[AutoDiff] Update method-style differential operators. (#395)

Use top-level differential operators instead of method-style ones, which have
been removed. Method-style differential operators have been removed for a full
release cycle now.

Author: dan-zheng

docs/site/tutorials/custom_differentiation.ipynb

@@ -204,7 +204,7 @@
    "outputs": [],
    "source": [
     "var x: Float = 30\n",
-    "x.gradient { x -> Float in\n",
+    "gradient(at: x) { x -> Float in\n",
     "    // Print the partial derivative with respect to the result of `sin(x)`.\n",
     "    let a = sin(x).withDerivative { print(\"∂+/∂sin = \\($0)\") } \n",
     "    // Force the partial derivative with respect to `x` to be `0.5`.\n",
@@ -270,7 +270,7 @@
     "let y: Tensor<Float> = [0, 1, 1, 0]\n",
     "\n",
     "for _ in 0..<10 {\n",
-    "    let 𝛁model = classifier.gradient { classifier -> Tensor<Float> in\n",
+    "    let 𝛁model = gradient(at: classifier) { classifier -> Tensor<Float> in\n",
     "        let ŷ = classifier(x).withDerivative { print(\"∂L/∂ŷ =\", $0) }\n",
     "        let loss = (ŷ - y).squared().mean()\n",
     "        print(\"Loss: \\(loss)\")\n",
@@ -378,7 +378,7 @@
     "}\n",
     "\n",
     "// Differentiate `f(x) = (cos(x))^2`.\n",
-    "let (output, backprop) = input.valueWithPullback { input -> Float in\n",
+    "let (output, backprop) = valueWithPullback(at: input) { input -> Float in\n",
     "    return square(cos(input))\n",
     "}\n",
     "print(\"Running backpropagation...\")\n",
@@ -598,7 +598,7 @@
     "    print(\"Starting training step \\(i)\")\n",
     "    print(\"  Running original computation...\")\n",
     "    let (logits, backprop) = model.appliedForBackpropagation(to: x)\n",
-    "    let (loss, dL_dŷ) = logits.valueWithGradient { logits in\n",
+    "    let (loss, dL_dŷ) = valueWithGradient(at: logits) { logits in\n",
     "        softmaxCrossEntropy(logits: logits, labels: y)\n",
     "    }\n",
     "    print(\"  Loss: \\(loss)\")\n",

docs/site/tutorials/model_training_walkthrough.ipynb

@@ -750,7 +750,7 @@
    },
    "outputs": [],
    "source": [
-    "let (loss, grads) = model.valueWithGradient { model -> Tensor<Float> in\n",
+    "let (loss, grads) = valueWithGradient(at: model) { model -> Tensor<Float> in\n",
     "    let logits = model(firstTrainFeatures)\n",
     "    return softmaxCrossEntropy(logits: logits, labels: firstTrainLabels)\n",
     "}\n",
@@ -871,7 +871,7 @@
     "    var epochAccuracy: Float = 0\n",
     "    var batchCount: Int = 0\n",
     "    for batch in trainDataset {\n",
-    "        let (loss, grad) = model.valueWithGradient { (model: IrisModel) -> Tensor<Float> in\n",
+    "        let (loss, grad) = valueWithGradient(at: model) { (model: IrisModel) -> Tensor<Float> in\n",
     "            let logits = model(batch.features)\n",
     "            return softmaxCrossEntropy(logits: logits, labels: batch.labels)\n",
     "        }\n",