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

arXiv: https://arxiv.org/abs/2603.25103 · HTML: https://mlsanity.com/paper/2603.25103/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 49 references that are in the map.
- First posted on arXiv 26 Mar 2026.

## Builds on (most cited first, 25 of 25)

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- [ViLBERT: Pretraining Task-Agnostic Visiolinguistic Representations for Vision-and-Language Tasks](https://mlsanity.com/paper/1908.02265/) (2019)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [LXMERT: Learning Cross-Modality Encoder Representations from Transformers](https://mlsanity.com/paper/1908.07490/) (2019)
- [Contrastive Multiview Coding](https://mlsanity.com/paper/1906.05849/) (2019)
- [Virtual Adversarial Training: A Regularization Method for Supervised and Semi-Supervised Learning](https://mlsanity.com/paper/1704.03976/) (2017)
- [Look, Listen and Learn](https://mlsanity.com/paper/1705.08168/) (2017)
- [VATT: Transformers for Multimodal Self-Supervised Learning from Raw Video, Audio and Text](https://mlsanity.com/paper/2104.11178/) (2021)
- [Objects that Sound](https://mlsanity.com/paper/1712.06651/) (2017)
- [Cooperative Learning of Audio and Video Models from Self-Supervised Synchronization](https://mlsanity.com/paper/1807.00230/) (2018)
- [Sorting out Lipschitz function approximation](https://mlsanity.com/paper/1811.05381/) (2018)
- [Are Multimodal Transformers Robust to Missing Modality?](https://mlsanity.com/paper/2204.05454/) (2022)
- [Understanding Gradient Clipping in Private SGD: A Geometric Perspective](https://mlsanity.com/paper/2006.15429/) (2020)
- [Learning Representations from Audio-Visual Spatial Alignment](https://mlsanity.com/paper/2011.01819/) (2020)
- [Watch or Listen: Robust Audio-Visual Speech Recognition with Visual Corruption Modeling and Reliability Scoring](https://mlsanity.com/paper/2303.08536/) (2023)
- [Decoupling Common and Unique Representations for Multimodal Self-supervised Learning](https://mlsanity.com/paper/2309.05300/) (2023)
- [Understanding and Improving Feature Learning for Out-of-Distribution Generalization](https://mlsanity.com/paper/2304.11327/) (2023)
- [Learning Continually by Spectral Regularization](https://mlsanity.com/paper/2406.06811/) (2024)
- [Certified Robustness via Dynamic Margin Maximization and Improved Lipschitz Regularization](https://mlsanity.com/paper/2310.00116/) (2023)
- [Local Disentanglement in Variational Auto-Encoders Using Jacobian L1 Regularization](https://mlsanity.com/paper/2106.02923/) (2021)
- [Robust Multimodal Learning via Representation Decoupling](https://mlsanity.com/paper/2407.04458/) (2024)
- [Toward Robust Incomplete Multimodal Sentiment Analysis via Hierarchical Representation Learning](https://mlsanity.com/paper/2411.02793/) (2024)
- [The Survey on Multi-Source Data Fusion in Cyber-Physical-Social Systems:Foundational Infrastructure for Industrial Metaverses and Industries 5.0](https://mlsanity.com/paper/2404.07476/) (2024)
- [A Multimodal Lightweight Approach to Fault Diagnosis of Induction Motors in High-Dimensional Dataset](https://mlsanity.com/paper/2501.03746/) (2025)
- [Stabilizing Multimodal Autoencoders: A Theoretical and Empirical Analysis of Fusion Strategies](https://mlsanity.com/paper/2512.20749/) (2025)

## Abstract (arXiv)

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.