Shi-Jun Zhang

A sharp width--magnitude tradeoff at fixed depth is established using one elementary bounded $1$-Lipschitz Dyadic--Triangular Activation and yields a continuum of statistically optimal choices, ranging from unit parameter radius to fixed network size.

A fixed-dimensional latent space can achieve vanishing approximation error in neural networks, challenging conventional beliefs about the necessity of high-dimensional representations.

Fixed-size neural networks can achieve arbitrary Sobolev approximation accuracy with new activation functions, challenging traditional limits on network size and complexity.

Depth in neural networks isn't just about the final output; this work shows how each intermediate layer can be a progressively refined approximation, with error explicitly tied to the layer's geometric scale.