arXiv:2607. 09097v1 Announce Type: cross Abstract: We study stochastic fixed-point equations $\mathbf{T}(\mathbf{x}) = \mathbf{x}$ over normed spaces $(\mathcal{E}, \|\cdot\|)$, where the operator $\mathbf{T}$ is nonexpansive or contractive and is accessed only through unbiased stochastic evaluations with bounded second central moment.
By Jelena Diakonikolas
arXiv:2607. 16384v1 Announce Type: new Abstract: For stochastic gradient descent (SGD) with a constant stepsize $\alpha$, the invariant law of the iterates, centered at a minimizer, describes the behavior of the algorithm over long time horizons.
By Jingyi Zhang, Cheng Mao, Debankur Mukherjee
arXiv:2608. 06687v1 Announce Type: cross Abstract: We develop a rigorous theory of discrete residual least-squares approximation for elliptic spectral equations $\mathfrak L_\beta u=f$ using linearized ReLU$^k$ neural networks on the sphere, where $\mathfrak L_\beta$ is a positive elliptic spectral multiplier of order $\beta$.
By Xinliang Liu, Tong Mao, Jinchao Xu
arXiv:2509. 08726v3 Announce Type: replace-cross Abstract: This paper focuses on the decentralized stochastic optimization problem $f(\mathbf{x})=\frac{1}{m}\sum_{i=1}^m f_i(\mathbf{x})$ over a connected network of $n$ agents, where each local function has the form of $f_i(\mathbf{x}) = {\mathbb E}\left[F(\mathbf{x};{\boldsymbol \xi}_i)\right]$ which satisfies the $(L_0,L_1)$-smooth condition but possibly nonconvex and each random variable ${\boldsymbol \xi}_i$ follows distribution ${\mathcal D}_i$.
By Luo Luo, Xue Cui, Tingkai Jia, Cheng Chen
arXiv:2603. 10485v3 Announce Type: replace-cross Abstract: In this work, we study the convergence properties of the Dual Space Preconditioned Gradient Descent, encompassing optimizers such as Normalized Gradient Descent and Gradient Clipping.
By Reza Ghane, Danil Akhtiamov, Babak Hassibi
arXiv:2410. 23212v3 Announce Type: replace-cross Abstract: In graph-based data analysis, $k$-nearest neighbor ($k$NN) graphs are widely used due to their adaptivity to local data densities.
By Xiuyuan Cheng, Yixuan Tan, Nan Wu