Memorization capacity of deep ReLU neural networks characterized by width and depth

ArXi:2603.09589v1 Announce Type: new This paper studies the memorization capacity of deep neural networks with ReLU activation. Specifically, we investigate the minimal size of such networks to memorize any $N$ data points in the unit ball with pairwise separation distance $\delta$ and discrete labels. Most prior studies characterize the memorization capacity by the number of parameters or neurons. We generalize these results by constructing neural networks, whose width $W$ and depth $L$ satisfy $W^2L^2= \mathcal{O}(N\log(\delta^{-1}))$, that can memorize any $N$ data samples.