# Copyright 2020 The JAX Authors.
#
# 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 __future__ import annotations
from collections.abc import Sequence
import dataclasses
from functools import update_wrapper, reduce, partial
import inspect
from typing import Any, Callable, Generic, TypeVar
from jax._src import config
from jax._src import core
from jax._src import custom_api_util
from jax._src.custom_transpose import custom_transpose
from jax._src import dtypes
from jax._src import effects
from jax._src import linear_util as lu
from jax._src import traceback_util
from jax._src.ad_util import (
stop_gradient_p, SymbolicZero, Zero, zeros_like_aval)
from jax._src.api_util import argnums_partial, flatten_fun_nokwargs
from jax._src.core import raise_to_shaped
from jax._src.errors import UnexpectedTracerError
from jax._src.interpreters import ad
from jax._src.interpreters import batching
from jax._src.interpreters import mlir
from jax._src.interpreters import partial_eval as pe
from jax._src.interpreters import xla
from jax._src.interpreters.batching import not_mapped
from jax._src.lax import lax
from jax._src.tree_util import (tree_flatten, tree_unflatten, tree_map,
treedef_is_leaf, treedef_tuple,
register_pytree_node_class, tree_leaves,
tree_flatten_with_path, keystr)
from jax._src.util import (cache, safe_zip, safe_map, split_list, Unhashable,
unzip2)
traceback_util.register_exclusion(__file__)
map = safe_map
zip = safe_zip
### util
def _resolve_kwargs(fun, args, kwargs):
if isinstance(fun, partial):
# functools.partial should have an opaque signature.
fun = lambda *args, **kwargs: None
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 pe.close_jaxpr(pe.convert_constvars_jaxpr(jaxpr))
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
# like the api_util.py function, but also grabs output avals for error checking
@lu.transformation_with_aux
def _flatten_fun_nokwargs(in_tree, *args_flat):
py_args = tree_unflatten(in_tree, args_flat)
ans = yield py_args, {}
ans_flat, ans_tree = tree_flatten(ans)
ans_avals = [core.raise_to_shaped(core.get_aval(x)) for x in ans_flat]
yield ans_flat, (ans_tree, ans_avals)
### JVPs
ReturnValue = TypeVar('ReturnValue')
[docs]
@custom_api_util.register_custom_decorator_type
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
"""
fun: Callable[..., ReturnValue]
nondiff_argnums: tuple[int, ...]
jvp: Callable[..., tuple[ReturnValue, ReturnValue]] | None = None
symbolic_zeros: bool = False
[docs]
def __init__(self,
fun: Callable[..., ReturnValue],
nondiff_argnums: tuple[int, ...] = (),
):
update_wrapper(self, fun)
self.fun = fun
self.nondiff_argnums = nondiff_argnums
__getattr__ = custom_api_util.forward_attr
def defjvp(self,
jvp: Callable[..., tuple[ReturnValue, ReturnValue]],
symbolic_zeros: bool = False,
) -> Callable[..., tuple[ReturnValue, ReturnValue]]:
"""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.
symbolic_zeros: boolean, indicating whether the rule should be passed
objects representing static symbolic zeros in its tangent argument in
correspondence with unperturbed values; otherwise, only standard JAX
types (e.g. array-likes) are passed. Setting this option to ``True``
allows a JVP rule to detect whether certain inputs are not involved in
differentiation, but at the cost of needing special handling for these
objects (which e.g. can't be passed into jax.numpy functions). Default
``False``.
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
self.symbolic_zeros = symbolic_zeros
return jvp
def defjvps(self, *jvps: Callable[..., ReturnValue] | None):
"""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_map(_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
primal_name = getattr(self.fun, '__name__', str(self.fun))
if not self.jvp:
msg = f"No JVP defined for custom_jvp function {primal_name} using defjvp."
raise AttributeError(msg)
jvp_name = getattr(self.jvp, '__name__', str(self.jvp))
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 # type: ignore
jvp = lu.wrap_init(self.jvp)
args_flat, in_tree = tree_flatten(dyn_args)
flat_fun, out_type1 = _flatten_fun_nokwargs(f_, in_tree)
flat_jvp, out_type2 = _flatten_jvp(jvp, primal_name, jvp_name, in_tree,
out_type1)
out_flat = custom_jvp_call_p.bind(flat_fun, flat_jvp, *args_flat,
symbolic_zeros=self.symbolic_zeros)
_, (out_tree, _) = lu.merge_linear_aux(out_type1, out_type2)
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)
@partial(lu.transformation_with_aux, use_eq_store=True)
def _flatten_jvp(primal_name, jvp_name, in_tree, maybe_out_type, *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 = (f"Custom JVP rule {jvp_name} for function {primal_name} "
"must produce a pair (list or tuple of length two) representing "
f"primal and tangent outputs, but got {pair_out}.")
raise TypeError(msg)
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)
primal_avals = [core.raise_to_shaped(core.get_aval(x)) for x in primals_out]
if out_tree != out_tree2:
msg = (f"Custom JVP rule {jvp_name} for function {primal_name} must "
"produce primal and tangent outputs with equal container (pytree) "
f"structures, but got {out_tree} and {out_tree2} respectively.")
raise TypeError(msg)
# If the primal function already ran, check out_tree agreement.
try: out_type_ = maybe_out_type()
except lu.StoreException: out_type_ = None
if out_type_ is not None:
out_tree_, primal_avals_ = out_type_
ty_tree = tree_unflatten(out_tree , [a.str_short() for a in primal_avals])
ty_tree_ = tree_unflatten(out_tree_, [a.str_short() for a in primal_avals_])
if out_tree_ != out_tree:
m = (f"Custom JVP rule {jvp_name} for function {primal_name} must "
"produce a pair (list or tuple of length two) "
"where the first element represents the primal output "
"(equal in value to the output of the custom_jvp-decorated function "
f"{primal_name}, "
"and in particular of the same container/pytree structure), but "
"instead the JVP rule output's first element had container/pytree "
"structure:\n"
f""" {str(ty_tree ).replace("'", "")}\n"""
f"while the custom_jvp-decorated function {primal_name} had output "
"container/pytree structure:\n"
f""" {str(ty_tree_).replace("'", "")}.""")
raise TypeError(m)
if not all(map(core.typematch, primal_avals, primal_avals_)):
m = (f"Custom JVP rule {jvp_name} for function {primal_name} must "
"produce a pair (list or tuple of length two) "
"where the first element represents the primal output "
"(equal in value to the output of the custom_jvp-decorated function "
f"{primal_name}, "
"and in particular with leaves of the same shape/dtype), but "
"instead the JVP rule output's first element had shapes/dtypes of:\n"
f""" {str(ty_tree ).replace("'", "")}\n"""
f"while the custom_jvp-decorated function {primal_name} had output "
"shapes/dtypes of:\n"
f""" {str(ty_tree_).replace("'", "")}""")
raise TypeError(m)
# 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()
if type(t) is not SymbolicZero else t.aval.strip_weak_type()
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 = (
f" primal {av1.str_short()} for tangent {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, primal_avals)
class CustomJVPCallPrimitive(core.Primitive):
multiple_results = True
def bind(self, fun, jvp, *args, symbolic_zeros):
args = map(core.full_lower, args)
top_trace = core.find_top_trace(args)
fun, env_trace_todo1 = process_env_traces(
fun, self, top_trace and top_trace.level, False)
jvp, env_trace_todo2 = process_env_traces(
jvp, self, top_trace and top_trace.level, True)
tracers = map(top_trace.full_raise, args) # type: ignore
outs = top_trace.process_custom_jvp_call(self, fun, jvp, tracers, # type: ignore
symbolic_zeros=symbolic_zeros) # type: ignore
_, env_trace_todo = lu.merge_linear_aux(env_trace_todo1, env_trace_todo2)
return core.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, jvp_was_run: bool):
return trace.post_process_custom_jvp_call(out_tracers, jvp_was_run)
def get_bind_params(self, params):
new_params = dict(params)
call_jaxpr = new_params.pop('call_jaxpr')
num_consts = new_params.pop('num_consts')
jvp_jaxpr_thunk = new_params.pop('jvp_jaxpr_thunk')
fun = lu.wrap_init(core.jaxpr_as_fun(call_jaxpr))
jvp = lift_jvp(num_consts, jvp_jaxpr_thunk)
return [fun, jvp], new_params
def lift_jvp(num_consts: int, jvp_jaxpr_thunk: Callable) -> lu.WrappedFun:
@lu.wrap_init
def jvp(*xs):
n, ragged = divmod(len(xs), 2)
assert not ragged
primals, tangents = xs[num_consts:n], xs[n+num_consts:]
zeros = [type(t) is SymbolicZero for t in tangents]
jvp_jaxpr, jvp_consts, out_zeros = jvp_jaxpr_thunk(*zeros)
nonzero_tangents = [t for t in tangents if type(t) is not SymbolicZero]
out = core.eval_jaxpr(jvp_jaxpr, jvp_consts, *primals, *nonzero_tangents)
out_primals, nz_out_tangents = split_list(out, [len(out_zeros)])
nz_out_tangents_ = iter(nz_out_tangents)
out_tangents = [SymbolicZero(core.get_aval(p).at_least_vspace())
if z else next(nz_out_tangents_)
for p, z in zip(out_primals, out_zeros)]
assert next(nz_out_tangents_, None) is None
return [*out_primals, *out_tangents]
return jvp
@partial(lu.transformation_with_aux, use_eq_store=True)
def process_env_traces(primitive, level: int, jvp_was_run: bool, *args):
outs = yield args, {}
todo = []
while True:
tracers = [x for x in outs if isinstance(x, core.Tracer)
and (level is None or x._trace.level > level)]
if tracers:
ans = max(tracers, key=lambda x: x._trace.level)
else:
break
trace = ans._trace.main.with_cur_sublevel()
outs = map(trace.full_raise, outs)
outs, cur_todo = primitive.post_process(trace, outs, jvp_was_run)
todo.append(cur_todo)
yield outs, tuple(todo) # Ensure the aux output is immutable
effects.custom_derivatives_allowed_effects.add_type(lax.InOutFeedEffect)
custom_jvp_call_p = CustomJVPCallPrimitive('custom_jvp_call')
def _custom_jvp_call_typecheck(_, *in_avals, call_jaxpr, jvp_jaxpr_thunk,
num_consts, symbolic_zeros):
# TODO(mattjj): could do more checking here...
del in_avals, jvp_jaxpr_thunk, num_consts
disallowed_effects = effects.custom_derivatives_allowed_effects.filter_not_in(call_jaxpr.effects)
if disallowed_effects:
raise NotImplementedError(
f'Effects not supported in `custom_jvp`: {disallowed_effects}')
return call_jaxpr.out_avals, call_jaxpr.effects
core.custom_typechecks[custom_jvp_call_p] = _custom_jvp_call_typecheck
def _custom_jvp_call_mlir_translation(ctx, *args, call_jaxpr, jvp_jaxpr_thunk,
num_consts, symbolic_zeros):
del jvp_jaxpr_thunk, num_consts, symbolic_zeros
args_ = map(mlir.wrap_singleton_ir_values, args)
consts = mlir._ir_consts(call_jaxpr.consts)
out, tokens = mlir.jaxpr_subcomp(ctx.module_context, call_jaxpr.jaxpr,
ctx.name_stack, ctx.tokens_in, consts,
*args_, dim_var_values=ctx.dim_var_values)
ctx.set_tokens_out(tokens)
return out
mlir.register_lowering(custom_jvp_call_p, _custom_jvp_call_mlir_translation)
# If a (multi)linear function is defined with a custom jvp, then
# custom_jvp_call_ can appear in jaxprs to be transposed. Since it's already
# been linearized, we can drop the jvp rule.
def _custom_jvp_call_transpose(params, jaxpr, args, ct, _):
del params
return ad.backward_pass(jaxpr.jaxpr, None, jaxpr.consts, args, ct)
ad.primitive_transposes[custom_jvp_call_p] = _custom_jvp_call_transpose
### VJPs
[docs]
@custom_api_util.register_custom_decorator_type
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
"""
[docs]
def __init__(self,
fun: Callable[..., ReturnValue],
nondiff_argnums: tuple[int, ...] = ()):
update_wrapper(self, fun)
self.fun = fun
self.nondiff_argnums = nondiff_argnums
self.fwd: Callable[..., tuple[ReturnValue, Any]] | None = None
self.bwd: Callable[..., tuple[Any, ...]] | None = None
self.symbolic_zeros = False
__getattr__ = custom_api_util.forward_attr
def defvjp(self,
fwd: Callable[..., tuple[ReturnValue, Any]],
bwd: Callable[..., tuple[Any, ...]],
symbolic_zeros: bool = False,
) -> 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.
symbolic_zeros: boolean, determining whether to indicate symbolic zeros
to the ``fwd`` and ``bwd`` rules. Enabling this option allows custom
derivative rules to detect when certain inputs, and when certain
output cotangents, are not involved in differentiation. If ``True``:
* ``fwd`` must accept, in place of each leaf value ``x`` in
the pytree comprising an argument to the original function,
an object (of type
``jax.custom_derivatives.CustomVJPPrimal``) with two
attributes instead: ``value`` and ``perturbed``. The
``value`` field is the original primal argument, and
``perturbed`` is a boolean. The ``perturbed`` bit indicates
whether the argument is involved in differentiation (i.e.,
if it is ``False``, then the corresponding Jacobian "column"
is zero).
* ``bwd`` will be passed objects representing static symbolic zeros in
its cotangent argument in correspondence with unperturbed values;
otherwise, only standard JAX types (e.g. array-likes) are passed.
Setting this option to ``True`` allows these rules to detect whether
certain inputs and outputs are not involved in differentiation, but at
the cost of special handling. For instance:
* The signature of ``fwd`` changes, and the objects it is passed cannot
be output from the rule directly.
* The ``bwd`` rule is passed objects that are not entirely array-like,
and that cannot be passed to most ``jax.numpy`` functions.
* Any custom pytree nodes involved in the primal function's arguments
must accept, in their unflattening functions, the two-field record
objects that are given as input leaves to the ``fwd`` rule.
Default ``False``.
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
self.symbolic_zeros = symbolic_zeros
@traceback_util.api_boundary
def __call__(self, *args: Any, **kwargs: Any) -> ReturnValue: # pytype: disable=invalid-annotation
primal_name = getattr(self.fun, '__name__', str(self.fun))
if not self.fwd or not self.bwd:
msg = f"No VJP defined for custom_vjp function {primal_name} using defvjp."
raise AttributeError(msg)
fwd_name = getattr(self.fwd, '__name__', str(self.fwd))
args = _resolve_kwargs(self.fun, args, kwargs)
if config.enable_custom_vjp_by_custom_transpose.value:
if self.nondiff_argnums:
raise NotImplementedError(
'nondiff_argnums not implemented for new custom_vjp')
return custom_vjp_by_custom_transpose(self.fun, self.fwd, self.bwd)(*args)
else:
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_type = _flatten_fun_nokwargs(f_, in_tree)
flat_fwd, out_trees = _flatten_fwd(fwd, self.symbolic_zeros, primal_name,
fwd_name, in_tree, out_type)
flat_bwd = _flatten_bwd(bwd, in_tree, in_avals, out_trees).call_wrapped
out_flat = custom_vjp_call_p.bind(flat_fun, flat_fwd, flat_bwd,
*args_flat, out_trees=out_trees,
symbolic_zeros=self.symbolic_zeros)
_, (out_tree, _) = lu.merge_linear_aux(out_type, out_trees)
return tree_unflatten(out_tree, out_flat)
@dataclasses.dataclass
class CustomVJPPrimal:
"""Primal to a ``custom_vjp``'s forward rule when ``symbolic_zeros`` is set"""
value: Any
perturbed: bool
def custom_vjp_primal_tree_values(tree):
"""Strips away perturbation information from forward rule arguments.
This is a helper function for user with the ``symbolic_zeros`` option to
the ``defvjp`` method of a ``custom_vjp``-decorated function.
In ``symbolic_zeros`` mode, the custom forward rule receives arguments
whose pytree leaves are records with a ``value`` attribute that carries
the primal argument. This is a way to convert such argument trees back to
their original form, replacing each such record with its carried value at
each leaf.
"""
def value(leaf):
if type(leaf) is not CustomVJPPrimal:
raise TypeError(f"unexpected leaf type {type(leaf)}")
return leaf.value
return tree_map(value, tree)
def _check_for_tracers(x):
for leaf in tree_leaves(x):
if isinstance(leaf, 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.")
raise UnexpectedTracerError(msg)
@partial(lu.transformation_with_aux, use_eq_store=True)
def _flatten_fwd(symbolic_zeros, primal_name, fwd_name, in_tree, maybe_out_type,
*args):
if symbolic_zeros:
args = [CustomVJPPrimal(x, z) for x, z in zip(args[::2], args[1::2])]
else:
args = args[::2]
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 = (f"Custom VJP fwd rule {fwd_name} for function {primal_name} "
"must produce a pair (list or tuple of length two) where the first "
"element represents the primal output (equal to those of the "
f"custom_vjp-decorated function {primal_name}) and the "
"second element represents residuals (i.e. values stored from the "
"forward pass for use on the backward pass), but "
f"instead of a pair the fwd rule {fwd_name} produced {pair_out}.")
raise TypeError(msg)
py_primals_out, res = pair_out
primals_out, out_tree = tree_flatten(py_primals_out)
res, res_tree = tree_flatten(res)
primal_avals = [core.raise_to_shaped(core.get_aval(x)) for x in primals_out]
# If the primal function already ran, check out_tree agreement.
try: out_type_ = maybe_out_type()
except lu.StoreException: out_type_ = None
if out_type_ is not None:
out_tree_, primal_avals_ = out_type_
ty_tree = tree_unflatten(out_tree , [a.str_short() for a in primal_avals])
ty_tree_ = tree_unflatten(out_tree_, [a.str_short() for a in primal_avals_])
if out_tree_ != out_tree:
m = (f"Custom VJP fwd rule {fwd_name} for function {primal_name} "
"must produce a pair (list or tuple of length two) where the first "
"element represents the primal output "
"(equal to the output of the custom_vjp-decorated function "
f"{primal_name}) and the "
"second element represents residuals (i.e. values stored from the "
"forward pass for use on the backward pass), but "
"instead the fwd rule output's first element had container/pytree "
"structure:\n"
f""" {str(ty_tree ).replace("'", "")}\n"""
f"while the custom_vjp-decorated function {primal_name} had output "
"container/pytree structure:\n"
f""" {str(ty_tree_).replace("'", "")}.""")
raise TypeError(m)
if not all(map(core.typematch, primal_avals, primal_avals_)):
m = (f"Custom VJP fwd rule {fwd_name} for function {primal_name} must "
"produce a pair (list or tuple of length two) "
"where the first element represents the primal output "
"(equal to the output of the custom_vjp-decorated function "
f"{primal_name}) and the second element represents residuals "
"(i.e. values stored from the forward pass for use on the "
"backward pass), but "
"instead the fwd rule output's first element had shapes/dtypes of:\n"
f""" {str(ty_tree ).replace("'", "")}\n"""
f"while the custom_vjp-decorated function {primal_name} had output "
"shapes/dtypes of:\n"
f""" {str(ty_tree_).replace("'", "")}""")
raise TypeError(m)
yield (*res, *primals_out), (out_tree, res_tree)
@lu.transformation
def _flatten_bwd(in_tree, in_avals, out_trees, *args):
out_tree, res_tree = out_trees()
assert len(args) == res_tree.num_leaves + out_tree.num_leaves
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)
keypaths, _ = unzip2(tree_flatten_with_path(dummy)[0])
cts_in_flat = []
def append(x, d):
num_leaves = len(tree_flatten(d)[0])
if x is None and d is not None:
cts_in_flat.extend([zero] * num_leaves)
elif x is not None:
cts_in_flat.extend([x] * num_leaves)
return x
try:
if not isinstance(py_cts_in, tuple):
raise ValueError
tree_map(append, py_cts_in, dummy, is_leaf=lambda x: x is None)
except ValueError:
_, in_tree2 = tree_flatten(py_cts_in)
msg = ("Custom VJP bwd 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 bwd output "
"structure {} for primal input structure {}.")
raise TypeError(msg.format(in_tree2, in_tree)) from None
results = []
for kp, a, ct in zip(keypaths, in_avals, cts_in_flat):
if ct is zero or a != a.at_least_vspace():
results.append(Zero(a.at_least_vspace()))
elif type(ct) is SymbolicZero:
if not core.typecompat(a.at_least_vspace(), a_ := ct.aval):
msg = ("Custom VJP bwd rule produced a SymbolicZero with a shape/dtype "
"that does not match the corresponding input tangent shape/dtype: "
f"the SymbolicZero had shape/dtype {a_.str_short()} while the "
f"corresponding input had shape/dtype {a.str_short()}. "
"Consider just returning a None here instead of a SymbolicZero "
"object.")
raise ValueError(msg)
results.append(Zero(ct.aval))
else:
if (not core.typecompat(a.at_least_vspace(), a_ := core.get_aval(ct))
and not (_temporary_dtype_exception(a, a_) or
_temporary_shape_exception(a, a_))):
msg = ("Custom VJP bwd rule must produce an output with the same "
"shape/dtypes as the args tuple of the primal function, but at "
f"output{keystr(kp)} the bwd rule produced an output of "
f"shape/dtype {raise_to_shaped(a_).str_short()} corresponding "
f"to an input of shape/dtype {a.str_short()}.")
raise ValueError(msg)
results.append(ct)
yield results
# TODO(mattjj): remove both these exceptions to cotangent compatibility check
def _temporary_dtype_exception(a, a_) -> bool:
if isinstance(a, core.ShapedArray) and isinstance(a_, core.ShapedArray):
return (a.shape == a_.shape and
(dtypes.issubdtype(a_.dtype, dtypes.extended) or
dtypes.issubdtype(a.dtype, dtypes.np.inexact)))
return False
# TODO(mattjj): remove both these exceptions to cotangent compatibility check
def _temporary_shape_exception(a, a_) -> bool:
return config.custom_vjp_disable_shape_check.value
class CustomVJPCallPrimitive(core.CallPrimitive):
initial_style: core.Primitive
def bind(self, fun, fwd, bwd, *args, out_trees, symbolic_zeros):
args = map(core.full_lower, args)
top_trace = core.find_top_trace(args)
fun, env_trace_todo1 = process_env_traces(
fun, self, top_trace and top_trace.level, False)
fwd, env_trace_todo2 = process_env_traces_fwd(
fwd, top_trace and top_trace.level, out_trees)
tracers = map(top_trace.full_raise, args) # type: ignore
bwd_ = lambda *args: bwd(*args)
outs = top_trace.process_custom_vjp_call(self, fun, fwd, bwd_, tracers,
out_trees=out_trees,
symbolic_zeros=symbolic_zeros)
fst, env_trace_todo = lu.merge_linear_aux(env_trace_todo1, env_trace_todo2)
if fst:
return core.apply_todos(env_trace_todo, map(core.full_lower, outs))
else:
env_trace_todo, bwd_transform = env_trace_todo
bwd = _apply_bwd_transform(bwd_transform, bwd)
return core.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')
@partial(lu.transformation_with_aux, use_eq_store=True)
def process_env_traces_fwd(level: int, out_trees, *args):
outs = yield args, {}
todo = []
bwd_transforms = []
while True:
tracers = [x for x in outs if isinstance(x, core.Tracer)
and (level is None or x._trace.level > level)]
if tracers:
ans = max(tracers, key=lambda x: x._trace.level)
else:
break
trace = ans._trace.main.with_cur_sublevel()
outs = map(trace.full_raise, outs)
outs, cur_todo, bwd_xform = trace.post_process_custom_vjp_call_fwd(outs, out_trees)
todo.append(cur_todo)
bwd_transforms.append(bwd_xform)
yield outs, (tuple(todo), tuple(bwd_transforms))
def _apply_bwd_transform(todos, bwd):
todos_list = list(todos)
while todos_list:
bwd = todos_list.pop()(bwd)
return bwd
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, **__):
disallowed_effects = effects.custom_derivatives_allowed_effects.filter_not_in(fun_jaxpr.effects)
if disallowed_effects:
raise NotImplementedError(
f'Effects not supported in `custom_vjp`: {disallowed_effects}')
return fun_jaxpr.out_avals, fun_jaxpr.effects
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_effectful_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]]],
num_consts: int, bwd: Callable, out_trees: Callable, symbolic_zeros: bool):
_, 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()
zeros = [type(t) is not Zero for t in args_dot]
fwd_jaxpr, fwd_consts = fwd_jaxpr_thunk(*zeros) # consts can be tracers!
_, res_tree = out_trees()
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]
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)
tangents_out = ad.custom_lin_p.bind(
*res, *args_dot, num_res=res_tree.num_leaves, bwd=bwd,
out_avals=avals_out, symbolic_zeros=symbolic_zeros)
tangents_out = map(lax.tie_p.bind, primals_out, tangents_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(
spmd_axis_name, axis_size, axis_name, main_type, args, in_dims, *,
fun_jaxpr: core.ClosedJaxpr,
fwd_jaxpr_thunk: Callable[..., tuple[core.Jaxpr, Sequence[Any]]],
num_consts: int, bwd: Callable, out_trees: Callable, symbolic_zeros: bool):
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, spmd_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(*zeros):
fwd_jaxpr = core.ClosedJaxpr(*fwd_jaxpr_thunk(*zeros)) # consts can be tracers
batched_fwd_jaxpr, out_batched = batching.batch_jaxpr(
fwd_jaxpr, axis_size, args_batched, False, axis_name, spmd_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,
spmd_axis_name)
batched_outs = custom_vjp_call_jaxpr_p.bind(
*args, fun_jaxpr=batched_fun_jaxpr,
fwd_jaxpr_thunk=batched_fwd_jaxpr_thunk, bwd=batched_bwd,
num_consts=num_consts, out_trees=out_trees, symbolic_zeros=symbolic_zeros)
out_dims = out_dims2[0] if out_dims2 else out_dims1
return batched_outs, out_dims
batching.spmd_axis_primitive_batchers[custom_vjp_call_jaxpr_p] = \
_custom_vjp_call_jaxpr_vmap
batching.axis_primitive_batchers[custom_vjp_call_jaxpr_p] = partial(
_custom_vjp_call_jaxpr_vmap, None)
xla.register_initial_style_primitive(custom_vjp_call_jaxpr_p)
batching.primitive_batchers[ad.custom_lin_p] = ad.raise_custom_vjp_error_on_jvp
mlir.register_lowering(ad.custom_lin_p, ad.raise_custom_vjp_error_on_jvp)
[docs]
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 Haskell-like signature
``a -> b``, then the Python callable ``fun`` should have the 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: (g * y, g * x)
...
>>> print(f(3., 4.))
12.0
>>> print(jax.grad(f, argnums=(0, 1))(3., 4.))
(Array(4., dtype=float32, weak_type=True), Array(3., dtype=float32, weak_type=True))
"""
@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: Callable, *example_args) -> tuple[Callable, list[Any]]:
"""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.check_tracer_leaks.value:
return _closure_convert_for_avals.__wrapped__(fun, in_tree, in_avals)
else:
return _closure_convert_for_avals(fun, in_tree, in_avals)
def _maybe_perturbed(x: Any) -> bool:
# False if x can't represent an AD-perturbed value (i.e. a value
# with a nontrivial tangent attached), up to heuristics, and True otherwise.
# See https://github.com/google/jax/issues/6415 for motivation.
x = core.full_lower(x)
if not isinstance(x, core.Tracer):
# If x is not a Tracer, it can't be perturbed.
return False
elif isinstance(x, pe.DynamicJaxprTracer):
# If x is a DynamicJaxprTracer then we're staging out; differentiation could
# happen later, but some types always have trivial tangents.
vspace = x.aval.at_least_vspace()
return not (vspace is core.abstract_token or
getattr(vspace, 'dtype', None) == dtypes.float0)
elif not isinstance(x, ad.JVPTracer):
# If x is not a JVPTracer, recursively check its contents.
return any(_maybe_perturbed(attr) for name, attr in x._contents())
else:
return True # We can't be sure!
@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(_maybe_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 `Haskell-like 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.)
Array(12., dtype=float32, weak_type=True)
>>> transpose(partial(div_add, denom=3.), 1.)(18.) # custom
Array(24., dtype=float32, weak_type=True)
>>> transpose(lambda x: x + x / 3., 1.)(18.) # reference
Array(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 necessarily 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)``.
.. _Haskell-like type signatures: https://wiki.haskell.org/Type_signature
"""
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_initial_style_primitive(linear_call_p)
mlir.register_lowering(linear_call_p, mlir.lower_fun(
_linear_call_impl, multiple_results=True))
# A stageable primitive that fails when evaluated
unreachable_p: core.Primitive = core.Primitive('unreachable')
unreachable_p.multiple_results = True
def unreachable_impl(*_, out_avals, exc_type, message):
del out_avals
raise exc_type(message)
# Evaluation raises an exception
unreachable_p.def_impl(unreachable_impl)
# Translation raises an exception
# TODO(frostig,mattjj): We have no good way to translate a function
# that errs. Since MLIR lowering over-approximates concrete evaluation,
# we err on MLIR lowering for the time being.
mlir.register_lowering(unreachable_p, unreachable_impl)
# Abstract evaluation proceeds without issue, to allow for staging
unreachable_p.def_abstract_eval(lambda *_, out_avals, **__: out_avals)
def unreachable(*args, out_avals=None, exc_type=TypeError,
message='unreachable'):
"""Fail when evaluated concretely (but allow for staging).
This function allows one to assert an impossibility of
evaluation. It can be used to guarantee that evaluation does not
"reach" a certain point in the sense that it does not execute, but
it can nonetheless be staged out by JAX without error.
Args:
*args: The arbitrary pytree of arguments to the function.
out_avals: Optional specification of the output types of this
function invocation from the point of view of staging. If
``None``, these are chosen as equal to types of input arguments.
exc_type: Optional constructor for the Python exception raised if
evaluated.
message: Optional string message for the Python exception raised
if evaluated.
"""
if out_avals is None:
out_avals = tree_map(core.get_aval, args)
args_flat, in_tree = tree_flatten(args)
out_avals_flat, out_tree = tree_flatten(out_avals)
out = unreachable_p.bind(*args_flat, out_avals=out_avals_flat,
exc_type=exc_type, message=message)
return tree_unflatten(out_tree, out)
disallow_jvp = partial(
unreachable,
exc_type=TypeError,
message="can't apply forward-mode autodiff (jvp) to a custom_vjp function.")
def custom_vjp_by_custom_transpose(fun, fwd, bwd):
fun = custom_jvp(fun)
@fun.defjvp
def jvp(primals, tangents):
outs, residuals = fwd(*primals)
tan_out_types = tree_map(lambda o: core.get_aval(o).at_least_vspace(), outs)
tan_fn = custom_transpose(partial(disallow_jvp, out_avals=tan_out_types))
tan_fn.def_transpose(bwd)
return outs, tan_fn(tan_out_types, residuals, tangents)
return fun
# TODO(mattjj): remove these stubs, which exist to avoid breaking internal users
custom_jvp_call_jaxpr_p = core.Primitive("custom_jvp_call_jaxpr")
