arXiv subjects

Alok Kumar Pandey

Publications and source records attributed to Alok Kumar Pandey.

5 recordsLinked to original sources

arXiv2026

AOS: Adaptive Optimizer Switching via Training-State Signals for Faster Convergence and Better Generalization

Single-optimizer training is a poor fit for the distinct phases of deep network optimization: adaptive methods handle noisy early gradients well but overshoot flat minima, while SGD with momentum generalizes better in the late phase but converges slowly early on. We introduce AOS-R (Adaptive Optimizer Switching, Rule-Based), a lightweight controller that monitors six online gradient-space signals -- gradient noise scale (GNS), Hutchinson curvature trace, loss stagnation, update stability ratio, gradient stability index (GSI), and loss improvement ratio (LIR) -- and switches among AdamW, SGD-M, and Lion as the optimization landscape evolves. State-preserving momentum transfer and a 400-step learning-rate bridge prevent accuracy degradation at every transition point. On CIFAR-100/WRN-28x10, AOS-R reaches 78% top-1 in 81 epochs -- 26% fewer than AdamW (109), 43% fewer than SGD-M (143), and 16% fewer than Lion (96). Across eight model-dataset benchmarks, AOS-R achieves best accuracy on 6 of 8 combinations with a mean +0.4 pp gain and 0.80x convergence speedup over AdamW under a single shared hyperparameter configuration.

cs.LG↗

arXiv2025

Finsler structure of the Apollonian weak metric on the unit disc

In this paper, we {\it find} the Finsler structure of the Apollonian weak metric on the open unit disc in $\mathbb{R}^2$, which turns out to be a Randers type Finsler structure and we call it as Apollonian weak-Finsler structure. In fact the Apollonian weak-Finsler structure is the deformation of the hyperbolic Poincar\'e metric in the unit disc by a closed $1$-form. As a cosequence, the trajectories of the geodesic of this Apollonian weak-Finsler structure pointwise agrees with the geodesic of hyperbolic Poincar\'e metric in the open unit disc. Further, we explicitly calculate its $S$-curvature, Riemann curvature, Ricci curvature and flag curvature. It turns out that the $S$-curvature of the Apollonian weak-Finsler structure in the unit disc is bounded below by $\frac{3}{2}$, while its flag curvature $K$ satisfies $-\infty< K<-1$, in particular, it becomes a Hadamard manifold.

math.DG↗

arXiv2024

On Generalized Transmuted Lifetime Distribution

This article presents a new class of generalized transmuted lifetime distributions which includes a large number of lifetime distributions as sub-family. Several important mathematical quantities such as density function, distribution function, quantile function, moments, moment generating function, stress-strength reliability function, order statistics, R\'enyi and q-entropy, residual and reversed residual life function, and cumulative information generating function are obtained. The methods of maximum likelihood, ordinary least square, weighted least square, Cram\'er-von Mises, Anderson Darling, and Right-tail Anderson Darling are considered to estimate the model parameters in a general way. Further, a well-organized Monte Carlo simulation experiments have been performed to observe the behavior of the estimators. Finally, two real data have also been analyzed to demonstrate the effectiveness of the proposed distribution in real-life modeling.

stat.ME↗

arXiv2024

Record-based transmuted unit omega distribution: different methods of estimation and applications

Dombi et al. (2019) introduced a three parameter omega distribution and showed that its asymptotic distribution is the Weibull model. We propose a new record-based transmuted generalization of the unit omega distribution by considering Balakrishnan and He (2021) approach. We call it the RTUOMG distribution. We derive expressions for some statistical quantities, like, probability density function, distribution, hazard function, quantile function, moments, incomplete moments, inverted moments, moment generating function, Lorenz curve, and Bonferroni curve of the proposed distribution. The numerical values of various measures of central tendency and coefficient of skewness and kurtosis are also presented. Concepts of stochastic ordering and some results related to ordered statistics of the RTUOMG distribution are discussed. The parameters of the RTUOMG distribution are estimated using five distinct estimators. Additionally, the Monte Carlo simulations are performed to assess the performance of these estimators. Finally, two real data sets are analyzed to demonstrate the utility of the RTUOMG distribution.

math.ST↗

arXiv2022

Extreme-ultraviolet structured beams via high harmonic generation

Vigorous efforts to harness the topological properties of light have enabled a multitude of novel applications. Translating the applications of structured light to higher spatial and temporal resolutions mandates their controlled generation, manipulation, and thorough characterization in the short-wavelength regime. Here, we resort to high-order harmonic generation (HHG) in a noble gas to upconvert near-infrared (IR) vector, vortex, and vector-vortex driving beams that are tailored respectively in their Spin Angular Momentum (SAM), Orbital Angular Momentum (OAM), and simultaneously in their SAM and OAM. We show that HHG enables the controlled generation of extreme-ultraviolet (EUV) vector beams exhibiting various spatially-dependent polarization distributions, or EUV vortex beams with a highly twisted phase. Moreover, we demonstrate the generation of EUV vector-vortex beams (VVB) bearing combined characteristics of vector and vortex beams. We rely on EUV wavefront sensing to unambiguously affirm the topological charge scaling of the HHG beams with the harmonic order. Interestingly, our work shows that HHG allows for a synchronous controlled manipulation of SAM and OAM. These EUV structured beams bring in the promising scenario of their applications at nanometric spatial and sub-femtosecond temporal resolutions using a table-top harmonic source.

physics.optics↗