Data valuation quantifies the intrinsic quality of individual samples to enable principled data curation, quality control, and robust learning. For time series in critical domains such as healthcare, finance, and industrial monitoring, effective valuation methods are essential yet fundamentally lacking. Existing approaches are either model-dependent, limiting their generalizability, or designed for i.i.d. data and thus fail to capture temporal dependencies, multi-scale patterns, and non-stationary dynamics inherent to sequential data. We introduce TimeLAVA, a learning-agnostic framework that values temporal segments by their marginal contribution to minimizing distributional discrepancy between evaluated and reference data. At its core is a novel Selective Wavelet-based Wasserstein discrepancy combining multi-scale wavelet transforms for temporal localization with unbalanced optimal transport for robustness to distributional shifts. Segment values are efficiently computed via sensitivity analysis without requiring model training and aggregated into point-wise scores. We provide theoretical guarantees linking valuation to model-agnostic generalization and prove bounded sensitivity to outlier contamination. Extensive experiments across anomaly detection, data pruning, and label noise detection demonstrate that TimeLAVA produces significantly more informative value scores than existing methods on diverse real-world datasets.

In 2020, the U.S. Census Bureau adopted differential privacy for the Decennial Census by injecting integer-valued Gaussian noise into published census tabulations. Exactly evaluating the privacy guarantees of these data releases would enable the Bureau to determine the absolute minimum noise required to satisfy a given privacy budget, preventing the injection of unnecessary excess noise and thereby substantially enhancing the statistical utility of the data for downstream applications such as federal funding allocation and political redistricting. In this paper, we introduce a computationally efficient and mathematically rigorous quadrature method to evaluate the exact privacy profile of practical, large-scale census releases under the composition of heterogeneous discrete Gaussian mechanisms. Mathematically, this problem reduces to evaluating the tail probabilities of high-dimensional convolutions of integer-valued random variables sampled from heterogeneous discrete Gaussian distributions under exceptionally stringent numerical error tolerances (e.g., $10^{-35}$). By recasting the exact privacy accounting as a numerical integration problem via the discrete Fourier transform, we explicitly exploit the exponential convergence of the trapezoidal rule for complex analytic, periodic characteristic functions. Furthermore, to overcome the computational bottleneck of evaluating highly oscillatory integrands in high dimensions, we develop a sieve algorithm that identifies and prunes negligible quadrature nodes, accelerating the computation by three orders of magnitude. Taken together, these numerical innovations enable the first exact, assumption-free privacy accounting for the 2020 Census Demographic and Housing Characteristics File, achieving a 1,824-fold speedup over prior methods while maintaining census-mandated error tolerances.

Modern machine learning models struggle to maintain performance in dynamic environments where temporal distribution shifts, i.e., concept drift, are prevalent. Temporal Domain Generalization (TDG) seeks to enable model generalization across evolving domains, yet existing approaches typically assume smooth incremental changes, struggling with complex real-world drifts involving both long-term structure (incremental evolution/periodicity) and local uncertainties. To overcome these limitations, we introduce FreKoo, which tackles these challenges through a novel frequency-domain analysis of parameter trajectories. It leverages the Fourier transform to disentangle parameter evolution into distinct spectral bands. Specifically, the low-frequency components with dominant dynamics are learned and extrapolated using the Koopman operator, robustly capturing diverse drift patterns including both incremental and periodic drifts. Simultaneously, potentially disruptive high-frequency variations are smoothed via targeted temporal regularization, preventing overfitting to transient noise and domain uncertainties. In addition, this dual-spectral strategy is rigorously grounded through theoretical analysis, providing stability guarantees for the Koopman prediction, a principled Bayesian justification for the high-frequency regularization, and culminating in a multiscale generalization bound connecting spectral dynamics to improved generalization. Extensive experiments demonstrate FreKoo's significant superiority over state-of-the-art TDG methods, particularly excelling in real-world streaming scenarios with complex drifts and uncertainties.

We consider the task of interpolating a k-sparse band-limited signal from a small collection of noisy time-domain samples. Exploiting a new analytic framework for hierarchical frequency decomposition that performs systematic noise cancellation, we give the first polynomial-time algorithm with a provable (3+ 2+ε)approximation guarantee for continuous interpolation. Our method breaks the long-standing C > 100 barrier set by the best previous algorithms, sharply reducing the gap to optimal recovery and establishing a new state of the art for high-accuracy band-limited interpolation. We also give a refined "shrinking-range" variant that achieves a ( 2+ε+c)-approximation on any sub-interval (1 c)T for some c (0,1), which gives even higher interpolation accuracy.

Fast Fourier Transforms (FFT) are widely used to reduce memory and computational costs in deep learning. However, existing implementations, including standard FFT and real FFT (rFFT), cannot achieve true in-place computation.

Normalizing flows are deep generative models that achieve efficient likelihood estimation and sampling through invertible transformations. A key challenge is designing linear layers that enhance expressiveness while enabling efficient computation of the Jacobian determinant and inverse. In this work, we introduce a novel invertible linear layer based on the product of circulant and diagonal matrices. This decomposition provides a parameter-and computation-efficient formulation, reducing the parameter complexity from $\mathcal{O}(n^2)$ to $\mathcal{O}(mn)$ by using $m$ diagonal matrices together with $m-1$ circulant matrices, while approximating arbitrary linear transformations.Furthermore, leveraging the Fast Fourier Transform (FFT), our method reduces the time complexity of matrix inversion from $\mathcal{O}(n^{3})$ to $\mathcal{O}(mn \log n)$ and matrix log-determinant from $\mathcal{O}(n^{3})$ to $\mathcal{O}(mn)$, where $n$ is the input dimension. Building upon this, we introduce a novel normalizing flow model called Circulant-Diagonal Flow (CDFlow). Empirical results demonstrate that CDFlow excels in density estimation for natural image datasets and effectively models data with inherent periodicity. In terms of computational efficiency, our method speeds up the matrix inverse and log-determinant computations by $1.17\times$ and $4.31\times$, respectively, compared to the general dense matrix, when the number of channels is set to 96.

Ultra-high-resolution (UHR) text-to-image (T2I) generation has seen notable progress. However, two key challenges remain: 1) the absence of a large-scale high-quality UHR T2I dataset, and (2) the neglect of tailored training strategies for fine-grained detail synthesis in UHR scenarios. To tackle the first challenge, we introduce \textbf{UltraHR-100K}, a high-quality dataset of 100K UHR images with rich captions, offering diverse content and strong visual fidelity. Each image exceeds 3K resolution and is rigorously curated based on detail richness, content complexity, and aesthetic quality. To tackle the second challenge, we propose a frequency-aware post-training method that enhances fine-detail generation in T2I diffusion models. Specifically, we design (i) \textit{Detail-Oriented Timestep Sampling (DOTS)} to focus learning on detail-critical denoising steps, and (ii) \textit{Soft-Weighting Frequency Regularization (SWFR)}, which leverages Discrete Fourier Transform (DFT) to softly constrain frequency components, encouraging high-frequency detail preservation. Extensive experiments on our proposed UltraHR-eval4K benchmarks demonstrate that our approach significantly improves the fine-grained detail quality and overall fidelity of UHR image generation.

Gaussian graphical models in the spectral domain offer a principled approach for recovering conditional dependence structures in stationary high-dimensional time series. Inference on the spectral precision matrix at a fixed frequency enables tests of frequency-specific conditional associations among time series components. The problem is challenging because finite-sample discrete Fourier transforms induce truncation and smoothing biases, while the complex-valued nature of the spectral precision matrix complicates high-dimensional variance estimation, rendering methods for i.i.d. samples not directly applicable. Existing approaches do not provide full likelihood-based inference for the discrete Fourier transforms. We propose a high-dimensional inference framework for sparse spectral precision matrices using the full likelihood of neighboring discrete Fourier transforms. We construct a debiased complex graphical lasso estimator at any fixed frequency. Using asymptotic theory for quadratic forms of multivariate time series, we establish its asymptotic normality and construct entry-wise consistent covariance estimators by aggregating information across neighboring frequencies. The key theoretical contribution is the simultaneous control of regularization, finite-sample truncation, and smoothing biases, enabling valid inference. Simulation studies show reliable coverage away from zero frequency and improved detection power over the benchmark, with false discovery rates near the desired level.

Diffusion models have demonstrated strong performance in time series modeling due to their ability to progressively capture complex data distributions through iterative denoising. However, existing approaches struggle with frequency-sensitive denoising, high-frequency reconstruction and balancing global trends with local dynamics. To address these limitations, we propose \textbf{HyFAD}, a \textbf{Hy}brid time-frequency \textbf{D}iffusion model with \textbf{F}requency-\textbf{A}ware embedding for time series imputation. Built upon the DDPM paradigm, HyFAD adopts a coupled time-frequency diffusion framework, in which the reverse denoising proceeds sequentially from the time domain to the frequency domain, enabling coarse-to-fine generation. Specifically, the time-domain diffusion process captures low-frequency global trends, while the frequency-domain diffusion process refines high-frequency spectral components. We further introduce a frequency-aware step embedding that exploits the relationship between diffusion steps and spectral components, providing step-dependent spectral guidance and facilitates more accurate band-wise reconstruction. Extensive experiments on multiple benchmark datasets demonstrate that HyFAD achieves state-of-the-art performance. Our source code is available at https://github.com/hongfangao/HyFAD.

As illustrated by the success of integer linear programming, linear integer arithmetic is a powerful tool for modelling combinatorial problems. Furthermore, the probabilistic extension of linear programming has been used to formulate problems in neurosymbolic AI. However, two key problems persist that prevent the adoption of neurosymbolic techniques beyond toy problems. First, probabilistic inference is inherently hard, #P-hard to be precise. Second, the discrete nature of integers renders the construction of meaningful gradients challenging, which is problematic for learning. In order to mitigate these issues, we formulate linear arithmetic over integer-valued random variables as tensor manipulations that can be implemented in a straightforward fashion using modern deep learning libraries. At the core of our formulation lies the observation that the addition of two integer-valued random variables can be performed by adapting the fast Fourier transform to probabilities in the log-domain. By relying on tensor operations we obtain a differentiable data structure, which unlocks, virtually for free, gradient-based learning. In our experimental validation we show that tensorising probabilistic linear integer arithmetic and leveraging the fast Fourier transform allows us to push the state of the art by several orders of magnitude in terms of inference and learning times.