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from __future__ import with_statement
import mdp
import bimdp
from mdp import numx, numx_rand
class TestGradientExtension(object):
def test_sfa_gradient(self):
"""Test gradient for combination of SFA nodes."""
sfa_node1 = bimdp.nodes.SFABiNode(output_dim=8)
sfa_node2 = bimdp.nodes.SFABiNode(output_dim=7)
sfa_node3 = bimdp.nodes.SFABiNode(output_dim=5)
flow = sfa_node1 + sfa_node2 + sfa_node3
x = numx_rand.random((300, 10))
flow.train(x)
x = numx_rand.random((2, 10))
mdp.activate_extension("gradient")
try:
flow.execute(x, {"method": "gradient"})
finally:
mdp.deactivate_extension("gradient")
def test_gradient_product(self):
"""Test that the product of gradients is calculated correctly."""
sfa_node1 = bimdp.nodes.SFABiNode(output_dim=5)
sfa_node2 = bimdp.nodes.SFABiNode(output_dim=3)
flow = sfa_node1 + sfa_node2
x = numx_rand.random((300, 10))
flow.train(x)
mdp.activate_extension("gradient")
try:
x1 = numx_rand.random((2, 10))
x2, msg = sfa_node1.execute(x1, {"method": "gradient"})
grad1 = msg["grad"]
_, msg = sfa_node2.execute(x2, {"method": "gradient"})
grad2 = msg["grad"]
grad12 = flow.execute(x1, {"method": "gradient"})[1]["grad"]
# use a different way to calculate the product of the gradients,
# this method is too memory intensive for large data
ref_grad = numx.sum(grad2[:,:,numx.newaxis,:] *
numx.transpose(grad1[:,numx.newaxis,:,:], (0,1,3,2)),
axis=3)
assert numx.amax(abs(ref_grad - grad12)) < 1E-9
finally:
mdp.deactivate_extension("gradient")
def test_quadexpan_gradient1(self):
"""Test validity of gradient for QuadraticExpansionBiNode."""
node = mdp.nodes.QuadraticExpansionNode()
x = numx.array([[1, 3, 4]])
node.execute(x)
mdp.activate_extension("gradient")
try:
result = node._gradient(x)
grad = result[1]["grad"]
reference = numx.array(
[[[ 1, 0, 0], # x1
[ 0, 1, 0], # x2
[ 0, 0, 1], # x3
[ 2, 0, 0], # x1x1
[ 3, 1, 0], # x1x2
[ 4, 0, 1], # x1x3
[ 0, 6, 0], # x2x2
[ 0, 4, 3], # x2x3
[ 0, 0, 8]]]) # x3x3
assert numx.all(grad == reference)
finally:
mdp.deactivate_extension("gradient")
def test_quadexpan_gradient2(self):
"""Test gradient with multiple data points."""
node = mdp.nodes.QuadraticExpansionNode()
x = numx_rand.random((3,5))
node.execute(x)
mdp.activate_extension("gradient")
try:
result = node._gradient(x)
gradient = result[1]["grad"]
assert gradient.shape == (3,20,5)
finally:
mdp.deactivate_extension("gradient")
def test_sfa2_gradient(self):
sfa2_node1 = bimdp.nodes.SFA2BiNode(output_dim=5)
sfa2_node2 = bimdp.nodes.SFA2BiNode(output_dim=3)
flow = sfa2_node1 + sfa2_node2
x = numx_rand.random((300, 6))
flow.train(x)
x = numx_rand.random((2, 6))
mdp.activate_extension("gradient")
try:
flow.execute(x, {"method": "gradient"})
finally:
mdp.deactivate_extension("gradient")
def test_sfa2_gradient2(self):
def _alt_sfa2_grad(self, x):
"""Reference grad method based on quadratic forms."""
# note that the H and f arrays are cached in the node and remain even
# after the extension has been deactivated
if not hasattr(self, "__gradient_Hs"):
quad_forms = [self.get_quadratic_form(i)
for i in range(self.output_dim)]
self.__gradient_Hs = numx.vstack((quad_form.H[numx.newaxis]
for quad_form in quad_forms))
self.__gradient_fs = numx.vstack((quad_form.f[numx.newaxis]
for quad_form in quad_forms))
grad = (numx.dot(x, self.__gradient_Hs) +
numx.repeat(self.__gradient_fs[numx.newaxis,:,:],
len(x), axis=0))
return grad
sfa2_node = bimdp.nodes.SFA2BiNode(output_dim=3)
x = numx_rand.random((300, 6))
sfa2_node.train(x)
sfa2_node.stop_training()
x = numx_rand.random((2, 6))
mdp.activate_extension("gradient")
try:
result1 = sfa2_node.execute(x, {"method": "gradient"})
grad1 = result1[1]["grad"]
grad2 = _alt_sfa2_grad(sfa2_node, x)
assert numx.amax(abs(grad1 - grad2)) < 1E-9
finally:
mdp.deactivate_extension("gradient")
def test_layer_gradient(self):
"""Test gradient for a simple layer."""
node1 = mdp.nodes.SFA2Node(input_dim=4, output_dim=3)
node2 = mdp.nodes.SFANode(input_dim=6, output_dim=2)
layer = mdp.hinet.Layer([node1, node2])
x = numx_rand.random((100,10))
layer.train(x)
layer.stop_training()
mdp.activate_extension("gradient")
try:
x = numx_rand.random((7,10))
result = layer._gradient(x)
grad = result[1]["grad"]
# get reference result
grad1 = node1._gradient(x[:, :node1.input_dim])[1]["grad"]
grad2 = node2._gradient(x[:, node1.input_dim:])[1]["grad"]
ref_grad = numx.zeros(((7,5,10)))
ref_grad[:, :node1.output_dim, :node1.input_dim] = grad1
ref_grad[:, node1.output_dim:, node1.input_dim:] = grad2
assert numx.all(grad == ref_grad)
finally:
mdp.deactivate_extension("gradient")
def test_clonebilayer_gradient(self):
"""Test gradient for a simple layer."""
layer = bimdp.hinet.CloneBiLayer(
bimdp.nodes.SFA2BiNode(input_dim=5, output_dim=2),
n_nodes=3)
x = numx_rand.random((100,15))
layer.train(x)
layer.stop_training()
mdp.activate_extension("gradient")
try:
x = numx_rand.random((7,15))
result = layer._gradient(x)
grad = result[1]["grad"]
assert grad.shape == (7,6,15)
finally:
mdp.deactivate_extension("gradient")
def test_switchboard_gradient1(self):
"""Test that gradient is correct for a tiny switchboard."""
sboard = mdp.hinet.Switchboard(input_dim=4, connections=[2,0])
x = numx_rand.random((2,4))
mdp.activate_extension("gradient")
try:
result = sboard._gradient(x)
grad = result[1]["grad"]
ref_grad = numx.array([[[0,0,1,0], [1,0,0,0]],
[[0,0,1,0], [1,0,0,0]]], dtype=grad.dtype)
assert numx.all(grad == ref_grad)
finally:
mdp.deactivate_extension("gradient")
def test_switchboard_gradient2(self):
"""Test gradient for a larger switchboard."""
dim = 100
connections = [int(i) for i in numx.random.random((dim,)) * (dim-1)]
sboard = mdp.hinet.Switchboard(input_dim=dim, connections=connections)
x = numx.random.random((10, dim))
# assume a 5-dimensional gradient at this stage
grad = numx.random.random((10, dim, 5))
# original reference implementation
def _switchboard_grad(self, x):
grad = numx.zeros((self.output_dim, self.input_dim))
grad[range(self.output_dim), self.connections] = 1
return numx.tile(grad, (len(x), 1, 1))
with mdp.extension("gradient"):
result = sboard._gradient(x, grad)
ext_grad = result[1]["grad"]
tmp_grad = _switchboard_grad(sboard, x)
ref_grad = numx.asarray([numx.dot(tmp_grad[i], grad[i])
for i in range(len(tmp_grad))])
assert numx.all(ext_grad == ref_grad)
def test_network_gradient(self):
"""Test gradient for a small SFA network."""
sfa_node = bimdp.nodes.SFABiNode(input_dim=4*4, output_dim=5)
switchboard = bimdp.hinet.Rectangular2dBiSwitchboard(
in_channels_xy=8,
field_channels_xy=4,
field_spacing_xy=2)
flownode = bimdp.hinet.BiFlowNode(bimdp.BiFlow([sfa_node]))
sfa_layer = bimdp.hinet.CloneBiLayer(flownode,
switchboard.output_channels)
flow = bimdp.BiFlow([switchboard, sfa_layer])
train_gen = [numx_rand.random((10, switchboard.input_dim))
for _ in range(3)]
flow.train([None, train_gen])
# now can test the gradient
mdp.activate_extension("gradient")
try:
x = numx_rand.random((3, switchboard.input_dim))
result = flow(x, {"method": "gradient"})
grad = result[1]["grad"]
assert grad.shape == (3, sfa_layer.output_dim,
switchboard.input_dim)
finally:
mdp.deactivate_extension("gradient")
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