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. Additionally, ResNets with a block width of $\min\{d_x+d_y, \max\{2d_x+1,d_y\}\}$ can achieve uniform approximation under the same inner width constraint. The paper also proves that any ResNet with a block width less than $\max\{d_x, d_y\}$ cannot approximate all target functions, irrespective of their inner width. AI
IMPACT Establishes theoretical limits for a specific neural network architecture, informing future model design.
RANK_REASON Academic paper detailing theoretical findings on neural network architecture. [lever_c_demoted from research: ic=1 ai=1.0]
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