Researchers have established new theoretical bounds for the universal approximation capabilities of residual neural networks (ResNets) with an inner width of one. The study demonstrates that for $L^p$ approximation on compact domains, the minimum block width required is $\max\{d_x, d_y\}$, where $d_x$ and $d_y$ are the input and output dimensions, respectively. Furthermore, the paper proves that ResNets with a block width less than $\max\{d_x, d_y\}$ cannot achieve universal approximation, irrespective of their inner width. AI
IMPACT Establishes theoretical limits for residual neural network expressivity, informing future architectural designs.
RANK_REASON The cluster contains a research paper published on arXiv detailing theoretical findings about neural network approximation properties.
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