chainer.functions.bilinear¶
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chainer.functions.
bilinear
(e1, e2, W, V1=None, V2=None, b=None)[source]¶ Applies a bilinear function based on given parameters.
This is a building block of Neural Tensor Network (see the reference paper below). It takes two input variables and one or four parameters, and outputs one variable.
To be precise, denote six input arrays mathematically by \(e^1\in \mathbb{R}^{I\cdot J}\), \(e^2\in \mathbb{R}^{I\cdot K}\), \(W\in \mathbb{R}^{J \cdot K \cdot L}\), \(V^1\in \mathbb{R}^{J \cdot L}\), \(V^2\in \mathbb{R}^{K \cdot L}\), and \(b\in \mathbb{R}^{L}\), where \(I\) is mini-batch size. In this document, we call \(V^1\), \(V^2\), and \(b\) linear parameters.
The output of forward propagation is calculated as
\[y_{il} = \sum_{jk} e^1_{ij} e^2_{ik} W_{jkl} + \ \sum_{j} e^1_{ij} V^1_{jl} + \sum_{k} e^2_{ik} V^2_{kl} + b_{l}.\]Note that V1, V2, b are optional. If these are not given, then this function omits the last three terms in the above equation.
Note
This function accepts an input variable
e1
ore2
of a non-matrix array. In this case, the leading dimension is treated as the batch dimension, and the other dimensions are reduced to one dimension.Note
In the original paper, \(J\) and \(K\) must be equal and the author denotes \([V^1 V^2]\) (concatenation of matrices) by \(V\).
Parameters: Returns: Output variable.
Return type: - See:
- Reasoning With Neural Tensor Networks for Knowledge Base Completion [Socher+, NIPS2013].