Its low-rank QTT structure arises from intrinsic spectral smoothness in continuous models, or from spectral energy concentration as the number of components D grows in discrete models. We demonstrate this on weighted sums of Bernoulli and lognormal random variables. In the latter, the approach reaches high-resolution discretizations of N = 230 frequency modes on standard hardware, far beyond the N =224 ceiling of dense implementations. These compressed representations enable efficient computation of Value at Risk (VaR) and Expected Shortfall (ES), supporting applications in quantitative finance and beyond. I. INTRODUCTION Weighted sums of independent random variables constitute a basic probabilistic model, describing macroscopic behavior arising from the aggregation of microscopic stochastic components. These models arise in a wide range of applications. Their probability distribution generally lacks a closed-form expression, and their evaluation involves multidimensional convolution integrals that are susceptible to the curse of dimensionality. Consequently, evaluating these models relies on specializednumericalmethods. Whilethese methods have been adapted for discrete settings [18, 19], they are frequently hampered by persistent Gibbs oscillations, which arise from distributional discontinuities and preclude uniform convergence [20, 21]. No existing method simultaneously achieves an accurate approximation of the exact, fully non-Gaussian target distribution while remaining scalable to larger, practically relevant system sizes. In this work, we introduce a new algorithm that combines the Fourier spectral method with tensor-network techniques.

The coefficients in this RF expansion are optimized to fit the given data of input-output pairs.

The key observation is that the success4 of the proposed method depends solely on the intrinsic property of the data manifold instead of specific sampling5 procedures (Theorem 4.2),whichmakesourextension non-trivial. About the curvature estimation method: we apologize for not including enough details in the description of the15 proposed curvature estimation method. When estimating the curvature at some pointp, our method requires (Sect. What is the dimension of the NRPCA space, is it two? Is the neighborhood patch defined with respect to Xi or Xi?