Thursday, January 16, 2025

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2025-01-17 / 09:00 ~ 10:30
학과 세미나/콜로퀴엄 - 응용수학 세미나: 인쇄
by ()
We propose a general learning based framework for solving nonsmooth and nonconvex inverse problems with application to low-dose CT (LDCT) reconstruction. We model the regularization function as the combination of a sparsity enhancing and a non-local smoothing regularization. We develop an efficient learned descent-type algorithm (ELDA) to solve the nonsmooth nonconvex minimization problem by leveraging the Nesterov’s smoothing technique and incorporating the residual learning structure. We proved the convergence of the algorithm and generate the network, whose architecture follows the algorithm exactly. Our method is versatile as one can employ various modern network structures into the regularization, and the resulting network inherits the convergence properties, and hence is interpretable. We also show that the proposed network is parameter-efficient and its performance compares favorably to the state-of-the-art methods.
2025-01-21 / 16:30 ~ 17:30
IBS-KAIST 세미나 - 이산수학: Bounded size modifications in time $2^{{\sf poly}(k)}\cdot n^2$ 인쇄
by Laure Morelle(LIRMM)
A replacement action is a function $\mathcal L$ that maps each graph to a collection of subgraphs of smaller size. Given a graph class $\mathcal H$, we consider a general family of graph modification problems, called “$\mathcal L$-Replacement to $\mathcal H$”, where the input is a graph $G$ and the question is whether it is possible to replace some induced subgraph $H_1$ of $G$ on at most $k$ vertices by a graph $H_2$ in ${\mathcal L}(H_1)$ so that the resulting graph belongs to $\mathcal H$. “$\mathcal L$-Replacement to $\mathcal H$” can simulate many graph modification problems including vertex deletion, edge deletion/addition/edition/contraction, vertex identification, subgraph complementation, independent set deletion, (induced) matching deletion/contraction, etc. We prove here that, for any minor-closed graph class $\mathcal H$ and for any action $\mathcal L$ that is hereditary, there is an algorithm that solves “$\mathcal L$-Replacement to $\mathcal H$” in time $2^{{\sf poly}(k)}\cdot |V(G)|^2$, where $\sf poly$ is a polynomial whose degree depends on $\mathcal H$.
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