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@bilzard
Created March 30, 2023 12:32
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{
"cells": [
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The lab_black extension is already loaded. To reload it, use:\n",
" %reload_ext lab_black\n",
"The autoreload extension is already loaded. To reload it, use:\n",
" %reload_ext autoreload\n"
]
}
],
"source": [
"%load_ext lab_black\n",
"%load_ext autoreload\n",
"%autoreload 2"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"\n",
"# Softmax function\n",
"def softmax(logits):\n",
" exp_logits = np.exp(logits)\n",
" return exp_logits / np.sum(exp_logits, axis=1, keepdims=True)\n",
"\n",
"\n",
"# Hinge loss function\n",
"def hinge_loss(y_pred):\n",
" return np.maximum(0, 1 - y_pred)\n",
"\n",
"\n",
"# Cross entropy loss function\n",
"def cross_entropy_loss(y_pred_prob):\n",
" return -np.log(y_pred_prob)\n",
"\n",
"\n",
"# Cross entropy loss with label smoothing function\n",
"def cross_entropy_loss_label_smoothing(y_pred_prob, label_smoothing=0.1):\n",
" return -(\n",
" (1 - label_smoothing) * np.log(y_pred_prob)\n",
" + label_smoothing * np.log(1 - y_pred_prob)\n",
" )\n",
"\n",
"\n",
"# Create an array of model logits from -3 to 3\n",
"logits = np.linspace(-10, 10, 1000)\n",
"\n",
"# Calculate the softmax probabilities\n",
"probs = softmax(np.column_stack((logits, np.zeros_like(logits))))\n",
"\n",
"# Calculate loss values for each prediction\n",
"hinge_losses = hinge_loss(logits)\n",
"ce_losses = cross_entropy_loss(probs[:, 0])\n",
"ce_losses_label_smoothing = cross_entropy_loss_label_smoothing(probs[:, 0])\n",
"\n",
"_, ax = plt.subplots()\n",
"# Plot the losses\n",
"ax.plot(logits, hinge_losses, label=\"Hinge Loss\")\n",
"ax.plot(logits, ce_losses, label=\"Cross Entropy Loss\")\n",
"ax.plot(\n",
" logits,\n",
" ce_losses_label_smoothing,\n",
" label=\"Cross Entropy Loss with Label Smoothing (0.1)\",\n",
")\n",
"\n",
"# Add labels and legend\n",
"ax.set(xlabel=\"Model Logits\", ylabel=\"Loss\", title=\"Comparison of Loss Curve\")\n",
"ax.legend()\n",
"\n",
"# Show the plot\n",
"plt.show()"
]
}
],
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