Just because 2 things are dual, doesn't mean they're just opposites

The 2 Aspects

Boolean Algebra, Arithmetic POV

(written long time ago, publish or languish)

discontinuous linear functions

Let \(H > \mathbb{Nat}\) be unlimited.

Continuous vs Bounded

Nonstandard analysis gives a nice link between continuous and bounded functions, which are small and large-scale notions.1

  1. Credit to Takuma Imamura for showing me this definition 

Minimal Surfaces

GPT-4 did this in 1 shot.

November 2, 2023

Been going through Mosteller’s 50 challenging problems in probability.

NTK reparametrization

I’ve been learning about the neural tangent kernel and some things confused me.

Kate from Vancouver, please email me

You replied to my dissection post and I decided then that I wished to be your friend. You didn’t leave your email, but asked how old I was in earth years. My email is alokbeniwal@gmail.com, please reach out if you see this.

ChatGPT Session: Emotions, Etymology, Hyperfiniteness

List as many emotions as you can. Then list their etymologies

Some ChatGPT Sessions

No particular theme. Quoted text is me, rest is GPT.

2016 ML thoughts

(Old notes from 2016 that I stumbled upon).

My biggest takeaway from Redwood Research REMIX

I just finished a 1 month research program called REMIX (Redwood Research Mechanistic Interpretability Experiment).

finite, actual infinity, potential infinity

For a finite set, one can describe a uniform distribution. There isn’t a natural way to do so for a countable set. But for a hyperfinite set, one can describe a uniform distribution through a probability density. So in some ways the countable is “bigger”.

Actions and Flows

What is an action?

PSA: reward is part of the habit loop too

The usual setup of a habit is

a kernel of lie theory

just like how infinitesimals are useful because they’re indiscernible from 0, but have the advantage of being able to be divided by.