Vision-Language Models (VLMs) inherit adversarial vulnerabilities of Large Language Models (LLMs), which are further exacerbated by their multimodal nature. Existing defenses, including adversarial training, input transformations, and heuristic detection, are computationally expensive, architecture-dependent, and fragile against adaptive attacks. We introduce EigenShield, an inference-time defense leveraging Random Matrix Theory to quantify adversarial disruptions in high-dimensional VLM representations. Unlike prior methods that rely on empirical heuristics, EigenShield employs the spiked covariance model to detect structured spectral deviations. Using a Robustness-based Nonconformity Score (RbNS) and quantile-based thresholding, it separates causal eigenvectors, which encode semantic information, from correlational eigenvectors that are susceptible to adversarial artifacts. By projecting embeddings onto the causal subspace, EigenShield filters adversarial noise without modifying model parameters or requiring adversarial training. This architecture-independent, attack-agnostic approach significantly reduces the attack success rate, establishing spectral analysis as a principled alternative to conventional defenses. Our results demonstrate that EigenShield consistently outperforms all existing defenses, including adversarial training, UNIGUARD, and CIDER.

Modern time series forecasting methods, such as Transformer and its variants, have shown strong ability in sequential data modeling. To achieve high performance, they usually rely on redundant or unexplainable structures to model complex relations between variables and tune the parameters with large-scale data. Many real-world data mining tasks, however, lack sufficient variables for relation reasoning, and therefore these methods may not properly handle such forecasting problems. With insufficient data, time series appear to be affected by many exogenous variables, and thus, the modeling becomes unstable and unpredictable. To tackle this critical issue, in this paper, we develop a novel algorithmic framework for inferring the intrinsic latent factors implied by the observable time series. The inferred factors are used to form multiple independent and predictable signal components that enable not only sparse relation reasoning for long-term efficiency but also reconstructing the future temporal data for accurate prediction. To achieve this, we introduce three characteristics, i.e., predictability, sufficiency, and identifiability, and model these characteristics via the powerful deep latent dynamics models to infer the predictable signal components. Empirical results on multiple real datasets show the efficiency of our method for different kinds of time series forecasting. The statistical analysis validates the predictability of the learned latent factors.

This work introduces an asymptotic study of Hotelling-type tensor deflation in the presence of noise, in the regime of large tensor dimensions. Specifically, we consider a low-rank asymmetric tensor model of the form $\sum_{i=1}^r \beta_i{\mathcal{A}}_i + {\mathcal{W}}$ where $\beta_i\geq 0$ and the ${\mathcal{A}}_i$'s are unit-norm rank-one tensors such that $\left| \langle {\mathcal{A}}_i, {\mathcal{A}}_j \rangle \right| \in [0, 1]$ for $i\neq j$ and ${\mathcal{W}}$ is an additive noise term. Assuming that the dominant components are successively estimated from the noisy observation and subsequently subtracted, we leverage recent advances in random tensor theory in the regime of asymptotically large tensor dimensions to analytically characterize the estimated singular values and the alignment of estimated and true singular vectors at each step of the deflation procedure. Furthermore, this result can be used to construct estimators of the signal-to-noise ratios $\beta_i$ and the alignments between the estimated and true rank-1 signal components.

Leveraging on recent advances in random tensor theory, we consider in this paper a rank-$r$ asymmetric spiked tensor model of the form $\sum_{i=1}^r \beta_i A_i + W$ where $\beta_i\geq 0$ and the $A_i$'s are rank-one tensors such that $\langle A_i, A_j \rangle\in [0, 1]$ for $i\neq j$, based on which we provide an asymptotic study of Hotelling-type tensor deflation in the large dimensional regime. Specifically, our analysis characterizes the singular values and alignments at each step of the deflation procedure, for asymptotically large tensor dimensions. This can be used to construct consistent estimators of different quantities involved in the underlying problem, such as the signal-to-noise ratios $\beta_i$ or the alignments between the different signal components $\langle A_i, A_j \rangle$.

Noise in seismic data arises from numerous sources and is continually evolving. The use of supervised deep learning procedures for denoising of seismic datasets often results in poor performance: this is due to the lack of noise-free field data to act as training targets and the large difference in characteristics between synthetic and field datasets. Self-supervised, blind-spot networks typically overcome these limitation by training directly on the raw, noisy data. However, such networks often rely on a random noise assumption, and their denoising capabilities quickly decrease in the presence of even minimally-correlated noise. Extending from blind-spots to blind-masks can efficiently suppress coherent noise along a specific direction, but it cannot adapt to the ever-changing properties of noise. To preempt the network's ability to predict the signal and reduce its opportunity to learn the noise properties, we propose an initial, supervised training of the network on a frugally-generated synthetic dataset prior to fine-tuning in a self-supervised manner on the field dataset of interest. Considering the change in peak signal-to-noise ratio, as well as the volume of noise reduced and signal leakage observed, we illustrate the clear benefit in initialising the self-supervised network with the weights from a supervised base-training. This is further supported by a test on a field dataset where the fine-tuned network strikes the best balance between signal preservation and noise reduction. Finally, the use of the unrealistic, frugally-generated synthetic dataset for the supervised base-training includes a number of benefits: minimal prior geological knowledge is required, substantially reduced computational cost for the dataset generation, and a reduced requirement of re-training the network should recording conditions change, to name a few.

Image-based anomaly detection systems are of vital importance in various manufacturing applications. The resolution and acquisition rate of such systems is increasing significantly in recent years under the fast development of image sensing technology. This enables the detection of tiny defects in real-time. However, such a high resolution and acquisition rate of image data not only slows down the speed of image processing algorithms but also increases data storage and transmission cost. To tackle this problem, we propose a fast and data-efficient method with theoretical performance guarantee that is suitable for sparse anomaly detection in images with a smooth background (smooth plus sparse signal). The proposed method, named Compressed Smooth Sparse Decomposition (CSSD), is a one-step method that unifies the compressive image acquisition and decomposition-based image processing techniques. To further enhance its performance in a high-dimensional scenario, a Kronecker Compressed Smooth Sparse Decomposition (KronCSSD) method is proposed. Compared to traditional smooth and sparse decomposition algorithms, significant transmission cost reduction and computational speed boost can be achieved with negligible performance loss. Simulation examples and several case studies in various applications illustrate the effectiveness of the proposed framework.

This paper is concerned with the inverse problem of recovering the unknown signal components, along with extraction of their instantaneous frequencies (IFs), governed by the adaptive harmonic model (AHM), from discrete (and possibly non-uniform) samples of the blind-source composite signal. None of the existing decomposition methods and algorithms, including the most popular empirical mode decomposition (EMD) computational scheme and its current modifications, is capable of solving this inverse problem. In order to meet the AHM formulation and to extract the IFs of the decomposed components, called intrinsic mode functions (IMFs), each IMF of EMD is extended to an analytic function in the upper half of the complex plane via the Hilbert transform, followed by taking the real part of the polar form of the analytic extension. Unfortunately, this approach most often fails to resolve the inverse problem satisfactorily. More recently, to resolve the inverse problem, the notion of synchrosqueezed wavelet transform (SST) was proposed by Daubechies and Maes, and further developed in many other papers, while a more direct method, called signal separation operation (SSO), was proposed and developed in our previous work published in the journal, Applied and Computational Harmonic Analysis, vol. 30(2):243-261, 2016. In the present paper, we propose a synthesis of SSO using a deep neural network, based directly on a discrete sample set, that may be non-uniformly sampled, of the blind-source signal. Our method is localized, as illustrated by a number of numerical examples, including components with different signal arrival and departure times. It also yields short-term prediction of the signal components, along with their IFs. Our neural networks are inspired by theory, designed so that they do not require any training in the traditional sense.

We propose Deep Multiset Canonical Correlation Analysis (dMCCA) as an extension to representation learning using CCA when the underlying signal is observed across multiple (more than two) modalities. We use deep learning framework to learn non-linear transformations from different modalities to a shared subspace such that the representations maximize the ratio of between- and within-modality covariance of the observations. Unlike linear discriminant analysis, we do not need class information to learn these representations, and we show that this model can be trained for complex data using mini-batches. Using synthetic data experiments, we show that dMCCA can effectively recover the common signal across the different modalities corrupted by multiplicative and additive noise. We also analyze the sensitivity of our model to recover the correlated components with respect to mini-batch size and dimension of the embeddings. Performance evaluation on noisy handwritten datasets shows that our model outperforms other CCA-based approaches and is comparable to deep neural network models trained end-to-end on this dataset.

Over-the-air computation (AirComp) shows great promise to support fast data fusion in Internet-of-Things (IoT) networks. AirComp typically computes desired functions of distributed sensing data by exploiting superposed data transmission in multiple access channels. To overcome its reliance on channel station information (CSI), this work proposes a novel blind over-the-air computation (BlairComp) without requiring CSI access, particularly for low complexity and low latency IoT networks. To solve the resulting non-convex optimization problem without the initialization dependency exhibited by the solutions of a number of recently proposed efficient algorithms, we develop a Wirtinger flow solution to the BlairComp problem based on random initialization. To analyze the resulting efficiency, we prove its statistical optimality and global convergence guarantee. Specifically, in the first stage of the algorithm, the iteration of randomly initialized Wirtinger flow given sufficient data samples can enter a local region that enjoys strong convexity and strong smoothness within a few iterations. We also prove the estimation error of BlairComp in the local region to be sufficiently small. We show that, at the second stage of the algorithm, its estimation error decays exponentially at a linear convergence rate.

The measurement and analysis of Electrodermal Activity (EDA) offers applications in diverse areas ranging from market research, to seizure detection, to human stress analysis. Unfortunately, the analysis of EDA signals is made difficult by the superposition of numerous components which can obscure the signal information related to a user's response to a stimulus. We show how simple pre-processing followed by a novel compressed sensing based decomposition can mitigate the effects of the undesired noise components and help reveal the underlying physiological signal. The proposed framework allows for decomposition of EDA signals with provable bounds on the recovery of user responses. We test our procedure on both synthetic and real-world EDA signals from wearable sensors and demonstrate that our approach allows for more accurate recovery of user responses as compared to the existing techniques.