Things I've Worked On 🍜

Abstract: This paper reproduces and stress-tests MEMIT, a method for editing factual knowledge into LLM weights, finding it works perfectly on GPT-J but transfers poorly to Llama 3.1 8B. Even when edits succeed, clever adversarial prompts can trick the model into recalling its original, pre-edit knowledge over 65% of the time.

Abstract: Developed a novel data structure for efficiently analyzing product metrics by extending classical range tree techniques. Designed and implemented greedy range trees in Python to optimize multi-dimensional queries, improving speed and scalability for large datasets. This enables faster, more accurate analysis of product metrics, including trends, anomalies, and usage patterns.

Abstract: A compilation of selected problems and solutions from research in advanced graph theory, covering topics such as graph colorings, connectivity, planarity, and extremal problems.

Abstract: In 1928, Emil Artin and Helmut Hasse introduced the Artin–Hasse exponential, a p-adic analogue. After introducing the basics of p-adic analysis, including why \(\mathbb{Q}_p\) is the completion of \(\mathbb{Q}\), this paper shows that the exponential and logarithm remain inverses, with intuition drawn from metric spaces and topology. The core is an inductive-based proof of Dwork's Lemma, used to prove the integrality of the Artin–Hasse Exponential.

Abstract: Building on Christiaan Huygens' discovery of coupled pendulum synchronization, this paper examines how string length affects synchronization time on a moving platform. Experiments showed that shorter strings generally synchronize faster. Behaviors like brief pauses and in-phase vs. anti-phase motion are explained using classical mechanics. The paper also models motion and energy using Lagrangian techniques.