Graph upsampling by transposed convolution.

Upsamples a graph using a transposed convolution op. The map from input vertices to the upsampled graph is specified by the reverse of pool_map. The inputs pool_map and sizes are the same as used for pooling:

pooled = pool(data, pool_map, sizes)
upsampled = upsample_transposed_convolution(pooled, pool_map, sizes, ...)

The shorthands used below are V1: The number of vertices in the inputs. V2: The number of vertices in the upsampled output. C: The number of channels in the inputs.

In the following, A1 to A3 are optional batch dimensions. Only up to three batch dimensions are supported due to limitations with TensorFlow's dense-sparse multiplication.

Please see the documentation for graph_pooling.pool for a detailed interpretation of the inputs pool_map and sizes.

data A float tensor with shape [A1, ..., A3, V1, C].
pool_map A SparseTensor with the same type as data and with shape [A1, ..., A3, V1, V2]. pool_map will be interpreted in the same way as the pool_map argument of graph_pooling.pool, namely v_i_map = [..., v_i, :] are the upsampled vertices corresponding to vertex v_i. Additionally, for transposed convolution a fixed number of entries in each v_i_map (equal to kernel_size) are expected: |v_i_map| = kernel_size. When this is not the case, the map is either truncated or the last element repeated. Furthermore, upsampled vertex indices should not be repeated across maps otherwise the output is nondeterministic. Specifically, to avoid nondeterminism we must have intersect([a1, ..., an, v_i, :],[a1, ..., a3, v_j, :]) = {}, i != j.
sizes An int tensor of shape [A1, ..., A3, 2] indicating the true input sizes in case of padding (sizes=None indicates no padding): sizes[A1, ..., A3, 0] <= V1 and sizes[A1, ..., A3, 1] <= V2.
kernel_size The kernel size for transposed convolution.
transposed_convolution_op A callable transposed convolution op with the form y = transposed_convolution_op(x), where x has shape [1, 1, D1, C] and y must have shape [1, 1, kernel_size * D1, C]. transposed_convolution_op maps each row of x to kernel_size rows in y. An example: transposed_convolution_op = tf.keras.layers.Conv2DTranspose( filters=C, kernel_size=(1, kernel_size), strides=(1, kernel_size), padding='valid', ...) </td> </tr><tr> <td>name` A name for this op. Defaults to 'graph_pooling_upsample_transposed_convolution'.

Tensor with shape [A1, ..., A3, V2, C].

TypeError if the input types are invalid.
TypeError if transposed_convolution_op is not a callable.
ValueError if the input dimensions are invalid.