wehub-resource-sync
47 lines
1.6 KiB
ReStructuredText
47 lines
1.6 KiB
ReStructuredText
.. _guide-message-passing:
|
|
|
|
Chapter 2: Message Passing
|
|
==========================
|
|
|
|
:ref:`(中文版) <guide_cn-message-passing>`
|
|
|
|
Message Passing Paradigm
|
|
------------------------
|
|
|
|
Let :math:`x_v\in\mathbb{R}^{d_1}` be the feature for node :math:`v`,
|
|
and :math:`w_{e}\in\mathbb{R}^{d_2}` be the feature for edge
|
|
:math:`({u}, {v})`. The **message passing paradigm** defines the
|
|
following node-wise and edge-wise computation at step :math:`t+1`:
|
|
|
|
.. math:: \text{Edge-wise: } m_{e}^{(t+1)} = \phi \left( x_v^{(t)}, x_u^{(t)}, w_{e}^{(t)} \right) , ({u}, {v},{e}) \in \mathcal{E}.
|
|
|
|
.. math:: \text{Node-wise: } x_v^{(t+1)} = \psi \left(x_v^{(t)}, \rho\left(\left\lbrace m_{e}^{(t+1)} : ({u}, {v},{e}) \in \mathcal{E} \right\rbrace \right) \right).
|
|
|
|
In the above equations, :math:`\phi` is a **message function**
|
|
defined on each edge to generate a message by combining the edge feature
|
|
with the features of its incident nodes; :math:`\psi` is an
|
|
**update function** defined on each node to update the node feature
|
|
by aggregating its incoming messages using the **reduce function**
|
|
:math:`\rho`.
|
|
|
|
Roadmap
|
|
-------
|
|
|
|
This chapter introduces DGL's message passing APIs, and how to efficiently use them on both nodes and edges.
|
|
The last section of it explains how to implement message passing on heterogeneous graphs.
|
|
|
|
* :ref:`guide-message-passing-api`
|
|
* :ref:`guide-message-passing-efficient`
|
|
* :ref:`guide-message-passing-part`
|
|
* :ref:`guide-message-passing-heterograph`
|
|
|
|
.. toctree::
|
|
:maxdepth: 1
|
|
:hidden:
|
|
:glob:
|
|
|
|
message-api
|
|
message-efficient
|
|
message-part
|
|
message-heterograph
|