4 ms·

Why waste a slot on -0?

• saulpw 6mo ago
  Because it means "infinitesimal negative" which is distinct from "infinitesimal positive".
  • Dylan16807 6mo ago
    That sounds pretty niche. What's a use case where you have less than 8 bits and that distinction is more important than having an extra finite value? I don't think AI is one.
    • jlokier 6mo ago
      For neural net gradient descent, automatic differentiation etc, the widely used ReLU function has infornation carrying derivatives at +0 and –0 if those are infinitesimals.
      • Dylan16807 6mo ago
        Barely any information. After surviving RELU that signed zero is probably getting added to another value and then oops the information is gone. It sounds a lot worse than properly spaced values.
        • saulpw 6mo ago
          sign = most important bit of information
          • Dylan16807 6mo ago
            If you were looking at the entire number line, sign would roughly be the most important part. But you still have all the other numbers carrying sign info. This is only the sign of denormals and that's way less valuable. Outside of particular equations it ends up added to something else and disappearing entirely. It would be way better to cut it and have either half the smallest existing positive value or double the largest existing value as a replacement. Or many other options.
      • deleted 6mo ago
        [deleted]
• adampunk 6mo ago
  You need it if you want the idea of total ordering over the extended Reals. There's +/- infinity--an affine closure, not projective (point at infinity)--so to make that math work you need to give 0 a sign.