# An Efficient Approach to Regression Problems with Tensor Neural Networks

arXiv: https://arxiv.org/abs/2406.09694 · HTML: https://mlsanity.com/paper/2406.09694/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 35 references that are in the map.
- First posted on arXiv 14 Jun 2024.

## Builds on (most cited first, 5 of 5)

- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)

## Abstract (arXiv)

This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex, high-dimensional functions. The TNN demonstrates superior performance compared to conventional Feed-Forward Networks (FFN) and Radial Basis Function Networks (RBN) in terms of both approximation accuracy and generalization capacity, even with a comparable number of parameters. A significant innovation in our approach is the integration of statistical regression and numerical integration within the TNN framework. This allows for efficient computation of high-dimensional integrals associated with the regression function and provides detailed insights into the underlying data structure. Furthermore, we employ gradient and Laplacian analysis on the regression outputs to identify key dimensions influencing the predictions, thereby guiding the design of subsequent experiments. These advancements make TNN a powerful tool for applications requiring precise high-dimensional data analysis and predictive modeling.