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| Format: | Preprint |
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2026
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| Online-Zugang: | https://arxiv.org/abs/2603.13602 |
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| _version_ | 1866908885603844096 |
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| author | Hammami, Cheima Magoarou, Luc Le Monochristou, Christos González-Ovejero, David Momeni, Ali Fleury, Romain del Hougne, Philipp |
| author_facet | Hammami, Cheima Magoarou, Luc Le Monochristou, Christos González-Ovejero, David Momeni, Ali Fleury, Romain del Hougne, Philipp |
| contents | Wave-based signal processing conventionally encodes input data into the input wavefront, making it challenging to implement non-linear operations. Programmable wave systems enable an alternative approach: encoding the input data into the scattering properties of tunable components. With such structural input encoding, two potentially non-linear mappings are involved: first, from the input data to the tunable components' scattering characteristics, and, second, from these scattering characteristics to the output wavefront. In this paper, we systematically examine the expressivity of a wave-based physical neural network (WPNN) with structural input encoding. Our analysis is based on a physics-consistent multiport-network model of a compact D-band rich-scattering cavity parametrized by a 100-element programmable metasurface. We separately control encoding non-linearity, structural non-linearity, and network depth in order to examine their interplay, considering a controlled scalar regression task. With phase encoding and strong inter-element mutual coupling (MC), both aforementioned mappings are strongly non-linear and the WPNN performs very well even with a single layer. We further observe that additional layers can partially compensate for weak inter-element MC. In addition, we demonstrate that WPNN depth can improve expressivity even when it is not associated with an increase in trainable weights. Altogether, our results provide a physics-consistent picture of how encoding choice, MC strength, and depth jointly govern the expressive power of PM-based WPNNs, informing design choices for future experimental implementations of WPNNs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_13602 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Expressivity of Programmable-Metasurface-Based Physical Neural Networks: Encoding Non-Linearity, Structural Non-Linearity, and Depth Hammami, Cheima Magoarou, Luc Le Monochristou, Christos González-Ovejero, David Momeni, Ali Fleury, Romain del Hougne, Philipp Signal Processing Wave-based signal processing conventionally encodes input data into the input wavefront, making it challenging to implement non-linear operations. Programmable wave systems enable an alternative approach: encoding the input data into the scattering properties of tunable components. With such structural input encoding, two potentially non-linear mappings are involved: first, from the input data to the tunable components' scattering characteristics, and, second, from these scattering characteristics to the output wavefront. In this paper, we systematically examine the expressivity of a wave-based physical neural network (WPNN) with structural input encoding. Our analysis is based on a physics-consistent multiport-network model of a compact D-band rich-scattering cavity parametrized by a 100-element programmable metasurface. We separately control encoding non-linearity, structural non-linearity, and network depth in order to examine their interplay, considering a controlled scalar regression task. With phase encoding and strong inter-element mutual coupling (MC), both aforementioned mappings are strongly non-linear and the WPNN performs very well even with a single layer. We further observe that additional layers can partially compensate for weak inter-element MC. In addition, we demonstrate that WPNN depth can improve expressivity even when it is not associated with an increase in trainable weights. Altogether, our results provide a physics-consistent picture of how encoding choice, MC strength, and depth jointly govern the expressive power of PM-based WPNNs, informing design choices for future experimental implementations of WPNNs. |
| title | Expressivity of Programmable-Metasurface-Based Physical Neural Networks: Encoding Non-Linearity, Structural Non-Linearity, and Depth |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2603.13602 |