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Author

Haizhao Yang

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Preprint Sep 2026

Finite Expression Approximation of High-Dimensional PDEs Without the Curse of Dimensionality

We establish that finite expressions form a symbolic representation class capable of overcoming the curse of dimensionality for several classes of high-dimensional partial differential equations. For semilinear heat equations, we show how finite expression approximations of the terminal condition and nonlinearity can b...

Zhi-Heng Liu, Hai-Zhao Yang · 0 citations
#machine learning Preprint Sep 2026

Optimal Tradeoffs Between Network Size and Parameter Magnitude in Neural Approximation and Minimax Regression

The statistical accuracy of neural networks depends on both their approximation power and the complexity of the class fitted from data. While increasing network size is a natural way to improve approximation, parameter magnitude provides another resource whose role must be quantified in both respects. We establish a sh...

Bai-Chen Li, Zuo-Wei Shen, Hai-Zhao Yang et al. · 0 citations

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