Stabilizing Multimodal Autoencoders: A Theoretical and Empirical Analysis of Fusion Strategies

TL;DR

The paper tackles stability in multimodal autoencoders by rigorously analyzing Lipschitz properties of fusion methods and proposing a Lipschitz-regularized, attention-based fusion. It derives theoretical bounds for aggregation and attention, proves that concatenation generally has lower Lipschitz constants than summation, and develops normalization and regularization strategies to control gradient behavior. The authors validate their theory with extensive experiments on synthetic and real industrial datasets (MuJoCo UR5, ABB welding, RoboMNIST), showing that attention-based fusion with spectral normalization and regularization yields superior training stability, convergence, and downstream fault detection. The work provides a solid theoretical foundation for stable multimodal fusion and demonstrates practical benefits for industrial perception tasks.

Abstract

In recent years, the development of multimodal autoencoders has gained significant attention due to their potential to handle multimodal complex data types and improve model performance. Understanding the stability and robustness of these models is crucial for optimizing their training, architecture, and real-world applicability. This paper presents an analysis of Lipschitz properties in multimodal autoencoders, combining both theoretical insights and empirical validation to enhance the training stability of these models. We begin by deriving the theoretical Lipschitz constants for aggregation methods within the multimodal autoencoder framework. We then introduce a regularized attention-based fusion method, developed based on our theoretical analysis, which demonstrates improved stability and performance during training. Through a series of experiments, we empirically validate our theoretical findings by estimating the Lipschitz constants across multiple trials and fusion strategies. Our results demonstrate that our proposed fusion function not only aligns with theoretical predictions but also outperforms existing strategies in terms of consistency, convergence speed, and accuracy. This work provides a solid theoretical foundation for understanding fusion in multimodal autoencoders and contributes a solution for enhancing their performance.

Figures (22)

• Figure 1: Four camera samples of the ABB robots within the RobotStudio cooperative welding simulation environment.
• Figure 2: Four camera samples of the RoboMNIST dataset.
• Figure 3: Multimodal autoencoder including the three aggregation methods. The sum aggregation is represented in blue, concatenation in green, and multimodal attention-based fusion in orange. The SN block represents the spectral normalization, and the MUX block represents a multiplexer.
• Figure 4: Estimated Lipschitz constants of each submodel in the multimodal autoencoder during training on the MuJoCo UR5 dataset, using summation, concatenation, and attention. Solid lines show the mean across trials; shaded areas indicate variation.
• Figure 5: Impact of norm scaling and regularization on the Lipschitz constant in the attention-based aggregation of the multimodal autoencoder on the MuJoCo UR5 dataset, averaged over 10 trials. Solid lines indicate the mean and shaded areas show variation.

Theorems & Definitions (20)

• Definition 3.1
• Lemma 3.1
• Lemma 3.2
• Lemma 3.3
• Theorem 3.1
• Theorem 3.2
• Theorem 3.3
• Definition 4.1
• Theorem 4.1
• Lemma 4.1