Looping back: Circular nodes revisited with novel applications in the radio frequency domain

Tim Marrinan, Bill Kay, Audun Myers, Rachel Wofford, Tegan Emerson
Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:176-190, 2026.

Abstract

In domains with complex-structured data, some relationships cannot be easily modeled using only real-valued Euclidean features. In spite of this misalignment, most modern machine learning methods default to representing data in just that way. By failing to appropriately encode the data structure, the performance and reliability of the resulting machine learning models can be degraded. In prior work, Kirby and Miranda introduced the concept of a circular node, a type of artificial neuron engineered to represent periodic data or angular information [11]. These nodes can be implemented directly in many traditional neural network architectures to more faithfully model periodic relationships. However, since they have garnered relatively little attention compared to their non-circular counterparts, circular nodes have largely been excluded from open-source machine learning libraries. In this paper, we re-investigate circular nodes in the context of modern machine learning libraries, and demonstrate the advantages of circular representations in applications with complex-structured data. Our experiments center around radio frequency signals, which naturally encode circular relationships. We illustrate that a neural network composed of a single circular node can learn the phase offset of a radio frequency signal. We show that a fully-connected neural network made up of multiple layers of circular nodes can successfully classify digital modulation constellation points, and demonstrates accuracy gains over its traditional counterpart when the model size is small. Finally, we demonstrate notable performance improvements on the task of automatic modulation classification through the integration of a circular node layer into traditional convolutional networks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v321-marrinan26a, title = {Looping back: {C}ircular nodes revisited with novel applications in the radio frequency domain}, author = {Marrinan, Tim and Kay, Bill and Myers, Audun and Wofford, Rachel and Emerson, Tegan}, booktitle = {Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025)}, pages = {176--190}, year = {2026}, editor = {Bernardez Gil, Guillermo and Black, Mitchell and Cloninger, Alexander and Doster, Timothy and Emerson, Tegan and Garcı́a-Rodondo, Ińes and Holtz, Chester and Kotak, Mit and Kvinge, Henry and Mishne, Gal and Papillon, Mathilde and Pouplin, Alison and Rainey, Katie and Rieck, Bastian and Telyatnikov, Lev and Yeats, Eric and Wang, Qingsong and Wang, Yusu and Wayland, Jeremy}, volume = {321}, series = {Proceedings of Machine Learning Research}, month = {01--02 Dec}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v321/main/assets/marrinan26a/marrinan26a.pdf}, url = {https://proceedings.mlr.press/v321/marrinan26a.html}, abstract = {In domains with complex-structured data, some relationships cannot be easily modeled using only real-valued Euclidean features. In spite of this misalignment, most modern machine learning methods default to representing data in just that way. By failing to appropriately encode the data structure, the performance and reliability of the resulting machine learning models can be degraded. In prior work, Kirby and Miranda introduced the concept of a circular node, a type of artificial neuron engineered to represent periodic data or angular information [11]. These nodes can be implemented directly in many traditional neural network architectures to more faithfully model periodic relationships. However, since they have garnered relatively little attention compared to their non-circular counterparts, circular nodes have largely been excluded from open-source machine learning libraries. In this paper, we re-investigate circular nodes in the context of modern machine learning libraries, and demonstrate the advantages of circular representations in applications with complex-structured data. Our experiments center around radio frequency signals, which naturally encode circular relationships. We illustrate that a neural network composed of a single circular node can learn the phase offset of a radio frequency signal. We show that a fully-connected neural network made up of multiple layers of circular nodes can successfully classify digital modulation constellation points, and demonstrates accuracy gains over its traditional counterpart when the model size is small. Finally, we demonstrate notable performance improvements on the task of automatic modulation classification through the integration of a circular node layer into traditional convolutional networks.} }
Endnote
%0 Conference Paper %T Looping back: Circular nodes revisited with novel applications in the radio frequency domain %A Tim Marrinan %A Bill Kay %A Audun Myers %A Rachel Wofford %A Tegan Emerson %B Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025) %C Proceedings of Machine Learning Research %D 2026 %E Guillermo Bernardez Gil %E Mitchell Black %E Alexander Cloninger %E Timothy Doster %E Tegan Emerson %E Ińes Garcı́a-Rodondo %E Chester Holtz %E Mit Kotak %E Henry Kvinge %E Gal Mishne %E Mathilde Papillon %E Alison Pouplin %E Katie Rainey %E Bastian Rieck %E Lev Telyatnikov %E Eric Yeats %E Qingsong Wang %E Yusu Wang %E Jeremy Wayland %F pmlr-v321-marrinan26a %I PMLR %P 176--190 %U https://proceedings.mlr.press/v321/marrinan26a.html %V 321 %X In domains with complex-structured data, some relationships cannot be easily modeled using only real-valued Euclidean features. In spite of this misalignment, most modern machine learning methods default to representing data in just that way. By failing to appropriately encode the data structure, the performance and reliability of the resulting machine learning models can be degraded. In prior work, Kirby and Miranda introduced the concept of a circular node, a type of artificial neuron engineered to represent periodic data or angular information [11]. These nodes can be implemented directly in many traditional neural network architectures to more faithfully model periodic relationships. However, since they have garnered relatively little attention compared to their non-circular counterparts, circular nodes have largely been excluded from open-source machine learning libraries. In this paper, we re-investigate circular nodes in the context of modern machine learning libraries, and demonstrate the advantages of circular representations in applications with complex-structured data. Our experiments center around radio frequency signals, which naturally encode circular relationships. We illustrate that a neural network composed of a single circular node can learn the phase offset of a radio frequency signal. We show that a fully-connected neural network made up of multiple layers of circular nodes can successfully classify digital modulation constellation points, and demonstrates accuracy gains over its traditional counterpart when the model size is small. Finally, we demonstrate notable performance improvements on the task of automatic modulation classification through the integration of a circular node layer into traditional convolutional networks.
APA
Marrinan, T., Kay, B., Myers, A., Wofford, R. & Emerson, T.. (2026). Looping back: Circular nodes revisited with novel applications in the radio frequency domain. Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), in Proceedings of Machine Learning Research 321:176-190 Available from https://proceedings.mlr.press/v321/marrinan26a.html.

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