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math.NA2026
Regularization and compression of integral operator kernels with tensor paraproducts
Oluwadamilola Fasina, Ronald R. Coifman
We present a new perspective on integral operator kernels given by a nonlinear function of the distance. This perspective is useful since it permits one to quasilinearize the nonli…
math.NA2025
Intrinsic and Extrinsic Organized Attention: Softmax Invariance and Network Sparsity
Oluwadamilola Fasina, Ruben V. C. Pohle, Pei-Chun Su +1
We examine the intrinsic (within the attention head) and extrinsic (amongst the attention heads) structure of the self-attention mechanism in transformers. Theoretical evidence for…
math.NA2025
Extracting Dual Analytic Geometries of Linear Transformations to Achieve Efficient Computation
Pei-Chun Su, Ronald R. Coifman
We generalize the Calderon-Zygmund methodology for operator analysis and the Rokhlin-Greengard fast multipole algorithms, in which the domain and range of an operator are jointly o…