Vivan Doshi

Vivan Doshi, Mengyuan Li

The proliferation of Large Language Models (LLMs) raises a critical question about what it means to be human when we share an increasingly symbiotic relationship with persuasive and creative machines. This paper examines patterns of human-AI coevolution in creative writing, investigating how human craft and agency are adapting alongside machine capabilities. We challenge the prevailing notion of stylistic homogenization by examining diverse patterns in longitudinal writing data. Using a large-scale corpus spanning the pre- and post-LLM era, we observe patterns suggestive of a "Dual-Track Evolution": thematic convergence around AI-related topics, coupled with structured stylistic differentiation. Our analysis reveals three emergent adaptation patterns: authors showing increased similarity to AI style, those exhibiting decreased similarity, and those maintaining stylistic stability while engaging with AI-related themes. This Creative Archetype Map illuminates how authorship is coevolving with AI, contributing to discussions about human-AI collaboration, detection challenges, and the preservation of creative diversity.

Vivan Doshi

The discovery of conservation laws is a cornerstone of scientific progress. However, identifying these invariants from observational data remains a significant challenge. We propose a hybrid framework to automate the discovery of conserved quantities from noisy trajectory data. Our approach integrates three components: (1) a Neural Ordinary Differential Equation (Neural ODE) that learns a continuous model of the system's dynamics, (2) a Transformer that generates symbolic candidate invariants conditioned on the learned vector field, and (3) a symbolic-numeric verifier that provides a strong numerical certificate for the validity of these candidates. We test our framework on canonical physical systems and show that it significantly outperforms baselines that operate directly on trajectory data. This work demonstrates the robustness of a decoupled learn-then-search approach for discovering mathematical principles from imperfect data.