[atum47]

I've been wondering about something and I don't know if this is the place to ask it, but here it goes. I saw a video the other day about how the Nintendo 64 did not have the ability to calculate sine, so they used a lookup table from 0 to 2PI (with some clever trick to reduce the size of the table). Would it have been possibly to train a NN and store the weights or even a function and store the coefficients to calculate the sine, cosine?

[mandibles]

Neural networks often have trigonometric functions internally, so it would be massively more computation than necessary.

If you have a few spare CPU cycles, a hybrid approximation could start with a sparse lookup table of values as the initial guess for a few rounds of a numerical approximation technique. Or you just store the first few coefficients of a polynomial approximation (as in the OP's work).

[CamperBob2]

Take a look at CORDIC if you aren't familiar with it; that was a common trig hack back in the day, and still sees some use in the embedded space.

Neural nets can be useful when you have samples of a function but no idea how to approximate it, but that's not the case here.

[EdgeExplorer]

Obviously you could train some kind of neural net to calculate any function, but this would never make sense for a well-known function like sine. Neural nets are a great solution when you need to evaluate something that isn't easy to analyze mathematically, but there are already many known techniques for calculating and approximating trigonometric functions.

Training a neural net to calculate sines is like the math equivalent of using an LLM to reverse a string. Sure, you *can*, but the idea only makes sense if you don't understand how fundamentally solvable the problem is with a more direct approach.

It's always worth looking if mathematicians already have a solution to a problem before reaching for AI/ML techniques. Unfortunately, a lot of effort is probably being spent these days programming some kind of AI/ML to solve problems that have a known, efficient, maybe even proven optimal solution that developers just don't know about.

[o11c]

> using an LLM to reverse a string.

  Input: Please reverse the string "Dlrow, Olleh!"
  Output (chatgpt): Sure! The reversed string is "!helleO ,worldD"
  Output (liquid): The reversed string is "!ehT, Llord!"
  Output (llama): The reversed string is "Hellol, Wlod."
  Output (phi): The reversed string of "Dlrow, Olleh!" is "!HoleL ,owrdL" or "Hello, World!" backwards.
  Output (qwen): The reversed string of "Dlrow, Olleh!" is "!hlelo ,wolrD".

Honestly some of them are doing better than I expected.

[magicalhippo]

A neural network is essentially just a curve fitter, so yeah. You might find this[1] video illuminating.

The main strength of a neural network comes into play when there's a lot of different inputs, not just a handful. For the simpler cases like sin(x) we have other tools like the one posted here.

[1]: https://www.youtube.com/watch?v=FBpPjjhJGhk But what is a neural network REALLY?

[kevin_thibedeau]

The usual conservation trick is to have a table from 0 to PI/2 and use two additional index bits to generate the other three quadrants.