def visit_Expr(self, node):
# We need to special-case pushes, e.g. utils.push(_stack,x,op_id)
adjoint = []
if (isinstance(node.value, gast.Call)
and anno.getanno(node.value, 'func') == utils.push):
orig_src = quoting.unquote(node)
stack, val, op_id = node.value.args
push_template = grads.adjoints[utils.push]
adjoint_rhs = template.replace(push_template,
namer=self.namer,
stack=stack,
val=val,
op_id=op_id)
# Walk the RHS adjoint AST to find temporary adjoint variables to
# sum
accumulation = template.replace(
'd[xi] = add_grad(d[xi], dxi_partial)',
namer=self.namer,
replace_grad=template.Replace.FULL,
xi=val,
dxi_partial=ast_.copy_node(adjoint_rhs[0].targets[0]),
add_grad=utils.ADD_GRAD)
adjoint = adjoint_rhs + [accumulation]
for i, adj in enumerate(adjoint):
adjoint[i] = comments.add_comment(adj,
'Grad of: %s' % orig_src)
return node, adjoint
def primal_and_adjoint_for_tracing(self, node):
"""Build the primal and adjoint of a traceable function.
Args:
node: ast.Call node of a function we wish to trace, instead of transform
Returns:
primal: new ast.Assign node to replace the original primal call
adjoint: new ast.Assign node using the VJP generated in primal to
calculate the adjoint.
"""
primal_template = grads.primals[tracing.Traceable]
adjoint_template = grads.adjoints[tracing.Traceable]
# Prep
to_pack = node.args
target = ast_.copy_node(self.orig_target)
vjp = quoting.quote(self.namer.unique('%s_grad' % node.func.id))
tmp = create.create_temp(quoting.quote('tmp'), self.namer)
assert len(node.keywords) == 0
# Full replacement of primal
# TODO: do we need to set 'pri_call' on this?
primal = template.replace(
primal_template,
namer=self.namer,
result=target,
fn=node.func,
tmp=tmp,
vjp=vjp,
args=gast.Tuple(elts=to_pack, ctx=gast.Load()))
# Building adjoint using the vjp generated with the primal
dto_pack = gast.Tuple(
elts=[create.create_temp_grad(arg, self.namer) for arg in to_pack],
ctx=gast.Store())
adjoint = template.replace(
adjoint_template,
namer=self.namer,
result=target,
vjp=vjp,
dargs=dto_pack)
return primal, adjoint
def visit_For(self, node):
if node.orelse:
raise ValueError
# Construct the primal and adjoint of the loop
body, adjoint_body = self.visit_statements(node.body)
# We create a loop counter which will be pushed on the stack
push, pop, op_id = get_push_pop()
counter = self.namer.counter()
# In `for i in range ...` the variable `i` is the target, which we
# temporarily set aside each iteration to push to the stack later
push_target, pop_target, op_id_target = get_push_pop()
tmp_target = create.create_temp(node.target, self.namer)
primal_template = grads.primals[gast.For]
primal = template.replace(
primal_template,
body=body,
i=counter,
push=push,
target=node.target,
iter_=node.iter,
push_target=push_target,
_target=tmp_target,
_stack=self.stack,
op_id_iter=op_id,
op_id_target=op_id_target)
adjoint_template = grads.adjoints[gast.For]
adjoint = template.replace(
adjoint_template,
adjoint_body=adjoint_body,
i=counter,
pop=pop,
pop_target=pop_target,
target=ast_.copy_node(node.target),
_stack=self.stack,
op_id_iter=op_id,
op_id_target=op_id_target)
return primal, adjoint
def visit_Return(self, node):
orig_retval = ast_.copy_node(node.value)
retval = node.value
if isinstance(retval, (gast.Name, gast.Subscript)):
retval = gast.Tuple(
elts=[create.create_grad(retval, self.namer, tangent=True)],
ctx=gast.Load())
elif isinstance(retval, gast.Tuple):
retval.elts = [
create.create_grad(elt, self.namer, tangent=True)
for elt in retval.elts
]
else:
raise ValueError
for n in retval.elts:
n.ctx = gast.Load()
if self.preserve_result:
retval.elts.append(orig_retval)
node.value = retval
return node
def visit_Name(self, node):
if node.id in self.replacements:
# NOTE In principle we don't want to copy, because it might break
# references held in annotations, but we will copy if we have to to
# avoid duplicate nodes
if node.id in self.seen:
new_nodes = ast_.copy_node(self.replacements[node.id])
else:
self.seen.add(node.id)
new_nodes = self.replacements[node.id]
if isinstance(new_nodes, gast.AST):
new_nodes = [new_nodes]
for new_node in new_nodes:
anno.setanno(new_node, 'replacement', node, safe=False)
if 'ctx' in new_node._fields:
new_node.ctx = node.ctx
if len(new_nodes) == 1:
new_nodes, = new_nodes
return new_nodes
else:
return node
def visit_Call(self, node):
"""Create adjoint for call.
We don't allow unpacking of parameters, so we know that each argument
gets passed in explicitly, allowing us to create partials for each.
However, templates might perform parameter unpacking (for cases where
the number of arguments is variable) and express their gradient as a
tuple. In this case, we have to unpack this tuple of partials.
"""
# Find the function we are differentiating
func = anno.getanno(node, 'func')
if func in non_differentiable.NON_DIFFERENTIABLE:
return node, []
if func == tracing.Traceable:
return self.primal_and_adjoint_for_tracing(node)
if func in grads.UNIMPLEMENTED_ADJOINTS:
raise errors.ReverseNotImplementedError(func)
# If we don't have an adjoint, we will have to step into the called
# function and differentiate it
if func not in grads.adjoints:
active_args = tuple(i for i, arg in enumerate(node.args)
if arg.id in self.active_variables)
already_counted = False
for f, a in self.required:
if f.__name__ == func.__name__ and set(a) == set(active_args):
already_counted = True
break
if not already_counted:
self.required.append((func, active_args))
pri_name = naming.primal_name(func, active_args)
pri_call = gast.Call(
func=gast.Name(id=pri_name, ctx=gast.Load(), annotation=None),
args=[self.substack] + node.args,
keywords=node.keywords)
anno.setanno(pri_call, 'pri_call', True)
dy = create.create_grad(self.target, self.namer)
dy.ctx = gast.Load()
dx = create.create_grad(node.args[0], self.namer)
dx.ctx = gast.Store()
adj_name = naming.adjoint_name(func, active_args)
adj_call = gast.Call(
func=gast.Name(id=adj_name, ctx=gast.Load(), annotation=None),
args=[self.substack, dy] + node.args,
keywords=node.keywords)
anno.setanno(adj_call, 'adj_call', True)
adjoint = [template.replace('dxs = dfx', namer=self.namer, dfx=adj_call)]
for j, i in enumerate(active_args):
adjoint.append(template.replace('d[x] = dxs[i]', namer=self.namer,
x=node.args[i].id, i=gast.Num(n=j)))
return pri_call, adjoint
# We have a template for the gradient that we need to fill in
template_ = grads.adjoints[func]
# Match the function call to the template
sig = funcsigs.signature(template_)
sig = sig.replace(parameters=list(sig.parameters.values())[1:])
kwargs = dict((keyword.arg, keyword.value) for keyword in node.keywords)
bound_args = sig.bind(*node.args, **kwargs)
# Fill in any missing kwargs with the defaults from the template
args = quoting.parse_function(template_).body[0].args
kwargs = dict(zip(*map(reversed, [args.args, args.defaults])))
kwargs.update(dict(zip(args.kwonlyargs, args.kw_defaults)))
for arg, val in kwargs.items():
if arg.id not in bound_args.arguments:
bound_args.arguments[arg.id] = val
# Let's fill in the template. The first argument is the output, which
# was stored in a temporary variable
output_name = six.get_function_code(template_).co_varnames[0]
arg_replacements = {output_name: ast_.copy_node(self.target)}
arg_replacements.update(bound_args.arguments)
# If the template uses *args, then we pack the corresponding inputs
packing = []
flags = six.get_function_code(template_).co_flags
if flags & inspect.CO_VARARGS:
to_pack = node.args[six.get_function_code(template_).co_argcount - 1:]
vararg_name = six.get_function_code(template_).co_varnames[-1]
target = gast.Name(annotation=None, id=vararg_name, ctx=gast.Store())
value = gast.Tuple(elts=to_pack, ctx=gast.Load())
packing = [gast.Assign(targets=[target], value=value)]
# And we fill in the packed tuple into the template
arg_replacements[six.get_function_code(
template_).co_varnames[-1]] = target
adjoint = template.replace(template_, namer=self.namer, **arg_replacements)
unpacking = []
if flags & inspect.CO_VARARGS:
# If the template packs arguments, then we have to unpack the
# derivatives afterwards
# We also have to update the replacements tuple then
dto_pack = [create.create_temp_grad(arg, self.namer)
for arg in to_pack]
value = create.create_grad(target, self.namer)
target = gast.Tuple(elts=dto_pack, ctx=gast.Store())
unpacking = [gast.Assign(targets=[target], value=value)]
return node, packing + adjoint + unpacking
def visit_Assign(self, node):
"""Visit assignment statement."""
if len(node.targets) != 1:
raise ValueError('no support for chained assignment')
# Before the node gets modified, get a source code representation
# to add as a comment later on
if anno.hasanno(node, 'pre_anf'):
orig_src = anno.getanno(node, 'pre_anf')
else:
orig_src = quoting.unquote(node)
# Set target for the RHS visitor to access
self.orig_target = ast_.copy_node(node.targets[0])
# If we know we're going to be putting another stack on the stack,
# we should try to make that explicit
if isinstance(node.value, gast.Call) and \
anno.hasanno(node.value, 'func') and \
anno.getanno(node.value, 'func') in (utils.Stack, utils.pop_stack):
push, pop, op_id = get_push_pop_stack()
else:
push, pop, op_id = get_push_pop()
push_stack, pop_stack, op_id_stack = get_push_pop_stack()
# Every assignment statement requires us to store the pre-value, and in the
# adjoint restore the value, and reset the gradient
store = template.replace(
'push(_stack, y, op_id)',
push=push,
y=self.orig_target,
_stack=self.stack,
op_id=op_id)
create_substack = template.replace(
'substack = tangent.Stack()', substack=self.substack)
store_substack = template.replace(
'push(stack, substack, op_id)',
push=push_stack,
stack=self.stack,
substack=self.substack,
op_id=op_id_stack)
restore = template.replace(
'y = pop(_stack, op_id)',
_stack=self.stack,
pop=pop,
y=ast_.copy_node(self.orig_target),
op_id=op_id)
restore_substack = template.replace(
'substack = pop(stack, op_id)',
pop=pop_stack,
stack=self.stack,
substack=self.substack,
op_id=op_id_stack)
reset = template.replace(
'd[y] = init_grad(y, allow_lazy_initializer=True)',
y=self.orig_target,
init_grad=utils.INIT_GRAD,
namer=self.namer,
replace_grad=template.Replace.FULL)
# If there are no active nodes, we don't need to find an adjoint
# We simply store and restore the state, and reset the gradient
if not self.is_active(node):
return [store, node], [restore, reset]
# We create a temporary variable for the target that the RHS can use
self.target = create.create_temp(self.orig_target, self.namer)
create_tmp = template.replace(
'tmp = y', tmp=self.target, y=self.orig_target)
# Get the primal and adjoint of the RHS expression
try:
fx, adjoint_rhs = self.visit(node.value)
except ValueError as e:
context = [t.id if hasattr(t, 'id') else t for t in node.targets]
raise ValueError(
'Failed to process assignment to: %s. Error: %s' % (context, e))
if not isinstance(adjoint_rhs, list):
adjoint_rhs = [adjoint_rhs]
# Walk the RHS adjoint AST to find temporary adjoint variables to sum
accumulations = []
for n in adjoint_rhs:
for succ in gast.walk(n):
if anno.hasanno(succ, 'temp_adjoint_var'):
xi = anno.getanno(succ, 'temp_adjoint_var')
dxi_partial = ast_.copy_node(succ)
accumulations.append(template.replace(
'd[xi] = add_grad(d[xi], dxi_partial)',
namer=self.namer, replace_grad=template.Replace.FULL,
xi=xi, dxi_partial=dxi_partial, add_grad=utils.ADD_GRAD))
# The primal consists of storing the state and then performing the
# assignment with the new primal.
# The primal `fx` may be optionally (but rarely) redefined when the
# adjoint is generated, in `fx, adjoint_rhs = self.visit(node.value)`.
# If we see that the primal value is an Assign node, or a list of nodes
# (with at least one being an Assign) node, we allow the primal to change.
# Otherwise, we'll build our own Assign node.
if isinstance(fx, gast.Assign):
assign = [fx]
elif (isinstance(fx, list) and
any([isinstance(ifx, gast.Assign) for ifx in fx])):
assign = fx
else:
assign = template.replace(
'y = fx', y=ast_.copy_node(self.orig_target), fx=fx)
assign = [assign]
primal = [store, create_substack, store_substack] + assign
# The adjoint involves creating the temporary, restoring the store,
# calculating the adjoint, resetting the gradient, and finally accumulating
# the partials
adjoint = [create_tmp, restore_substack, restore
] + adjoint_rhs + [reset] + accumulations
# If the LHS is a subscript assignment with variable index, we need to
# store and restore that as well
if (isinstance(self.orig_target, gast.Subscript) and
isinstance(self.orig_target.slice.value, gast.Name)):
push, pop, op_id = get_push_pop()
i = self.orig_target.slice.value
push_index = template.replace(
'push(_stack, i, op_id)',
push=push,
i=i,
_stack=self.stack,
op_id=op_id)
pop_index = template.replace(
'i = pop(_stack, op_id)',
pop=pop,
i=i,
_stack_=self.stack,
op_id=op_id)
primal.insert(len(primal), push_index)
adjoint.insert(0, pop_index)
# Add a comment in the backwards pass, indicating which
# lines in the forward pass generated the adjoint
for i, adj in enumerate(adjoint):
adjoint[i] = comments.add_comment(adj, 'Grad of: %s' % orig_src)
return primal, adjoint
def visit_FunctionDef(self, node):
# Construct a namer to guarantee we create unique names that don't
# override existing names
self.namer = naming.Namer.build(node)
# Check that this function has exactly one return statement at the end
return_nodes = [n for n in gast.walk(node) if isinstance(n, gast.Return)]
if ((len(return_nodes) > 1) or not isinstance(node.body[-1], gast.Return)):
raise ValueError('function must have exactly one return statement')
return_node = ast_.copy_node(return_nodes[0])
# Perform AD on the function body
body, adjoint_body = self.visit_statements(node.body[:-1])
# Annotate the first statement of the primal and adjoint as such
if body:
body[0] = comments.add_comment(body[0], 'Beginning of forward pass')
if adjoint_body:
adjoint_body[0] = comments.add_comment(
adjoint_body[0], 'Beginning of backward pass')
# Before updating the primal arguments, extract the arguments we want
# to differentiate with respect to
dx = gast.Tuple([create.create_grad(node.args.args[i], self.namer)
for i in self.wrt], ctx=gast.Load())
if self.preserve_result:
# Append an extra Assign operation to the primal body
# that saves the original output value
stored_result_node = quoting.quote(self.namer.unique('result'))
assign_stored_result = template.replace(
'result=orig_result',
result=stored_result_node,
orig_result=return_node.value)
body.append(assign_stored_result)
dx.elts.append(stored_result_node)
for _dx in dx.elts:
_dx.ctx = gast.Load()
return_dx = gast.Return(value=dx)
# We add the stack as first argument of the primal
node.args.args = [self.stack] + node.args.args
# Rename the function to its primal name
func = anno.getanno(node, 'func')
node.name = naming.primal_name(func, self.wrt)
# The new body is the primal body plus the return statement
node.body = body + node.body[-1:]
# Find the cost; the first variable of potentially multiple return values
# The adjoint will receive a value for the initial gradient of the cost
y = node.body[-1].value
if isinstance(y, gast.Tuple):
y = y.elts[0]
dy = gast.Name(id=self.namer.grad(y.id), ctx=gast.Param(),
annotation=None)
# Construct the adjoint
adjoint_template = grads.adjoints[gast.FunctionDef]
adjoint, = template.replace(adjoint_template, namer=self.namer,
adjoint_body=adjoint_body, return_dx=return_dx)
adjoint.args.args.extend([self.stack, dy])
adjoint.args.args.extend(node.args.args[1:])
adjoint.name = naming.adjoint_name(func, self.wrt)
return node, adjoint
def substack(self):
if not hasattr(self, '_substack'):
self._substack = quoting.quote(self.namer.unique(naming.SUBSTACK_NAME))
return ast_.copy_node(self._substack)
