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math.NA2025
Low-rank cross approximation of function-valued tensors for reduced-order modeling of parametric PDEs
Stanislav Budzinskiy, Vladimir Kazeev, Maxim Olshanskii
The paper considers function-valued tensors, viewed as multidimensional arrays with entries in an abstract Hilbert space. Despite the absence of the algebraic structure of a field,…
math.NA2025
Numerical stability analysis of large language models
Stanislav Budzinskiy, Wenyi Fang, Longbin Zeng +1
Transformers are the state-of-the-art architecture for large language models, and a key to their scalability is the strategic usage of low-precision arithmetic. We develop a mixed-…