# Bilinear¶

class torch.nn.Bilinear(in1_features, in2_features, out_features, bias=True, device=None, dtype=None)[source]

Applies a bilinear transformation to the incoming data: $y = x_1^T A x_2 + b$

Parameters
• in1_features – size of each first input sample

• in2_features – size of each second input sample

• out_features – size of each output sample

• bias – If set to False, the layer will not learn an additive bias. Default: True

Shape:
• Input1: $(*, H_{in1})$ where $H_{in1}=\text{in1\_features}$ and $*$ means any number of additional dimensions including none. All but the last dimension of the inputs should be the same.

• Input2: $(*, H_{in2})$ where $H_{in2}=\text{in2\_features}$.

• Output: $(*, H_{out})$ where $H_{out}=\text{out\_features}$ and all but the last dimension are the same shape as the input.

Variables
• ~Bilinear.weight (torch.Tensor) – the learnable weights of the module of shape $(\text{out\_features}, \text{in1\_features}, \text{in2\_features})$. The values are initialized from $\mathcal{U}(-\sqrt{k}, \sqrt{k})$, where $k = \frac{1}{\text{in1\_features}}$

• ~Bilinear.bias – the learnable bias of the module of shape $(\text{out\_features})$. If bias is True, the values are initialized from $\mathcal{U}(-\sqrt{k}, \sqrt{k})$, where $k = \frac{1}{\text{in1\_features}}$

Examples:

>>> m = nn.Bilinear(20, 30, 40)
>>> input1 = torch.randn(128, 20)
>>> input2 = torch.randn(128, 30)
>>> output = m(input1, input2)
>>> print(output.size())
torch.Size([128, 40])