Math
Expositions
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Behavior of Infinitely Wide Neural Networks [pdf] I discuss the neural tangent kernel, some RKHS theory, and what happens during initialization and throughout gradient descent for infinitely wide neural networks.
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Ratatouille: RL for Micromouse [pdf] This one is not really mathy, but I design an environment to make it conducive for an agent to learn the Micromouse task (which I do in real life!).
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Strong Law of Large Numbers and Kingman’s Subadditive Ergodic Theorem [pdf] I approach the Strong Law of Large Numbers from the ergodic point of view, which is really interesting (and becomes perhaps more obvious). Plus Kingman’s Theorem, which is helpful in the case when “addition” is not commutative.
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Elliptic Functions and Plane Cubics [pdf] I discuss this mysteriously fancy-sounding object called “elliptic functions”, and reveal that the plane cubics they induce admit a certain additive structure, which can be seen by just drawing straight (tangent) lines.
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Risk-averse Dynamic Programming for Tree-based Controlled Markov Decision Processes [pdf] (FUSRP 2024) We generalize a technique on using dynamic programming to minimize convex dynamic risk measures on controlled MDPs, from the sequential case to the tree-based case. We also illustrate certain difficulties when generalizing this further to a DAG-based process.
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Harmony in Randomness: the Laplacian and the Heat Equation [pdf] (UChicago REU Apprentice 2023) I discuss the heat equation, the analytic way to solve it, and its probabilistic interpretations. Personally I think complementing it with the probabilistic point of view is not only interesting, but it also provides a strong intuition of things that ought to be true.