# Tensor Network Based Feature Learning Model

arXiv: https://arxiv.org/abs/2512.02547 · HTML: https://mlsanity.com/paper/2512.02547/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 39 references that are in the map.
- First posted on arXiv 2 Dec 2025.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Bayesian Deep Convolutional Networks with Many Channels are Gaussian Processes](https://mlsanity.com/paper/1810.05148/) (2018)
- [Variational Fourier features for Gaussian processes](https://mlsanity.com/paper/1611.06740/) (2016)
- [Reproducing Kernel Hilbert Space, Mercer's Theorem, Eigenfunctions, Nystr"om Method, and Use of Kernels in Machine Learning: Tutorial and Survey](https://mlsanity.com/paper/2106.08443/) (2021)
- [Supervised Learning with Projected Entangled Pair States](https://mlsanity.com/paper/2009.09932/) (2020)
- [Parallelized Tensor Train Learning of Polynomial Classifiers](https://mlsanity.com/paper/1612.06505/) (2016)
- [Large-Scale Learning with Fourier Features and Tensor Decompositions](https://mlsanity.com/paper/2109.01545/) (2021)
- [Tensor Network alternating linear scheme for MIMO Volterra system identification](https://mlsanity.com/paper/1607.00127/) (2016)
- [Multi-output Polynomial Networks and Factorization Machines](https://mlsanity.com/paper/1705.07603/) (2017)
- [Quantized Fourier and Polynomial Features for more Expressive Tensor Network Models](https://mlsanity.com/paper/2309.05436/) (2023)
- [String and Membrane Gaussian Processes](https://mlsanity.com/paper/1507.06977/) (2015)

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

- [Laplace Approximation for Bayesian Tensor Network Kernel Machines](https://mlsanity.com/paper/2604.26673/) (2026)
- [Tensor Computing Interface: An Application-Oriented, Lightweight Interface for Portable High-Performance Tensor Network Applications](https://mlsanity.com/paper/2512.23917/) (2025)
- [Tensor Network Kernel Machines: A JAX Framework for Machine Learning and Nonlinear System Identification](https://mlsanity.com/paper/2608.07043/) (2026)

## Abstract (arXiv)

Many approximations were suggested to circumvent the cubic complexity of kernel-based algorithms, allowing their application to large-scale datasets. One strategy is to consider the primal formulation of the learning problem by mapping the data to a higher-dimensional space using tensor-product structured polynomial and Fourier features. The curse of dimensionality due to these tensor-product features was effectively solved by a tensor network reparameterization of the model parameters. However, another important aspect of model training - identifying optimal feature hyperparameters - has not been addressed and is typically handled using the standard cross-validation approach. In this paper, we introduce the Feature Learning (FL) model, which addresses this issue by representing tensor-product features as a learnable Canonical Polyadic Decomposition (CPD). By leveraging this CPD structure, we efficiently learn the hyperparameters associated with different features alongside the model parameters using an Alternating Least Squares (ALS) optimization method. We prove the effectiveness of the FL model through experiments on real data of various dimensionality and scale. The results show that the FL model can be consistently trained 3-5 times faster than and have the prediction quality on par with a standard cross-validated model.