Source code for jax._src.custom_derivatives

# coding=utf-8
# Copyright 2020 Google LLC
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

from functools import update_wrapper, reduce, partial
import inspect
import operator as op
from typing import (Callable, Generic, Optional, Sequence, Tuple, List, TypeVar,
                    Any)

from jax import core
from jax import linear_util as lu
from jax.tree_util import (tree_flatten, tree_unflatten, tree_map,
                        tree_multimap, treedef_is_leaf, treedef_tuple,
                        register_pytree_node_class)
from jax._src.util import cache, safe_zip, safe_map, split_list, Unhashable
from jax._src.api_util import flatten_fun_nokwargs, argnums_partial
from jax.core import raise_to_shaped
from jax.errors import UnexpectedTracerError
from jax._src.ad_util import Zero, zeros_like_aval, stop_gradient_p
from jax.interpreters import partial_eval as pe
from jax.interpreters import ad
from jax.interpreters import batching
from jax.interpreters import mlir
from jax.interpreters import xla
from jax.interpreters.batching import not_mapped
from jax.config import config

from jax._src import traceback_util
traceback_util.register_exclusion(__file__)

map = safe_map
zip = safe_zip


### util

def _resolve_kwargs(fun, args, kwargs):
  ba = inspect.signature(fun).bind(*args, **kwargs)
  ba.apply_defaults()
  if ba.kwargs:
    raise TypeError("keyword arguments could not be resolved to positions")
  else:
    return ba.args

def _initial_style_jaxpr(fun, in_avals):
  jaxpr, _, consts = pe.trace_to_jaxpr_dynamic(fun, in_avals)
  return jaxpr, consts

def _close_jaxpr(jaxpr):
  return core.ClosedJaxpr(pe.convert_constvars_jaxpr(jaxpr), ())

def _initial_style_staging() -> bool:
  return core.thread_local_state.trace_state.initial_style

def _sum_tangents(_, x, *xs):
  return reduce(ad.add_tangents, xs, x)

def _zeros_like_pytree(x):
  return tree_map(Zero.from_value, x)

@partial(partial, tree_map)
def _stop_gradient(x):
  if isinstance(x, core.Tracer):
    return stop_gradient_p.bind(x)
  else:
    return x


### JVPs
ReturnValue = TypeVar('ReturnValue')

[docs]class custom_jvp(Generic[ReturnValue]): """Set up a JAX-transformable function for a custom JVP rule definition. This class is meant to be used as a function decorator. Instances are callables that behave similarly to the underlying function to which the decorator was applied, except when a differentiation transformation (like :py:func:`jax.jvp` or :py:func:`jax.grad`) is applied, in which case a custom user-supplied JVP rule function is used instead of tracing into and performing automatic differentiation of the underlying function's implementation. There are two instance methods available for defining the custom JVP rule: :py:func:`~jax.custom_jvp.defjvp` for defining a *single* custom JVP rule for all the function's inputs, and for convenience :py:func:`~jax.custom_jvp.defjvps`, which wraps :py:func:`~jax.custom_jvp.defjvp`, and allows you to provide separate definitions for the partial derivatives of the function w.r.t. each of its arguments. For example:: @jax.custom_jvp def f(x, y): return jnp.sin(x) * y @f.defjvp def f_jvp(primals, tangents): x, y = primals x_dot, y_dot = tangents primal_out = f(x, y) tangent_out = jnp.cos(x) * x_dot * y + jnp.sin(x) * y_dot return primal_out, tangent_out For a more detailed introduction, see the tutorial_. .. _tutorial: https://jax.readthedocs.io/en/latest/notebooks/Custom_derivative_rules_for_Python_code.html """ def __init__(self, fun: Callable[..., ReturnValue], nondiff_argnums: Tuple[int, ...] = ()): self.fun = fun self.nondiff_argnums = nondiff_argnums self.jvp: Optional[Callable[..., Tuple[ReturnValue, ReturnValue]]] = None update_wrapper(self, fun)
[docs] def defjvp(self, jvp: Callable[..., Tuple[ReturnValue, ReturnValue]]) -> None: """Define a custom JVP rule for the function represented by this instance. Args: jvp: a Python callable representing the custom JVP rule. When there are no ``nondiff_argnums``, the ``jvp`` function should accept two arguments, where the first is a tuple of primal inputs and the second is a tuple of tangent inputs. The lengths of both tuples are equal to the number of parameters of the ``custom_jvp`` function. The ``jvp`` function should produce as output a pair where the first element is the primal output and the second element is the tangent output. Elements of the input and output tuples may be arrays or any nested tuples/lists/dicts thereof. Returns: None. Example:: @jax.custom_jvp def f(x, y): return jnp.sin(x) * y @f.defjvp def f_jvp(primals, tangents): x, y = primals x_dot, y_dot = tangents primal_out = f(x, y) tangent_out = jnp.cos(x) * x_dot * y + jnp.sin(x) * y_dot return primal_out, tangent_out """ self.jvp = jvp
[docs] def defjvps(self, *jvps: Optional[Callable[..., ReturnValue]]): """Convenience wrapper for defining JVPs for each argument separately. This convenience wrapper cannot be used together with ``nondiff_argnums``. Args: *jvps: a sequence of functions, one for each positional argument of the ``custom_jvp`` function. Each function takes as arguments the tangent value for the corresponding primal input, the primal output, and the primal inputs. See the example below. Returns: None. Example:: @jax.custom_jvp def f(x, y): return jnp.sin(x) * y f.defjvps(lambda x_dot, primal_out, x, y: jnp.cos(x) * x_dot * y, lambda y_dot, primal_out, x, y: jnp.sin(x) * y_dot) """ if self.nondiff_argnums: raise TypeError("Can't use ``defjvps`` with ``nondiff_argnums``.") def jvp(primals, tangents): primal_out = self(*primals) zeros = _zeros_like_pytree(primal_out) all_tangents_out = [jvp(t, primal_out, *primals) if jvp else zeros for t, jvp in zip(tangents, jvps)] tangent_out = tree_multimap(_sum_tangents, primal_out, *all_tangents_out) return primal_out, tangent_out self.defjvp(jvp)
@traceback_util.api_boundary def __call__(self, *args: Any, **kwargs: Any) -> ReturnValue: # pytype: disable=invalid-annotation if not self.jvp: msg = "No JVP defined for custom_jvp function {} using defjvp." raise AttributeError(msg.format(self.__name__)) args = _resolve_kwargs(self.fun, args, kwargs) if self.nondiff_argnums: nondiff_argnums = set(self.nondiff_argnums) args = tuple(_stop_gradient(x) if i in nondiff_argnums else x for i, x in enumerate(args)) diff_argnums = [i for i in range(len(args)) if i not in nondiff_argnums] f_, dyn_args = argnums_partial(lu.wrap_init(self.fun), diff_argnums, args, require_static_args_hashable=False) static_args = [args[i] for i in self.nondiff_argnums] jvp = _add_args(lu.wrap_init(self.jvp), static_args) else: f_, dyn_args = lu.wrap_init(self.fun), args jvp = lu.wrap_init(self.jvp) args_flat, in_tree = tree_flatten(dyn_args) flat_fun, out_tree1 = flatten_fun_nokwargs(f_, in_tree) flat_jvp, out_tree2 = _flatten_jvp(jvp, in_tree) out_flat = custom_jvp_call_p.bind(flat_fun, flat_jvp, *args_flat) _, out_tree = lu.merge_linear_aux(out_tree1, out_tree2) return tree_unflatten(out_tree, out_flat)
def _add_args(f, extra_args): return _add_args_(f, tuple(Unhashable(arg) for arg in extra_args)) @lu.transformation def _add_args_(extra_args, *args, **kwargs): extra_args = tuple([arg.val for arg in extra_args]) all_args = (extra_args + args) yield (yield all_args, kwargs) @lu.transformation_with_aux def _flatten_jvp(in_tree, *args): primals_in, tangents_in = split_list(args, [len(args) // 2]) py_primals = tree_unflatten(in_tree, primals_in) py_tangents = tree_unflatten(in_tree, tangents_in) pair_out = yield (py_primals, py_tangents), {} if not isinstance(pair_out, (list, tuple)) or len(pair_out) != 2: msg = ("Custom JVP rule must produce a pair (list or tuple of length two) " "representing primal and tangent outputs, got {}.") raise TypeError(msg.format(pair_out)) py_primals_out, py_tangents_out = pair_out primals_out, out_tree = tree_flatten(py_primals_out) tangents_out, out_tree2 = tree_flatten(py_tangents_out) if out_tree != out_tree2: msg = ("Custom JVP rule must produce primal and tangent outputs with equal " "container (pytree) structures, but got {} and {} respectively.") raise TypeError(msg.format(out_tree, out_tree2)) # TODO(mattjj): compare primals' tangent types to tangent objects' types primal_avals_out = [ raise_to_shaped(core.get_aval(x), weak_type=False).strip_named_shape() for x in primals_out] tangent_avals_out = [ raise_to_shaped(core.get_aval(t), weak_type=False).strip_named_shape() for t in tangents_out] if primal_avals_out != tangent_avals_out: if len(primal_avals_out) == 1: (av1,), (av2,) = primal_avals_out, tangent_avals_out msg = ("Custom JVP rule must produce primal and tangent outputs with " "equal shapes and dtypes, but got {} and {} respectively.") raise TypeError(msg.format(av1.str_short(), av2.str_short())) else: msg = ("Custom JVP rule must produce primal and tangent outputs with " "equal shapes and dtypes, but got:\n{}") disagreements = ( " primal {} for tangent {}".format(av1.str_short(), av2.str_short()) for av1, av2 in zip(primal_avals_out, tangent_avals_out) if av1 != av2) raise TypeError(msg.format('\n'.join(disagreements))) yield primals_out + tangents_out, out_tree class CustomJVPCallPrimitive(core.CallPrimitive): initial_style: core.Primitive def bind(self, fun, jvp, *args): args = map(core.full_lower, args) top_trace = core.find_top_trace(args) fun, env_trace_todo1 = core.process_env_traces( fun, self, top_trace and top_trace.level, (), None) jvp, env_trace_todo2 = core.process_env_traces( jvp, self, top_trace and top_trace.level, (), None) tracers = map(top_trace.full_raise, args) # type: ignore outs = top_trace.process_custom_jvp_call(self, fun, jvp, tracers) # type: ignore _, env_trace_todo = lu.merge_linear_aux(env_trace_todo1, env_trace_todo2) return _apply_todos(env_trace_todo, map(core.full_lower, outs)) def impl(self, fun, _, *args): with core.new_sublevel(): return fun.call_wrapped(*args) def post_process(self, trace, out_tracers, params): return trace.post_process_custom_jvp_call(out_tracers, params) def _apply_todos(todos, outs): todos_list = list(todos) while todos_list: outs = map(core.full_lower, todos_list.pop()(outs)) return outs custom_jvp_call_p = CustomJVPCallPrimitive('custom_jvp_call') def _custom_jvp_call_jaxpr_impl(*args, fun_jaxpr: core.ClosedJaxpr, **params): del params # other params ignored because we're just executing the primal fun return core.jaxpr_as_fun(fun_jaxpr)(*args) def _custom_jvp_call_jaxpr_abstract_eval(*args, fun_jaxpr: core.ClosedJaxpr, **params): del args, params return fun_jaxpr.out_avals custom_jvp_call_jaxpr_p = core.AxisPrimitive('custom_jvp_call_jaxpr') custom_jvp_call_jaxpr_p.multiple_results = True custom_jvp_call_jaxpr_p.def_impl(_custom_jvp_call_jaxpr_impl) custom_jvp_call_jaxpr_p.def_abstract_eval(_custom_jvp_call_jaxpr_abstract_eval) CustomJVPCallPrimitive.initial_style = custom_jvp_call_jaxpr_p mlir.register_lowering(custom_jvp_call_jaxpr_p, mlir.lower_fun( _custom_jvp_call_jaxpr_impl, multiple_results=True)) def _custom_jvp_call_jaxpr_jvp( primals, tangents, *, fun_jaxpr: core.ClosedJaxpr, jvp_jaxpr_thunk: Callable[[], Tuple[core.Jaxpr, Sequence[Any]]], num_consts: int): _, args = split_list(primals, [num_consts]) consts_dot, args_dot = split_list(tangents, [num_consts]) if any(type(t) is not Zero for t in consts_dot): raise ad.CustomJVPException() jvp_jaxpr, jvp_consts = jvp_jaxpr_thunk() # consts can be tracers! args_dot = map(ad.instantiate_zeros, args_dot) # Cast float0 to zeros with the primal dtype because custom jvp rules don't # currently handle float0s args_dot = map(ad.replace_float0s, args, args_dot) outs = core.eval_jaxpr(jvp_jaxpr, jvp_consts, *args, *args_dot) primals_out, tangents_out = split_list(outs, [len(outs) // 2]) tangents_out = map(ad.recast_to_float0, primals_out, tangents_out) return primals_out, tangents_out ad.primitive_jvps[custom_jvp_call_jaxpr_p] = _custom_jvp_call_jaxpr_jvp def _custom_jvp_call_jaxpr_vmap( axis_size, axis_name, main_type, args, in_dims, *, fun_jaxpr: core.ClosedJaxpr, jvp_jaxpr_thunk: Callable[[], Tuple[core.Jaxpr, Sequence[Any]]], num_consts: int): args = [batching.moveaxis(x, d, 0) if d is not not_mapped and d != 0 else x for x, d in zip(args, in_dims)] num_out = len(fun_jaxpr.out_avals) in_batched = [d is not not_mapped for d in in_dims] batched_fun_jaxpr, out_batched = batching.batch_jaxpr( fun_jaxpr, axis_size, in_batched, False, axis_name, main_type) out_dims1 = [0 if b else not_mapped for b in out_batched] out_dims2 = [] # mutable cell updated by batched_jvp_jaxpr_thunk @pe._memoize def batched_jvp_jaxpr_thunk(): jvp_jaxpr = core.ClosedJaxpr(*jvp_jaxpr_thunk()) # consts can be tracers _, args_batched = split_list(in_batched, [num_consts]) _, all_batched = batching.batch_jaxpr(jvp_jaxpr, axis_size, args_batched * 2, False, axis_name, main_type) primals_batched, tangents_batched = split_list(all_batched, [num_out]) out_batched = map(op.or_, primals_batched, tangents_batched) out_dims2.append([0 if b else not_mapped for b in out_batched]) batched_jvp_jaxpr, _ = batching.batch_jaxpr( jvp_jaxpr, axis_size, args_batched * 2, out_batched * 2, axis_name, main_type) return batched_jvp_jaxpr.jaxpr, batched_jvp_jaxpr.consts batched_outs = custom_jvp_call_jaxpr_p.bind( *args, fun_jaxpr=batched_fun_jaxpr, jvp_jaxpr_thunk=batched_jvp_jaxpr_thunk, num_consts=num_consts) out_dims = out_dims2[0] if out_dims2 else out_dims1 return batched_outs, out_dims batching.axis_primitive_batchers[custom_jvp_call_jaxpr_p] = _custom_jvp_call_jaxpr_vmap xla.register_translation( custom_jvp_call_jaxpr_p, xla.lower_fun(_custom_jvp_call_jaxpr_impl, new_style=True, multiple_results=True), initial_style=True) # If a (multi)linear function is defined with a custom jvp, then # custom_jvp_call_jaxpr can appear in jaxprs to be transposed. Since it's # already been linearized, we can drop the jvp rule. def _custom_jvp_call_jaxpr_transpose(reduce_axes, cts, *args, fun_jaxpr, jvp_jaxpr_thunk, num_consts): del jvp_jaxpr_thunk, num_consts return ad.backward_pass( fun_jaxpr.jaxpr, reduce_axes, fun_jaxpr.consts, args, cts) ad.reducing_transposes[custom_jvp_call_jaxpr_p] = _custom_jvp_call_jaxpr_transpose def custom_jvp_jaxpr_custom_partial_eval_rule( saveable: Callable[..., bool], unks_in: List[bool], inst_in: List[bool], eqn: core.JaxprEqn ) -> Tuple[Optional[core.JaxprEqn], core.JaxprEqn, List[bool], List[bool], List[core.Var]]: # It doesn't make sense to unzip (i.e. break up) a custom_jvp function into # constituent parts, so we always perform full remat. An alternative would be # to allow the policy function to decide whether the value of a # custom_jvp-decorated function's application should be saved or not. # TODO(mattjj,jekbradbury): the user writing the custom_jvp-decorated function # probably has a better idea for what to do under remat (e.g. if the function # contains dots or not), so we should allow for more expressive interaction # (e.g. allow the policy to depend on which custom_jvp-decorated function is # being applied, or annotating the behavior where custom_vjp is called.) inst_out = [True] * len(eqn.outvars) new_inst = [x for x, inst in zip(eqn.invars, inst_in) if type(x) is core.Var and not inst] if any(unks_in): unks_out = [True] * len(eqn.outvars) return None, eqn, unks_out, inst_out, new_inst else: unks_out = [False] * len(eqn.outvars) return eqn, eqn, unks_out, inst_out, new_inst pe.partial_eval_jaxpr_custom_rules[custom_jvp_call_jaxpr_p] = \ custom_jvp_jaxpr_custom_partial_eval_rule # type: ignore ### VJPs
[docs]class custom_vjp(Generic[ReturnValue]): """Set up a JAX-transformable function for a custom VJP rule definition. This class is meant to be used as a function decorator. Instances are callables that behave similarly to the underlying function to which the decorator was applied, except when a reverse-mode differentiation transformation (like :py:func:`jax.grad`) is applied, in which case a custom user-supplied VJP rule function is used instead of tracing into and performing automatic differentiation of the underlying function's implementation. There is a single instance method, :py:func:`~jax.custom_vjp.defvjp`, which may be used to define the custom VJP rule. This decorator precludes the use of forward-mode automatic differentiation. For example:: @jax.custom_vjp def f(x, y): return jnp.sin(x) * y def f_fwd(x, y): return f(x, y), (jnp.cos(x), jnp.sin(x), y) def f_bwd(res, g): cos_x, sin_x, y = res return (cos_x * g * y, sin_x * g) f.defvjp(f_fwd, f_bwd) For a more detailed introduction, see the tutorial_. .. _tutorial: https://jax.readthedocs.io/en/latest/notebooks/Custom_derivative_rules_for_Python_code.html """ def __init__(self, fun: Callable[..., ReturnValue], nondiff_argnums: Tuple[int, ...] = ()): self.fun = fun self.nondiff_argnums = nondiff_argnums self.fwd: Optional[Callable[..., Tuple[ReturnValue, Any]]] = None self.bwd: Optional[Callable[..., Tuple[Any, ...]]] = None update_wrapper(self, fun)
[docs] def defvjp(self, fwd: Callable[..., Tuple[ReturnValue, Any]], bwd: Callable[..., Tuple[Any, ...]]) -> None: """Define a custom VJP rule for the function represented by this instance. Args: fwd: a Python callable representing the forward pass of the custom VJP rule. When there are no ``nondiff_argnums``, the ``fwd`` function has the same input signature as the underlying primal function. It should return as output a pair, where the first element represents the primal output and the second element represents any "residual" values to store from the forward pass for use on the backward pass by the function ``bwd``. Input arguments and elements of the output pair may be arrays or nested tuples/lists/dicts thereof. bwd: a Python callable representing the backward pass of the custom VJP rule. When there are no ``nondiff_argnums``, the ``bwd`` function takes two arguments, where the first is the "residual" values produced on the forward pass by ``fwd``, and the second is the output cotangent with the same structure as the primal function output. The output of ``bwd`` must be a tuple of length equal to the number of arguments of the primal function, and the tuple elements may be arrays or nested tuples/lists/dicts thereof so as to match the structure of the primal input arguments. Returns: None. Example:: @jax.custom_vjp def f(x, y): return jnp.sin(x) * y def f_fwd(x, y): return f(x, y), (jnp.cos(x), jnp.sin(x), y) def f_bwd(res, g): cos_x, sin_x, y = res return (cos_x * g * y, sin_x * g) f.defvjp(f_fwd, f_bwd) """ self.fwd = fwd self.bwd = bwd
@traceback_util.api_boundary def __call__(self, *args: Any, **kwargs: Any) -> ReturnValue: # pytype: disable=invalid-annotation if not self.fwd or not self.bwd: msg = "No VJP defined for custom_vjp function {} using defvjp." raise AttributeError(msg.format(self.__name__)) args = _resolve_kwargs(self.fun, args, kwargs) if self.nondiff_argnums: for i in self.nondiff_argnums: _check_for_tracers(args[i]) nondiff_argnums = set(self.nondiff_argnums) dyn_argnums = [i for i in range(len(args)) if i not in nondiff_argnums] f_, dyn_args = argnums_partial(lu.wrap_init(self.fun), dyn_argnums, args, require_static_args_hashable=False) static_args = [args[i] for i in self.nondiff_argnums] fwd, _ = argnums_partial(lu.wrap_init(self.fwd), dyn_argnums, args, require_static_args_hashable=False) bwd = _add_args(lu.wrap_init(self.bwd), static_args) else: f_, dyn_args = lu.wrap_init(self.fun), args fwd, bwd = lu.wrap_init(self.fwd), lu.wrap_init(self.bwd) args_flat, in_tree = tree_flatten(dyn_args) in_avals = [core.raise_to_shaped(core.get_aval(x)) for x in args_flat] flat_fun, out_tree = flatten_fun_nokwargs(f_, in_tree) flat_fwd, out_trees = _flatten_fwd(fwd, in_tree) flat_bwd = _flatten_bwd(bwd, in_tree, in_avals, out_trees) out_flat = custom_vjp_call_p.bind(flat_fun, flat_fwd, flat_bwd, *args_flat, out_trees=out_trees) fst, aux = lu.merge_linear_aux(out_tree, out_trees) out_tree = aux if fst else aux[0] return tree_unflatten(out_tree, out_flat)
@partial(partial, tree_map) def _check_for_tracers(x): if isinstance(x, core.Tracer): msg = ("Found a JAX Tracer object passed as an argument to a custom_vjp " "function in a position indicated by nondiff_argnums as " "non-differentiable. Tracers cannot be passed as non-differentiable " "arguments to custom_vjp functions; instead, nondiff_argnums should " "only be used for arguments that can't be or contain JAX tracers, " "e.g. function-valued arguments. In particular, array-valued " "arguments should typically not be indicated as nondiff_argnums. " "\n\n" "This behavior recently changed in JAX. " "See https://github.com/google/jax/blob/main/docs/custom_vjp_update.md " "for more information.") raise UnexpectedTracerError(msg) @lu.transformation_with_aux def _flatten_fwd(in_tree, *args): py_args = tree_unflatten(in_tree, args) pair_out = yield py_args, {} if not isinstance(pair_out, (list, tuple)) or len(pair_out) != 2: msg = ("Custom VJP fwd function must produce a pair (list or tuple of " "length two) representing primal outputs and residuals (values " "stored from the forward pass for use on the backward pass), " "got {}.") raise TypeError(msg.format(pair_out)) py_outs, res = pair_out out, out_tree = tree_flatten(py_outs) res, res_tree = tree_flatten(res) yield res + out, (out_tree, res_tree) @lu.transformation def _flatten_bwd(in_tree, in_avals, out_trees, *args): out_tree, res_tree = out_trees() res, cts_out = split_list(args, [res_tree.num_leaves]) py_res = tree_unflatten(res_tree, res) py_cts_out = tree_unflatten(out_tree, cts_out) py_cts_in = yield (py_res, py_cts_out), {} # For each None in py_cts_in, indicating an argument for which the rule # produces no cotangent, we replace it with a pytree with the structure of the # corresponding subtree of in_tree and with leaves of a non-pytree sentinel # object, to be replaced with Nones in the final returned result. zero = object() # non-pytree sentinel to replace Nones in py_cts_in dummy = tree_unflatten(in_tree, [object()] * in_tree.num_leaves) cts_in_flat = [] append_cts = lambda x, d: cts_in_flat.extend([x] * len(tree_flatten(d)[0])) try: if not isinstance(py_cts_in, tuple): raise ValueError tree_multimap(append_cts, tuple(zero if ct is None else ct for ct in py_cts_in), dummy) except ValueError: _, in_tree2 = tree_flatten(py_cts_in) msg = ("Custom VJP rule must produce an output with the same container " "(pytree) structure as the args tuple of the primal function, " "and in particular must produce a tuple of length equal to the " "number of arguments to the primal function, but got VJP output " "structure {} for primal input structure {}.") raise TypeError(msg.format(in_tree2, in_tree)) from None # Ignore any None cotangents, and any corresponding to inputs for which the # type doesn't equal the tangent type (i.e. float0s) # TODO(mattjj): change this to check if tangent type represents 0dim vspace yield [Zero(a.at_least_vspace()) if ct is zero or a != a.at_least_vspace() else ct for a, ct in zip(in_avals, cts_in_flat)] class CustomVJPCallPrimitive(core.CallPrimitive): initial_style: core.Primitive def bind(self, fun, fwd, bwd, *args, out_trees): args = map(core.full_lower, args) top_trace = core.find_top_trace(args) fun, env_trace_todo1 = core.process_env_traces( fun, self, top_trace and top_trace.level, (), None) fwd, env_trace_todo2 = core.process_env_traces( fwd, self, top_trace and top_trace.level, (), None) tracers = map(top_trace.full_raise, args) # type: ignore outs = top_trace.process_custom_vjp_call(self, fun, fwd, bwd, tracers, out_trees=out_trees) _, env_trace_todo = lu.merge_linear_aux(env_trace_todo1, env_trace_todo2) return _apply_todos(env_trace_todo, map(core.full_lower, outs)) def impl(self, fun, fwd, bwd, *args, out_trees): del fwd, bwd, out_trees with core.new_sublevel(): return fun.call_wrapped(*args) def post_process(self, trace, out_tracers, params): return trace.post_process_custom_vjp_call(out_tracers, params) custom_vjp_call_p = CustomVJPCallPrimitive('custom_vjp_call') def _custom_vjp_call_jaxpr_impl(*args, fun_jaxpr, **_): return core.jaxpr_as_fun(fun_jaxpr)(*args) def _custom_vjp_call_jaxpr_abstract_eval(*_, fun_jaxpr, **__): return fun_jaxpr.out_avals custom_vjp_call_jaxpr_p = core.AxisPrimitive('custom_vjp_call_jaxpr') custom_vjp_call_jaxpr_p.multiple_results = True custom_vjp_call_jaxpr_p.def_impl(_custom_vjp_call_jaxpr_impl) custom_vjp_call_jaxpr_p.def_abstract_eval(_custom_vjp_call_jaxpr_abstract_eval) CustomVJPCallPrimitive.initial_style = custom_vjp_call_jaxpr_p mlir.register_lowering(custom_vjp_call_jaxpr_p, mlir.lower_fun( _custom_vjp_call_jaxpr_impl, multiple_results=True)) def _custom_vjp_call_jaxpr_jvp( primals, tangents, *, fun_jaxpr: core.ClosedJaxpr, fwd_jaxpr_thunk: Callable[[], Tuple[core.Jaxpr, Sequence[Any]]], bwd: lu.WrappedFun, out_trees: Callable, num_consts: int): _, args = split_list(primals, [num_consts]) consts_dot, args_dot = split_list(tangents, [num_consts]) if any(type(t) is not Zero for t in consts_dot): raise ad.CustomVJPException() fwd_jaxpr, fwd_consts = fwd_jaxpr_thunk() # consts can be tracers! out_tree, res_tree = out_trees() args_dot = map(ad.instantiate_zeros, args_dot) # Cast float0 to zeros with the primal dtype because custom vjp rules don't # currently handle float0s args_dot = map(ad.replace_float0s, args, args_dot) res_and_primals_out = core.eval_jaxpr(fwd_jaxpr, fwd_consts, *args) res, primals_out = split_list(res_and_primals_out, [res_tree.num_leaves]) avals_out = [raise_to_shaped(core.get_aval(x)) for x in primals_out] tangents_out = ad.custom_lin_p.bind( *res, *args_dot, num_res=res_tree.num_leaves, bwd=bwd, out_avals=avals_out) tangents_out = map(ad.recast_to_float0, primals_out, tangents_out) return primals_out, tangents_out ad.primitive_jvps[custom_vjp_call_jaxpr_p] = _custom_vjp_call_jaxpr_jvp def _custom_vjp_call_jaxpr_vmap( axis_size, axis_name, main_type, args, in_dims, *, fun_jaxpr: core.ClosedJaxpr, fwd_jaxpr_thunk: Callable[[], Tuple[core.Jaxpr, Sequence[Any]]], bwd: lu.WrappedFun, out_trees: Callable, num_consts: int): args = [batching.moveaxis(x, d, 0) if d is not not_mapped and d != 0 else x for x, d in zip(args, in_dims)] in_batched = [d is not not_mapped for d in in_dims] _, args_batched = split_list(in_batched, [num_consts]) batched_fun_jaxpr, out_batched = batching.batch_jaxpr( fun_jaxpr, axis_size, in_batched, False, axis_name, main_type) out_dims1 = [0 if b else not_mapped for b in out_batched] out_dims2 = [] @pe._memoize def batched_fwd_jaxpr_thunk(): fwd_jaxpr = core.ClosedJaxpr(*fwd_jaxpr_thunk()) # consts can be tracers batched_fwd_jaxpr, out_batched = batching.batch_jaxpr( fwd_jaxpr, axis_size, args_batched, False, axis_name, main_type) out_dims2.append([0 if b else not_mapped for b in out_batched]) return batched_fwd_jaxpr.jaxpr, batched_fwd_jaxpr.consts fwd_args_batched = [0 if b else not_mapped for b in args_batched] fwd_out_dims = lambda: out_dims2[0] batched_bwd = batching.batch_custom_vjp_bwd(bwd, axis_name, axis_size, fwd_out_dims, fwd_args_batched, main_type) batched_outs = custom_vjp_call_jaxpr_p.bind( *args, fun_jaxpr=batched_fun_jaxpr, fwd_jaxpr_thunk=batched_fwd_jaxpr_thunk, bwd=batched_bwd, out_trees=out_trees, num_consts=num_consts) out_dims = out_dims2[0] if out_dims2 else out_dims1 return batched_outs, out_dims batching.axis_primitive_batchers[custom_vjp_call_jaxpr_p] = _custom_vjp_call_jaxpr_vmap xla.register_translation( custom_vjp_call_jaxpr_p, xla.lower_fun(_custom_vjp_call_jaxpr_impl, new_style=True, multiple_results=True), initial_style=True) batching.primitive_batchers[ad.custom_lin_p] = ad._raise_custom_vjp_error_on_jvp xla.register_translation(ad.custom_lin_p, ad._raise_custom_vjp_error_on_jvp) pe.partial_eval_jaxpr_custom_rules[custom_vjp_call_jaxpr_p] = \ custom_jvp_jaxpr_custom_partial_eval_rule # type: ignore def custom_gradient(fun): """Convenience function for defining custom VJP rules (aka custom gradients). While the canonical way to define custom VJP rules is via ``jax.custom_vjp``, the ``custom_gradient`` convenience wrapper follows TensorFlow's ``tf.custom_gradient`` API. The difference here is that ``custom_gradient`` can be used as a decorator on one function that returns both the primal value (representing the output of the mathematical function to be differentiated) and the VJP (gradient) function. See https://www.tensorflow.org/api_docs/python/tf/custom_gradient. If the mathematical function to be differentiated has type signature ``a -> b``, then the Python callable ``fun`` should have signature ``a -> (b, CT b --o CT a)`` where we use ``CT x`` to denote a cotangent type for ``x`` and the ``--o`` arrow to denote a linear function. See the example below. That is, ``fun`` should return a pair where the first element represents the value of the mathematical function to be differentiated and the second element is a function to be called on the backward pass of reverse-mode automatic differentiation (i.e. the "custom gradient" function). The function returned as the second element of the output of ``fun`` can close over intermediate values computed when evaluating the function to be differentiated. That is, use lexical closure to share work between the forward pass and the backward pass of reverse-mode automatic differentiation. However, it cannot perform Python control flow which depends on the values of the closed-over intermediate values or its cotangent arguments; if the function includes such control flow, an error is raised. Args: fun: a Python callable specifying both the mathematical function to be differentiated and its reverse-mode differentiation rule. It should return a pair consisting of an output value and a Python callable that represents the custom gradient function. Returns: A Python callable that accepts the same arguments as ``fun`` and returns the output value specified by the first element of ``fun``'s output pair. For example: >>> @jax.custom_gradient ... def f(x): ... return x ** 2, lambda g: (g * x,) ... >>> print(f(3.)) 9.0 >>> print(jax.grad(f)(3.)) 3.0 An example with a function on two arguments, so that the VJP function must return a tuple of length two: >>> @jax.custom_gradient ... def f(x, y): ... return x * y, lambda g: (y, x) ... >>> print(f(3., 4.)) 12.0 >>> print(jax.grad(f, argnums=(0, 1))(3., 4.)) (4.0, 3.0) """ @custom_vjp def wrapped_fun(*args, **kwargs): ans, _ = fun(*args, **kwargs) return ans def fwd(*args, **kwargs): ans, rule = fun(*args, **kwargs) ans_flat, out_tree = tree_flatten((ans,)) rule, in_tree = flatten_fun_nokwargs(lu.wrap_init(rule), out_tree) ans_avals = [core.get_aval(x).at_least_vspace() for x in ans_flat] jaxpr, _, consts = pe.trace_to_jaxpr_dynamic(rule, ans_avals) return ans, Residuals(jaxpr, in_tree(), out_tree, consts) def bwd(res, cts): jaxpr, in_tree, out_tree, consts = res cts_flat, out_tree_ = tree_flatten((cts,)) if out_tree != out_tree_: raise TypeError(f'{out_tree}\n!=\n{out_tree_}') cts_out = core.eval_jaxpr(jaxpr, consts, *cts_flat) cts_out = tree_unflatten(in_tree, cts_out) if treedef_is_leaf(in_tree): cts_out = (cts_out,) return cts_out wrapped_fun.defvjp(fwd, bwd) return wrapped_fun @register_pytree_node_class class Residuals: def __init__(self, jaxpr, in_tree, out_tree, consts): self.jaxpr = jaxpr self.in_tree = in_tree self.out_tree = out_tree self.consts = consts def __iter__(self): return iter((self.jaxpr, self.in_tree, self.out_tree, self.consts)) def tree_flatten(self): return self.consts, (self.jaxpr, self.in_tree, self.out_tree) @classmethod def tree_unflatten(cls, aux, consts): jaxpr, in_tree, out_tree = aux return cls(jaxpr, in_tree, out_tree, consts)
[docs]def closure_convert(fun, *example_args): """Closure conversion utility, for use with higher-order custom derivatives. To define custom derivatives such as with ``jax.custom_vjp(f)``, the target function ``f`` must take, as formal arguments, all values involved in differentiation. If ``f`` is a higher-order function, in that it accepts as an argument a Python function ``g``, then values stored away in ``g``'s closure will not be visible to the custom derivative rules, and attempts at AD involving these values will fail. One way around this is to convert the closure by extracting these values, and to pass them as explicit formal arguments across the custom derivative boundary. This utility carries out that conversion. More precisely, it closure-converts the function ``fun`` specialized to the types of the arguments given in ``example_args``. When we refer here to "values in the closure" of ``fun``, we do not mean the values that are captured by Python directly when ``fun`` is defined (e.g. the Python objects in ``fun.__closure__``, if the attribute exists). Rather, we mean values encountered during the execution of ``fun`` on ``example_args`` that determine its output. This may include, for instance, arrays captured transitively in Python closures, i.e. in the Python closure of functions called by ``fun``, the closures of the functions that they call, and so forth. The function ``fun`` must be a pure function. Example usage:: def minimize(objective_fn, x0): converted_fn, aux_args = closure_convert(objective_fn, x0) return _minimize(converted_fn, x0, *aux_args) @partial(custom_vjp, nondiff_argnums=(0,)) def _minimize(objective_fn, x0, *args): z = objective_fn(x0, *args) # ... find minimizer x_opt ... return x_opt def fwd(objective_fn, x0, *args): y = _minimize(objective_fn, x0, *args) return y, (y, args) def rev(objective_fn, res, g): y, args = res y_bar = g # ... custom reverse-mode AD ... return x0_bar, *args_bars _minimize.defvjp(fwd, rev) Args: fun: Python callable to be converted. Must be a pure function. example_args: Arrays, scalars, or (nested) standard Python containers (tuples, lists, dicts, namedtuples, i.e., pytrees) thereof, used to determine the types of the formal arguments to ``fun``. This type-specialized form of ``fun`` is the function that will be closure converted. Returns: A pair comprising (i) a Python callable, accepting the same arguments as ``fun`` followed by arguments corresponding to the values hoisted from its closure, and (ii) a list of values hoisted from the closure. """ flat_args, in_tree = tree_flatten(example_args) in_avals = tuple(map(abstractify, flat_args)) if config.jax_check_tracer_leaks: return _closure_convert_for_avals.__wrapped__(fun, in_tree, in_avals) else: return _closure_convert_for_avals(fun, in_tree, in_avals)
def _is_perturbed(x: Any) -> bool: if isinstance(x, ad.JVPTracer): return True elif isinstance(x, core.Tracer): return any(_is_perturbed(attr) for name, attr in x._contents()) else: return False @cache() def _closure_convert_for_avals(fun, in_tree, in_avals): wrapped_fun, out_tree = flatten_fun_nokwargs(lu.wrap_init(fun), in_tree) jaxpr, out_pvals, consts = pe.trace_to_jaxpr_dynamic(wrapped_fun, in_avals) out_tree = out_tree() (closure_consts, hoisted_consts), merge = partition_list(_is_perturbed, consts) num_consts = len(hoisted_consts) def converted_fun(*args_hconsts): num_args = len(args_hconsts) - num_consts args, hoisted_consts = split_list(args_hconsts, [num_args]) consts = merge(closure_consts, hoisted_consts) all_args, in_tree2 = tree_flatten(tuple(args)) assert in_tree == in_tree2 out_flat = core.eval_jaxpr(jaxpr, consts, *all_args) return tree_unflatten(out_tree, out_flat) return converted_fun, hoisted_consts def partition_list(choice, lst): out = [], [] which = [out[choice(elt)].append(elt) or choice(elt) for elt in lst] def merge(l1, l2): i1, i2 = iter(l1), iter(l2) return [next(i2 if snd else i1) for snd in which] return out, merge def abstractify(x): return core.raise_to_shaped(core.get_aval(x)) ### Custom transposition def linear_call(fun: Callable, fun_transpose: Callable, residual_args, linear_args): """Call a linear function, with a custom implementation for its transpose. The type signatures of ``fun`` and ``fun_transpose`` are: .. code-block:: haskell fun :: r -> a -o b fun_transpose :: r -> b -o a where the ``-o`` arrow indicates a linear function, ``r`` is the residual input type and ``a`` is the linear input type. The functions ``fun`` and ``fun_transpose`` are coupled as transposes of one another. Specifically, the transpose of a ``linear_call`` primitive is another ``linear_call`` to ``fun_transpose``, with ``fun`` as its custom transposition. For example: >>> def f(r, x): ... return x / r >>> def t(r, t): ... return t / r >>> def div_add(x, denom): ... return x + linear_call(f, t, denom, x) >>> def transpose(f, x_example): ... def transposed(y): ... x, = jax.linear_transpose(f, x_example)(y) ... return x ... return transposed >>> div_add(9., 3.) DeviceArray(12., dtype=float32, weak_type=True) >>> transpose(partial(div_add, denom=3.), 1.)(18.) # custom DeviceArray(24., dtype=float32, weak_type=True) >>> transpose(lambda x: x + x / 3., 1.)(18.) # reference DeviceArray(24., dtype=float32, weak_type=True) The above definition of ``f`` illustrates the purpose of a residual argument: division is linear in one of its inputs (the dividend ``x``) but not the other (the divisor ``r``). As another example: >>> def custom_id(x): ... def f(_, x): return x ... def t(_, t): return 7. ... return linear_call(f, t, (), x) >>> custom_id(1.) 1.0 >>> transpose(custom_id, 1.)(1.) 7.0 >>> transpose(transpose(custom_id, 1.), 1.)(1.) 1.0 >>> transpose(transpose(transpose(custom_id, 1.), 1.), 1.)(1.) 7.0 Args: fun: a Python callable specifying a linear function. It should take two arguments: one of "residual" inputs (type ``r``), i.e. inputs in which the function is not necessarly linear, and one of "linear" inputs (type ``a``). It should return output whose components are linear in the linear input (type ``b``). fun_transpose: a Python callable specifying a structurally linear function that is the transpose of ``fun`` with respect to its linear inputs. Its first argument is the same residual inputs (``r``) as ``fun``. Its second argument is of type ``b``. Finally, its output is of type ``a`` and each of its component are linear in its second argument (the ``b`` inputs). residual_args: Argument in which ``fun`` and ``fun_transpose`` are not necessarily linear. Not involved in transposition. linear_args: Argument in which ``fun`` and ``fun_transpose`` are linear and with respect to which the two are transposes. Returns: The call result, i.e. ``fun(residual_args, linear_args)``. """ operands_res, res_tree = tree_flatten(residual_args) operands_lin, lin_tree = tree_flatten(linear_args) f_in_tree = treedef_tuple((res_tree, lin_tree)) f, out_tree = flatten_fun_nokwargs(lu.wrap_init(fun), f_in_tree) res_avals = map(abstractify, operands_res) lin_avals = map(abstractify, operands_lin) f_jaxpr, f_consts = _initial_style_jaxpr(f, (*res_avals, *lin_avals)) f_jaxpr = _close_jaxpr(f_jaxpr) out_avals = map(core.raise_to_shaped, f_jaxpr.out_avals) t_in_tree = treedef_tuple((res_tree, out_tree())) t, t_out_tree = flatten_fun_nokwargs(lu.wrap_init(fun_transpose), t_in_tree) t_jaxpr, t_consts = _initial_style_jaxpr(t, (*res_avals, *out_avals)) t_jaxpr = _close_jaxpr(t_jaxpr) if t_out_tree() != lin_tree: raise TypeError( 'transpose output pytree structure must match that of linear inputs, ' f'got output structure {t_out_tree()} ' f'and input structure {lin_tree}.') out = linear_call_p.bind(*f_consts, *t_consts, *operands_res, *operands_lin, callee=f_jaxpr, transpose=t_jaxpr, num_callee_consts=len(f_consts), num_transpose_consts=len(t_consts), num_res=len(operands_res)) return tree_unflatten(out_tree(), out) def _linear_call_impl(*args, callee, transpose, num_callee_consts, num_transpose_consts, num_res): del transpose consts, _, operands_res, operands_lin = split_list( args, [num_callee_consts, num_transpose_consts, num_res]) return core.eval_jaxpr(callee.jaxpr, (), *consts, *operands_res, *operands_lin) def _linear_call_transpose_rule(cts, *args, callee, transpose, num_callee_consts, num_transpose_consts, num_res): f_consts, t_consts, operands_res, operands_lin = split_list( args, [num_callee_consts, num_transpose_consts, num_res]) _, _, cts_avals = split_list( transpose.in_avals, [num_transpose_consts, num_res]) assert all(ad.is_undefined_primal(x) for x in operands_lin) assert all(not ad.is_undefined_primal(x) for x in operands_res) cts = [zeros_like_aval(a) if type(ct) is Zero else ct for ct, a in zip(cts, cts_avals)] cts_out = linear_call_p.bind(*t_consts, *f_consts, *operands_res, *cts, callee=transpose, transpose=callee, num_callee_consts=len(t_consts), num_transpose_consts=len(f_consts), num_res=len(operands_res)) return [None] * (num_callee_consts + num_transpose_consts + num_res) + cts_out def _linear_call_abstract_eval(*args, **kwargs): return map(core.raise_to_shaped, kwargs['callee'].out_avals) linear_call_p = core.Primitive('linear_call') linear_call_p.multiple_results = True linear_call_p.def_impl(_linear_call_impl) linear_call_p.def_abstract_eval(_linear_call_abstract_eval) ad.primitive_transposes[linear_call_p] = _linear_call_transpose_rule xla.register_translation(linear_call_p, xla.lower_fun(_linear_call_impl, new_style=True, multiple_results=True), initial_style=True) mlir.register_lowering(linear_call_p, mlir.lower_fun( _linear_call_impl, multiple_results=True))