diff --git a/Notebooks/Chap08/8_3_Double_Descent.ipynb b/Notebooks/Chap08/8_3_Double_Descent.ipynb
index f60f12f1..aaac87e5 100644
--- a/Notebooks/Chap08/8_3_Double_Descent.ipynb
+++ b/Notebooks/Chap08/8_3_Double_Descent.ipynb
@@ -4,8 +4,7 @@
"metadata": {
"colab": {
"provenance": [],
- "gpuType": "T4",
- "include_colab_link": true
+ "gpuType": "T4"
},
"kernelspec": {
"name": "python3",
@@ -17,16 +16,6 @@
"accelerator": "GPU"
},
"cells": [
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "view-in-github",
- "colab_type": "text"
- },
- "source": [
- ""
- ]
- },
{
"cell_type": "markdown",
"source": [
@@ -51,10 +40,45 @@
"!pip install git+https://github.com/greydanus/mnist1d"
],
"metadata": {
- "id": "fn9BP5N5TguP"
+ "id": "fn9BP5N5TguP",
+ "outputId": "3ba15b8f-2395-4b1a-8a66-8ed80e9b5138",
+ "colab": {
+ "base_uri": "https://localhost:8080/"
+ }
},
- "execution_count": null,
- "outputs": []
+ "execution_count": 29,
+ "outputs": [
+ {
+ "output_type": "stream",
+ "name": "stdout",
+ "text": [
+ "Collecting git+https://github.com/greydanus/mnist1d\n",
+ " Cloning https://github.com/greydanus/mnist1d to /tmp/pip-req-build-cbhxd1j8\n",
+ " Running command git clone --filter=blob:none --quiet https://github.com/greydanus/mnist1d /tmp/pip-req-build-cbhxd1j8\n",
+ " Resolved https://github.com/greydanus/mnist1d to commit 350929d12f4c9a4b7355e0c96604e41b9239bdb4\n",
+ " Installing build dependencies ... \u001b[?25l\u001b[?25hdone\n",
+ " Getting requirements to build wheel ... \u001b[?25l\u001b[?25hdone\n",
+ " Preparing metadata (pyproject.toml) ... \u001b[?25l\u001b[?25hdone\n",
+ "Requirement already satisfied: requests in /usr/local/lib/python3.10/dist-packages (from mnist1d==0.0.2.post9) (2.31.0)\n",
+ "Requirement already satisfied: numpy in /usr/local/lib/python3.10/dist-packages (from mnist1d==0.0.2.post9) (1.25.2)\n",
+ "Requirement already satisfied: matplotlib in /usr/local/lib/python3.10/dist-packages (from mnist1d==0.0.2.post9) (3.7.1)\n",
+ "Requirement already satisfied: scipy in /usr/local/lib/python3.10/dist-packages (from mnist1d==0.0.2.post9) (1.11.4)\n",
+ "Requirement already satisfied: contourpy>=1.0.1 in /usr/local/lib/python3.10/dist-packages (from matplotlib->mnist1d==0.0.2.post9) (1.2.1)\n",
+ "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.10/dist-packages (from matplotlib->mnist1d==0.0.2.post9) (0.12.1)\n",
+ "Requirement already satisfied: fonttools>=4.22.0 in /usr/local/lib/python3.10/dist-packages (from matplotlib->mnist1d==0.0.2.post9) (4.53.0)\n",
+ "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.10/dist-packages (from matplotlib->mnist1d==0.0.2.post9) (1.4.5)\n",
+ "Requirement already satisfied: packaging>=20.0 in /usr/local/lib/python3.10/dist-packages (from matplotlib->mnist1d==0.0.2.post9) (24.1)\n",
+ "Requirement already satisfied: pillow>=6.2.0 in /usr/local/lib/python3.10/dist-packages (from matplotlib->mnist1d==0.0.2.post9) (9.4.0)\n",
+ "Requirement already satisfied: pyparsing>=2.3.1 in /usr/local/lib/python3.10/dist-packages (from matplotlib->mnist1d==0.0.2.post9) (3.1.2)\n",
+ "Requirement already satisfied: python-dateutil>=2.7 in /usr/local/lib/python3.10/dist-packages (from matplotlib->mnist1d==0.0.2.post9) (2.8.2)\n",
+ "Requirement already satisfied: charset-normalizer<4,>=2 in /usr/local/lib/python3.10/dist-packages (from requests->mnist1d==0.0.2.post9) (3.3.2)\n",
+ "Requirement already satisfied: idna<4,>=2.5 in /usr/local/lib/python3.10/dist-packages (from requests->mnist1d==0.0.2.post9) (3.7)\n",
+ "Requirement already satisfied: urllib3<3,>=1.21.1 in /usr/local/lib/python3.10/dist-packages (from requests->mnist1d==0.0.2.post9) (2.0.7)\n",
+ "Requirement already satisfied: certifi>=2017.4.17 in /usr/local/lib/python3.10/dist-packages (from requests->mnist1d==0.0.2.post9) (2024.6.2)\n",
+ "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.10/dist-packages (from python-dateutil>=2.7->matplotlib->mnist1d==0.0.2.post9) (1.16.0)\n"
+ ]
+ }
+ ]
},
{
"cell_type": "code",
@@ -73,10 +97,22 @@
"print('Using:', DEVICE)"
],
"metadata": {
- "id": "hFxuHpRqTgri"
+ "id": "hFxuHpRqTgri",
+ "outputId": "2a246d1e-8568-4605-df0a-28dad08935ec",
+ "colab": {
+ "base_uri": "https://localhost:8080/"
+ }
},
- "execution_count": null,
- "outputs": []
+ "execution_count": 30,
+ "outputs": [
+ {
+ "output_type": "stream",
+ "name": "stdout",
+ "text": [
+ "Using: cuda\n"
+ ]
+ }
+ ]
},
{
"cell_type": "code",
@@ -99,13 +135,28 @@
"# data['x'], data['y'], data['x_test'], and data['y_test']\n",
"print(\"Examples in training set: {}\".format(len(data['y'])))\n",
"print(\"Examples in test set: {}\".format(len(data['y_test'])))\n",
- "print(\"Length of each example: {}\".format(data['x'].shape[-1]))"
+ "print(\"Dimensionality of each example: {}\".format(data['x'].shape[-1]))"
],
"metadata": {
- "id": "PW2gyXL5UkLU"
+ "id": "PW2gyXL5UkLU",
+ "outputId": "a4186965-3025-4d00-b780-441baab421de",
+ "colab": {
+ "base_uri": "https://localhost:8080/"
+ }
},
- "execution_count": null,
- "outputs": []
+ "execution_count": 31,
+ "outputs": [
+ {
+ "output_type": "stream",
+ "name": "stdout",
+ "text": [
+ "Did or could not load data from ./mnist1d_data.pkl. Rebuilding dataset...\n",
+ "Examples in training set: 4000\n",
+ "Examples in test set: 4000\n",
+ "Dimensionality of each example: 40\n"
+ ]
+ }
+ ]
},
{
"cell_type": "code",
@@ -141,13 +192,13 @@
"metadata": {
"id": "hAIvZOAlTnk9"
},
- "execution_count": null,
+ "execution_count": 32,
"outputs": []
},
{
"cell_type": "code",
"source": [
- "def fit_model(model, data):\n",
+ "def fit_model(model, data, n_epoch):\n",
"\n",
" # choose cross entropy loss function (equation 5.24)\n",
" loss_function = torch.nn.CrossEntropyLoss()\n",
@@ -164,9 +215,6 @@
" # load the data into a class that creates the batches\n",
" data_loader = DataLoader(TensorDataset(x_train,y_train), batch_size=100, shuffle=True, worker_init_fn=np.random.seed(1))\n",
"\n",
- " # loop over the dataset n_epoch times\n",
- " n_epoch = 1000\n",
- "\n",
" for epoch in range(n_epoch):\n",
" # loop over batches\n",
" for i, batch in enumerate(data_loader):\n",
@@ -200,7 +248,19 @@
"metadata": {
"id": "AazlQhheWmHk"
},
- "execution_count": null,
+ "execution_count": 33,
+ "outputs": []
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "def count_parameters(model):\n",
+ " return sum(p.numel() for p in model.parameters() if p.requires_grad)"
+ ],
+ "metadata": {
+ "id": "AQNCmFNV6JpV"
+ },
+ "execution_count": 34,
"outputs": []
},
{
@@ -226,42 +286,333 @@
"# This code will take a while (~30 mins on GPU) to run! Go and make a cup of coffee!\n",
"\n",
"hidden_variables = np.array([2,4,6,8,10,14,18,22,26,30,35,40,45,50,55,60,70,80,90,100,120,140,160,180,200,250,300,400]) ;\n",
+ "\n",
"errors_train_all = np.zeros_like(hidden_variables)\n",
"errors_test_all = np.zeros_like(hidden_variables)\n",
+ "total_weights_all = np.zeros_like(hidden_variables)\n",
+ "\n",
+ "# loop over the dataset n_epoch times\n",
+ "n_epoch = 1000\n",
"\n",
"# For each hidden variable size\n",
"for c_hidden in range(len(hidden_variables)):\n",
" print(f'Training model with {hidden_variables[c_hidden]:3d} hidden variables')\n",
" # Get a model\n",
" model = get_model(hidden_variables[c_hidden]) ;\n",
+ " # Count and store number of weights\n",
+ " total_weights_all[c_hidden] = count_parameters(model)\n",
" # Train the model\n",
- " errors_train, errors_test = fit_model(model, data)\n",
+ " errors_train, errors_test = fit_model(model, data, n_epoch)\n",
" # Store the results\n",
" errors_train_all[c_hidden] = errors_train\n",
- " errors_test_all[c_hidden]= errors_test"
+ " errors_test_all[c_hidden]= errors_test\n",
+ "\n",
+ ""
],
"metadata": {
- "id": "K4OmBZGHWXpk"
+ "id": "K4OmBZGHWXpk",
+ "outputId": "62a7aaf0-793a-4ab2-960e-c1127f15717c",
+ "colab": {
+ "base_uri": "https://localhost:8080/"
+ }
},
- "execution_count": null,
- "outputs": []
+ "execution_count": 35,
+ "outputs": [
+ {
+ "output_type": "stream",
+ "name": "stdout",
+ "text": [
+ "Training model with 2 hidden variables\n",
+ "Epoch 0, train loss 2.280202, train error 89.05, test loss 2.276196, test error 89.18\n",
+ "Epoch 100, train loss 1.925899, train error 71.75, test loss 1.761014, test error 70.57\n",
+ "Epoch 200, train loss 1.912995, train error 71.20, test loss 1.747572, test error 69.07\n",
+ "Epoch 300, train loss 1.908751, train error 71.32, test loss 1.741206, test error 69.07\n",
+ "Epoch 400, train loss 1.906859, train error 71.05, test loss 1.737478, test error 70.00\n",
+ "Epoch 500, train loss 1.906671, train error 71.43, test loss 1.732123, test error 68.95\n",
+ "Epoch 600, train loss 1.903380, train error 71.28, test loss 1.741086, test error 69.65\n",
+ "Epoch 700, train loss 1.902236, train error 70.88, test loss 1.733666, test error 69.22\n",
+ "Epoch 800, train loss 1.903633, train error 71.88, test loss 1.734591, test error 70.57\n",
+ "Epoch 900, train loss 1.901804, train error 71.03, test loss 1.742573, test error 68.10\n",
+ "Training model with 4 hidden variables\n",
+ "Epoch 0, train loss 2.267358, train error 86.97, test loss 2.269902, test error 87.62\n",
+ "Epoch 100, train loss 1.716064, train error 62.22, test loss 1.519437, test error 58.25\n",
+ "Epoch 200, train loss 1.705652, train error 61.88, test loss 1.507422, test error 58.40\n",
+ "Epoch 300, train loss 1.696660, train error 60.62, test loss 1.507704, test error 57.58\n",
+ "Epoch 400, train loss 1.691092, train error 61.60, test loss 1.499592, test error 56.85\n",
+ "Epoch 500, train loss 1.684060, train error 61.05, test loss 1.513196, test error 57.95\n",
+ "Epoch 600, train loss 1.677890, train error 61.10, test loss 1.504343, test error 56.85\n",
+ "Epoch 700, train loss 1.677930, train error 61.10, test loss 1.509796, test error 58.15\n",
+ "Epoch 800, train loss 1.676683, train error 61.17, test loss 1.506790, test error 58.28\n",
+ "Epoch 900, train loss 1.676809, train error 61.53, test loss 1.505417, test error 57.72\n",
+ "Training model with 6 hidden variables\n",
+ "Epoch 0, train loss 2.290775, train error 89.18, test loss 2.284365, test error 87.57\n",
+ "Epoch 100, train loss 1.634348, train error 58.42, test loss 1.467763, test error 55.67\n",
+ "Epoch 200, train loss 1.602023, train error 57.25, test loss 1.456007, test error 55.38\n",
+ "Epoch 300, train loss 1.587963, train error 56.50, test loss 1.453522, test error 55.33\n",
+ "Epoch 400, train loss 1.587952, train error 56.55, test loss 1.453863, test error 54.92\n",
+ "Epoch 500, train loss 1.579495, train error 56.42, test loss 1.452398, test error 55.40\n",
+ "Epoch 600, train loss 1.590881, train error 56.67, test loss 1.473001, test error 56.28\n",
+ "Epoch 700, train loss 1.581218, train error 56.58, test loss 1.470745, test error 55.90\n",
+ "Epoch 800, train loss 1.575105, train error 56.30, test loss 1.455353, test error 55.92\n",
+ "Epoch 900, train loss 1.579539, train error 56.15, test loss 1.449462, test error 55.67\n",
+ "Training model with 8 hidden variables\n",
+ "Epoch 0, train loss 2.278947, train error 85.18, test loss 2.266557, test error 84.68\n",
+ "Epoch 100, train loss 1.593652, train error 55.60, test loss 1.449531, test error 56.00\n",
+ "Epoch 200, train loss 1.557044, train error 53.92, test loss 1.453447, test error 55.03\n",
+ "Epoch 300, train loss 1.544829, train error 53.38, test loss 1.457726, test error 55.22\n",
+ "Epoch 400, train loss 1.538902, train error 54.05, test loss 1.456941, test error 55.33\n",
+ "Epoch 500, train loss 1.538077, train error 54.28, test loss 1.469433, test error 56.20\n",
+ "Epoch 600, train loss 1.529778, train error 53.60, test loss 1.470659, test error 55.72\n",
+ "Epoch 700, train loss 1.522470, train error 53.42, test loss 1.476947, test error 55.95\n",
+ "Epoch 800, train loss 1.520377, train error 53.22, test loss 1.481796, test error 56.55\n",
+ "Epoch 900, train loss 1.522042, train error 53.42, test loss 1.489359, test error 56.15\n",
+ "Training model with 10 hidden variables\n",
+ "Epoch 0, train loss 2.250067, train error 83.80, test loss 2.238750, test error 81.28\n",
+ "Epoch 100, train loss 1.570056, train error 55.80, test loss 1.444564, test error 54.62\n",
+ "Epoch 200, train loss 1.512308, train error 53.33, test loss 1.417375, test error 53.70\n",
+ "Epoch 300, train loss 1.485546, train error 52.62, test loss 1.415674, test error 53.62\n",
+ "Epoch 400, train loss 1.465965, train error 50.22, test loss 1.415631, test error 52.95\n",
+ "Epoch 500, train loss 1.450910, train error 50.50, test loss 1.412722, test error 52.70\n",
+ "Epoch 600, train loss 1.437163, train error 49.65, test loss 1.409063, test error 52.92\n",
+ "Epoch 700, train loss 1.430005, train error 49.38, test loss 1.402299, test error 52.83\n",
+ "Epoch 800, train loss 1.420938, train error 49.17, test loss 1.398151, test error 52.22\n",
+ "Epoch 900, train loss 1.417372, train error 49.25, test loss 1.407553, test error 52.58\n",
+ "Training model with 14 hidden variables\n",
+ "Epoch 0, train loss 2.250147, train error 84.45, test loss 2.224496, test error 83.50\n",
+ "Epoch 100, train loss 1.467325, train error 49.22, test loss 1.371005, test error 51.35\n",
+ "Epoch 200, train loss 1.371697, train error 46.47, test loss 1.341893, test error 49.60\n",
+ "Epoch 300, train loss 1.338310, train error 45.25, test loss 1.345958, test error 49.47\n",
+ "Epoch 400, train loss 1.329984, train error 44.95, test loss 1.364456, test error 49.85\n",
+ "Epoch 500, train loss 1.312067, train error 44.70, test loss 1.368620, test error 49.67\n",
+ "Epoch 600, train loss 1.307369, train error 44.00, test loss 1.383248, test error 49.97\n",
+ "Epoch 700, train loss 1.302358, train error 44.10, test loss 1.384645, test error 49.78\n",
+ "Epoch 800, train loss 1.309552, train error 44.42, test loss 1.399194, test error 50.60\n",
+ "Epoch 900, train loss 1.305113, train error 43.70, test loss 1.416064, test error 51.28\n",
+ "Training model with 18 hidden variables\n",
+ "Epoch 0, train loss 2.159715, train error 80.35, test loss 2.139665, test error 80.20\n",
+ "Epoch 100, train loss 1.385202, train error 47.75, test loss 1.362450, test error 51.58\n",
+ "Epoch 200, train loss 1.265389, train error 43.55, test loss 1.335479, test error 49.20\n",
+ "Epoch 300, train loss 1.224858, train error 41.67, test loss 1.384820, test error 48.47\n",
+ "Epoch 400, train loss 1.186068, train error 40.70, test loss 1.428581, test error 49.33\n",
+ "Epoch 500, train loss 1.167748, train error 39.30, test loss 1.472766, test error 49.95\n",
+ "Epoch 600, train loss 1.160923, train error 38.45, test loss 1.499211, test error 50.65\n",
+ "Epoch 700, train loss 1.145295, train error 38.40, test loss 1.528852, test error 50.67\n",
+ "Epoch 800, train loss 1.141608, train error 38.08, test loss 1.569496, test error 51.33\n",
+ "Epoch 900, train loss 1.132156, train error 38.22, test loss 1.602549, test error 51.35\n",
+ "Training model with 22 hidden variables\n",
+ "Epoch 0, train loss 2.211529, train error 79.80, test loss 2.206877, test error 79.95\n",
+ "Epoch 100, train loss 1.282252, train error 42.90, test loss 1.323739, test error 48.38\n",
+ "Epoch 200, train loss 1.161285, train error 38.65, test loss 1.423607, test error 50.78\n",
+ "Epoch 300, train loss 1.103865, train error 36.65, test loss 1.482603, test error 50.70\n",
+ "Epoch 400, train loss 1.070859, train error 36.42, test loss 1.543965, test error 51.38\n",
+ "Epoch 500, train loss 1.044615, train error 34.82, test loss 1.574064, test error 51.38\n",
+ "Epoch 600, train loss 1.030322, train error 34.82, test loss 1.633871, test error 51.47\n",
+ "Epoch 700, train loss 1.016668, train error 33.93, test loss 1.711600, test error 52.30\n",
+ "Epoch 800, train loss 0.997430, train error 32.82, test loss 1.763077, test error 52.95\n",
+ "Epoch 900, train loss 1.001320, train error 33.82, test loss 1.814692, test error 52.95\n",
+ "Training model with 26 hidden variables\n",
+ "Epoch 0, train loss 2.200904, train error 81.43, test loss 2.190686, test error 80.72\n",
+ "Epoch 100, train loss 1.189043, train error 39.80, test loss 1.398701, test error 51.97\n",
+ "Epoch 200, train loss 1.032893, train error 34.72, test loss 1.504426, test error 52.15\n",
+ "Epoch 300, train loss 0.975272, train error 33.55, test loss 1.621815, test error 53.30\n",
+ "Epoch 400, train loss 0.939880, train error 32.05, test loss 1.739801, test error 54.03\n",
+ "Epoch 500, train loss 0.907610, train error 30.85, test loss 1.822161, test error 54.30\n",
+ "Epoch 600, train loss 0.893433, train error 30.55, test loss 1.929679, test error 54.80\n",
+ "Epoch 700, train loss 0.864689, train error 29.20, test loss 1.968643, test error 54.75\n",
+ "Epoch 800, train loss 0.847545, train error 28.82, test loss 2.045258, test error 54.97\n",
+ "Epoch 900, train loss 0.843597, train error 28.97, test loss 2.113636, test error 55.55\n",
+ "Training model with 30 hidden variables\n",
+ "Epoch 0, train loss 2.105095, train error 78.75, test loss 2.046595, test error 77.50\n",
+ "Epoch 100, train loss 1.139368, train error 36.85, test loss 1.384092, test error 50.33\n",
+ "Epoch 200, train loss 0.948281, train error 31.70, test loss 1.521346, test error 50.53\n",
+ "Epoch 300, train loss 0.866517, train error 28.10, test loss 1.689052, test error 51.30\n",
+ "Epoch 400, train loss 0.822552, train error 26.95, test loss 1.871116, test error 53.58\n",
+ "Epoch 500, train loss 0.793155, train error 26.53, test loss 2.016083, test error 53.45\n",
+ "Epoch 600, train loss 0.747390, train error 25.15, test loss 2.175583, test error 54.60\n",
+ "Epoch 700, train loss 0.739243, train error 24.82, test loss 2.375611, test error 55.90\n",
+ "Epoch 800, train loss 0.705187, train error 23.97, test loss 2.521607, test error 56.12\n",
+ "Epoch 900, train loss 0.678345, train error 22.30, test loss 2.623145, test error 56.05\n",
+ "Training model with 35 hidden variables\n",
+ "Epoch 0, train loss 2.133684, train error 77.95, test loss 2.105965, test error 78.03\n",
+ "Epoch 100, train loss 1.025999, train error 34.07, test loss 1.387318, test error 49.42\n",
+ "Epoch 200, train loss 0.801432, train error 27.22, test loss 1.734866, test error 52.33\n",
+ "Epoch 300, train loss 0.665120, train error 22.30, test loss 2.111001, test error 54.28\n",
+ "Epoch 400, train loss 0.603412, train error 20.30, test loss 2.516824, test error 55.53\n",
+ "Epoch 500, train loss 0.557454, train error 19.50, test loss 2.875285, test error 55.90\n",
+ "Epoch 600, train loss 0.541823, train error 18.70, test loss 3.230060, test error 56.78\n",
+ "Epoch 700, train loss 0.489021, train error 16.43, test loss 3.542463, test error 56.67\n",
+ "Epoch 800, train loss 0.487397, train error 16.50, test loss 3.868127, test error 56.67\n",
+ "Epoch 900, train loss 0.452621, train error 15.62, test loss 4.107164, test error 57.90\n",
+ "Training model with 40 hidden variables\n",
+ "Epoch 0, train loss 2.131664, train error 78.45, test loss 2.104819, test error 79.57\n",
+ "Epoch 100, train loss 0.916092, train error 29.90, test loss 1.443106, test error 50.62\n",
+ "Epoch 200, train loss 0.637736, train error 20.70, test loss 1.931214, test error 52.22\n",
+ "Epoch 300, train loss 0.477490, train error 15.45, test loss 2.592646, test error 54.35\n",
+ "Epoch 400, train loss 0.375117, train error 11.97, test loss 3.317954, test error 55.75\n",
+ "Epoch 500, train loss 0.320583, train error 10.82, test loss 4.105999, test error 56.25\n",
+ "Epoch 600, train loss 0.282808, train error 9.62, test loss 4.787386, test error 56.17\n",
+ "Epoch 700, train loss 0.270115, train error 9.78, test loss 5.615366, test error 57.00\n",
+ "Epoch 800, train loss 0.271310, train error 10.05, test loss 6.246390, test error 56.17\n",
+ "Epoch 900, train loss 0.298141, train error 11.35, test loss 6.893893, test error 56.62\n",
+ "Training model with 45 hidden variables\n",
+ "Epoch 0, train loss 2.124081, train error 78.05, test loss 2.105962, test error 77.93\n",
+ "Epoch 100, train loss 0.826444, train error 26.68, test loss 1.503941, test error 49.47\n",
+ "Epoch 200, train loss 0.488764, train error 15.75, test loss 2.213665, test error 52.97\n",
+ "Epoch 300, train loss 0.339090, train error 11.00, test loss 3.221352, test error 54.25\n",
+ "Epoch 400, train loss 0.239335, train error 8.18, test loss 4.424680, test error 55.75\n",
+ "Epoch 500, train loss 0.163451, train error 4.93, test loss 5.617220, test error 55.38\n",
+ "Epoch 600, train loss 0.099984, train error 3.05, test loss 6.670816, test error 55.85\n",
+ "Epoch 700, train loss 0.015253, train error 0.00, test loss 7.652980, test error 55.70\n",
+ "Epoch 800, train loss 0.008259, train error 0.00, test loss 8.460521, test error 55.85\n",
+ "Epoch 900, train loss 0.005923, train error 0.00, test loss 8.991735, test error 55.92\n",
+ "Training model with 50 hidden variables\n",
+ "Epoch 0, train loss 2.164114, train error 78.28, test loss 2.153555, test error 78.55\n",
+ "Epoch 100, train loss 0.760776, train error 23.62, test loss 1.521621, test error 49.42\n",
+ "Epoch 200, train loss 0.388589, train error 11.07, test loss 2.433003, test error 52.42\n",
+ "Epoch 300, train loss 0.212128, train error 5.60, test loss 3.755425, test error 54.70\n",
+ "Epoch 400, train loss 0.101783, train error 2.12, test loss 5.258374, test error 55.00\n",
+ "Epoch 500, train loss 0.024106, train error 0.03, test loss 6.485045, test error 56.25\n",
+ "Epoch 600, train loss 0.010166, train error 0.00, test loss 7.247528, test error 56.03\n",
+ "Epoch 700, train loss 0.007013, train error 0.00, test loss 7.764050, test error 56.17\n",
+ "Epoch 800, train loss 0.005290, train error 0.00, test loss 8.180995, test error 56.25\n",
+ "Epoch 900, train loss 0.004218, train error 0.00, test loss 8.507399, test error 56.30\n",
+ "Training model with 60 hidden variables\n",
+ "Epoch 0, train loss 2.054841, train error 76.82, test loss 2.010036, test error 77.35\n",
+ "Epoch 100, train loss 0.533140, train error 15.78, test loss 1.685822, test error 50.55\n",
+ "Epoch 200, train loss 0.092306, train error 0.62, test loss 3.330975, test error 53.12\n",
+ "Epoch 300, train loss 0.018351, train error 0.00, test loss 4.631015, test error 54.05\n",
+ "Epoch 400, train loss 0.008906, train error 0.00, test loss 5.276160, test error 54.12\n",
+ "Epoch 500, train loss 0.005695, train error 0.00, test loss 5.702274, test error 54.15\n",
+ "Epoch 600, train loss 0.004078, train error 0.00, test loss 6.026574, test error 54.28\n",
+ "Epoch 700, train loss 0.003147, train error 0.00, test loss 6.281788, test error 54.22\n",
+ "Epoch 800, train loss 0.002537, train error 0.00, test loss 6.493565, test error 54.30\n",
+ "Epoch 900, train loss 0.002114, train error 0.00, test loss 6.669685, test error 54.45\n",
+ "Training model with 80 hidden variables\n",
+ "Epoch 0, train loss 2.028571, train error 74.40, test loss 1.985185, test error 75.28\n",
+ "Epoch 100, train loss 0.244489, train error 4.47, test loss 2.115000, test error 51.50\n",
+ "Epoch 200, train loss 0.020814, train error 0.00, test loss 3.415434, test error 51.40\n",
+ "Epoch 300, train loss 0.008094, train error 0.00, test loss 3.970142, test error 51.72\n",
+ "Epoch 400, train loss 0.004785, train error 0.00, test loss 4.299542, test error 51.83\n",
+ "Epoch 500, train loss 0.003310, train error 0.00, test loss 4.534029, test error 51.70\n",
+ "Epoch 600, train loss 0.002490, train error 0.00, test loss 4.716822, test error 51.78\n",
+ "Epoch 700, train loss 0.001978, train error 0.00, test loss 4.864742, test error 51.75\n",
+ "Epoch 800, train loss 0.001629, train error 0.00, test loss 4.988203, test error 51.80\n",
+ "Epoch 900, train loss 0.001378, train error 0.00, test loss 5.096081, test error 51.78\n",
+ "Training model with 120 hidden variables\n",
+ "Epoch 0, train loss 1.962679, train error 72.30, test loss 1.879106, test error 71.68\n",
+ "Epoch 100, train loss 0.048203, train error 0.00, test loss 2.235627, test error 49.70\n",
+ "Epoch 200, train loss 0.009333, train error 0.00, test loss 2.851372, test error 49.85\n",
+ "Epoch 300, train loss 0.004629, train error 0.00, test loss 3.129520, test error 49.95\n",
+ "Epoch 400, train loss 0.002970, train error 0.00, test loss 3.309089, test error 49.83\n",
+ "Epoch 500, train loss 0.002143, train error 0.00, test loss 3.442119, test error 49.92\n",
+ "Epoch 600, train loss 0.001658, train error 0.00, test loss 3.548133, test error 49.80\n",
+ "Epoch 700, train loss 0.001341, train error 0.00, test loss 3.635033, test error 49.72\n",
+ "Epoch 800, train loss 0.001120, train error 0.00, test loss 3.709674, test error 49.72\n",
+ "Epoch 900, train loss 0.000957, train error 0.00, test loss 3.774692, test error 49.65\n",
+ "Training model with 200 hidden variables\n",
+ "Epoch 0, train loss 1.913651, train error 70.00, test loss 1.842174, test error 72.20\n",
+ "Epoch 100, train loss 0.021130, train error 0.00, test loss 1.918857, test error 46.60\n",
+ "Epoch 200, train loss 0.006089, train error 0.00, test loss 2.209828, test error 46.88\n",
+ "Epoch 300, train loss 0.003314, train error 0.00, test loss 2.356240, test error 46.92\n",
+ "Epoch 400, train loss 0.002209, train error 0.00, test loss 2.455862, test error 46.85\n",
+ "Epoch 500, train loss 0.001633, train error 0.00, test loss 2.532098, test error 46.70\n",
+ "Epoch 600, train loss 0.001284, train error 0.00, test loss 2.592178, test error 46.67\n",
+ "Epoch 700, train loss 0.001051, train error 0.00, test loss 2.644237, test error 46.80\n",
+ "Epoch 800, train loss 0.000885, train error 0.00, test loss 2.687477, test error 46.78\n",
+ "Epoch 900, train loss 0.000762, train error 0.00, test loss 2.726535, test error 46.72\n",
+ "Training model with 360 hidden variables\n",
+ "Epoch 0, train loss 1.881302, train error 67.10, test loss 1.826783, test error 69.07\n",
+ "Epoch 100, train loss 0.012637, train error 0.00, test loss 1.789455, test error 46.08\n",
+ "Epoch 200, train loss 0.004398, train error 0.00, test loss 1.978857, test error 45.70\n",
+ "Epoch 300, train loss 0.002526, train error 0.00, test loss 2.081702, test error 45.45\n",
+ "Epoch 400, train loss 0.001732, train error 0.00, test loss 2.153348, test error 45.22\n",
+ "Epoch 500, train loss 0.001301, train error 0.00, test loss 2.208247, test error 45.28\n",
+ "Epoch 600, train loss 0.001034, train error 0.00, test loss 2.252916, test error 45.28\n",
+ "Epoch 700, train loss 0.000853, train error 0.00, test loss 2.290226, test error 45.40\n",
+ "Epoch 800, train loss 0.000724, train error 0.00, test loss 2.322630, test error 45.42\n",
+ "Epoch 900, train loss 0.000626, train error 0.00, test loss 2.351381, test error 45.33\n",
+ "Training model with 680 hidden variables\n",
+ "Epoch 0, train loss 1.808186, train error 63.28, test loss 1.783419, test error 66.82\n",
+ "Epoch 100, train loss 0.008044, train error 0.00, test loss 1.678780, test error 44.55\n",
+ "Epoch 200, train loss 0.003155, train error 0.00, test loss 1.810078, test error 44.47\n",
+ "Epoch 300, train loss 0.001885, train error 0.00, test loss 1.886664, test error 44.42\n",
+ "Epoch 400, train loss 0.001322, train error 0.00, test loss 1.939946, test error 44.35\n",
+ "Epoch 500, train loss 0.001008, train error 0.00, test loss 1.982137, test error 44.45\n",
+ "Epoch 600, train loss 0.000809, train error 0.00, test loss 2.015580, test error 44.45\n",
+ "Epoch 700, train loss 0.000673, train error 0.00, test loss 2.044045, test error 44.28\n",
+ "Epoch 800, train loss 0.000574, train error 0.00, test loss 2.068916, test error 44.28\n",
+ "Epoch 900, train loss 0.000499, train error 0.00, test loss 2.090607, test error 44.28\n"
+ ]
+ }
+ ]
},
{
"cell_type": "code",
"source": [
+ "import matplotlib.pyplot as plt\n",
+ "import numpy as np\n",
+ "\n",
+ "# Assuming data['y'] is available and contains the training examples\n",
+ "num_training_examples = len(data['y'])\n",
+ "\n",
+ "# Find the index where total_weights_all is closest to num_training_examples\n",
+ "closest_index = np.argmin(np.abs(np.array(total_weights_all) - num_training_examples))\n",
+ "\n",
+ "# Get the corresponding value of hidden variables\n",
+ "hidden_variable_at_num_training_examples = hidden_variables[closest_index]\n",
+ "\n",
"# Plot the results\n",
"fig, ax = plt.subplots()\n",
- "ax.plot(hidden_variables, errors_train_all,'r-',label='train')\n",
- "ax.plot(hidden_variables, errors_test_all,'b-',label='test')\n",
- "ax.set_ylim(0,100);\n",
- "ax.set_xlabel('No hidden variables'); ax.set_ylabel('Error')\n",
+ "ax.plot(hidden_variables, errors_train_all, 'r-', label='train')\n",
+ "ax.plot(hidden_variables, errors_test_all, 'b-', label='test')\n",
+ "\n",
+ "# Add a vertical line at the point where total weights equal the number of training examples\n",
+ "ax.axvline(x=hidden_variable_at_num_training_examples, color='g', linestyle='--', label='N(weights) = N(train)')\n",
+ "\n",
+ "ax.set_ylim(0, 100)\n",
+ "ax.set_xlabel('No. hidden variables')\n",
+ "ax.set_ylabel('Error')\n",
"ax.legend()\n",
"plt.show()\n"
],
"metadata": {
- "id": "Rw-iRboTXbck"
+ "id": "Rw-iRboTXbck",
+ "outputId": "4b2ec111-9a74-4e10-821c-6f5129c4e109",
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 455
+ }
+ },
+ "execution_count": 36,
+ "outputs": [
+ {
+ "output_type": "display_data",
+ "data": {
+ "text/plain": [
+ ""
+ ],
+ "image/png": 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\n"
+ },
+ "metadata": {}
+ }
+ ]
+ },
+ {
+ "cell_type": "code",
+ "source": [],
+ "metadata": {
+ "id": "KT4X8_hE5NFb"
+ },
+ "execution_count": 36,
+ "outputs": []
+ },
+ {
+ "cell_type": "code",
+ "source": [],
+ "metadata": {
+ "id": "iGKZSfVF2r4z"
},
- "execution_count": null,
+ "execution_count": 36,
"outputs": []
}
]
![\"Open](\"https://colab.research.google.com/assets/colab-badge.svg\"){kind=icon}