{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/surreal-frechet-mean-and-distance-transform","title":"SurReal: Fréchet Mean and Distance Transform for Complex-Valued Deep Learning","arxiv_id":"1906.10048","date":"2019-06-24","proceeding":null,"authors":["Rudrasis Chakraborty","Jiayun Wang","Stella X. Yu"],"abstract":"We develop a novel deep learning architecture for naturally complex-valued data, which is often subject to complex scaling ambiguity. We treat each sample as a field in the space of complex numbers. With the polar form of a complex-valued number, the general group that acts in this space is the product of planar rotation and non-zero scaling. This perspective allows us to develop not only a novel convolution operator using weighted Fr\\'echet mean (wFM) on a Riemannian manifold, but also a novel fully connected layer operator using the distance to the wFM, with natural equivariant properties to non-zero scaling and planar rotation for the former and invariance properties for the latter. Compared to the baseline approach of learning real-valued neural network models on the two-channel real-valued representation of complex-valued data, our method achieves surreal performance on two publicly available complex-valued datasets: MSTAR on SAR images and RadioML on radio frequency signals. On MSTAR, at 8% of the baseline model size and with fewer than 45,000 parameters, our model improves the target classification accuracy from 94% to 98% on this highly imbalanced dataset. On RadioML, our model achieves comparable RF modulation classification accuracy at 10% of the baseline model size.","url_abs":"https://arxiv.org/abs/1906.10048v1","url_pdf":"https://arxiv.org/pdf/1906.10048v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"surreal-frechet-mean-and-distance-transform","repo_url":"https://github.com/xingyifei2016/RotLieNet","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"classification","task_name":"General Classification"}],"methods":[{"method_slug":"convolution","method_name":"Convolution"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}