James Berkeley Larsen

James Berkeley Larsen

UMich PhD student in Applied Math & Scientific Computing, interested in simulating quantum systems

Arch Madness

less than 1 minute read

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Sorry for the lack of blog posts the past few months, things have been a little crazy.

Arch Madness

Every month, Jane Street launches a new puzzle. This month, they unveiled something called “Arch Madness”, which is an absolutely beautiful little game. After showing their puzzle to my friends David P and James S, we spent many hours late into the night figuring it out. But these clever friends of mine didn’t stop there! David P went ahead and vibe-coded a little tool to help solve the puzzles.

I have always loved little daily puzzle games, and I saw the potential to turn David’s tool into a beautiful quick puzzle game. So, after an afternoon date with Cursor, I am launching my daily puzzle game, check it out here. Please let me know what you think! And if you like it, try to make puzzles of your own with the explorer tool. If you make a particularly good one and send me the json, it may just be featured!

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POMDP

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Minesweeper as a Markov Process

As promised two weeks ago, I’ve started my attempt to formulate Minesweeper in the language of reinforcement learning (RL). The mathematical backbone of RL is a Markov decision process (MDP), consisting of a state space $\mathcal{S}$, an action space $\mathcal{A}_s$ for each state $s \in \mathcal{S}$, transition probabilities $P_a(s,s’)$ for states $s,s’\in\mathcal{S}$ and action $a \in \mathcal{A}_s$, and the reward functions $R_a(s,s’)$. The goal of the MDP is to find the policy $\pi$ that determines the best action $a$ from any given state, i.e., \begin{equation} \pi^* = \arg\max_\pi \mathbb{E}_{s \sim \pi, a \sim \pi(s)} \left[ \sum_{t=0}^\infty \gamma^t R_a(s_t, a_t) \right] \end{equation} for some discount factor $\gamma \in [0,1]$.

Rich Sutton Plays Minesweeper

2 minute read

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Month Two

Turns out, a new year’s resolution to blog every week is too ambitious. Maybe I can update that to once a month? Here goes a simple February blog post, coming back into the CompCath sandbox to see what I can put together.

New Year, New Me

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Trajectory

With the arrival of the arbitrarily chosen day set aside by our society as the first of the year comes the ritualistic resolutions meant to change our behavior. One such resolution of mine was to revive Computational Catharsis as a sandbox for my thoughts. Here goes nothing.

Hello World

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Genesis

With November quickly fading away, I am thinking ahead to future iterations of the universe. Why not include a personal online blog/CV in such future iterations? Hence, the birth of Computational Catharsis.