Deep convolutional neural networks (CNN) have achieved great success. On the other hand, modeling structural information has been proved critical in many vision problems. It is of great interest to integrate them effectively. In a classical neural network, there is no message passing between neurons in the same layer. In this paper, we propose a CRF-CNN framework which can simultaneously model structural information in both output and hidden feature layers in a probabilistic way, and it is applied to human pose estimation. A message passing scheme is proposed, so that in various layers each body joint receives messages from all the others in an efficient way. Such message passing can be implemented with convolution between features maps in the same layer, and it is also integrated with feedforward propagation in neural networks. Finally, a neural network implementation of end-to-end learning CRF-CNN is provided. Its effectiveness is demonstrated through experiments on two benchmark datasets.

Property prediction on molecular graphs is an important application of Graph Neural Networks (GNNs).

However, empirically, we find that, directly using the native transformer to model IMU sequences results in unacceptable jitter and inaccurate postures.

Although various normalization schemes havebeen proposed, theyallfollowacommon theme: normalize acrossspatialdimensions and discard the extracted statistics.

Textual network embedding leverages rich text information associated with the network to learn low-dimensional vectorial representations of vertices.