  Recent years have witnessed a surge of interest in integrating
high-dimensional data captured by multisource sensors, driven by the impressive
success of neural networks in the integration of multimodal data. However, the
integration of heterogeneous multimodal data poses a significant challenge, as
confounding effects and dependencies among such heterogeneous data sources
introduce unwanted variability and bias, leading to suboptimal performance of
multimodal models. Therefore, it becomes crucial to normalize the low- or
high-level features extracted from data modalities before their fusion takes
place. This paper introduces a novel approach for the normalization of
multimodal data, called RegBN, that incorporates regularization. RegBN uses the
Frobenius norm as a regularizer term to address the side effects of confounders
and underlying dependencies among different data sources. The proposed method
generalizes well across multiple modalities and eliminates the need for
learnable parameters, simplifying training and inference. We validate the
effectiveness of RegBN on eight databases from five research areas,
encompassing diverse modalities such as language, audio, image, video, depth,
tabular, and 3D MRI. The proposed method demonstrates broad applicability
across different architectures such as multilayer perceptrons, convolutional
neural networks, and vision transformers, enabling effective normalization of
both low- and high-level features in multimodal neural networks. RegBN is
available at \url{https://github.com/mogvision/regbn}.
