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Cake day: July 9th, 2023

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  • A quadratic function is just one possible polynomial. They’re also not really related to big-O complexity, where you mostly just care about what the highest exponent is: O(n^2) vs O(n^3).

    For most short programs it’s fairly easy to determine the complexity. Just count how many nested loops you have. If there’s no loops, it’s probably O(1) unless you’re calling other functions that hide the complexity.

    If there’s one loop that runs N times, it’s O(n), and if you have a nested loop, it’s likely O(n^2).

    You throw out any constant-time portion, so your function’s actual runtime might be the polynomial: 5n^3 + 2n^2 + 6n + 20. But the big-O notation would simply be O(n^3) in that case.

    I’m simplifying a little, but that’s the overview. I think a lot of people just memorize that certain algorithms have a certain complexity, like binary search being O(log n) for example.









  • This graph actually shows a little more about what’s happening with the randomness or “temperature” of the LLM.
    It’s actually predicting the probability of every word (token) it knows of coming next, all at once.
    The temperature then says how random it should be when picking from that list of probable next words. A temperature of 0 means it always picks the most likely next word, which in this case ends up being 42.
    As the temperature increases, it gets more random (but you can see it still isn’t a perfect random distribution with a higher temperature value)