Continuous Simplicial Neural Networks
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915572695957504 |
|---|---|
| author | Einizade, Aref Thanou, Dorina Malliaros, Fragkiskos D. Giraldo, Jhony H. |
| author_facet | Einizade, Aref Thanou, Dorina Malliaros, Fragkiskos D. Giraldo, Jhony H. |
| contents | Simplicial complexes provide a powerful framework for modeling higher-order interactions in structured data, making them particularly suitable for applications such as trajectory prediction and mesh processing. However, existing simplicial neural networks (SNNs), whether convolutional or attention-based, rely primarily on discrete filtering techniques, which can be restrictive. In contrast, partial differential equations (PDEs) on simplicial complexes offer a principled approach to capture continuous dynamics in such structures. In this work, we introduce continuous simplicial neural network (COSIMO), a novel SNN architecture derived from PDEs on simplicial complexes. We provide theoretical and experimental justifications of COSIMO's stability under simplicial perturbations. Furthermore, we investigate the over-smoothing phenomenon, a common issue in geometric deep learning, demonstrating that COSIMO offers better control over this effect than discrete SNNs. Our experiments on real-world datasets demonstrate that COSIMO achieves competitive performance compared to state-of-the-art SNNs in complex and noisy environments. The implementation codes are available in https://github.com/ArefEinizade2/COSIMO. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12919 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Continuous Simplicial Neural Networks Einizade, Aref Thanou, Dorina Malliaros, Fragkiskos D. Giraldo, Jhony H. Machine Learning Simplicial complexes provide a powerful framework for modeling higher-order interactions in structured data, making them particularly suitable for applications such as trajectory prediction and mesh processing. However, existing simplicial neural networks (SNNs), whether convolutional or attention-based, rely primarily on discrete filtering techniques, which can be restrictive. In contrast, partial differential equations (PDEs) on simplicial complexes offer a principled approach to capture continuous dynamics in such structures. In this work, we introduce continuous simplicial neural network (COSIMO), a novel SNN architecture derived from PDEs on simplicial complexes. We provide theoretical and experimental justifications of COSIMO's stability under simplicial perturbations. Furthermore, we investigate the over-smoothing phenomenon, a common issue in geometric deep learning, demonstrating that COSIMO offers better control over this effect than discrete SNNs. Our experiments on real-world datasets demonstrate that COSIMO achieves competitive performance compared to state-of-the-art SNNs in complex and noisy environments. The implementation codes are available in https://github.com/ArefEinizade2/COSIMO. |
| title | Continuous Simplicial Neural Networks |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2503.12919 |