Can anyone explain how conv works in that graph. You have a tensor of shape [2,4,16] and you convolve with a kernel of shape [4,16,8] and that gives you a [2,8] tensor? How's that possible?
* 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.
Thanks. What was confusing me is the kernel size 4. Normally in (2D) convolutions you have (in_channels, out_channels, k, k) for a kxk kernel size. In the example above it the k is the first dimension instead of the last. This is in PyTorch, not sure about Keras
phillengel|2 years ago
*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.
potac|2 years ago