Neural Operator-Grounded Continuous Tensor Function Representation and Its Applications

• URL: http://arxiv.org/abs/2603.01812v1
• Date: Mon, 02 Mar 2026 12:47:17 GMT
• Title: Neural Operator-Grounded Continuous Tensor Function Representation and Its Applications
• Authors: Ruoyang Su, Xi-Le Zhao, Sheng Liu, Wei-Hao Wu, Yisi Luo, Michael K. Ng,
• Abstract summary: We propose a neural operator-grounded continuous tensor function representation (abbreviated as NO-CTR), which can more faithfully represent complex real-world data.<n>Experiments on regular mesh grids, on mesh girds with different resolutions and beyond mesh grids demonstrate NO-CTR's superiority.
• Score: 47.55853502720306
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recently, continuous tensor functions have attracted increasing attention, because they can unifiedly represent data both on mesh grids and beyond mesh grids. However, since mode-$n$ product is essentially discrete and linear, the potential of current continuous tensor function representations is still locked. To break this bottleneck, we suggest neural operator-grounded mode-$n$ operators as a continuous and nonlinear alternative of discrete and linear mode-$n$ product. Instead of mapping the discrete core tensor to the discrete target tensor, proposed mode-$n$ operator directly maps the continuous core tensor function to the continuous target tensor function, which provides a genuine continuous representation of real-world data and can ameliorate discretization artifacts. Empowering with continuous and nonlinear mode-$n$ operators, we propose a neural operator-grounded continuous tensor function representation (abbreviated as NO-CTR), which can more faithfully represent complex real-world data compared with classic discrete tensor representations and continuous tensor function representations. Theoretically, we also prove that any continuous tensor function can be approximated by NO-CTR. To examine the capability of NO-CTR, we suggest an NO-CTR-based multi-dimensional data completion model. Extensive experiments across various data on regular mesh grids (multi-spectral images and color videos), on mesh girds with different resolutions (Sentinel-2 images) and beyond mesh grids (point clouds) demonstrate the superiority of NO-CTR.

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