arXiv subjects

Abhash Kumar Jha

Publications and source records attributed to Abhash Kumar Jha.

6 recordsLinked to original sources

arXiv2026

Amortizing Scaling Law Construction Costs

Scaling laws guide the design choices for training large foundation models, but deriving them involves training an exhaustive grid over hyperparameters, token budgets, and parameter counts, which is computationally expensive. Fitting a scaling law, however, only requires the best-loss frontier across compute scales, discarding most of the trained configurations. We propose a framework for efficient scaling law construction that formulates data collection as a Bayesian optimization problem, and introduce metrics for comparing scaling law fitting methods under constrained compute budgets. We find that progressively expanding the compute budget during acquisition, mirroring the compute-ordered evaluation of configurations in practice, substantially improves recovery efficiency. Augmenting the observed configurations with surrogate-fantasized evaluations then recovers the broader experimental grid, allowing accurate scaling law fitting without training every configuration. Together, these can closely match scaling law fits over a full dense grid at computational savings of up to $10\text{--}100\times$.

cs.LG↗

arXiv2025

confopt: A Library for Implementation and Evaluation of Gradient-based One-Shot NAS Methods

Gradient-based one-shot neural architecture search (NAS) has significantly reduced the cost of exploring architectural spaces with discrete design choices, such as selecting operations within a model. However, the field faces two major challenges. First, evaluations of gradient-based NAS methods heavily rely on the DARTS benchmark, despite the existence of other available benchmarks. This overreliance has led to saturation, with reported improvements often falling within the margin of noise. Second, implementations of gradient-based one-shot NAS methods are fragmented across disparate repositories, complicating fair and reproducible comparisons and further development. In this paper, we introduce Configurable Optimizer (confopt), an extensible library designed to streamline the development and evaluation of gradient-based one-shot NAS methods. Confopt provides a minimal API that makes it easy for users to integrate new search spaces, while also supporting the decomposition of NAS optimizers into their core components. We use this framework to create a suite of new DARTS-based benchmarks, and combine them with a novel evaluation protocol to reveal a critical flaw in how gradient-based one-shot NAS methods are currently assessed. The code can be found at https://github.com/automl/ConfigurableOptimizer.

cs.LG↗

arXiv2024

An asymptotic expansion for a Lambert series associated to Siegel cusp forms of degree $n$

Utilizing inverse Mellin transform of the symmetric square $L$-function attached to Ramanujan tau function, Hafner and Stopple proved a conjecture of Zagier, which states that the constant term of the automorphic function $y^{12}|Δ(z)|^2$ i.e., the Lambert series $y^{12}\sum_{n=1}^\infty τ(n)^2 e^{-4 πn y}$ can be expressed in terms of the non-trivial zeros of the Riemann zeta function. This study examines certain Lambert series associated to Siegel cusp forms of degree $n$ twisted by a character $χ$ and observes a similar phenomenon.

math.NT↗

arXiv2023

Asymptotics and sign patterns for coefficients in expansions of Habiro elements

We prove asymptotics and study sign patterns for coefficients in expansions of elements in the Habiro ring which satisfy a strange identity. As an application, we prove asymptotics and discuss positivity for the generalized Fishburn numbers which arise from the Kontsevich-Zagier series associated to the colored Jones polynomial for a family of torus knots. This extends Zagier's result on asymptotics for the Fishburn numbers.

math.NT↗

arXiv2023

An asymptotic expansion for a Lambert series associated to Siegel cusp forms

In 2000, Hafner and Stopple proved a conjecture of Zagier which states that the constant term of the automorphic function $|Δ(x+iy)|^2$ i.e., the Lambert series $\sum_{n=1}^\infty τ(n)^2 e^{-4 πn y}$ can be expressed in terms of the non-trivial zeros of the Riemann zeta function. In this article, we study a certain Lambert series associated to Siegel cusp forms and observe a similar phenomenon.

math.NT↗

arXiv2016

Construction of cusp forms using Rankin-Cohen brackets

For a fix modular form g and a non negative ineteger ν, by using Rankin-Cohen bracket we first define a linear map $T_{g,ν}$ on the space of modular forms. We explicitly compute the adjoint of this map and show that the n-th Fourier coefficients of the image of the cusp form f under this map is, upto a constant a special value of Rankin-Selberg convolution of f and g.

math.NT↗