Shijun Zhang

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.