Derives the asymptotic ratio of storage capacities between real-constrained and complex pre-activations in complex neural networks using Gardner volumes and the HCIZ formula.
Pseudo-differential neural operator: Generalized fourier neural operator for learning solution operators of partial differential equations, 2024
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cs.LG 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
LFNO is a dual-branch neural operator combining Laplace and Fourier methods to explicitly decompose and model transient and steady-state dynamics, outperforming baselines on ODE benchmarks and remaining competitive on PDEs.
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Shortcomings and capacities of real-constrained neural networks in complex spaces
Derives the asymptotic ratio of storage capacities between real-constrained and complex pre-activations in complex neural networks using Gardner volumes and the HCIZ formula.
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LFNO: Bridging Laplace and Fourier via Transient-Steady Decomposition
LFNO is a dual-branch neural operator combining Laplace and Fourier methods to explicitly decompose and model transient and steady-state dynamics, outperforming baselines on ODE benchmarks and remaining competitive on PDEs.