Abstract Reliable non-destructive hardness measurement, such as using magnetic properties, is a critical requirement in industrial quality assurance and structural health monitoring, where destructive testing is impractical or economically infeasible. Despite its importance, extracting physically meaningful and predictive features from frequency-domain magnetic signals remains challenging, particularly in scenarios where annotated measurement data are scarce and expensive to obtain. In this study, the challenge of extracting physically meaningful features from limited data is addressed by proposing a complex-valued autoencoder. This architecture is designed to jointly encode magnitude and frequency information into a compact latent representation, thereby preserving phase-sensitive structural dependencies that are typically lost in standard approaches. The method was evaluated on a real-world dataset of high-strength alloys with sparse annotations. It is demonstrated that the proposed complex-valued representations yield significantly improved regression performance, characterized by lower prediction error and reduced variance compared to a classical real-valued baseline. These results indicate that leveraging the algebraic structure of complex-valued networks offers a superior approach for non-destructive testing in low-data regimes, enabling more stable and accurate industrial inspection systems.

Ensuring the stability and robustness of multimodal autoencoders is critical for their optimization and deployment in safety-critical industrial environments. This paper presents a rigorous analysis of Lipschitz properties in multimodal fusion, identifying theoretical vulnerabilities in standard summation and concatenation strategies. We derive explicit Lipschitz bounds for these methods, demonstrating their susceptibility to gradient instability and noise propagation as the number of modalities increases. To address this, we introduce a Lipschitz-regularized attention-based fusion mechanism that explicitly bounds gradient sensitivity through spectral normalization and dimension scaling. Empirical validation on four industrial robotic datasets, including the real-world RoboMNIST dataset, confirms our theoretical findings. On the RoboMNIST dataset, our method achieves an improvement of 54.7% in bimodal and 57.4% in trimodal reconstruction over standard attention, alongside a 20.5% gain in subordinated fault detection, while effectively regularizing the Lipschitz of the gradients.

Neural network architectures designed for function parameterization, such as the Bag-of-Functions (BoF) framework, bridge the gap between the expressivity of deep learning and the interpretability of classical signal processing. However, these models are inherently sensitive to parameter initialization, as traditional data-agnostic schemes fail to capture the structural properties of the target signals, often leading to suboptimal convergence. In this work, we propose a prior-informed design strategy that leverages the intrinsic spectral and temporal structure of the data to guide both network initialization and architectural configuration for the Bag-of-Functions. A principled methodology is introduced that uses the Fast Fourier Transform to extract dominant seasonal priors, informing model depth and initial states, and a residual-based regression approach to parameterize trend components. Crucially, this structural alignment enables a substantial reduction in encoder dimensionality without compromising reconstruction fidelity. A supporting theoretical analysis provides guidance on trend estimation under finite-sample regimes. Extensive experiments demonstrate the effectiveness of this approach: the informed initialization reduces reconstruction error by 15.1% on complex real-world benchmarks. Furthermore, the trend-informed dimensionality reduction yields up to a 30% decrease in model parameters and computational complexity, accelerating inference and stabilizing optimization without altering the core training procedure. • Data-driven spectral priors guide neural network initialization and depth selection. • Trend-informed initialization enables compact architectures without accuracy loss. • Informed priors stabilize optimization and accelerate convergence across datasets. • Improved efficiency achieved with reduced parameters and computational cost.

• Rigorous analysis proving the marginal convexity for multimodal autoencoders. • Block-wise optimization strategy for multimodal architectures. • Novel Lipschitz-based adaptive learning rate for scale mismatch. • Evaluation on real-world heterogeneous multimodal datasets.

Multimodal learning is critical for robust perception in complex systems, yet integrating diverse modalities while ensuring fault tolerance remains a significant challenge. This paper presents a novel approach for fusing multimodal latent representations using a denoising variational autoencoder framework, where the fusion is achieved through the multiplication of probability density functions corresponding to each modality. By modeling each modality as a Gaussian distribution in the latent space, we derive a fused representation that optimally combines information from all modalities while preserving their probabilistic structure. We introduce a failure injection mechanism during training, where non-linear transformations simulate realistic faults in individual modalities. Experiments on industrial datasets demonstrate that our approach achieves superior reconstruction accuracy and robustness compared to existing methods, even in the presence of corrupted or missing modalities.

Drone delivery systems are increasingly gaining importance in modern logistics due to their efficiency and potential to revolutionize the supply chain. However, among the various stages of drone operations, the landing phase stands out as the most critical, as it requires precise navigation and control to ensure the safe and successful delivery of goods. Therefore, testing simulations are required to accurately replicate the complex dynamics of real-world environments. In this paper, we propose a CycleGAN-based framework for bidirectional domain translation between simulated and real-world data, with a focus on GPS features. The proposed architecture facilitates seamless transfer learning by enabling simulation-trained controllers to operate effectively in real-world environments and vice versa. Additionally, we integrate the translated data into a downstream control framework for autonomous landing tasks, validating the practicality of the approach.

Deep networks have been successfully applied to industrial applications for clean unimodal data (e.g., sensors, images, or audio). Leveraging multimodal data is a common approach to enhance performance, guided by the principle that a larger quantity of data leads to improvement. However, performance may decline considerably if corruption in the data is present (e.g., noise, blur, failure). Although researchers have explored various data augmentation methods to improve the generalization capacity, these methods are not adapted for industrial settings. The primary distinction is that current augmentation methods are designed to enhance model generalization capabilities and not realistically simulate real-world industry scenarios. In this paper, we present industry-related augmentation methods for temporal and spatial data for multimodal fusion with deep neural networks. Our methods are specifically designed to encourage modality collaboration and reinforce generalization capability. The impact of the proposed data extension strategy to train multimodal fusion models is assessed on a synthetic dataset from an industrial UR5 robot with varying degrees of imbalance. In our study, we analyze different combinations of methods and evaluate their performance. Through these experiments, we are able to identify the challenges in multimodal fusion with deep learning models in an industrial setting.

Deep networks have been successfully applied to unsupervised feature learning and supervised classification and regression for unimodal data (e.g., sensors, images, or audio). Multimodal data is often used to improve the performance of networks according to the slogan: the more, the better. Limited research is available to compensate for corrupted signals from multimodal approaches. In this work, we propose a novel regularization method for deep networks to learn features over multiple modalities designed to compensate for relative sensor weaknesses, such as sensor malfunction, inaccuracy, restricted spatial coverage, and uncertainty. We have used a special augmentation strategy for image and time series modalities to enhance the dataset of underrepresented industrial failure cases. The primary objective is to prevent these cases from negatively impacting the model's predictions. Our approach involves incorporating a fuzzy regularizer that can modify the intensity of activations depending on the quality of the signal, enabling disturbances from various modalities to be identified based on the activations. Our experiments on a simulated Universal Robots UR5 dataset demonstrate the effectiveness of our proposed regularization in increasing the model's stability, accuracy, and generalization to uncertainties and failures in the input signals. By incorporating fuzzy regularization in deep fusion models, their efficiency on complex tasks can be improved while reducing the complexity of the architectures.