def gen_data(lmbda: float, size: int):
forward_arrow = CompositeArrow(name="forward")
in_port1 = forward_arrow.add_port()
make_in_port(in_port1)
in_port2 = forward_arrow.add_port()
make_in_port(in_port2)
out_port = forward_arrow.add_port()
make_out_port(out_port)
subtraction = SubArrow()
absolute = AbsArrow()
forward_arrow.add_edge(in_port1, subtraction.in_ports()[0])
forward_arrow.add_edge(in_port2, subtraction.in_ports()[1])
forward_arrow.add_edge(subtraction.out_ports()[0], absolute.in_ports()[0])
forward_arrow.add_edge(absolute.out_ports()[0], out_port)
assert forward_arrow.is_wired_correctly()
inverse_arrow = CompositeArrow(name="inverse")
in_port = inverse_arrow.add_port()
make_in_port(in_port)
param_port_1 = inverse_arrow.add_port()
make_in_port(param_port_1)
make_param_port(param_port_1)
param_port_2 = inverse_arrow.add_port()
make_in_port(param_port_2)
make_param_port(param_port_2)
out_port_1 = inverse_arrow.add_port()
make_out_port(out_port_1)
out_port_2 = inverse_arrow.add_port()
make_out_port(out_port_2)
inv_sub = InvSubArrow()
inv_abs = InvAbsArrow()
inverse_arrow.add_edge(in_port, inv_abs.in_ports()[0])
inverse_arrow.add_edge(param_port_1, inv_abs.in_ports()[1])
inverse_arrow.add_edge(inv_abs.out_ports()[0], inv_sub.in_ports()[0])
inverse_arrow.add_edge(param_port_2, inv_sub.in_ports()[1])
inverse_arrow.add_edge(inv_sub.out_ports()[0], out_port_1)
inverse_arrow.add_edge(inv_sub.out_ports()[1], out_port_2)
assert inverse_arrow.is_wired_correctly()
eps = 1e-5
data = []
dist = ExponentialRV(lmbda)
for _ in range(size):
x = tuple(dist.sample(shape=[2]))
y = np.abs(x[0] - x[1])
theta = (np.sign(x[0] - x[1]), x[1])
y_ = apply(forward_arrow, list(x))
x_ = apply(inverse_arrow, [y, theta[0], theta[1]])
assert np.abs(y_[0] - y) < eps
assert np.abs(x_[0] - x[0]) < eps
assert np.abs(x_[1] - x[1]) < eps
data.append((x, theta, y))
return data, forward_arrow, inverse_arrow
def unparam(arrow: Arrow, nnet: Arrow = None):
"""Unparameerize an arrow by sticking a tfArrow between its normal inputs,
and any parametric inputs
Args:
arrow: Y x Theta -> X
nnet: Y -> Theta
Returns:
Y -> X
"""
c = CompositeArrow(name="%s_unparam" % arrow.name)
in_ports = [p for p in arrow.in_ports() if not is_param_port(p)]
param_ports = [p for p in arrow.in_ports() if is_param_port(p)]
if nnet is None:
nnet = TfArrow(n_in_ports=len(in_ports), n_out_ports=len(param_ports))
for i, in_port in enumerate(in_ports):
c_in_port = c.add_port()
make_in_port(c_in_port)
transfer_labels(in_port, c_in_port)
c.add_edge(c_in_port, in_port)
c.add_edge(c_in_port, nnet.in_port(i))
for i, param_port in enumerate(param_ports):
c.add_edge(nnet.out_port(i), param_port)
for out_port in arrow.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)
transfer_labels(out_port, c_out_port)
c.add_edge(out_port, c_out_port)
assert c.is_wired_correctly()
return c
def __init__(self, lmbda: float) -> None:
comp_arrow = CompositeArrow(name="ExponentialRVQuantile")
in_port = comp_arrow.add_port()
make_in_port(in_port)
out_port = comp_arrow.add_port()
make_out_port(out_port)
lmbda_source = SourceArrow(lmbda)
one_source = SourceArrow(1.0)
one_minus_p = SubArrow()
comp_arrow.add_edge(one_source.out_ports()[0],
one_minus_p.in_ports()[0])
comp_arrow.add_edge(in_port, one_minus_p.in_ports()[1])
ln = LogArrow()
comp_arrow.add_edge(one_minus_p.out_ports()[0], ln.in_ports()[0])
negate = NegArrow()
comp_arrow.add_edge(ln.out_ports()[0], negate.in_ports()[0])
div_lmbda = DivArrow()
comp_arrow.add_edge(negate.out_ports()[0], div_lmbda.in_ports()[0])
comp_arrow.add_edge(lmbda_source.out_ports()[0],
div_lmbda.in_ports()[1])
comp_arrow.add_edge(div_lmbda.out_ports()[0], out_port)
assert comp_arrow.is_wired_correctly()
self.quantile = comp_arrow
def SumNArrow(ninputs: int):
"""
Create arrow f(x1, ..., xn) = sum(x1, ..., xn)
Args:
n: number of inputs
Returns:
Arrow of n inputs and one output
"""
assert ninputs > 1
c = CompositeArrow(name="SumNArrow")
light_port = c.add_port()
make_in_port(light_port)
for _ in range(ninputs - 1):
add = AddArrow()
c.add_edge(light_port, add.in_port(0))
dark_port = c.add_port()
make_in_port(dark_port)
c.add_edge(dark_port, add.in_port(1))
light_port = add.out_port(0)
out_port = c.add_port()
make_out_port(out_port)
c.add_edge(add.out_port(0), out_port)
assert c.is_wired_correctly()
assert c.num_in_ports() == ninputs
return c
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 create_arrow(arrow: CompositeArrow, equiv_thetas, port_attr, valid_ports,
symbt_ports):
# New parameter space should have nclasses elements
nclasses = num_unique_elem(equiv_thetas)
new_arrow = CompositeArrow(name="%s_elim" % arrow.name)
for out_port in arrow.out_ports():
c_out_port = new_arrow.add_port()
make_out_port(c_out_port)
transfer_labels(out_port, c_out_port)
if is_error_port(out_port):
make_error_port(c_out_port)
new_arrow.add_edge(out_port, c_out_port)
flat_shape = SourceArrow(np.array([nclasses], dtype=np.int32))
flatten = ReshapeArrow()
new_arrow.add_edge(flat_shape.out_port(0), flatten.in_port(1))
slim_param_flat = flatten.out_port(0)
batch_size = None
for in_port in arrow.in_ports():
if in_port in valid_ports:
symbt = symbt_ports[in_port]['symbolic_tensor']
indices = []
for theta in symbt.symbols:
setid = equiv_thetas[theta]
indices.append(setid)
shape = get_port_shape(in_port, port_attr)
if len(shape) > 1:
if batch_size is not None:
assert shape[0] == batch_size
batch_size = shape[0]
gather = GatherArrow()
src = SourceArrow(np.array(indices, dtype=np.int32))
shape_shape = SourceArrow(np.array(shape, dtype=np.int32))
reshape = ReshapeArrow()
new_arrow.add_edge(slim_param_flat, gather.in_port(0))
new_arrow.add_edge(src.out_port(0), gather.in_port(1))
new_arrow.add_edge(gather.out_port(0), reshape.in_port(0))
new_arrow.add_edge(shape_shape.out_port(0), reshape.in_port(1))
new_arrow.add_edge(reshape.out_port(0), in_port)
else:
new_in_port = new_arrow.add_port()
make_in_port(new_in_port)
if is_param_port(in_port):
make_param_port(new_in_port)
transfer_labels(in_port, new_in_port)
new_arrow.add_edge(new_in_port, in_port)
assert nclasses % batch_size == 0
slim_param = new_arrow.add_port()
make_in_port(slim_param)
make_param_port(slim_param)
new_arrow.add_edge(slim_param, flatten.in_port(0))
set_port_shape(slim_param, (batch_size, nclasses // batch_size))
assert new_arrow.is_wired_correctly()
return new_arrow
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
def g_from_g_theta(inv: Arrow, g_theta: Arrow):
"""
Construct an amoritzed random variable g from a parametric inverse `inv`
and function `g_theta` which constructs parameters for `inv`
Args:
g_theta: Y x Y ... Y x Z -> Theta
Returns:
Y x Y x .. x Z -> X x ... X x Error x ... Error
"""
c = CompositeArrow(name="%s_g_theta" % inv.name)
inv_in_ports, inv_param_ports, inv_out_ports, inv_error_ports = split_ports(
inv)
g_theta_in_ports, g_theta_param_ports, g_theta_out_ports, g_theta_error_ports = split_ports(
g_theta)
assert len(g_theta_out_ports) == len(inv_param_ports)
# Connect y to g_theta and f
for i in range(len(inv_in_ports)):
y_in_port = c.add_port()
make_in_port(y_in_port)
c.add_edge(y_in_port, g_theta.in_port(i))
c.add_edge(y_in_port, inv_in_ports[i])
# conect up noise input to g_theta
z_in_port = c.add_port()
make_in_port(z_in_port)
c.add_edge(z_in_port, g_theta.in_port(len(inv_in_ports)))
# connect g_theta to inv
for i in range(len(g_theta_out_ports)):
c.add_edge(g_theta.out_port(i), inv_param_ports[i])
for inv_out_port in inv_out_ports:
out_port = c.add_port()
make_out_port(out_port)
c.add_edge(inv_out_port, out_port)
for inv_error_port in inv_error_ports:
error_port = c.add_port()
make_out_port(error_port)
make_error_port(error_port)
c.add_edge(inv_error_port, error_port)
assert c.is_wired_correctly()
return c
def reparam(comp_arrow: CompositeArrow,
phi_shape: Tuple,
nn_takes_input=True):
"""Reparameterize an arrow. All parametric inputs now function of phi
Args:
comp_arrow: Arrow to reparameterize
phi_shape: Shape of parameter input
"""
reparam = CompositeArrow(name="%s_reparam" % comp_arrow.name)
phi = reparam.add_port()
set_port_shape(phi, phi_shape)
make_in_port(phi)
make_param_port(phi)
n_in_ports = 1
if nn_takes_input:
n_in_ports += comp_arrow.num_in_ports() - comp_arrow.num_param_ports()
nn = TfArrow(n_in_ports=n_in_ports, n_out_ports=comp_arrow.num_param_ports())
reparam.add_edge(phi, nn.in_port(0))
i = 0
j = 1
for port in comp_arrow.ports():
if is_param_port(port):
reparam.add_edge(nn.out_port(i), port)
i += 1
else:
re_port = reparam.add_port()
if is_out_port(port):
make_out_port(re_port)
reparam.add_edge(port, re_port)
if is_in_port(port):
make_in_port(re_port)
reparam.add_edge(re_port, port)
if nn_takes_input:
reparam.add_edge(re_port, nn.in_port(j))
j += 1
if is_error_port(port):
make_error_port(re_port)
for label in get_port_labels(port):
add_port_label(re_port, label)
assert reparam.is_wired_correctly()
return reparam
def ConcatShuffleArrow(n_inputs: int, ndims: int):
"""Concatenate n_inputs inputs and shuffle
Arrow first n_inputs inputs are arrays to shuffle
last input is permutation vector
Args:
n_inputs"""
c = CompositeArrow(name="ConcatShuffle")
stack = StackArrow(n_inputs, axis=0)
for i in range(n_inputs):
in_port = c.add_port()
make_in_port(in_port)
c.add_edge(in_port, stack.in_port(i))
# Permutation vector
perm = c.add_port()
make_in_port(perm)
set_port_dtype(perm, 'int32')
gather = GatherArrow()
c.add_edge(stack.out_port(0), gather.in_port(0))
c.add_edge(perm, gather.in_port(1))
# Switch the first and last dimension
# FIXME: I do this only because gather seems to affect only first dimension
# There's a better way, probably using gather_nd
a = [i for i in range(ndims + 1)]
tp_perm = [a[i + 1] for i in range(len(a) - 1)] + [a[0]]
transpose = TransposeArrow(tp_perm)
c.add_edge(gather.out_port(0), transpose.in_port(0))
out = c.add_port()
make_out_port(out)
c.add_edge(transpose.out_port(0), out)
assert c.is_wired_correctly()
return c
def set_gan_arrow(arrow: Arrow,
cond_gen: Arrow,
disc: Arrow,
n_fake_samples: int,
ndims: int,
x_shapes=None,
z_shape=None) -> CompositeArrow:
"""
Arrow wihch computes loss for amortized random variable using set gan.
Args:
arrow: Forward function
cond_gen: Y x Z -> X - Conditional Generators
disc: X^n -> {0,1}^n
n_fake_samples: n, number of samples seen by discriminator at once
ndims: dimensionality of dims
Returns:
CompositeArrow: X x Z x ... Z x RAND_PERM -> d_Loss x g_Loss x Y x ... Y
"""
# TODO: Assumes that f has single in_port and single out_port, generalize
c = CompositeArrow(name="%s_set_gan" % arrow.name)
assert cond_gen.num_in_ports(
) == 2, "don't handle case of more than one Y input"
cond_gens = [deepcopy(cond_gen) for i in range(n_fake_samples)]
comp_in_ports = []
# Connect x to arrow in puts
for i in range(arrow.num_in_ports()):
in_port = c.add_port()
make_in_port(in_port)
comp_in_ports.append(in_port)
c.add_edge(in_port, arrow.in_port(i))
if x_shapes is not None:
set_port_shape(in_port, x_shapes[i])
# Connect f(x) to generator
for i in range(n_fake_samples):
for j in range(arrow.num_out_ports()):
c.add_edge(arrow.out_port(j), cond_gens[i].in_port(j))
# Connect noise input to generator second inport
for i in range(n_fake_samples):
noise_in_port = c.add_port()
make_in_port(noise_in_port)
if z_shape is not None:
set_port_shape(noise_in_port, z_shape)
cg_noise_in_port_id = cond_gens[i].num_in_ports() - 1
c.add_edge(noise_in_port, cond_gens[i].in_port(cg_noise_in_port_id))
stack_shuffles = []
rand_perm_in_port = c.add_port()
make_in_port(rand_perm_in_port)
set_port_shape(rand_perm_in_port, (n_fake_samples + 1, ))
set_port_dtype(rand_perm_in_port, 'int32')
# For every output of g, i.e. x and y if f(x, y) = z
# Stack all the Xs from the differet samples together and shuffle
cond_gen_non_error_out_ports = cond_gen.num_out_ports(
) - cond_gen.num_error_ports()
for i in range(cond_gen_non_error_out_ports):
stack_shuffle = ConcatShuffleArrow(n_fake_samples + 1, ndims)
stack_shuffles.append(stack_shuffle)
# Add each output from generator to shuffle set
for j in range(n_fake_samples):
c.add_edge(cond_gens[j].out_port(i), stack_shuffle.in_port(j))
# Add the posterior sample x to the shuffle set
c.add_edge(comp_in_ports[i], stack_shuffle.in_port(n_fake_samples))
c.add_edge(rand_perm_in_port,
stack_shuffle.in_port(n_fake_samples + 1))
gan_loss_arrow = GanLossArrow(n_fake_samples + 1)
# Connect output of each stack shuffle to discriminator
for i in range(cond_gen_non_error_out_ports):
c.add_edge(stack_shuffles[i].out_port(0), disc.in_port(i))
c.add_edge(disc.out_port(0), gan_loss_arrow.in_port(0))
c.add_edge(rand_perm_in_port, gan_loss_arrow.in_port(1))
# Add generator and discriminator loss ports
loss_d_port = c.add_port()
make_out_port(loss_d_port)
make_error_port(loss_d_port)
c.add_edge(gan_loss_arrow.out_port(0), loss_d_port)
loss_g_port = c.add_port()
make_out_port(loss_g_port)
make_error_port(loss_g_port)
c.add_edge(gan_loss_arrow.out_port(1), loss_g_port)
# Connect fake samples to output of composition
for i in range(n_fake_samples):
for j in range(cond_gen_non_error_out_ports):
sample = c.add_port()
make_out_port(sample)
c.add_edge(cond_gens[i].out_port(j), sample)
# Pipe up error ports
for cond_gen in cond_gens:
for i in range(cond_gen_non_error_out_ports, cond_gen.num_out_ports()):
error_port = c.add_port()
make_out_port(error_port)
c.add_edge(cond_gen.out_port(i), error_port)
assert c.is_wired_correctly()
return c