Layer-Specific Lipschitz Modulation for Fault-Tolerant Multimodal Representation Learning

arXiv cs.LG / 3/27/2026

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Key Points

The paper presents a fault-tolerant multimodal representation learning framework that uses Lipschitz- and Jacobian-based criteria to predict whether a neural operator amplifies or attenuates localized faults across modalities.
It unifies self-supervised anomaly detection and error correction in a single architecture, including a two-stage training strategy starting from clean-data multimodal convolutional autoencoder pretraining.
A learnable compute block with dense layers is added to perform correction alongside contrastive objectives for anomaly identification.
The approach introduces layer-specific Lipschitz modulation and gradient clipping to control sensitivity differently in detection versus correction modules.
Experiments on multimodal fault datasets reportedly improve both anomaly detection accuracy and reconstruction quality under sensor corruption, aiming to connect theoretical robustness guarantees with practical deployment needs.

Abstract

Modern multimodal systems deployed in industrial and safety-critical environments must remain reliable under partial sensor failures, signal degradation, or cross-modal inconsistencies. This work introduces a mathematically grounded framework for fault-tolerant multimodal representation learning that unifies self-supervised anomaly detection and error correction within a single architecture. Building upon a theoretical analysis of perturbation propagation, we derive Lipschitz- and Jacobian-based criteria that determine whether a neural operator amplifies or attenuates localized faults. Guided by this theory, we propose a two-stage self-supervised training scheme: pre-training a multimodal convolutional autoencoder on clean data to preserve localized anomaly signals in the latent space, and expanding it with a learnable compute block composed of dense layers for correction and contrastive objectives for anomaly identification. Furthermore, we introduce layer-specific Lipschitz modulation and gradient clipping as principled mechanisms to control sensitivity across detection and correction modules. Experimental results on multimodal fault datasets demonstrate that the proposed approach improves both anomaly detection accuracy and reconstruction under sensor corruption. Overall, this framework bridges the gap between analytical robustness guarantees and practical fault-tolerant multimodal learning.