3 ms·

I genuinely don't understand how anyone can use something like this and seriously think "oh yeah, this is revolutionary." It's almost complete garbage and can't

by dvt 3y ago

I genuinely don't understand how anyone can use something like this and seriously think "oh yeah, this is revolutionary." It's almost complete garbage and can't do anything remotely interesting. # a method that approximates the hyperbolic tangent (clamped tanh) def rational_tanh(x): return (x + 1) / (x - 1) Even gave it the BIG hint of a "clamped" and "rational" tanh, but that ain't it, chief. Forget GPT-4, I would be embarrassed to even show this as a tech demo.

afro88 3y ago
I use "something like this" (GPT4) all the time. Use a good model. Can't wait till proper open source models catch up, but they're not there yet. Here's GPT4's response: ``` import math def clamped_tanh(x, n_terms=10): """ Approximate the hyperbolic tangent (tanh) function using a Maclaurin series expansion. Args: x (float): The input value for which to compute the tanh. n_terms (int, optional): The number of terms to use in the Maclaurin series. Default is 10. Returns: float: The approximated tanh value. """ tanh_approx = 0 for n in range(n_terms): coef = ((-1) ** n) * (2 * n + 1) term = coef * (x ** (2 * n + 1)) / math.factorial(2 * n + 1) tanh_approx += term # Clamping the tanh approximation to the range [-1, 1] tanh_approx = max(-1, min(tanh_approx, 1)) return tanh_approx # Example usage x = 0.5 result = clamped_tanh(x) print(f"clamped_tanh({x}) = {result}") ```
- dvt 3y ago
  I don't mean to get in the weeds here, but this is still bad, as the Padé approximation[1] (which is what you're actually really looking for) is magnitudes better than the Maclaurin series (which is just a special case of the Taylor expansion). Keep in mind that I'm not even an expert (I merely earned a minor in math). In fact, I only know this because I did some research years ago on rational approximations of hyperbolic functions. The right answer gets clipped to -1 or 1 beyond (-3, 3), but it should look like: `x * ( 27 + x * x ) / ( 27 + 9 * x * x )`—though the coefficients (and clip range) can vary. [1] https://en.wikipedia.org/wiki/Pad%C3%A9_approximant https://en.wikipedia.org/wiki/Pad%C3%A9_approximant
  - afro88 3y ago
    Ah. It weakens my point, but I'll say it anyway: you do need to be able to tell the difference between good and bad responses to use it to make you more efficient. I definitely wouldn't use it blindly for things I don't know much about at this point. Pretending I know my Pade from my Maclaurian, I'd follow up with: "use the better Pade approximation".

by dvt 3y ago

afro88 3y ago

I use "something like this" (GPT4) all the time. Use a good model. Can't wait till proper open source models catch up, but they're not there yet. Here's GPT4's response: ``` import math def clamped_tanh(x, n_terms=10): """ Approximate the hyperbolic tangent (tanh) function using a Maclaurin series expansion. Args: x (float): The input value for which to compute the tanh. n_terms (int, optional): The number of terms to use in the Maclaurin series. Default is 10. Returns: float: The approximated tanh value. """ tanh_approx = 0 for n in range(n_terms): coef = ((-1) ** n) * (2 * n + 1) term = coef * (x ** (2 * n + 1)) / math.factorial(2 * n + 1) tanh_approx += term # Clamping the tanh approximation to the range [-1, 1] tanh_approx = max(-1, min(tanh_approx, 1)) return tanh_approx # Example usage x = 0.5 result = clamped_tanh(x) print(f"clamped_tanh({x}) = {result}") ```

dvt 3y ago
I don't mean to get in the weeds here, but this is still bad, as the Padé approximation[1] (which is what you're actually really looking for) is magnitudes better than the Maclaurin series (which is just a special case of the Taylor expansion). Keep in mind that I'm not even an expert (I merely earned a minor in math). In fact, I only know this because I did some research years ago on rational approximations of hyperbolic functions. The right answer gets clipped to -1 or 1 beyond (-3, 3), but it should look like: `x * ( 27 + x * x ) / ( 27 + 9 * x * x )`—though the coefficients (and clip range) can vary. [1] https://en.wikipedia.org/wiki/Pad%C3%A9_approximant https://en.wikipedia.org/wiki/Pad%C3%A9_approximant
- afro88 3y ago
  Ah. It weakens my point, but I'll say it anyway: you do need to be able to tell the difference between good and bad responses to use it to make you more efficient. I definitely wouldn't use it blindly for things I don't know much about at this point. Pretending I know my Pade from my Maclaurian, I'd follow up with: "use the better Pade approximation".