theano dot产品是如何播出的

Question

任何人都可以举例说明我是如何进行 theano dot 产品广播的。它似乎与 numpy 不同

import numpy
import theano
import theano.tensor as T

theano.config.compute_test_value = 'off'

W1val = numpy.random.rand(2, 5, 10, 4).astype(theano.config.floatX)

W1 = theano.shared(W1val, 'W1')

x  = T.tensor3('x')

func_of_W1 = W1

h1 = T.dot(x, func_of_W1)

f = theano.function([x], h1)

print f(numpy.random.rand(3, 5, 10)).shape

这是我用 theano 尝试的实验。

#   T.dot(x shape ,  W1 shape) = result shape

# (3, 5, 10) * (2, 5, 10, 4) = (3, 5, 2, 5, 4)

# (3, 10) * (2, 5, 10, 4) = (3, 2, 5, 4)

# (3, 10) * (10 ,4) = (3, 4)

# (3, 10) * (2, 10 ,4) = (3, 2, 4)

# (5,10) * (2, 10 ,10) = (5, 2, 10)

Answer 1

Theano 的广播功能就像 numpy 一样。为了演示，此代码直接比较 Theano 和 numpy：

import numpy

import theano
import theano.tensor as T

TENSOR_TYPES = dict([(0, T.scalar), (1, T.vector), (2, T.matrix), (3, T.tensor3), (4, T.tensor4)])

rand = numpy.random.rand


def theano_dot(x, y):
    sym_x = TENSOR_TYPES[x.ndim]('x')
    sym_y = TENSOR_TYPES[y.ndim]('y')
    return theano.function([sym_x, sym_y], theano.dot(sym_x, sym_y))(x, y)


def compare_dot(x, y):
    print theano_dot(x, y).shape, numpy.dot(x, y).shape


print compare_dot(rand(3, 5, 10), rand(2, 5, 10, 4))
print compare_dot(rand(3, 10), rand(2, 5, 10, 4))
print compare_dot(rand(3, 10), rand(10, 4))
print compare_dot(rand(3, 10), rand(2, 10, 4))
print compare_dot(rand(5, 10), rand(2, 10, 10))

输出是

(3L, 5L, 2L, 5L, 4L) (3L, 5L, 2L, 5L, 4L)
(3L, 2L, 5L, 4L) (3L, 2L, 5L, 4L)
(3L, 4L) (3L, 4L)
(3L, 2L, 4L) (3L, 2L, 4L)
(5L, 2L, 10L) (5L, 2L, 10L)

Theano 和 numpy 在您描述的每种情况下都会产生具有相同形状的结果。