Update RFC-00xx-automatic-implicit-differentiation.md

Author: 0x00b1

RFC-00xx-automatic-implicit-differentiation.md

@@ -261,6 +261,58 @@ def fixed_point(f: Callable, g: Callable):
     pass
 ```
 
+##### `@torch.optim.root_jvp`
+
+```Python
+from typing import Any, Callable, Tuple
+
+
+def root_jvp(
+        f: Callable,
+        g: Callable,
+        x: Tuple[Any],
+        y: Tuple[Any],
+        z: Any,
+):
+    """
+    Jacobian-vector product of a root.
+  
+    Args:
+      f: 
+      g: linear solver of the form ``g(a, b)``.
+      x: arguments.
+      y: tangents.
+      z: solution.
+    """
+    pass
+```
+
+##### `@torch.optim.root_vjp`
+
+```Python
+from typing import Any, Callable, Tuple
+
+
+def root_vjp(
+        f: Callable,
+        g: Callable,
+        x: Tuple[Any],
+        y: Tuple[Any],
+        z: Any,
+):
+    """
+    Add implicit differentiation to a fixed point method.
+  
+    Args:
+      f: 
+      g: linear solver of the form ``g(a, b)``.
+      x: arguments.
+      y: cotangents.
+      z: solution.
+    """
+    pass
+```
+
 #### Bracketing Optimizers
 
 PyTorch provides a variety of bracketing methods for univariate functions, or functions involving a single variable.