Created using Colab. 🔥

Author: RodolfoFerro

notebooks/01_Introducción_al_aprendizaje_profundo.ipynb

@@ -521,8 +521,8 @@
         "            error = y_pred - y_train\n",
         "\n",
         "            # Ajuste de pesos con gradientes\n",
-        "            #dz = error # BCE\n",
-        "            dz = 2 * error * self.sigmoid_derivative(y_pred) # MSE\n",
+        "            dz = error # BCE\n",
+        "            #dz = 2 * error * self.sigmoid_derivative(y_pred) # MSE\n",
         "            dw = X.T @ dz / n\n",
         "            db = np.sum(dz) / n\n",
         "            self.weights -= lr * dw\n",
@@ -534,6 +534,39 @@
         "        return history\n"
       ]
     },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "## ¿Por qué se calcula así?\n",
+        "\n",
+        "Para la función de binary **binary cross-entropy**, la derivada con respecto a la predicción es:\n",
+        "```\n",
+        "∂L/∂y_pred = (y_pred - y_train) / (y_pred * (1 - y_pred))\n",
+        "```\n",
+        "\n",
+        "Pero cuando combinamos esto con la derivada de la sigmoid (que ya está en la neurona), el término `y_pred * (1 - y_pred)` se cancela, quedando simplemente:\n",
+        "```\n",
+        "gradient = y_pred - y_train\n",
+        "````\n",
+        "\n",
+        "Para **MSE**, la función de pérdida es:\n",
+        "```\n",
+        "L = (1/n) * Σ(y_pred - y_train)²\n",
+        "```\n",
+        "La derivada con respecto a y_pred es:\n",
+        "```\n",
+        "∂L/∂y_pred = 2 * (y_pred - y_train)\n",
+        "```\n",
+        "Cuando aplicas la regla de la cadena con la sigmoid, obtenemos:\n",
+        "```\n",
+        "gradient = 2 * (y_pred - y_train) * sigmoid'(y_pred)\n",
+        "gradient = 2 * (y_pred - y_train) * y_pred * (1 - y_pred)\n",
+        "```"
+      ],
+      "metadata": {
+        "id": "-wj05Ow1Oavy"
+      }
+    },
     {
       "cell_type": "markdown",
       "metadata": {