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Hamid Mousavi

Publications and source records attributed to Hamid Mousavi.

8 recordsLinked to original sources
arXiv2025

On the Normalizer-Solubilizer Conjecture_V3

Let $G$ be a finite group and $x$ be an element of $G$. Define $\textrm{Sol}_G(x)$ as the set of all $y \in G$ such that $\langle {x,y}\rangle$ is soluble. We provide an equivalent condition for the normalizer-solubilizer conjecture, namely $|\mathcal{N}_G(\langle x\rangle)| \mid |\textrm{Sol}_G(x)|$, where $\mathcal{N}_G(\langle x\rangle)$ is the normalizer of $\langle x\rangle$. Furthermore, we demonstrate that the conjecture holds in the special case where $\mathcal{N}_G(\langle x\rangle)$ is a Frobenius group with kernel $\mathcal{C}_G(x)$, the centralizer of $x$, and $|\mathcal{N}_G(\langle x\rangle): \mathcal{C}_G(x)|$ is of prime order. Finally, we will classify all finite simple groups $G$ that contain an element $x$ for which $\textrm{Sol}_G(x)$ is a maximal subgroup of order $pq$, where $p$ and $q$ are prime numbers.

math.GR↗
arXiv2024

A note on meta and para-$\mathfrak{Nil}$-Hamiltonian groups_v3

Let $\mathfrak{Nil}$ be the class of nilpotent groups. This article explores the finiteness of meta and para-$\mathfrak{Nil}$-Hamiltonian groups or their derived subgroups when these groups contain a soluble subgroup of finite index or a non-nilpotent (or insoluble) subgroup of finite order respectively.

math.GR↗
arXiv2023

Groups whose non-normal subgroups are either nilpotent or minimal non-nilpotent

Let $\mathfrak{Nil}$ be the class of nilpotent groups and $G$ be a group. We call $G$ a meta-$\mathfrak{Nil}$-Hamiltonian group if any of its non-$\mathfrak{Nil}$ subgroups is normal. Also, we call $G$ a para-$\mathfrak{Nil}$-Hamiltonian group if $G$ is a non-$\mathfrak{Nil}$ group and every non-normal subgroup of $G$ is either a $\mathfrak{Nil}$-group or a minimal non-$\mathfrak{Nil}$ group. In this paper we investigate the class of finitely generated meta-$\mathfrak{Nil}$-Hamiltonian and para-$\mathfrak{Nil}$-Hamiltonian groups.

math.GR↗
arXiv2022

GTFLAT: Game Theory Based Add-On For Empowering Federated Learning Aggregation Techniques

GTFLAT, as a game theory-based add-on, addresses an important research question: How can a federated learning algorithm achieve better performance and training efficiency by setting more effective adaptive weights for averaging in the model aggregation phase? The main objectives for the ideal method of answering the question are: (1) empowering federated learning algorithms to reach better performance in fewer communication rounds, notably in the face of heterogeneous scenarios, and last but not least, (2) being easy to use alongside the state-of-the-art federated learning algorithms as a new module. To this end, GTFLAT models the averaging task as a strategic game among active users. Then it proposes a systematic solution based on the population game and evolutionary dynamics to find the equilibrium. In contrast with existing approaches that impose the weights on the participants, GTFLAT concludes a self-enforcement agreement among clients in a way that none of them is motivated to deviate from it individually. The results reveal that, on average, using GTFLAT increases the top-1 test accuracy by 1.38%, while it needs 21.06% fewer communication rounds to reach the accuracy.

cs.LG↗
arXiv2022

DASS: Differentiable Architecture Search for Sparse neural networks

The deployment of Deep Neural Networks (DNNs) on edge devices is hindered by the substantial gap between performance requirements and available processing power. While recent research has made significant strides in developing pruning methods to build a sparse network for reducing the computing overhead of DNNs, there remains considerable accuracy loss, especially at high pruning ratios. We find that the architectures designed for dense networks by differentiable architecture search methods are ineffective when pruning mechanisms are applied to them. The main reason is that the current method does not support sparse architectures in their search space and uses a search objective that is made for dense networks and does not pay any attention to sparsity. In this paper, we propose a new method to search for sparsity-friendly neural architectures. We do this by adding two new sparse operations to the search space and modifying the search objective. We propose two novel parametric SparseConv and SparseLinear operations in order to expand the search space to include sparse operations. In particular, these operations make a flexible search space due to using sparse parametric versions of linear and convolution operations. The proposed search objective lets us train the architecture based on the sparsity of the search space operations. Quantitative analyses demonstrate that our search architectures outperform those used in the stateof-the-art sparse networks on the CIFAR-10 and ImageNet datasets. In terms of performance and hardware effectiveness, DASS increases the accuracy of the sparse version of MobileNet-v2 from 73.44% to 81.35% (+7.91% improvement) with 3.87x faster inference time.

cs.CV↗
arXiv2020

Generic Unsupervised Optimization for a Latent Variable Model With Exponential Family Observables

Latent variable models (LVMs) represent observed variables by parameterized functions of latent variables. Prominent examples of LVMs for unsupervised learning are probabilistic PCA or probabilistic SC which both assume a weighted linear summation of the latents to determine the mean of a Gaussian distribution for the observables. In many cases, however, observables do not follow a Gaussian distribution. For unsupervised learning, LVMs which assume specific non-Gaussian observables have therefore been considered. Already for specific choices of distributions, parameter optimization is challenging and only a few previous contributions considered LVMs with more generally defined observable distributions. Here, we consider LVMs that are defined for a range of different distributions, i.e., observables can follow any (regular) distribution of the exponential family. The novel class of LVMs presented is defined for binary latents, and it uses maximization in place of summation to link the latents to observables. To derive an optimization procedure, we follow an EM approach for maximum likelihood parameter estimation. We show that a set of very concise parameter update equations can be derived which feature the same functional form for all exponential family distributions. The derived generic optimization can consequently be applied to different types of metric data as well as to different types of discrete data. Also, the derived optimization equations can be combined with a recently suggested variational acceleration which is likewise generically applicable to the LVMs considered here. So, the combination maintains generic and direct applicability of the derived optimization procedure, but, crucially, enables efficient scalability. We numerically verify our analytical results and discuss some potential applications such as learning of variance structure, noise type estimation and denoising.

cs.LG↗
arXiv2005

The Structure of $G/Φ(G)$ in Terms of $σ(G)$

Let $G$ be a finite group. We let $\f{m}(G)$ and $\sig(G)$ denote the number of maximal subgroups of $G$ and the least positive integer $n$ such that $G$ is written as the union of $n$ proper subgroups, respectively. In this paper we determine the structure of $G/Φ(G)$ when $G$ is a finite soluble group with $\f{m}(G)\leq 2\sig(G)$.

math.GR↗