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Tag: spectral

  • Perfect Clustering for Sparse Directed Stochastic Block Models

    Perfect Clustering for Sparse Directed Stochastic Block Models arXiv:2601.16427v1 Announce Type: new Abstract: Exact recovery in stochastic block models (SBMs) is well understood in undirected settings, but remains considerably less developed for directed and sparse networks, particularly when the number of communities diverges. Spectral methods for directed SBMs often lack stability in asymmetric, low-degree regimes,…

  • Deep learning estimation of the spectral density of functional time series on large domains

    Deep learning estimation of the spectral density of functional time series on large domains arXiv:2601.00284v1 Announce Type: cross Abstract: We derive an estimator of the spectral density of a functional time series that is the output of a multilayer perceptron neural network. The estimator is motivated by difficulties with the computation of existing spectral density…

  • Spectral Community Detection in Clinical Knowledge Graphs

    Spectral Community Detection in Clinical Knowledge Graphs Introduction How do we identify latent groups of patients in a large cohort? How can we find similarities among patients that go beyond the well-known comorbidity clusters associated with specific diseases? And more importantly, how can we extract quantitative signals that can be analyzed, compared, and reused across…

  • Spectral Identifiability for Interpretable Probe Geometry

    Spectral Identifiability for Interpretable Probe Geometry arXiv:2511.16288v1 Announce Type: new Abstract: Linear probes are widely used to interpret and evaluate neural representations, yet their reliability remains unclear, as probes may appear accurate in some regimes but collapse unpredictably in others. We uncover a spectral mechanism behind this phenomenon and formalize it as the Spectral Identifiability…

  • FreDN: Spectral Disentanglement for Time Series Forecasting via Learnable Frequency Decomposition

    FreDN: Spectral Disentanglement for Time Series Forecasting via Learnable Frequency Decomposition arXiv:2511.11817v1 Announce Type: new Abstract: Time series forecasting is essential in a wide range of real world applications. Recently, frequency-domain methods have attracted increasing interest for their ability to capture global dependencies. However, when applied to non-stationary time series, these methods encounter the $textit{spectral…

  • Spectral Thresholds for Identifiability and Stability:Finite-Sample Phase Transitions in High-Dimensional Learning

    Spectral Thresholds for Identifiability and Stability:Finite-Sample Phase Transitions in High-Dimensional Learning arXiv:2510.03809v1 Announce Type: new Abstract: In high-dimensional learning, models remain stable until they collapse abruptly once the sample size falls below a critical level. This instability is not algorithm-specific but a geometric mechanism: when the weakest Fisher eigendirection falls beneath sample-level fluctuations, identifiability fails.…

  • Spectral Algorithms in Misspecified Regression: Convergence under Covariate Shift

    Spectral Algorithms in Misspecified Regression: Convergence under Covariate Shift arXiv:2509.05106v1 Announce Type: new Abstract: This paper investigates the convergence properties of spectral algorithms — a class of regularization methods originating from inverse problems — under covariate shift. In this setting, the marginal distributions of inputs differ between source and target domains, while the conditional distribution…

  • Spectral Algorithms under Covariate Shift

    Spectral Algorithms under Covariate Shift arXiv:2504.12625v1 Announce Type: new Abstract: Spectral algorithms leverage spectral regularization techniques to analyze and process data, providing a flexible framework for addressing supervised learning problems. To deepen our understanding of their performance in real-world scenarios where the distributions of training and test data may differ, we conduct a rigorous investigation…

  • On the Robustness of Spectral Algorithms for Semirandom Stochastic Block Models

    On the Robustness of Spectral Algorithms for Semirandom Stochastic Block Models arXiv:2412.14315v1 Announce Type: new Abstract: In a graph bisection problem, we are given a graph $G$ with two equally-sized unlabeled communities, and the goal is to recover the vertices in these communities. A popular heuristic, known as spectral clustering, is to output an estimated…

  • Matrix Completion via Residual Spectral Matching

    Matrix Completion via Residual Spectral Matching arXiv:2412.10005v1 Announce Type: new Abstract: Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank constraints. However, minimizing the sum of squared residuals is not always efficient, as…

  • Spectral Differential Network Analysis for High-Dimensional Time Series

    Spectral Differential Network Analysis for High-Dimensional Time Series arXiv:2412.07905v1 Announce Type: cross Abstract: Spectral networks derived from multivariate time series data arise in many domains, from brain science to Earth science. Often, it is of interest to study how these networks change under different conditions. For instance, to better understand epilepsy, it would be interesting…