arXiv subjects

Jasdeep Sidhu

Publications and source records attributed to Jasdeep Sidhu.

3 recordsLinked to original sources

arXiv2024

An Evaluation Benchmark for Autoformalization in Lean4

Large Language Models (LLMs) hold the potential to revolutionize autoformalization. The introduction of Lean4, a mathematical programming language, presents an unprecedented opportunity to rigorously assess the autoformalization capabilities of LLMs. This paper introduces a novel evaluation benchmark designed for Lean4, applying it to test the abilities of state-of-the-art LLMs, including GPT-3.5, GPT-4, and Gemini Pro. Our comprehensive analysis reveals that, despite recent advancements, these LLMs still exhibit limitations in autoformalization, particularly in more complex areas of mathematics. These findings underscore the need for further development in LLMs to fully harness their potential in scientific research and development. This study not only benchmarks current LLM capabilities but also sets the stage for future enhancements in autoformalization.

cs.LG↗

arXiv2023

Subsquares in random Latin squares and rectangles

A $k \times n$ partial Latin rectangle is \textit{$C$-sparse} if the number of nonempty entries in each row and column is at most $C$ and each symbol is used at most $C$ times. We prove that the probability a uniformly random $k \times n$ Latin rectangle, where $k < (1/2 - α)n$, contains a $βn$-sparse partial Latin rectangle with $\ell$ nonempty entries is $(\frac{1 \pm \varepsilon}{n})^\ell$ for sufficiently large $n$ and sufficiently small $β$. Using this result, we prove that a uniformly random order-$n$ Latin square asymptotically almost surely has no Latin subsquare of order greater than $c\sqrt{n\log n}$ for an absolute constant $c$.

math.CO↗

arXiv2011

Significance of Ultra High Energy Cosmic Rays

The study of ultra high energy cosmic rays is a very important scientific problem. It is likely to have a huge impact in our understanding of the universe. Very high energy particles have been observed to hit the Earth whose origin is likely to be outside our Galaxy. Infact, particles with energies exceeding 10^ (20) electron volts which only hit the earth once in a century have been observed recently. The source of these high energy particles remains a deep and fascinating mystery yet to be resolved. Recently, a huge detector 30 times the size of the city of Paris is built by Pierre Auger Observatory to study these high energy particles. These detectors use the properties of Cherenkov radiation to identify the particles. Firstly, the paper will briefly explain the scientific motivation behind studying ultra high energy cosmic rays. Secondly, this paper will try to explain the reasons behind using water Cherenkov detectors. Thirdly, the paper within its limited scope, will try to give an overview of the exact process by which ultrahigh energy cosmic rays are detected using surface and water Cherenkov detectors.

astro-ph.HE↗