TypedLinear

class dgl.nn.pytorch.TypedLinear(in_size, out_size, num_types, regularizer=None, num_bases=None)

Bases: Module

Linear transformation according to types.

For each sample of the input batch \(x \in X\), apply linear transformation \(xW_t\), where \(t\) is the type of \(x\).

The module supports two regularization methods (basis-decomposition and block-diagonal-decomposition) proposed by “Modeling Relational Data with Graph Convolutional Networks”

The basis regularization decomposes \(W_t\) by:

\[W_t^{(l)} = \sum_{b=1}^B a_{tb}^{(l)}V_b^{(l)}\]

where \(B\) is the number of bases, \(V_b^{(l)}\) are linearly combined with coefficients \(a_{tb}^{(l)}\).

The block-diagonal-decomposition regularization decomposes \(W_t\) into \(B\) block-diagonal matrices. We refer to \(B\) as the number of bases:

\[W_t^{(l)} = \oplus_{b=1}^B Q_{tb}^{(l)}\]

where \(B\) is the number of bases, \(Q_{tb}^{(l)}\) are block bases with shape \(R^{(d^{(l+1)}/B)\times(d^{l}/B)}\).

Parameters:

• in_size (int) – Input feature size.

• out_size (int) – Output feature size.

• num_types (int) – Total number of types.

• regularizer (str, optional) –

  Which weight regularizer to use “basis” or “bdd”:

  • ”basis” is short for basis-decomposition.

  • ”bdd” is short for block-diagonal-decomposition.

  Default applies no regularization.

• num_bases (int, optional) – Number of bases. Needed when regularizer is specified. Typically smaller than num_types. Default: None.

Examples

No regularization.

>>> from dgl.nn import TypedLinear
>>> import torch
>>>
>>> x = torch.randn(100, 32)
>>> x_type = torch.randint(0, 5, (100,))
>>> m = TypedLinear(32, 64, 5)
>>> y = m(x, x_type)
>>> print(y.shape)
torch.Size([100, 64])

With basis regularization

>>> x = torch.randn(100, 32)
>>> x_type = torch.randint(0, 5, (100,))
>>> m = TypedLinear(32, 64, 5, regularizer='basis', num_bases=4)
>>> y = m(x, x_type)
>>> print(y.shape)
torch.Size([100, 64])

forward(x, x_type, sorted_by_type=False)

Forward computation.

Parameters:

• x (torch.Tensor) – A 2D input tensor. Shape: (N, D1)

• x_type (torch.Tensor) – A 1D integer tensor storing the type of the elements in x with one-to-one correspondenc. Shape: (N,)

• sorted_by_type (bool, optional) – Whether the inputs have been sorted by the types. Forward on pre-sorted inputs may be faster.

Returns:

y – The transformed output tensor. Shape: (N, D2)

Return type:

torch.Tensor

reset_parameters()

Reset parameters