ICML 2025

Tensor Product Neural Networks for Functional ANOVA Model
Seokhun Park 1 Insung Kong 2 Yongchan Choi 3 Chanmoo Park 1 4 Yongdai Kim 1
Abstract
Interpretability for machine learning models is
becoming more and more important as machine
learning models become more complex. The func-
tional ANOVA model, which decomposes a high-
dimensional function into a sum of lower dimen-
sional functions (commonly referred to as compo-
nents), is one of the most popular tools for inter-
pretable AI, and recently, various neural networks
have been developed for estimating each compo-
nent in the functional ANOVA model. However,
such neural networks are highly unstable when
estimating each component since the components
themselves are not uniquely defined. That is, there
are multiple functional ANOVA decompositions
for a given function. In this paper, we propose a
novel neural network which guarantees a unique
functional ANOVA decomposition and thus is
able to estimate each component stably. We call
our proposed neural network ANOVA Tensor Prod-
uct Neural Network (ANOVA-TPNN) since it is
motivated by the tensor product basis expansion.
Theoretically, we prove that ANOVA-TPNN can
approximate any smooth function well. Empiri-
cally, we show that ANOVA-TPNN provide much
more stable estimation of each component and
thus much more stable interpretation when train-
ing data and initial values of the model parameters
vary than existing neural networks do. Our source
code is released at https://github.com/
ParkSeokhun/ANOVA-TPNN
1. Introduction
Interpretability has become more important as artificial in-
telligence (AI) models have become more sophisticated and
complicated in recent years. Various methods such as LIME
1Department of Statistics, Seoul National University, Seoul, Re-
public of Korea 2Department of Applied Mathematics, University
of Twente, Enschede, Netherlands 3Toss Bank, Seoul, Republic of
Korea 4Samsung Electronics Co., Ltd, Republic of Korea. Corre-
spondence to: Yongdai ...