A common method of attacking deep learning models is through adversarial attacks, which occur when an attacker specifically modifies the input of a model to produce an incorrect result. Adversarial attacks have been deeply investigated in the image domain; however, there is less research in the time-series domain and very little for forecasting financial data. To address these concerns, this study aims to build upon previous research on adversarial attacks for time-series data by introducing two new slope-based methods aimed to alter the trends of the predicted stock forecast generated by an N-HiTS model. Compared to the normal N-HiTS predictions, the two new slope-based methods, the General Slope Attack and Least-Squares Slope Attack, can manipulate N-HiTS predictions by doubling the slope. These new slope attacks can bypass standard security mechanisms, such as a discriminator that filters real and perturbed inputs, reducing a 4-layered CNN's specificity to 28% and accuracy to 57%. Furthermore, the slope based methods were incorporated into a GAN architecture as a means of generating realistic synthetic data, while simultaneously fooling the model. Finally, this paper also proposes a sample malware designed to inject an adversarial attack in the model inference library, proving that ML-security research should not only focus on making the model safe, but also securing the entire pipeline.

In this paper, we utilize the emerging idea of "coded computation" to design a novel error-correcting-code inspired technique for solving linear inverse problems under specific iterative

In this paper, we propose the first non-linear coordination graph by extending CG value decomposition beyond the linear case.

Spectral methods play a fundamental role in machine learning, statistics, and data mining.

CoLA and discuss modifications to improve lower precision performance. In Appendix D we expand on the details of the experiments in the main text. We now present the linear algebra identities that we use to exploit structure in CoLA. I null Finally, for sum we have the Woodbury identity and its variants. Besides the compositional operators, we have some rules for some special operators.

Iterative method selection is crucial for solving sparse linear systems because these methods inherently lack robustness. Though image-based selection approaches have shown promise, their feature extraction techniques might encode distinct matrices into identical image representations, leading to the same selection and suboptimal method. In this paper, we introduce RAF (Relative-Absolute Fusion), an efficient feature extraction technique to enhance image-based selection approaches. By simultaneously extracting and fusing image representations as relative features with corresponding numerical values as absolute features, RAF achieves comprehensive matrix representations that prevent feature ambiguity across distinct matrices, thus improving selection accuracy and unlocking the potential of image-based selection approaches. We conducted comprehensive evaluations of RAF on SuiteSparse and our developed BMCMat (Balanced Multi-Classification Matrix dataset), demonstrating solution time reductions of 0.08s-0.29s for sparse linear systems, which is 5.86%-11.50% faster than conventional image-based selection approaches and achieves state-of-the-art (SOTA) performance. BMCMat is available at https://github.com/zkqq/BMCMat.

Green's function provides an inherent connection between theoretical analysis and numerical methods for elliptic partial differential equations, and general absence of its closed-form expression necessitates surrogate modeling to guide the design of effective solvers. Unfortunately, numerical computation of Green's function remains challenging due to its doubled dimensionality and intrinsic singularity. In this paper, we present a novel singularity-encoded learning approach to resolve these problems in an unsupervised fashion. Our method embeds the Green's function within a one-order higher-dimensional space by encoding its prior estimate as an augmented variable, followed by a neural network parametrization to manage the increased dimensionality. By projecting the trained neural network solution back onto the original domain, our deep surrogate model exploits its spectral bias to accelerate conventional iterative schemes, serving either as a preconditioner or as part of a hybrid solver. The effectiveness of our proposed method is empirically verified through numerical experiments with two and four dimensional Green's functions, achieving satisfactory resolution of singularities and acceleration of iterative solvers. Introduction Machine learning has achieved remarkable success across a wide range of engineering applications and scientific disciplines, emerging as an innovative methodology toward modern scientific computing [1, 2, 3, 4]. Owing to its universal approximation capability and mesh-free discretization [5, 6], the neural network-based method has become increasingly popular for the numerical solution of partial differential equations [7, 8], especially in high dimensions [9] where classical mesh-based methods exhibit limitations.

In this work, we propose a novel framework to enhance the efficiency and accuracy of neural operators through self-composition, offering both theoretical guarantees and practical benefits. Inspired by iterative methods in solving numerical partial differential equations (PDEs), we design a specific neural operator by repeatedly applying a single neural operator block, we progressively deepen the model without explicitly adding new blocks, improving the model's capacity. To train these models efficiently, we introduce an adaptive train-and-unroll approach, where the depth of the neural operator is gradually increased during training. This approach reveals an accuracy scaling law with model depth and offers significant computational savings through our adaptive training strategy. Our architecture achieves state-of-the-art (SOTA) performance on standard benchmarks. We further demonstrate its efficacy on a challenging high-frequency ultrasound computed tomography (USCT) problem, where a multigrid-inspired backbone enables superior performance in resolving complex wave phenomena. The proposed framework provides a computationally tractable, accurate, and scalable solution for large-scale data-driven scientific machine learning applications.