Homological Convolutional Neural Networks

Antonio Briola, Yuanrong Wang, Silvia Bartolucci, Tomaso Aste
Proceedings of the 2nd NeurIPS Workshop on Symmetry and Geometry in Neural Representations, PMLR 228:206-231, 2024.

Abstract

Deep learning methods have demonstrated outstanding performances on classification and regression tasks on homogeneous data types (e.g., image, audio, and text data). However, tabular data still pose a challenge, with classic machine learning approaches being often computationally cheaper and equally effective than increasingly complex deep learning architectures. The challenge arises from the fact that, in tabular data, the correlation among features is weaker than the one from spatial or semantic relationships in images or natural language, and the dependency structures need to be modeled without any prior information. In this work, we propose a novel deep learning architecture that exploits the data structural organization through topologically constrained network representations to gain relational information from sparse tabular inputs. The resulting model leverages the power of convolution and is centered on a limited number of concepts from network topology to guarantee: (i) a data-centric and deterministic building pipeline; (ii) a high level of interpretability over the inference process; and (iii) an adequate room for scalability. We test our model on $18$ benchmark datasets against $5$ classic machine learning and $3$ deep learning models, demonstrating that our approach reaches state-of-the-art performances on these challenging datasets. The code to reproduce all our experiments is provided at https://github.com/FinancialComputingUCL/HomologicalCNN.

Cite this Paper

BibTeX
@InProceedings{pmlr-v228-briola24a, title = {Homological Convolutional Neural Networks}, author = {Briola, Antonio and Wang, Yuanrong and Bartolucci, Silvia and Aste, Tomaso}, booktitle = {Proceedings of the 2nd NeurIPS Workshop on Symmetry and Geometry in Neural Representations}, pages = {206--231}, year = {2024}, editor = {Sanborn, Sophia and Shewmake, Christian and Azeglio, Simone and Miolane, Nina}, volume = {228}, series = {Proceedings of Machine Learning Research}, month = {16 Dec}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v228/main/assets/briola24a/briola24a.pdf}, url = {https://proceedings.mlr.press/v228/briola24a.html}, abstract = {Deep learning methods have demonstrated outstanding performances on classification and regression tasks on homogeneous data types (e.g., image, audio, and text data). However, tabular data still pose a challenge, with classic machine learning approaches being often computationally cheaper and equally effective than increasingly complex deep learning architectures. The challenge arises from the fact that, in tabular data, the correlation among features is weaker than the one from spatial or semantic relationships in images or natural language, and the dependency structures need to be modeled without any prior information. In this work, we propose a novel deep learning architecture that exploits the data structural organization through topologically constrained network representations to gain relational information from sparse tabular inputs. The resulting model leverages the power of convolution and is centered on a limited number of concepts from network topology to guarantee: (i) a data-centric and deterministic building pipeline; (ii) a high level of interpretability over the inference process; and (iii) an adequate room for scalability. We test our model on $18$ benchmark datasets against $5$ classic machine learning and $3$ deep learning models, demonstrating that our approach reaches state-of-the-art performances on these challenging datasets. The code to reproduce all our experiments is provided at https://github.com/FinancialComputingUCL/HomologicalCNN.} }
Endnote
%0 Conference Paper %T Homological Convolutional Neural Networks %A Antonio Briola %A Yuanrong Wang %A Silvia Bartolucci %A Tomaso Aste %B Proceedings of the 2nd NeurIPS Workshop on Symmetry and Geometry in Neural Representations %C Proceedings of Machine Learning Research %D 2024 %E Sophia Sanborn %E Christian Shewmake %E Simone Azeglio %E Nina Miolane %F pmlr-v228-briola24a %I PMLR %P 206--231 %U https://proceedings.mlr.press/v228/briola24a.html %V 228 %X Deep learning methods have demonstrated outstanding performances on classification and regression tasks on homogeneous data types (e.g., image, audio, and text data). However, tabular data still pose a challenge, with classic machine learning approaches being often computationally cheaper and equally effective than increasingly complex deep learning architectures. The challenge arises from the fact that, in tabular data, the correlation among features is weaker than the one from spatial or semantic relationships in images or natural language, and the dependency structures need to be modeled without any prior information. In this work, we propose a novel deep learning architecture that exploits the data structural organization through topologically constrained network representations to gain relational information from sparse tabular inputs. The resulting model leverages the power of convolution and is centered on a limited number of concepts from network topology to guarantee: (i) a data-centric and deterministic building pipeline; (ii) a high level of interpretability over the inference process; and (iii) an adequate room for scalability. We test our model on $18$ benchmark datasets against $5$ classic machine learning and $3$ deep learning models, demonstrating that our approach reaches state-of-the-art performances on these challenging datasets. The code to reproduce all our experiments is provided at https://github.com/FinancialComputingUCL/HomologicalCNN.
APA
Briola, A., Wang, Y., Bartolucci, S. & Aste, T.. (2024). Homological Convolutional Neural Networks. Proceedings of the 2nd NeurIPS Workshop on Symmetry and Geometry in Neural Representations, in Proceedings of Machine Learning Research 228:206-231 Available from https://proceedings.mlr.press/v228/briola24a.html.

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