch.tensor(y_train_array, dtype=torch.float32)\n",
    "    y_test = torch.tensor(y_test_array, dtype=torch.float32)\n",
    "    y_val = torch.tensor(y_val_array, dtype=torch.float32)\n",
    "    \n",
    "    train_ds = TensorDataset(X_train, y_train)\n",
    "    valid_ds = TensorDataset(X_val, y_val)\n",
    "    \n",
    "    batch_size = 32\n",
    "    train_dl = DataLoader(train_ds, batch_size, shuffle=True)\n",
    "    valid_dl = DataLoader(valid_ds, batch_size, shuffle=True)\n",
    "    \n",
    "    model = nn.Sequential(\n",
    "\n",
    "        nn.Conv2d(in_channels=1, out_channels=32, kernel_size=3, padding=1),\n",
    "        nn.ReLU(),\n",
    "        nn.MaxPool2d(kernel_size=2),\n",
    "        nn.Conv2d(in_channels=32, out_channels=64, kernel_size=3, padding=1),\n",
    "        nn.ReLU(),\n",
    "        nn.MaxPool2d(kernel_size=2),\n",
    "        nn.Flatten(),\n",
    "        nn.Linear(576, 256),\n",
    "        nn.ReLU(),\n",
    "        nn.Dropout(p=0.1),\n",
    "        nn.Linear(256, 1),\n",
    "        nn.Sigmoid()\n",
    "\n",
    "    )\n",
    "    \n",
    "    loss_fn = nn.BCELoss()\n",
    "    optimizer = torch.optim.Adam(model.parameters(), lr=0.001, weight_decay=0.001)  \n",
    "    \n",
    "    num_epochs = 20\n",
    "    torch.manual_seed(1)\n",
    "    \n",
    "    loss_hist_train, accuracy_hist_train, loss_hist_valid, accuracy_hist_valid, best_model = train(model, num_epochs, train_dl, valid_dl)\n",
    "    \n",
    "    pred = best_model(X_test)[:, 0]\n",
    "    is_correct = ((pred >= 0.5).float() == y_test).int()\n",
    "    test_accuracy = (is_correct.sum() / is_correct.shape[0]).item()\n",
    "    print(f'Tc guess = {Tc}, Test set accuracy = {test_accuracy} \\n\\n\\n')\n",
    "    \n",
    "    test_accuracies.append(test_accuracy)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f10b0958",
   "metadata": {},
   "source": [
    "### 6. Result: Classification accuracy vs. $\\beta_c$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "b63f9df8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 450x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "beta_c_estimate = Tc_values[2:-2][np.argmax(test_accuracies[2:-2])]\n",
    "\n",
    "plt.figure(figsize=(4.5, 5))\n",
    "plt.plot(Tc_values, test_accuracies, '--o', label=r'$n_s=50$')\n",
    "plt.grid(alpha=0.1)\n",
    "plt.axvline(x=beta_c_estimate, linestyle='dotted', color='red')\n",
    "plt.legend(frameon=True, edgecolor='k', fontsize=12)\n",
    "plt.text(x=beta_c_estimate+0.3, y=0.99, s=r'$\\beta_c$' + f' estimate: {beta_c_estimate}')\n",
    "plt.title('Phonon position snapshots ' + r'$\\{ x_{i} \\} $' +  '\\n (every ' + r'$n_s$' + ' measurement sweeps)')\n",
    "plt.ylabel('Accuracy', fontsize=16)\n",
    "plt.xlabel(r'$\\beta_c$', fontsize=16)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88887a4a",
   "metadata": {},
   "source": [
    "Here we observe the characteristic $W$ peak expected in the LBC method. It occurs at $\\beta_c \\approx 6$, which agrees quite well with the value known for the square lattice Holstein model ($\\beta_c = 6.0 \\pm 0.1$) [[Phys. Rev. Lett. 120, 187003]](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.120.187003). \n",
    "\n",
    "However, snapshots of the phonon field are just one set of measurements we can take during a Quantum Monte Carlo simulation of the Holstein model. What kind of measurements work best for discovering the critical point? In another notebook, <b>Methodology_and_Results.ipynb</b>, we explore the efficacy of various sets of training data in locating the phase transition with confusion scheme learning."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d72744b2",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}