octave convolution

**Octave Convolution (OctConv)** is a **convolution operation that processes features at two spatial resolutions simultaneously** — splitting feature maps into high-frequency (full resolution) and low-frequency (half resolution) components, reducing redundant spatial information. **How Does OctConv Work?** - **Split**: Divide channels into high-freq (H×W) and low-freq (H/2×W/2) groups. - **Four Paths**: H→H (intra-high), L→L (intra-low), H→L (high-to-low downsample), L→H (low-to-high upsample). - **Ratio**: $alpha$ controls the fraction of channels at low resolution (typically 0.5). - **Paper**: Chen et al. (2019). **Why It Matters** - **Efficiency**: Low-freq features at half resolution -> significant FLOPs reduction (30-50%). - **Accuracy**: Surprisingly, OctConv often improves accuracy while reducing compute (less spatial redundancy to overfit). - **Drop-In**: Replaces standard convolution with minimal architectural changes. **OctConv** is **dual-resolution convolution** — processing fine details at full resolution and coarse patterns at half resolution for efficiency and accuracy.