# Learning Tensors in Reproducing Kernel Hilbert Spaces with Multilinear Spectral Penalties

arXiv: https://arxiv.org/abs/1310.4977 · HTML: https://mlsanity.com/paper/1310.4977/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Oct 2013.

## Built on by (most cited first, 3 of 3)

- [Provable Adaptation across Multiway Domains via Representation Learning](https://mlsanity.com/paper/2106.06657/) (2021)
- [Approximation and learning of anisotropic and mixed smooth functions by deep ReLU neural networks](https://mlsanity.com/paper/2605.31152/) (2026)
- [Multi-Linear Kernel Regression and Imputation in Data Manifolds](https://mlsanity.com/paper/2304.03041/) (2023)

## Abstract (arXiv)

We present a general framework to learn functions in tensor product reproducing kernel Hilbert spaces (TP-RKHSs). The methodology is based on a novel representer theorem suitable for existing as well as new spectral penalties for tensors. When the functions in the TP-RKHS are defined on the Cartesian product of finite discrete sets, in particular, our main problem formulation admits as a special case existing tensor completion problems. Other special cases include transfer learning with multimodal side information and multilinear multitask learning. For the latter case, our kernel-based view is instrumental to derive nonlinear extensions of existing model classes. We give a novel algorithm and show in experiments the usefulness of the proposed extensions.