Gary Liang | Searcharxiv

arXiv2025

Automatically Detecting Amusing Games in Wordle

We explore automatically predicting which Wordle games Reddit users find amusing. We scrape approximately 80k reactions by Reddit users to Wordle games from Reddit, classify the reactions as expressing amusement or not using OpenAI's GPT-3.5 using few-shot prompting, and verify that GPT-3.5's labels roughly correspond to human labels. We then extract features from Wordle games that can predict user amusement. We demonstrate that the features indeed provide a (weak) signal that predicts user amusement as predicted by GPT-3.5. Our results indicate that user amusement at Wordle games can be predicted computationally to some extent. We explore which features of the game contribute to user amusement. We find that user amusement is predictable, indicating a measurable aspect of creativity infused into Wordle games through humor.

cs.CL↗

arXiv2020

Spanning trees in random regular uniform hypergraphs

Let $\mathcal{G}_{n,r,s}$ denote a uniformly random $r$-regular $s$-uniform hypergraph on the vertex set $\{1,2,\ldots, n\}$. We establish a threshold result for the existence of a spanning tree in $\mathcal{G}_{n,r,s}$, restricting to $n$ satisfying the necessary divisibility conditions. Specifically, we show that when $s\geq 5$, there is a positive constant $\rho(s)$ such that for any $r\geq 2$, the probability that $\mathcal{G}_{n,r,s}$ contains a spanning tree tends to 1 if $r > \rho(s)$, and otherwise this probability tends to zero. The threshold value $\rho(s)$ grows exponentially with $s$. As $\mathcal{G}_{n,r,s}$ is connected with probability which tends to 1, this implies that when $r \leq \rho(s)$, most $r$-regular $s$-uniform hypergraphs are connected but have no spanning tree. When $s=3,4$ we prove that $\mathcal{G}_{n,r,s}$ contains a spanning tree with probability which tends to 1, for any $r\geq 2$. Our proof also provides the asymptotic distribution of the number of spanning trees in $\mathcal{G}_{n,r,s}$ for all fixed integers $r,s\geq 2$. TPreviously, this asymptotic distribution was only known in the trivial case of 2-regular graphs, or for cubic graphs.

math.CO↗