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Reza Roohi Seraji

Publications and source records attributed to Reza Roohi Seraji.

5 recordsLinked to original sources
arXiv2025

Tame Riemannian Stochastic Approximation

We study the properties of stochastic approximation applied to a tame nondifferentiable function subject to constraints defined by a Riemannian manifold. The objective landscape of tame functions, arising in o-minimal topology extended to a geometric category when generalized to manifolds, exhibits some structure that enables theoretical guarantees of expected function decrease and asymptotic convergence for generic stochastic sub-gradient descent. Recent work has shown that this class of functions faithfully model the loss landscape of deep neural network training objectives, and the autograd operation used in deep learning packages implements a variant of subgradient descent with the correct properties for convergence. Riemannian optimization uses geometric properties of a constraint set to perform a minimization procedure while enforcing adherence to the the optimization variable lying on a Riemannian manifold. This paper presents the first study of tame optimization on Riemannian manifolds, highlighting the rich geometric structure of the problem and confirming the appropriateness of the canonical "SGD" for such a problem with the analysis and numerical reports of a simple Retracted SGD algorithm.

cs.LG↗
arXiv2025

Discrete Hilbert Transform And Discrete Mikhlin Multiplier On Discrete Variable Lebesgue Space

In this paper, by using continuous Hilbert transform and maximal operator boundedness property in the variable Lebesgue space $ L^{p(\cdot)}(\mathbb{R}) $ we show that the discrete Hilbert transform is bounded in the variable discrete Lebesgue space $ \ell^{p_n}(\mathbb{Z}) $. We show that the discrete Mikhlin multiplier $ \mathcal{T}_m $ is a bounded operator on $ \ell^{p_n}(\mathbb{Z}) $ when $ 1<\underline{p}_n<\bar{p}_n<\infty $.

math.FA↗
arXiv2024

Some Remarks on the Vector-Valued Variable Exponent Lebesgue Spaces $\ell^{q(\cdot)} (L^{p(\cdot)})$

In this paper, we investigate the geometric properties of the variable mixed Lebesgue-sequence space $\ell^{q(\cdot)} (L^{p(\cdot)})$ as a Banach space. We show that, if $ 1<q_-,p_-,q_+,p_+<\infty $, then $\ell^{q(\cdot)} (L^{p(\cdot)})$ is strictly and uniformly convex. We also prove that when $ 1\le q_-,p_-,q_+,p_+<\infty, $ the convergence in norm implies the convergence in measure, and under some conditions on exponents, the approximation identity holds in the space $ \ell^1(L^{\frac{p(\cdot)}{q(\cdot)}}) $.

math.FA↗
arXiv2022

On the reflexivity of the spaces of variable integrability and summability

In this paper, we show that under the condition $ 1<p_-, q_-, p_+, q_+<\infty$, the space $\ell^{q(\cdot)} (L^{p(\cdot)})$ is reflexive. In this way we give an answer to open problem posed by Hästö in 2017 about the reflexivity of the variable mixed Lebesgue-sequence spaces $\ell^{q(\cdot)} (L^{p(\cdot)})$. What is important here is that the dual space of $\ell^{q(\cdot)} (L^{p(\cdot)})$ is specified. As its direct corollary, we show that the corresponding Besov space $B^{s(\cdot)}_{p(\cdot)q(\cdot)}$ is reflexive.

math.FA↗