change title

Neural-Networks/2-MNIST.ipynb

@@ -551,17 +551,17 @@
     "\n",
     "    # learning_rate: how big of a step is taken while updating weights and biases\n",
     "\n",
-    "    def backward(self, output_gradient, learning_rate):\n",
-    "        # gradient: dC_dw = dC_da x da_dz x dz_dw\n",
-    "        da_dz = self.relu_derivative(self.last_output)  \n",
-    "        dC_dz = output_gradient * da_dz \n",
+    "    def backward(self, dC_da, learning_rate):\n",
+    "        # dC_da is the gradient of the cost with respect to the activation of this layer\n",
+    "        da_dz = self.relu_derivative(self.last_output)\n",
+    "        dC_dz = dC_da * da_dz\n",
     "        dC_dw = np.outer(dC_dz, self.last_input)\n",
-    "        dC_db = dC_dz \n",
+    "        dC_db = dC_dz\n",
+    "\n",
+    "        self.weights -= dC_dw * learning_rate\n",
+    "        self.bias -= np.sum(dC_db, axis=0) * learning_rate\n",
     "\n",
-    "        self.weights -= learning_rate * dC_dw.reshape(self.weights.shape)  # updates weights. gradient of the cost w.r.t. weight\n",
-    "        self.bias -= learning_rate * np.sum(dC_db)  # bias is a scalar & gradient could be a vector, so summed.\n",
-    "        \n",
-    "        dC_dx = np.dot(self.weights.T, dC_dz)   # gradient of the cost w.r.t. input of neuron\n",
+    "        dC_dx = np.dot(self.weights.T, dC_dz)\n",
     "        return dC_dx\n",
     "\n",
     "class Layer:\n",