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09d8e80 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 | # Copyright 2021 DeepMind Technologies Limited. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
"""Tests for optax.projections."""
from absl.testing import absltest
from absl.testing import parameterized
import chex
import jax
import jax.numpy as jnp
import numpy as np
from optax import projections as proj
import optax.tree_utils as otu
def projection_simplex_jacobian(projection):
"""Theoretical expression for the Jacobian of projection_simplex."""
support = (projection > 0).astype(jnp.int32)
cardinality = jnp.count_nonzero(support)
return jnp.diag(support) - jnp.outer(support, support) / cardinality
class ProjectionsTest(parameterized.TestCase):
def test_projection_non_negative(self):
with self.subTest('with an array'):
x = jnp.array([-1.0, 2.0, 3.0])
expected = jnp.array([0, 2.0, 3.0])
np.testing.assert_array_equal(proj.projection_non_negative(x), expected)
with self.subTest('with a tuple'):
np.testing.assert_array_equal(
proj.projection_non_negative((x, x)), (expected, expected)
)
with self.subTest('with nested pytree'):
tree_x = (-1.0, {'k1': 1.0, 'k2': (1.0, 1.0)}, 1.0)
tree_expected = (0.0, {'k1': 1.0, 'k2': (1.0, 1.0)}, 1.0)
chex.assert_trees_all_equal(
proj.projection_non_negative(tree_x), tree_expected
)
def test_projection_box(self):
with self.subTest('lower and upper are scalars'):
lower, upper = 0.0, 2.0
x = jnp.array([-1.0, 2.0, 3.0])
expected = jnp.array([0, 2.0, 2.0])
np.testing.assert_array_equal(
proj.projection_box(x, lower, upper), expected
)
with self.subTest('lower and upper values are arrays'):
lower_arr = jnp.ones(len(x)) * lower
upper_arr = jnp.ones(len(x)) * upper
np.testing.assert_array_equal(
proj.projection_box(x, lower_arr, upper_arr), expected
)
with self.subTest('lower and upper are tuples of arrays'):
lower_tuple = (lower, lower)
upper_tuple = (upper, upper)
chex.assert_trees_all_equal(
proj.projection_box((x, x), lower_tuple, upper_tuple),
(expected, expected),
)
with self.subTest('lower and upper are pytrees'):
tree = (-1.0, {'k1': 2.0, 'k2': (2.0, 3.0)}, 3.0)
expected = (0.0, {'k1': 2.0, 'k2': (2.0, 2.0)}, 2.0)
lower_tree = (0.0, {'k1': 0.0, 'k2': (0.0, 0.0)}, 0.0)
upper_tree = (2.0, {'k1': 2.0, 'k2': (2.0, 2.0)}, 2.0)
chex.assert_trees_all_equal(
proj.projection_box(tree, lower_tree, upper_tree), expected
)
def test_projection_hypercube(self):
x = jnp.array([-1.0, 2.0, 0.5])
with self.subTest('with default scale'):
expected = jnp.array([0, 1.0, 0.5])
np.testing.assert_array_equal(proj.projection_hypercube(x), expected)
with self.subTest('with scalar scale'):
expected = jnp.array([0, 0.8, 0.5])
np.testing.assert_array_equal(proj.projection_hypercube(x, 0.8), expected)
with self.subTest('with array scales'):
scales = jnp.ones(len(x)) * 0.8
np.testing.assert_array_equal(
proj.projection_hypercube(x, scales), expected
)
@parameterized.parameters(1.0, 0.8)
def test_projection_simplex_array(self, scale):
rng = np.random.RandomState(0)
x = rng.randn(50).astype(np.float32)
p = proj.projection_simplex(x, scale)
np.testing.assert_almost_equal(jnp.sum(p), scale, decimal=4)
self.assertTrue(jnp.all(0 <= p))
self.assertTrue(jnp.all(p <= scale))
@parameterized.parameters(1.0, 0.8)
def test_projection_simplex_pytree(self, scale):
pytree = {'w': jnp.array([2.5, 3.2]), 'b': 0.5}
new_pytree = proj.projection_simplex(pytree, scale)
np.testing.assert_almost_equal(otu.tree_sum(new_pytree), scale, decimal=4)
@parameterized.parameters(1.0, 0.8)
def test_projection_simplex_edge_case(self, scale):
p = proj.projection_simplex(jnp.array([0.0, 0.0, -jnp.inf]), scale)
np.testing.assert_array_almost_equal(
p, jnp.array([scale / 2, scale / 2, 0.0])
)
def test_projection_simplex_jacobian(self):
rng = np.random.RandomState(0)
x = rng.rand(5).astype(np.float32)
v = rng.randn(5).astype(np.float32)
jac_rev = jax.jacrev(proj.projection_simplex)(x)
jac_fwd = jax.jacfwd(proj.projection_simplex)(x)
with self.subTest('Check against theoretical expression'):
p = proj.projection_simplex(x)
jac_true = projection_simplex_jacobian(p)
np.testing.assert_array_almost_equal(jac_true, jac_fwd)
np.testing.assert_array_almost_equal(jac_true, jac_rev)
with self.subTest('Check against finite difference'):
jvp = jax.jvp(proj.projection_simplex, (x,), (v,))[1]
eps = 1e-4
jvp_finite_diff = (proj.projection_simplex(x + eps * v) -
proj.projection_simplex(x - eps * v)) / (2 * eps)
np.testing.assert_array_almost_equal(jvp, jvp_finite_diff, decimal=3)
with self.subTest('Check vector-Jacobian product'):
(vjp,) = jax.vjp(proj.projection_simplex, x)[1](v)
np.testing.assert_array_almost_equal(vjp, jnp.dot(v, jac_true))
with self.subTest('Check Jacobian-vector product'):
jvp = jax.jvp(proj.projection_simplex, (x,), (v,))[1]
np.testing.assert_array_almost_equal(jvp, jnp.dot(jac_true, v))
@parameterized.parameters(1.0, 0.8)
def test_projection_simplex_vmap(self, scale):
rng = np.random.RandomState(0)
x = rng.randn(3, 50).astype(np.float32)
scales = jnp.full(len(x), scale)
p = jax.vmap(proj.projection_simplex)(x, scales)
np.testing.assert_array_almost_equal(jnp.sum(p, axis=1), scales)
np.testing.assert_array_equal(True, 0 <= p)
np.testing.assert_array_equal(True, p <= scale)
if __name__ == '__main__':
absltest.main()
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