Adding the Xavier Initializer (#5270)

* Adding the Xavier Initializer
* Addressing code review feedback

python/paddle/v2/framework/initializer.py

 import paddle.v2.framework.framework as framework
+import numpy as np
 
-__all__ = ['ConstantInitializer', 'UniformInitializer']
+__all__ = [
+    'ConstantInitializer', 'UniformInitializer', 'NormalInitializer',
+    'XavierInitializer'
+]
 
 
 class Initializer(object):
@@ -20,6 +24,41 @@ class Initializer(object):
         """
         raise NotImplementedError()
 
+    def _compute_fans(self, var):
+        """Compute the fan_in and the fan_out for layers
+
+        This method computes the fan_in and the fan_out
+        for neural network layers, if not specified. It is
+        not possible to perfectly estimate fan_in and fan_out.
+        This method will estimate it correctly for matrix multiply and
+        convolutions.
+
+        Args:
+            var: variable for which fan_in and fan_out have to be computed
+
+        Returns:
+            tuple of two integers (fan_in, fan_out)
+        """
+        shape = var.shape
+        if not shape or len(shape) == 0:
+            fan_in = fan_out = 1
+        elif len(shape) == 1:
+            fan_in = fan_out = shape[0]
+        elif len(shape) == 2:
+            # This is the case for simple matrix multiply
+            fan_in = shape[0]
+            fan_out = shape[1]
+        else:
+            # Assume this to be a convolutional kernel
+            # In PaddlePaddle, the shape of the kernel is like:
+            # [num_filters, num_filter_channels, ...] where the remaining
+            # dimensions are the filter_size
+            receptive_field_size = np.prod(shape[2:])
+            fan_in = shape[1] * receptive_field_size
+            fan_out = shape[0] * receptive_field_size
+
+        return (fan_in, fan_out)
+
 
 class ConstantInitializer(Initializer):
     """Implements the constant initializer
@@ -156,3 +195,93 @@ class NormalInitializer(Initializer):
             })
         var.op = op
         return op
+
+
+class XavierInitializer(Initializer):
+    """Implements the Xavier initializer
+
+    This class implements the Xavier weight initializer from the paper
+    Understanding the difficulty of training deep feedforward neural
+    networks[1] by Xavier Glorot and Yoshua Bengio.
+
+    This initializer is designed to keep the scale of the gradients
+    approximately same in all the layers. In case of Uniform distribution,
+    the range is [-x, x], where x = sqrt(6 / (fan_in + fan_out)).
+    In case of Normal distribution, the mean is 0 and the standard deviation
+    is sqrt(2/ (fan_in + fan_out)).
+
+    References:
+        [1] Understanding the difficulty of training deep feedforward neural
+            networks. International conference on artificial intelligence and
+            statistics.
+            (http://proceedings.mlr.press/v9/glorot10a.html)
+    """
+
+    def __init__(self, uniform=True, fan_in=None, fan_out=None, seed=0):
+        """Constructor for XavierInitializer
+
+        Args:
+            uniform: whether to use uniform or normal distribution
+            fan_in: fan_in for Xavier initialization. If None, it is
+                    inferred from the variable.
+            fan_out: fan_out for Xavier initialization. If None, it is
+                     inferred from the variable.
+            seed: random seed
+
+        Note: It is recommended to set fan_in and fan_out to None for
+              most cases.
+        """
+        assert uniform is not None
+        assert seed is not None
+        super(XavierInitializer, self).__init__()
+        self._uniform = uniform
+        self._fan_in = fan_in
+        self._fan_out = fan_out
+        self._seed = seed
+
+    def __call__(self, var, block):
+        """Add xavier initialization ops for a variable
+
+        Args:
+            var: Variable that needs to be initialized
+            block: The block in which initialization ops
+                   should be added
+
+        Returns:
+            the initialization op
+        """
+        assert isinstance(var, framework.Variable)
+        assert isinstance(block, framework.Block)
+        f_in, f_out = self._compute_fans(var)
+
+        # If fan_in and fan_out are passed, use them
+        fan_in = f_in if self._fan_in is None else self._fan_in
+        fan_out = f_out if self._fan_out is None else self._fan_out
+
+        if self._uniform:
+            limit = np.sqrt(6.0 / float(fan_in + fan_out))
+            op = block.prepend_op(
+                type="uniform_random",
+                outputs={"Out": var},
+                attrs={
+                    "shape": var.shape,
+                    "data_type": int(var.data_type),
+                    "min": -limit,
+                    "max": limit,
+                    "seed": self._seed
+                })
+
+        else:
+            std = np.sqrt(2.0 / float(fan_in + fan_out))
+            op = block.prepend_op(
+                type="gaussian_random",
+                outputs={"Out": var},
+                attrs={
+                    "shape": var.shape,
+                    "data_type": int(var.data_type),
+                    "mean": 0.0,
+                    "std": std,
+                    "seed": self._seed
+                })
+        var.op = op
+        return op

python/paddle/v2/framework/tests/test_initializer.py

+import numpy as np
 import unittest
 
 import paddle.v2.framework.framework as framework
@@ -116,5 +117,111 @@ class TestNormalInitializer(unittest.TestCase):
         self.assertEqual(init_op.attr('seed'), 123)
 
 
+class TestXavierInitializer(unittest.TestCase):
+    def test_uniform_xavier_initializer(self):
+        """Test Xavier initializer with uniform distribution on
+           for matrix multiply.
+        """
+        program = framework.Program()
+        block = program.global_block()
+        param = block.create_parameter(
+            dtype="float32",
+            shape=[5, 10],
+            lod_level=0,
+            name="param",
+            initializer=initializer.XavierInitializer())
+        self.assertEqual(len(block.ops), 1)
+        init_op = block.ops[0]
+        self.assertEqual(init_op.type, 'uniform_random')
+        limit = np.sqrt(6.0 / (param.shape[0] + param.shape[1]))
+        self.assertAlmostEqual(init_op.attr('min'), -limit, delta=DELTA)
+        self.assertAlmostEqual(init_op.attr('max'), limit, delta=DELTA)
+        self.assertEqual(init_op.attr('seed'), 0)
+
+    def test_uniform_xavier_initializer_conv(self):
+        """Test Xavier initializer with uniform distribution on
+           for convolutions.
+        """
+        program = framework.Program()
+        block = program.global_block()
+        param = block.create_parameter(
+            dtype="float32",
+            shape=[5, 10, 15, 20],
+            lod_level=0,
+            name="param",
+            initializer=initializer.XavierInitializer())
+        self.assertEqual(len(block.ops), 1)
+        init_op = block.ops[0]
+        self.assertEqual(init_op.type, 'uniform_random')
+        receptive_field_size = float(15 * 20)
+        limit = np.sqrt(6.0 / (
+            (param.shape[0] + param.shape[1]) * receptive_field_size))
+        self.assertAlmostEqual(init_op.attr('min'), -limit, delta=DELTA)
+        self.assertAlmostEqual(init_op.attr('max'), limit, delta=DELTA)
+        self.assertEqual(init_op.attr('seed'), 0)
+
+    def test_normal_xavier_initializer(self):
+        """Test Xavier initializer with normal distribution on
+           for matrix multiply.
+        """
+        program = framework.Program()
+        block = program.global_block()
+        param = block.create_parameter(
+            dtype="float32",
+            shape=[5, 10],
+            lod_level=0,
+            name="param",
+            initializer=initializer.XavierInitializer(uniform=False))
+        self.assertEqual(len(block.ops), 1)
+        init_op = block.ops[0]
+        self.assertEqual(init_op.type, 'gaussian_random')
+        std = np.sqrt(2.0 / (param.shape[0] + param.shape[1]))
+        self.assertAlmostEqual(init_op.attr('mean'), 0.0, delta=DELTA)
+        self.assertAlmostEqual(init_op.attr('std'), std, delta=DELTA)
+        self.assertEqual(init_op.attr('seed'), 0)
+
+    def test_normal_xavier_initializer_conv(self):
+        """Test Xavier initializer with normal distribution on
+           for convolutions.
+        """
+        program = framework.Program()
+        block = program.global_block()
+        param = block.create_parameter(
+            dtype="float32",
+            shape=[5, 10, 15, 20],
+            lod_level=0,
+            name="param",
+            initializer=initializer.XavierInitializer(uniform=False))
+        self.assertEqual(len(block.ops), 1)
+        init_op = block.ops[0]
+        self.assertEqual(init_op.type, 'gaussian_random')
+        receptive_field_size = float(15 * 20)
+        std = np.sqrt(2.0 / (
+            (param.shape[0] + param.shape[1]) * receptive_field_size))
+        self.assertAlmostEqual(init_op.attr('mean'), 0.0, delta=DELTA)
+        self.assertAlmostEqual(init_op.attr('std'), std, delta=DELTA)
+        self.assertEqual(init_op.attr('seed'), 0)
+
+    def test_xavier_initializer_supplied_arguments(self):
+        """Test the Xavier initializer with supplied arguments
+        """
+        program = framework.Program()
+        block = program.global_block()
+        block.create_parameter(
+            dtype="float32",
+            shape=[5, 10],
+            lod_level=0,
+            name="param",
+            initializer=initializer.XavierInitializer(
+                fan_in=12, fan_out=23, seed=134))
+        self.assertEqual(len(block.ops), 1)
+        init_op = block.ops[0]
+        self.assertEqual(init_op.type, 'uniform_random')
+        limit = np.sqrt(6.0 / (12 + 23))
+        self.assertAlmostEqual(init_op.attr('min'), -limit, delta=DELTA)
+        self.assertAlmostEqual(init_op.attr('max'), limit, delta=DELTA)
+        self.assertEqual(init_op.attr('seed'), 134)
+
+
 if __name__ == '__main__':
     unittest.main()