no code implementations • 20 Dec 2023 • Yifei Duan, Yongqiang Cai
We prove that the control family $\mathcal{F}_1 = \mathcal{F}_0 \cup \{ \text{ReLU}(\cdot)\} $ is enough to generate flow maps that can uniformly approximate diffeomorphisms of $\mathbb{R}^d$ on any compact domain, where $\mathcal{F}_0 = \{x \mapsto Ax+b: A\in \mathbb{R}^{d\times d}, b \in \mathbb{R}^d\}$ is the set of linear maps and the dimension $d\ge2$.
no code implementations • 29 May 2023 • Li'ang Li, Yifei Duan, Guanghua Ji, Yongqiang Cai
In contrast, when the depth is unlimited, the width for UAP needs to be not less than the critical width $w^*_{\min}=\max(d_x, d_y)$, where $d_x$ and $d_y$ are the dimensions of the input and output, respectively.
no code implementations • 22 Sep 2022 • Yifei Duan, Li'ang Li, Guanghua Ji, Yongqiang Cai
In this paper, we back to the classical network structure and prove that the vanilla feedforward networks could also be a numerical discretization of dynamic systems, where the width of the network is equal to the dimension of the input and output.
no code implementations • 8 Jun 2019 • Yifei Duan, Paul B. Umbanhowar, Julio M. Ottino, Richard M. Lueptow
Individual constituent balance equations are often used to derive expressions for species specific segregation velocities in flows of dense granular mixtures.
Soft Condensed Matter
