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Remove dependency on epsilon for diagonal shampoo.

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PiperOrigin-RevId: 215857772
This commit is contained in:
A. Unique TensorFlower 2018-10-04 22:30:20 -07:00 committed by TensorFlower Gardener
parent 176e6993c5
commit 57d31aa599
2 changed files with 15 additions and 9 deletions
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16
tensorflow/contrib/opt/python/training/shampoo.py
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@ -108,7 +108,8 @@ class ShampooOptimizer(optimizer.Optimizer):
precond_update_interval: We should update the preconditioners after precond_update_interval: We should update the preconditioners after
this many steps. Default = 1. Usually less than this many steps. Default = 1. Usually less than
svd_interval. svd_interval.
epsilon: epsilon * I_n is added to each mat_gbar_j for stability epsilon: epsilon * I_n is added to each mat_gbar_j for stability for
non-diagonal version of shampoo.
alpha: total power of the preconditioners. alpha: total power of the preconditioners.
use_iterative_root: should the optimizer use SVD (faster) or the use_iterative_root: should the optimizer use SVD (faster) or the
iterative root method (for TPU) for finding the iterative root method (for TPU) for finding the
@ -394,15 +395,20 @@ class ShampooOptimizer(optimizer.Optimizer):
assert self._mat_gbar_decay == 1.0 assert self._mat_gbar_decay == 1.0
mat_g_updated = state_ops.scatter_add(mat_g, indices, mat_g_updated = state_ops.scatter_add(mat_g, indices,
mat_gbar_weight_t * grad_outer) mat_gbar_weight_t * grad_outer)
mat_h = math_ops.pow( mat_g_updated_slice = array_ops.gather(mat_g_updated, indices)
array_ops.gather(mat_g_updated, indices) + self._epsilon, mat_h = array_ops.where(
neg_alpha) math_ops.greater(mat_g_updated_slice, 0),
math_ops.pow(mat_g_updated_slice, neg_alpha),
array_ops.zeros_like(mat_g_updated_slice))
else: else:
mat_g_updated = self._weighted_average(mat_g, mat_g_updated = self._weighted_average(mat_g,
self._mat_gbar_decay, self._mat_gbar_decay,
mat_gbar_decay_t, mat_gbar_decay_t,
mat_gbar_weight_t * grad_outer) mat_gbar_weight_t * grad_outer)
mat_h = math_ops.pow(mat_g_updated + self._epsilon, neg_alpha) mat_h = array_ops.where(
math_ops.greater(mat_g_updated, 0),
math_ops.pow(mat_g_updated, neg_alpha),
array_ops.zeros_like(mat_g_updated))
# Need to do the transpose to ensure that the tensor becomes # Need to do the transpose to ensure that the tensor becomes
# a d_{i+1} x ... x d_n x d_0 x ... d_i tensor as described above. # a d_{i+1} x ... x d_n x d_0 x ... d_i tensor as described above.

8
tensorflow/contrib/opt/python/training/shampoo_test.py
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@ -279,7 +279,7 @@ class ShampooTest(test.TestCase, parameterized.TestCase):
# Update rule is var = var - lr * gg^{-0.5} * grad # Update rule is var = var - lr * gg^{-0.5} * grad
# lr = 1 # lr = 1
mat_g = (grad_np * grad_np) mat_g = (grad_np * grad_np)
new_val_np = init_var_np - np.power(mat_g + RIDGE_EPSILON, -0.5) * grad_np new_val_np = init_var_np - np.power(mat_g, -0.5) * grad_np
self.assertAllCloseAccordingToType( self.assertAllCloseAccordingToType(
new_val_np, new_val, atol=TOLERANCE, rtol=TOLERANCE) new_val_np, new_val, atol=TOLERANCE, rtol=TOLERANCE)
@ -288,7 +288,7 @@ class ShampooTest(test.TestCase, parameterized.TestCase):
new_val = sess.run(var) new_val = sess.run(var)
mat_g += (grad_np_2 * grad_np_2) mat_g += (grad_np_2 * grad_np_2)
new_val_np -= np.power(mat_g + RIDGE_EPSILON, -0.5) * grad_np_2 new_val_np -= np.power(mat_g, -0.5) * grad_np_2
self.assertAllCloseAccordingToType( self.assertAllCloseAccordingToType(
new_val_np, new_val, atol=TOLERANCE, rtol=TOLERANCE) new_val_np, new_val, atol=TOLERANCE, rtol=TOLERANCE)
@ -339,7 +339,7 @@ class ShampooTest(test.TestCase, parameterized.TestCase):
mat_g1 = np.sum( mat_g1 = np.sum(
grad_np * grad_np, axis=1, keepdims=True) / grad_np.shape[0] grad_np * grad_np, axis=1, keepdims=True) / grad_np.shape[0]
mat_left = np.power(mat_g1 + RIDGE_EPSILON, -0.25) mat_left = np.power(mat_g1, -0.25)
mat_g2 = np.dot(grad_np.transpose(), grad_np) / grad_np.shape[1] mat_g2 = np.dot(grad_np.transpose(), grad_np) / grad_np.shape[1]
mat_right = np_power(mat_g2 + RIDGE_EPSILON * np.eye(size[1]), -0.25) mat_right = np_power(mat_g2 + RIDGE_EPSILON * np.eye(size[1]), -0.25)
new_val_np = init_var_np - np.dot(grad_np * mat_left, mat_right) new_val_np = init_var_np - np.dot(grad_np * mat_left, mat_right)
@ -353,7 +353,7 @@ class ShampooTest(test.TestCase, parameterized.TestCase):
mat_g1 += np.sum( mat_g1 += np.sum(
grad_np_2 * grad_np_2, axis=1, keepdims=True) / grad_np_2.shape[0] grad_np_2 * grad_np_2, axis=1, keepdims=True) / grad_np_2.shape[0]
mat_left = np.power(mat_g1 + RIDGE_EPSILON, -0.25) mat_left = np.power(mat_g1, -0.25)
mat_g2 += np.dot(grad_np_2.transpose(), grad_np_2) / grad_np_2.shape[1] mat_g2 += np.dot(grad_np_2.transpose(), grad_np_2) / grad_np_2.shape[1]
mat_right = np_power(mat_g2 + RIDGE_EPSILON * np.eye(size[1]), -0.25) mat_right = np_power(mat_g2 + RIDGE_EPSILON * np.eye(size[1]), -0.25)
new_val_np -= np.dot(grad_np_2 * mat_left, mat_right) new_val_np -= np.dot(grad_np_2 * mat_left, mat_right)