Add interactive learning rate experiments and comparison visualizations

Co-authored-by: leestott <2511341+leestott@users.noreply.github.com>

lessons/3-NeuralNetworks/03-Perceptron/Perceptron.ipynb

@@ -384,6 +384,119 @@
     "plot_boundary(pos_examples,neg_examples,wts)"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Experimenting with Learning Rates\n",
+    "\n",
+    "Now let's explore how different learning rates affect the training process. The learning rate controls the step size in gradient descent - a crucial hyperparameter that affects both convergence speed and stability.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Compare different learning rates\n",
+    "learning_rates = [0.001, 0.01, 0.1, 1.0]\n",
+    "fig, axes = pylab.subplots(2, 2, figsize=(12, 10))\n",
+    "fig.suptitle('Effect of Different Learning Rates', fontsize=16)\n",
+    "\n",
+    "for idx, lr in enumerate(learning_rates):\n",
+    "    ax = axes[idx // 2, idx % 2]\n",
+    "    \n",
+    "    # Train with this learning rate\n",
+    "    weights_lr = train(pos_examples, neg_examples, num_iterations=100, learning_rate=lr)\n",
+    "    \n",
+    "    # Plot decision boundary\n",
+    "    if np.isclose(weights_lr[1], 0):\n",
+    "        if np.isclose(weights_lr[0], 0):\n",
+    "            x = y = np.array([-6, 6], dtype='float32')\n",
+    "        else:\n",
+    "            y = np.array([-6, 6], dtype='float32')\n",
+    "            x = -(weights_lr[1] * y + weights_lr[2])/weights_lr[0]\n",
+    "    else:\n",
+    "        x = np.array([-6, 6], dtype='float32')\n",
+    "        y = -(weights_lr[0] * x + weights_lr[2])/weights_lr[1]\n",
+    "    \n",
+    "    ax.set_xlim(-6, 6)\n",
+    "    ax.set_ylim(-6, 6)\n",
+    "    ax.plot(pos_examples[:, 0], pos_examples[:, 1], 'bo', label='Positive', alpha=0.7)\n",
+    "    ax.plot(neg_examples[:, 0], neg_examples[:, 1], 'ro', label='Negative', alpha=0.7)\n",
+    "    ax.plot(x, y, 'g-', linewidth=2)\n",
+    "    ax.set_title(f'Learning Rate = {lr}')\n",
+    "    ax.set_xlabel('Feature 1')\n",
+    "    ax.set_ylabel('Feature 2')\n",
+    "    ax.legend()\n",
+    "    ax.grid(True, alpha=0.3)\n",
+    "\n",
+    "pylab.tight_layout()\n",
+    "pylab.show()\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Interactive Learning Rate Experiment\n",
+    "\n",
+    "Use the slider below to interactively experiment with different learning rates and see how they affect the decision boundary:\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def train_and_plot_with_lr(learning_rate=0.01):\n",
+    "    \"\"\"Train perceptron with specified learning rate and plot results\"\"\"\n",
+    "    weights_lr = train(pos_examples, neg_examples, num_iterations=100, learning_rate=learning_rate)\n",
+    "    \n",
+    "    fig, (ax1, ax2) = pylab.subplots(1, 2, figsize=(14, 5))\n",
+    "    \n",
+    "    # Plot 1: Decision boundary\n",
+    "    if np.isclose(weights_lr[1], 0):\n",
+    "        if np.isclose(weights_lr[0], 0):\n",
+    "            x = y = np.array([-6, 6], dtype='float32')\n",
+    "        else:\n",
+    "            y = np.array([-6, 6], dtype='float32')\n",
+    "            x = -(weights_lr[1] * y + weights_lr[2])/weights_lr[0]\n",
+    "    else:\n",
+    "        x = np.array([-6, 6], dtype='float32')\n",
+    "        y = -(weights_lr[0] * x + weights_lr[2])/weights_lr[1]\n",
+    "    \n",
+    "    ax1.set_xlim(-6, 6)\n",
+    "    ax1.set_ylim(-6, 6)\n",
+    "    ax1.plot(pos_examples[:, 0], pos_examples[:, 1], 'bo', label='Positive', s=100, alpha=0.6)\n",
+    "    ax1.plot(neg_examples[:, 0], neg_examples[:, 1], 'ro', label='Negative', s=100, alpha=0.6)\n",
+    "    ax1.plot(x, y, 'g-', linewidth=3, label='Decision Boundary')\n",
+    "    ax1.set_title(f'Decision Boundary (lr={learning_rate})', fontsize=14)\n",
+    "    ax1.set_xlabel('Feature 1')\n",
+    "    ax1.set_ylabel('Feature 2')\n",
+    "    ax1.legend()\n",
+    "    ax1.grid(True, alpha=0.3)\n",
+    "    \n",
+    "    # Plot 2: Weight values\n",
+    "    ax2.bar(['w0', 'w1', 'bias'], weights_lr.flatten(), color=['blue', 'green', 'red'], alpha=0.7)\n",
+    "    ax2.set_title('Final Weight Values', fontsize=14)\n",
+    "    ax2.set_ylabel('Weight Value')\n",
+    "    ax2.grid(True, alpha=0.3, axis='y')\n",
+    "    ax2.axhline(y=0, color='black', linestyle='-', linewidth=0.5)\n",
+    "    \n",
+    "    pylab.tight_layout()\n",
+    "    pylab.show()\n",
+    "    \n",
+    "    print(f\"Final weights: {weights_lr.flatten()}\")\n",
+    "\n",
+    "# Create interactive widget\n",
+    "interact(train_and_plot_with_lr, \n",
+    "         learning_rate=widgets.FloatSlider(value=0.01, min=0.001, max=1.0, step=0.001, \n",
+    "                                          description='Learning Rate:', continuous_update=False))\n"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {