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A Number with a Shadow
- konmok 7mo agoNeato introduction, but the text reeks of LLMs so I stopped reading.
- cadamsdotcom 7mo agoReally let down by these short sentences. “Here’s where it gets interesting.” “That’s not a ____. It’s a _____.” I’ll gladly read this if the author does an editing pass and makes it read more naturally.
- nh23423fefe 7mo agolet e^2 = 0. the dual numbers are D = {x + ye | x,y in R}. let f(z) be some polynomial. Then by binomial theorem f(z + e) - f(z) = z^n + n*z^(n-1)*e + O(e^2) - z^n = f'(z)*e. And so df = df/dz * e
- zack-alex 7mo agoThat's a nice article, thanks! I learned something new from it (somehow I didn't know that typical finite difference error plot is linearly V-shaped). tang library looks cool, and I wonder whether it will become a modern full-fledged math library independent of ancient BLAS and solver libs... I wish it would, but that would require huge effort. A couple of nitpicks for the article: > The pathological function barely hits 10⁻⁵. Huh? The pathological function's error plot goes below 10⁻⁸. > What does that buy you? Watch two gradient descent particles race down Himmelblau's function The default value in the visualisation for h is 0.5. Of course it performs poorly! Switch to h=0.1 and the difference is gone. I wonder if there exists a more significant demonstration