Hyperbolic Manifold Constrained Tabular Neural Network

arXiv:2607.09710v2 Announce Type: replace Abstract: Tabular prediction is central to a wide range of real-world applications. Tabular data typically contain heterogeneous features as well as rich and complex relational information that can imply a latent structural manifold. Hyperbolic geometry can help capture complex structural relations in data. However, most existing tabular prediction models are constructed and optimized in Euclidean space. How to incorporate hyperbolic geometry into supervised tabular learning remains underexplored. We propose \textbf{HTNN}, a supervised hyperbolic manifold constrained tabular neural network for tabular prediction. HTNN consists of a hyperbolic feature-value representation layer for heterogeneous categorical and numerical features, followed by a conventional MLP predictor. HTNN employs a \emph{geometry-aware training} and \emph{geometry-free inference} optimization framework. The \emph{geometry-aware training} allows hyperbolic geometry to shape the latent representation learning of heterogeneous feature values. After training, the latent hyperbolic representations can be converted into ordinary Euclidean space for efficient \emph{geometry-free inference}. We conducted extensive experiments on the TALENT benchmark. HTNN ranks first among 36 methods on 200 classification datasets and third among 34 methods on 100 regression datasets. Experimental results show that the proposed hyperbolic manifold constrained tabular neural network is effective.

Abstract:Tabular prediction is central to a wide range of real-world applications. Tabular data typically contain heterogeneous features as well as rich and complex relational information that can imply a latent structural manifold. Hyperbolic geometry can help capture complex structural relations in data. However, most existing tabular prediction models are constructed and optimized in Euclidean space. How to incorporate hyperbolic geometry into supervised tabular learning remains underexplored. We propose \textbf{HTNN}, a supervised hyperbolic manifold constrained tabular neural network for tabular prediction. HTNN consists of a hyperbolic feature-value representation layer for heterogeneous categorical and numerical features, followed by a conventional MLP predictor. HTNN employs a \emph{geometry-aware training} and \emph{geometry-free inference} optimization framework. The \emph{geometry-aware training} allows hyperbolic geometry to shape the latent representation learning of heterogeneous feature values. After training, the latent hyperbolic representations can be converted into ordinary Euclidean space for efficient \emph{geometry-free inference}. We conducted extensive experiments on the TALENT benchmark. HTNN ranks first among 36 methods on 200 classification datasets and third among 34 methods on 100 regression datasets. Experimental results show that the proposed hyperbolic manifold constrained tabular neural network is effective.

Machine Learning (cs.LG); Machine Learning (stat.ML)

arXiv:2607.09710 [cs.LG]

(or arXiv:2607.09710v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.09710 Focus to learn more arXiv-issued DOI via DataCite

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Hyperbolic Manifold Constrained Tabular Neural Network

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