Related papers: Eigenbackground Revisited: Can We Model the Backgr…

We describe algorithms for computing eigenpairs (eigenvalue-eigenvector pairs) of a complex $n\times n$ matrix $A$. These algorithms are numerically stable, strongly accurate, and theoretically efficient (i.e., polynomial-time). We do not…

Predicting masked from visible parts of an image is a powerful self-supervised approach for visual representation learning. However, the common practice of masking random patches of pixels exhibits certain failure modes, which can prevent…

Representing a manifold of very high-dimensional data with generative models has been shown to be computationally efficient in practice. However, this requires that the data manifold admits a global parameterization. In order to represent…

Energy-based models (EBMs), a.k.a. un-normalized models, have had recent successes in continuous spaces. However, they have not been successfully applied to model text sequences. While decreasing the energy at training samples is…

Graphs (i.e., networks) have become an integral tool for the representation and analysis of relational data. Advances in data gathering have lead to multi-relational data sets which exhibit greater depth and scope. In certain cases, this…

A generalized eigenvector of a hypermatrix, called the universal (U-) eigenvector, is proposed, which extended the notion of diagonal (D-) eigenvectors in the literature. Using the semi-tensor product, the homogeneous U-eigenequation can be…

End-to-end autonomous driving has emerged as a dominant paradigm, yet its highly entangled black-box models pose significant challenges in terms of interpretability and safety assurance. To improve model transparency and training…

Autoencoders are certainly among the most studied and used Deep Learning models: the idea behind them is to train a model in order to reconstruct the same input data. The peculiarity of these models is to compress the information through a…

CNNs have become one of the most commonly used computational tool in the past two decades. One of the primary downsides of CNNs is that they work as a ``black box", where the user cannot necessarily know how the image data are analyzed, and…

An open-source middleware EigenKernel was developed for use with parallel generalized eigenvalue solvers or large-scale electronic state calculation to attain high scalability and usability. The middleware enables the users to choose the…

Backdoor-based fingerprinting has emerged as an effective technique for tracing the ownership of large language models. However, in real-world deployment scenarios, developers often instantiate multiple downstream models from a shared base…

We prove delocalization of eigenvectors of vertex-transitive graphs via elementary estimates of the spectral projector. We recover in this way known results which were formerly proved using representation theory. Similar techniques show…

Recent advances in representation learning reveal that widely used objectives, such as contrastive and non-contrastive, implicitly perform spectral decomposition of a contextual kernel, induced by the relationship between inputs and their…

We lay down the foundations of the Eigenvalue Method in coding theory. The method uses modern algebraic graph theory to derive upper bounds on the size of error-correcting codes for various metrics, addressing major open questions in the…

As a self-supervised learning paradigm, contrastive learning has been widely used to pre-train a powerful encoder as an effective feature extractor for various downstream tasks. This process requires numerous unlabeled training data and…

Foundation models have revolutionized computer vision by enabling broad generalization across diverse tasks. Yet, they remain highly susceptible to adversarial perturbations and targeted backdoor attacks. Mitigating such vulnerabilities…

Estimating eigenvectors and low-dimensional subspaces is of central importance for numerous problems in statistics, computer science, and applied mathematics. This paper characterizes the behavior of perturbed eigenvectors for a range of…

The research reported in this paper addresses the fundamental task of separation of locally moving or deforming image areas from a static or globally moving background. It builds on the latest developments in the field of robust principal…

We analyse the eigenvectors of the adjacency matrix of a random inhomogeneous graph constructed from a specified degree sequence. We assume that the empirical degree sequence has bounded mean and variance. We show that near the edges of the…

Anomaly detection relies on designing a score to determine whether a particular event is uncharacteristic of a given background distribution. One way to define a score is to use autoencoders, which rely on the ability to reconstruct certain…