orthogonal.py

#   Copyright (c) 2021 PaddlePaddle Authors. 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.

from ...fluid.initializer import Initializer
from ...fluid.data_feeder import check_variable_and_dtype
from ...fluid import framework
from ...tensor import diag, transpose, sign, qr, reshape
from paddle.utils import unique_name

__all__ = []


class Orthogonal(Initializer):
    """The orthogonal initializer. The initialized tensor is (semi) orthogonal.

    It's only applied to Tensor whose dimension is greater than or equal to 2. 
    
    For the Tensor whose dimension is greater than 2, the 0 dimension is seen as ``rows`` , 
    and the >=1 dimension are flattened as ``cols`` .

    Which can be describe as:

    .. code-block:: text

        rows = shape[0]
        cols = shape[1]·shape[2]···shape[N]
        
        if rows < cols:
            The rows are orthogonal vectors
        elif rows > cols:
            The columns are orthogonal vectors
        else rows = cols:
            Both rows and columns are orthogonal vectors

    Args:
        gain(float, optional): The multiplication coefficient for initialized tensor. Default: 1.0.
        name(str, optional): The default value is None. Normally there is no need for user to set this
            property. For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        A parameter initialized by orthogonal initialized.

    Examples:
        .. code-block:: python

            import paddle

            weight_attr = paddle.ParamAttr(initializer=paddle.nn.initializer.Orthogonal())
            linear = paddle.nn.Linear(10, 15, weight_attr=weight_attr)
            # linear.weight: X * X' = I

            linear = paddle.nn.Linear(15, 10, weight_attr=weight_attr)
            # linear.weight: X' * X = I
    """

    def __init__(self, gain=1.0, name=None):
        assert gain is not None, 'gain should not be None'
        super(Orthogonal, self).__init__()
        self._gain = gain

    def __call__(self, var, block=None):
        """Initialize the input tensor with orthogonal initializer.

        Args:
            var(Tensor): Tensor that needs to be initialized.
            block(Block, optional): The block in which initialization ops
                   should be added. Used in static graph only, default None.

        Returns:
            The last initialization op, it contain 8 ops in orthogonal initializer.
        """
        block = self._check_block(block)
        assert isinstance(var, framework.Parameter)
        assert isinstance(block, framework.Block)
        # 'qr' op only support float32/float64 now
        check_variable_and_dtype(var, "Out", ["float32", "float64"],
                                 "Orthogonal")

        self._seed = block.program.random_seed

        shape = var.shape
        assert len(
            shape
        ) >= 2, "Only Tensor with 2 or more dimensions can be initialized by Orthogonal"

        row = shape[0]
        col = 1
        for i in shape[1:]:
            col *= i

        flatten_shape = [max(row, col), min(row, col)]

        normal_var = block.create_var(
            name=unique_name.generate('.'.join(['gaussian_random', 'tmp'])),
            dtype=var.dtype,
            persistable=False,
            stop_gradient=True)
        block.append_op(
            type='gaussian_random',
            inputs={},
            outputs={'Out': normal_var},
            attrs={
                'mean': 0.0,
                'std': 1.0,
                'shape': flatten_shape,
                'seed': self._seed,
                'dtype': var.dtype
            },
            stop_gradient=True)

        q = block.create_var(
            name=unique_name.generate('.'.join(['qr', 'q', 'tmp'])),
            dtype=normal_var.dtype,
            persistable=False,
            stop_gradient=True)
        r = block.create_var(
            name=unique_name.generate('.'.join(['qr', 'r', 'tmp'])),
            dtype=normal_var.dtype,
            persistable=False,
            stop_gradient=True)
        block.append_op(
            type='qr',
            inputs={'X': [normal_var]},
            outputs={
                'Q': q,
                'R': r,
            },
            attrs={'mode': 'reduced'},
            stop_gradient=True)

        r_diag = block.create_var(
            name=unique_name.generate('.'.join(['diag', 'tmp'])),
            dtype=r.dtype,
            persistable=False,
            stop_gradient=True)
        block.append_op(
            type='diag_v2',
            inputs={'X': r},
            outputs={'Out': r_diag},
            attrs={'offset': 0,
                   'padding_value': 0},
            stop_gradient=True)

        r_sign = r_diag
        block.append_op(
            type='sign',
            inputs={'X': [r_diag]},
            outputs={'Out': r_sign},
            stop_gradient=True)

        block.append_op(
            type='elementwise_mul',
            inputs={'X': q,
                    'Y': r_sign},
            outputs={'Out': q},
            attrs={},
            stop_gradient=True)

        x_shape = block.create_var(
            name=unique_name.generate('.'.join(['transpose', 'shape', 'tmp'])),
            dtype=q.dtype,
            persistable=False,
            stop_gradient=True)
        if row < col:
            q_transpose = block.create_var(
                name=unique_name.generate('.'.join(['transpose', 'tmp'])),
                dtype=q.dtype,
                persistable=False,
                stop_gradient=True)
            block.append_op(
                type='transpose2',
                inputs={'X': q},
                outputs={'Out': q_transpose,
                         'XShape': x_shape},
                attrs={'axis': [1, 0]},
                stop_gradient=True)
            q = q_transpose

        block.append_op(
            type='reshape2',
            inputs={'X': q},
            outputs={'Out': q,
                     "XShape": x_shape},
            attrs={'shape': var.shape},
            stop_gradient=True)

        op = block.append_op(
            type='scale',
            inputs={'X': q},
            outputs={'Out': var},
            attrs={'scale': self._gain,
                   'bias': 0.0})

        return op