chainer.functions.local_convolution_2d(x, W, b=None, stride=1)[source]

Two-dimensional local convolution function.

Locally-connected function for 2D inputs. Works similarly to convolution_2d, except that weights are unshared, that is, a different set of filters is applied at each different patch of the input. It takes two or three variables: the input image x, the filter weight W, and optionally, the bias vector b.

Notation: here is a notation for dimensionalities.

  • \(n\) is the batch size.

  • \(c_I\) is the number of the input.

  • \(c_O\) is the number of output channels.

  • \(h\) and \(w\) are the height and width of the input image, respectively.

  • \(h_O\) and \(w_O\) are the height and width of the output image, respectively.

  • \(k_H\) and \(k_W\) are the height and width of the filters, respectively.


Output variable. Its shape is \((n, c_O, h_O, w_O)\).

Return type


Like Convolution2D, LocalConvolution2D function computes correlations between filters and patches of size \((k_H, k_W)\) in x. But unlike Convolution2D, LocalConvolution2D has a separate filter for each patch of the input

\((h_O, w_O)\) is determined by the equivalent equation of Convolution2D, without any padding

If the bias vector is given, then it is added to all spatial locations of the output of convolution.

See also

LocalConvolution2D to manage the model parameters W and b.


>>> x = np.random.uniform(0, 1, (2, 3, 7, 7))
>>> W = np.random.uniform(0, 1, (2, 5, 5, 3, 3, 3))
>>> b = np.random.uniform(0, 1, (2, 5, 5))
>>> y = F.local_convolution_2d(x, W, b)
>>> y.shape
(2, 2, 5, 5)