Use It or Lose It

In Spring 2024, I took ECE 513. To this day, I consider it the hardest class I've ever taken, and also the most rewarding in many ways. I'd always wanted to take a hard math class, and somewhat romanticized the notion of agonizing over a difficult problem set. Rest assured, I no longer romanticize math classes as such, and am indebted to the (very) smart classmates that endured many nights of me confusing myself. Though in retrospect, I did quite enjoy the puzzle nature of solving difficult problems, and hope to take another math class in grad school (most likely some form of abstract algebra).

Despite the trials of ECE 513, I seem to have utterly forgotten most of the formulas and theorems we learned in the class a mere 2 years later! Reading my old homeworks, I can vaguely understand the language and concepts at play, but if you asked me to derive the solutions again, I probably wouldn't have the foggiest idea how to do so! Some high-level concepts and a general familiarity with linear algebra have stuck with me though, and those are arguably very nice skills to have in the AI era.

Obviously abstract linear algebra and DSP are not my fields of research/work, but I apparently also forgot the chain rule at some point? Which I found out while trying to learn about how backpropagation works. And calculus fundamentals feel like a fairly important thing to retain for general knowledge purposes.

This note isn't really supposed to have any grand meaning, but some thoughts:

I'm (now even more) incredibly awed by the professors and grad students in my life who seem to have an almost eidetic recall of the coursework and papers they've studied in the past.
What is the "correct" amount of effort to spend reviewing or reinforcing content learned in past courses without impeding current work or research?
I wonder if limited recall is somehow attributable to the proliferation of search engines and online databases? Something something "incentivizing finding information repeatedly instead of recalling information long-term".

Can't imagine LLMs are doing anything to help point 3…