Comment by prvc
12 hours ago
This is neat, but could someone explain the significance or practical (or even theoretical) utility of it?
12 hours ago
This is neat, but could someone explain the significance or practical (or even theoretical) utility of it?
From the paper:
> Everyone learns many mathematical operations in school: fractions, roots, logarithms, and trigonometric functions (+, −, ×, /, sqrt, sin, cos, log, …), each with its own rules and a dedicated button on a scientific calculator. Higher mathematics reveals that many of these are redundant: for example, trigonometric ones reduce to the complex exponential. How far can this reduction go? We show that it goes all the way: a single operation, eml(x, y), replaces every one of them. A calculator with just two buttons, EML and the digit 1, can compute everything a full scientific calculator does. This is not a mere mathematical trick. Because one repeatable element suffices, mathematical expressions become uniform circuits, much like electronics built from identical transistors, opening new ways to encoding, evaluating, and discovering formulas across scientific computing.
Actually we know this for a long time. The universal approximation theorem states that any arbitrary function can be modelled through a nonlinear basis function so long as capacity is big enough. The practical bit here is knowing how many basis functions can be approximated with a two operators. That’s new!
Read the paper. On the third page is a "Significance statement".
eh, i didnt find that paragraph very helpful. it just restates what it means do decompose an expression into another one only relying on eml, and vaguely gestures at what this could mean, i was hoping for something more specific.
second, please help us laypeople here