| Abstract: |
| This talk explores the limitations of shallow neural networks in handling high-frequency functions and presents a solution through a novel multi-layer, multi-component neural network (MMNN) architecture. We show how shallow networks act as low-pass filters, struggling with high-frequency components due to machine precision and slow learning dynamics. The MMNN architecture addresses these challenges by efficiently decomposing complex functions, significantly improving accuracy and reducing computational costs. Numerical experiments demonstrate the effectiveness of this approach in capturing fine details in oscillatory functions. |
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