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

TL;DR

This paper presents a theoretically grounded, layer-specific Lipschitz modulation framework for fault-tolerant multimodal learning, enhancing anomaly detection and correction in safety-critical systems.

Contribution

It introduces a novel Lipschitz-based criteria and a two-stage training scheme for improving fault tolerance in multimodal neural networks.

Findings

Improved anomaly detection accuracy under sensor faults

Enhanced reconstruction quality during sensor degradation

Theoretical analysis linking Lipschitz properties to fault sensitivity

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.