S-GAI initializes sigmoidal MLPs by turning class-specific SVD principal directions into pairs of sigmoid gates, yielding stronger initial performance than Xavier on MNIST, Fashion-MNIST, and CIFAR-10.
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Two new DOD-based reduced-order models (DOD-DL-ROM and DOD+DFNN) are introduced for hybrid-type parabolic PDEs, with rigorous error bounds linking performance to optimal map regularity and conditions for outperforming POD methods.
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S-GAI: Spectral Geometry-Aware Initialization for Sigmoidal MLPs -- From Dataset Geometry to Network Weights
S-GAI initializes sigmoidal MLPs by turning class-specific SVD principal directions into pairs of sigmoid gates, yielding stronger initial performance than Xavier on MNIST, Fashion-MNIST, and CIFAR-10.
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A New Adaptive Deep Learning based Reduced Order Model for Hybrid-Type Parabolic PDEs: Rigorous Error Analysis and Applications
Two new DOD-based reduced-order models (DOD-DL-ROM and DOD+DFNN) are introduced for hybrid-type parabolic PDEs, with rigorous error bounds linking performance to optimal map regularity and conditions for outperforming POD methods.