short-term and long-term predictions can be predicted with the true observations without using the error-prone predictions. Thus error accumulation problem can be well addressed. Here, we output multi-step predictions with the the learned deep spatial-temporal features, and use the multi-step errors to train the model.

![image](Framework_big_v2.pdf){width="2\columnwidth" height="1.1\columnwidth"}

Spatial Transformer
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In this subsection, we first elaborate the four components of the proposed spatial transformer: spatial position-temporal embedding layer, graph convolution layer, dynamical graph convolution layer as gate mechanism for information fusion. More specifically, the spatial-temporal embedding layer is learned to incorporate spatial-temporal position information (e.g. topology, connectivity, timesteps.) into each node. The graph convolution layer is adopted to explore the road topology information for some fixed spatial dependency patterns, and the dynamical graph convolution layer is used to capture dynamical directed spatial dependencies evolving with time. In final, the learned fixed spatial and dynamical features are fused with gate mechanism. We further present that the proposed spatial transformer can be viewed as a general message passing graph neural network for dynamical graph construction and feature learning.

### Spatial-temporal Position Embedding

As the transformer contains only fully feed-forward structures, and there is no convolutional or recurrent operation, thus the spatial position 