def supervised_loss_arrow(arrow: Arrow,
DiffArrow=SquaredDifference) -> CompositeArrow:
"""
Creates an arrow that computes |f(y) - x|
Args:
Arrow: f: Y -> X - The arrow to modify
DiffArrow: d: X x X - R - Arrow for computing difference
Returns:
f: Y/Theta x .. Y/Theta x X -> |f^{-1}(y) - X| x X
Arrow with same input and output as arrow except that it takes an
addition input with label 'train_output' that should contain examples
in Y, and it returns an additional error output labelled
'supervised_error' which is the |f(y) - x|
"""
c = CompositeArrow(name="%s_supervised" % arrow.name)
# Pipe all inputs of composite to inputs of arrow
# Make all in_ports of inverse inputs to composition
for in_port in arrow.in_ports():
c_in_port = c.add_port()
make_in_port(c_in_port)
if is_param_port(in_port):
make_param_port(c_in_port)
c.add_edge(c_in_port, in_port)
# find difference between inputs to inverse and outputs of fwd
# make error port for each
for i, out_port in enumerate(arrow.out_ports()):
if is_error_port(out_port):
# if its an error port just pass through
error_port = c.add_port()
make_out_port(error_port)
make_error_port(error_port)
transfer_labels(out_port, error_port)
c.add_edge(out_port, error_port)
else:
# If its normal outport then pass through
c_out_port = c.add_port()
make_out_port(c_out_port)
c.add_edge(out_port, c_out_port)
# And compute the error
diff = DiffArrow()
in_port = c.add_port()
make_in_port(in_port)
add_port_label(in_port, "train_output")
c.add_edge(in_port, diff.in_port(0))
c.add_edge(out_port, diff.in_port(1))
error_port = c.add_port()
make_out_port(error_port)
make_error_port(error_port)
add_port_label(error_port, "supervised_error")
c.add_edge(diff.out_port(0), error_port)
assert c.is_wired_correctly()
return c
def inv_fwd_loss_arrow(arrow: Arrow,
inverse: Arrow,
DiffArrow=SquaredDifference) -> CompositeArrow:
"""
Arrow wihch computes |f(f^-1(y)) - y|
Args:
arrow: Forward function
Returns:
CompositeArrow
"""
c = CompositeArrow(name="%s_inv_fwd_loss" % arrow.name)
# Make all in_ports of inverse inputs to composition
for inv_in_port in inverse.in_ports():
in_port = c.add_port()
make_in_port(in_port)
if is_param_port(inv_in_port):
make_param_port(in_port)
c.add_edge(in_port, inv_in_port)
# Connect all out_ports of inverse to in_ports of f
for i, out_port in enumerate(inverse.out_ports()):
if not is_error_port(out_port):
c.add_edge(out_port, arrow.in_port(i))
c_out_port = c.add_port()
# add edge from inverse output to composition output
make_out_port(c_out_port)
c.add_edge(out_port, c_out_port)
# Pass errors (if any) of parametric inverse through as error_ports
for i, out_port in enumerate(inverse.out_ports()):
if is_error_port(out_port):
error_port = c.add_port()
make_out_port(error_port)
make_error_port(error_port)
add_port_label(error_port, "sub_arrow_error")
c.add_edge(out_port, error_port)
# find difference between inputs to inverse and outputs of fwd
# make error port for each
for i, out_port in enumerate(arrow.out_ports()):
diff = DiffArrow()
c.add_edge(c.in_port(i), diff.in_port(0))
c.add_edge(out_port, diff.in_port(1))
error_port = c.add_port()
make_out_port(error_port)
make_error_port(error_port)
add_port_label(error_port, "inv_fwd_error")
c.add_edge(diff.out_port(0), error_port)
assert c.is_wired_correctly()
return c
def comp(fwd: Arrow, right_inv: Arrow, DiffArrow=SquaredDifference):
"""Compositon: Pipe output of forward model into input of right inverse
Args:
fwd: X -> Y
right_inv: Y -> X x Error
Returns:
X -> X
"""
c = CompositeArrow(name="fwd_to_right_inv")
# Connect left boundar to fwd
for in_port in fwd.in_ports():
c_in_port = c.add_port()
make_in_port(c_in_port)
c.add_edge(c_in_port, in_port)
transfer_labels(in_port, c_in_port)
# Connect fwd to right_inv
for i, out_port in enumerate(fwd.out_ports()):
c.add_edge(out_port, right_inv.in_port(i))
# connect right_inv to right boundary
for out_port in right_inv.out_ports():
c_out_port = c.add_port()
make_out_port(c_out_port)
if is_error_port(out_port):
make_error_port(c_out_port)
c.add_edge(out_port, c_out_port)
transfer_labels(out_port, c_out_port)
# Find difference between X and right_inv(f(x))
right_inv_out_ports = list(filter(lambda port: not is_error_port(port),
right_inv.out_ports())) # len(X)
assert len(right_inv_out_ports) == len(c.in_ports())
for i, in_port in enumerate(c.in_ports()):
diff = DiffArrow()
c.add_edge(in_port, diff.in_port(0))
c.add_edge(right_inv_out_ports[i], diff.in_port(1))
error_port = c.add_port()
make_out_port(error_port)
make_error_port(error_port)
add_port_label(error_port, "supervised_error")
c.add_edge(diff.out_port(0), error_port)
assert c.is_wired_correctly()
return c