def _loss_fn(self, matrix, rels_reversed):
"""Given a numpy array with vectors for u, v and negative samples, computes loss value.
Parameters
----------
matrix : numpy.array
Array containing vectors for u, v and negative samples, of shape (2 + negative_size, dim).
Returns
-------
float
Computed loss value.
Warnings
--------
Only used for autograd gradients, since autograd requires a specific function signature.
"""
vector_u = matrix[0]
vectors_v = matrix[1:]
euclidean_dists = grad_np.linalg.norm(vector_u - vectors_v, axis=1)
norm = grad_np.linalg.norm(vector_u)
all_norms = grad_np.linalg.norm(vectors_v, axis=1)
poincare_dists = grad_np.arccosh(1 + 2 * ((euclidean_dists**2) /
((1 - norm**2) *
(1 - all_norms**2))))
if self.loss_type == 'nll':
return PoincareModel._nll_loss_fn(poincare_dists)
elif self.loss_type == 'neg':
return PoincareModel._neg_loss_fn(poincare_dists, self.neg_r,
self.neg_t, self.neg_mu)
elif self.loss_type == 'maxmargin':
return PoincareModel._maxmargin_loss_fn(poincare_dists,
self.maxmargin_margin)
else:
raise ValueError('Unknown loss type : ' + self.loss_type)
def test_dist(self):
x = self.man.rand() / 2
y = self.man.rand() / 2
correct_dist = np.sum(
np.arccosh(1 + 2 * la.norm(x - y, axis=0)**2 /
(1 - la.norm(x, axis=0)**2) /
(1 - la.norm(y, axis=0)**2))**2)
np_testing.assert_allclose(correct_dist, self.man.dist(x, y)**2)
def test_dist(self):
x = self.manifold.random_point() / 2
y = self.manifold.random_point() / 2
correct_dist = np.arccosh(
1
+ 2
* np.linalg.norm(x - y) ** 2
/ (1 - np.linalg.norm(x) ** 2)
/ (1 - np.linalg.norm(y) ** 2)
)
np_testing.assert_allclose(correct_dist, self.manifold.dist(x, y))
def test_arccosh():
fun = lambda x : 3.0 * np.arccosh(x)
d_fun = grad(fun)
check_grads(fun, npr.randn()**2 + 1)
check_grads(d_fun, npr.randn()**2 + 1)
def test_arccosh():
fun = lambda x : 3.0 * np.arccosh(x)
d_fun = grad(fun)
check_grads(fun, npr.randn()**2 + 1)
check_grads(d_fun, npr.randn()**2 + 1)
def test_arccosh():
fun = lambda x: 3.0 * np.arccosh(x)
check_grads(fun)(npr.randn()**2 + 1)
def test_arccosh():
fun = lambda x : 3.0 * np.arccosh(x)
check_grads(fun)(npr.randn()**2 + 1)
