Add doc explaining how it works (#6937)

experimental/torch_xla2/docs/how_it_works.md

@@ -0,0 +1,134 @@
+How it works
+============
+
+
+## Tensor subclass and eager mode
+
+The class `XLATensor2` is a `torch.Tensor` subclass
+that overrides `__torch_dispatch__`.
+
+It roughly looks like this (with some details removed):
+
+The complete class impl is at [tensor.py](../torch_xla2/tensor.py).
+
+```python
+class XLATensor2(torch.Tensor):
+
+  @staticmethod
+  def __new__(cls, elem):
+    return torch.Tensor._make_wrapper_subclass(
+        cls,
+        shape,
+        dtype=dtype,
+        device='meta',
+        requires_grad=False,
+    )
+
+  def __init__(self, elem: jax.Array):
+    super().__init__()
+    self._elem = elem
+
+  __torch_function__ = torch._C._disabled_torch_function_impl
+
+  @classmethod
+  def __torch_dispatch__(cls, func, types, args=(), kwargs=None):
+    # here assumes ALL tensors in args / kwargs are 
+    # instances of XLATensor2
+    args, kwargs = unwrap((args, kwargs))
+    jax_func = some_registry[func]
+    res = jax_func(*args, **kwargs)
+    return wrap(res)
+
+def wrap(tree):
+    # wrap jax.Array with XLATensor2
+    return pytree.tree_map_only(
+        jax.Array, XLATensor2, tree)
+
+def unwrap(tree):
+    # get jax.Array out ofXLATensor2
+    return pytree.tree_map_only(
+        XLATensor2, lambda x: x._elem, tree)
+```
+
+In other words, assuming that we have a function
+that takes `jax.Array` as input and returns `jax.Array`
+but otherwise implement the same semantics
+as a `ATen` op; then, using this tensor we would 
+be able to route the call to this jax function.
+
+[_ops.py](../torch_xla2/_ops.py) files defines some of those ops.
+
+Let's take `aten::add` as example:
+
+```python
+@op(torch.ops.aten.add)
+def _aten_add(x, y, *, alpha=1):
+  """if isinstance(x, jnp.ndarray) and isinstance(y, jnp.ndarray):
+
+  assert x.dtype == y.dtype, (x.dtype, y.dtype)
+  """
+  return x + y * alpha
+```
+
+The `@op` decorator just puts this function into `some_registry` dictionary.
+
+`_aten_add` has same signature as `torch.ops.aten.add` but takes `jax.Array` as
+input.
+
+![](dispatch.png)
+
+
+## fx Interpreter and dynamo mode
+
+Now, assuming we have this `some_registry` dict with key core Aten ops,
+and value the equivalent python Jax functions. We can also build a `fx.Interpreter`
+subclass that executes the jax function given a `fx.GraphModule`.
+
+
+```python
+class JaxInterpreter(torch.fx.Interpreter):
+
+  def call_function(self, target, args: Tuple, kwargs: Dict) -> Any:
+    if not isinstance(target,
+                      (torch._ops.OpOverloadPacket, torch._ops.OpOverload)):
+      return super().call_function(target, args, kwargs)
+
+    op = some_registry[target]
+    return op.func(*args, **kwargs)
+```
+
+There is no wrapping and unwrapping needed because `args` and `kwargs` are 
+already `jax.Array`'s.
+
+Using this interpreter we can build a dynamo backend:
+
+```python
+def backend(fxgraph):
+
+   def tojit(*args, *kwargs):
+    return JaxInterpreter(fxgraph).run(*args, **kwargs)
+   jitted = jax.jit(to_jit)
+
+   def f(*torchtensor):
+     jaxarrays = unwrap(torchtensors)
+     res = jitted(jax_array)
+     return wrap(res)
+
+   return f
+```
+
+The inner function `tojit` is a function that takes and returns 
+`jax.Array`'s. So it's suitable to be jitted with `jax.jit`.
+
+`f` is returned callable that takes `XLATensor2`; so can interop with 
+other torch codes.
+
+## nn.Modules and state management
+
+See [README.md](../README.md) for using `torch.func.functional_call` to 
+make `nn.Module`s interact well with `jax.jit`.
+
+See [Examples](../examples/README.md) for training using torch's optimizers or jax's
+optimizers.
+
+[def]: dispatch.png