arXiv subjects

Henry Jiang

Publications and source records attributed to Henry Jiang.

3 recordsLinked to original sources

arXiv2026

DARWIN: Dynamic Agentically Rewriting Self-Improving Network

DARWIN is an evolutionary GPT model, utilizing a genetic-algorithm like optimization structure with several independent GPT agents being trained individually using unique training code. Each iteration, the GPT models are prompted to modify the training code of one another in an attempt to improve their performance in a mutation-like manner, and the best GPT agents are then benchmarked and selected for the next iteration by genetic algorithm. For demonstration purposes and due to budget and time constraints, OpenAI API is used to prompt training code improvements and the nanoGPT framework is used as the training code. DARWIN also utilizes persistent JSON-based memory files to track previous reasoning and changes to code to correlate with improvement to model performance. and a bidirectional interface for HITL intervention allowing the model to request upgrades such as additional datasets, training scripts, and restructuring of file hierarchies. In experiments, DARWIN achieved a 1.26 percent improvement in model FLOPS utilization (MFU) and a 2.07 percent improvement to perplexity in 5 iterations of training over baseline configurations, demonstrating promising capabilities as a foundation for scaling evolutionary GPT training.

cs.NE↗

arXiv2025

The Axial Electric Potential and Length of a Torus Knot

Physical knot theory, where knots are treated like physical objects, is important to many fields. One natural problem is to give a knot a uniform charge, and analyze the resulting electric field and electric potential. There have been some results on the number of critical points of the electric potential from knots, such as by Lipton (2021) and Lipton, Townsend, and Strogatz (2022). However, little analysis has been done on the electric field and electric potential using calculations for specific knots. We focus on torus knots, specifically a parametrization that embeds it on a torus centered at the origin with rotational symmetry about the z-axis. Particularly, in this project, we analyze the electric field along the z-axis to take advantage of symmetry. We also analyze the length of the knot as a simpler integral. We show that the electric field is zero only at the origin, and investigate the extreme points of the electric field and electric potential using numerical methods and calculations. We also demonstrate a new way to apply methods for contour integration in complex analysis to calculate the length, electric potential, and electric field, and provide an explicit approximation for the length of a torus knot.

math.CV↗

arXiv2023

A weaker notion of the finite factorization property

An (additive) commutative monoid is called atomic if every given non-invertible element can be written as a sum of atoms (i.e., irreducible elements), in which case, such a sum is called a factorization of the given element. The number of atoms (counting repetitions) in the corresponding sum is called the length of the factorization. Following Geroldinger and Zhong, we say that an atomic monoid $M$ is a length-finite factorization monoid if each $b \in M$ has only finitely many factorizations of any prescribed length. An additive submonoid of $\mathbb{R}_{\ge 0}$ is called a positive monoid. Factorizations in positive monoids have been actively studied in recent years. The main purpose of this paper is to give a better understanding of the non-unique factorization phenomenon in positive monoids through the lens of the length-finite factorization property. To do so, we identify a large class of positive monoids which satisfy the length-finite factorization property. Then we compare the length-finite factorization property to the bounded and the finite factorization properties, which are two properties that have been systematically investigated for more than thirty years.

math.AC↗