*1. Input:*
* Tensor shape: [2,4,16] * `2`: This represents the *batch size*, meaning there are two independent data samples being processed. * `4`: This is the *input feature dimension*, indicating each sample has 4 features. * `16`: This is the *input channel dimension*, suggesting each feature has 16 channels of information.
*2. Kernel:*
* Shape: [4,16,8] * `4`: This is the *kernel size*, meaning the filter window used to convolve has a width of 4. * `16`: This matches the *input channel dimension*, ensuring the filter operates on the same number of channels as the input. * `8`: This is the *output channel dimension*, indicating the convolution produces 8 new channels of information per sample.
*3. Output:*
* Shape: [2,8] * `2`: This remains the *batch size* as the operation is applied to each sample independently. * `8`: This matches the *output channel dimension* of the kernel, signifying the final tensor has 8 new features extracted from the input.
*4. How is it possible?*
Despite the seemingly mismatched dimensions in the input and output, convolution on graphs works by leveraging the *neighborhood structure* of the graph. Here's a simplified explanation:
* The kernel slides across the graph, applying its weights to the features of the current node and its neighbors within a specific radius. * This weighted sum is then aggregated to form a new feature for the current node in each output channel. * As the kernel moves across the graph, it extracts information from the local neighborhood of each node, creating new features that capture relationships and patterns within the graph.
*Additional considerations:*
* The graph structure and edge weights likely play a role in how information propagates during the convolution process. * Specific details of the convolution implementation, including padding and stride, might also influence the output shape.