Floating-Point Formats and Deep Learning

https://eigenfoo.xyz/floating-point-deep-learning/

by _eigenfoo • 6 years ago

39 13 6 years ago

alecmg• 6 years ago

Hoped to see opinions on Unum [1]

Correct me if I'm wrong, but most machine learning does happen around 1.0. Unum should give more precision for same bits, same precision for less bits around 0 and 1. And some other interesting features.

But would require new hardware and software.

[1] https://en.wikipedia.org/wiki/Unum_(number_format)

quietbritishjim• 6 years ago

But even if you have extra precision around 1.0, assuming that weight is used for multiplication (of an output from the previous layer), surely you'll lose it as soon as you perform that multiplication? E.g. if the previous layer output is 3.5 and you multiply it by 1.00...0063, you'll get 3.500...02205, but you'll lose those trailing places on the output unless you have lots of precision around 3.5 too.

I tried to think about ways round that with traditional floating point formats and nonlinear functions (i.e. using exp to change the multiplication to addition) but it seems to come back to the same problem.

bsder2• 6 years ago

Please don't propagate Unums.

They have all the failure modes of interval arithmetic on top of their own brand of failure modes.

There are loads of engineers with stiff numerical problems that would welcome a better representation than standard floating point if it worked. Somehow, Gustafson never manages to demonstrate unums on any of these problems.

Until Gustafson grabs some real numerical code, implements it with unums and demonstrates how much better they are, he is not worth paying attention to.

kortex• 6 years ago

Type I and II unums are likely dead ends. Type III (posits) look promising. Facebook AI has developed their own type of "posit" with the terribly undescriptive name of "(8, 1, alpha, beta, gamma) log". Much less catchy than "posit" or "unum" but have been actually demonstrated to have numerical benefits.

https://engineering.fb.com/ai-research/floating-point-math/

daniel-cussen• 6 years ago

I read the book, the End of Error by John Gustafson. He works on a lot of numerical problems right there, providing code and results.

He also goes over the history of floats and numerical computation, highlighting how often the best method was never adopted, for reasons as simple as patents or it not being better by enough.

Unums are better by enough, and they're being used at LLNL in experiments. It's just a hard ask for people to switch the number system they use, even switching from decimal to binary was a huge slog in the early computer age.

xiphias2• 6 years ago

Companies with lots of deep learning applications, like Google/FB have better chance of experimenting with alternative hardware formats, as NVIDIA has to be compatible with older hardware. Still I'm hopeful that they will come, as they can give further scaling in AI.

_y5hn• 6 years ago

The moment floating-point precision errors become significant in your model, know that you're dealing with algorithmic BS.

tgv• 6 years ago

Didn't you know our neurons have a 384 bit resolution?

nine_k• 6 years ago

Source, if you don't mind?

sdenton4• 6 years ago

There's also the whole world of fixed point inference which isn't discussed here, but quite important. All of the hardware supports fast integer operations, and with fewer platform specific caveats, so you can get better guarantee of consistent behavior in deployments.

_5659• 6 years ago

Floating point? In MY deep learning?

It's more likely than you think.

Maybe not the most appropriate place for an "X? in MY y?" meme despite its relatively innocuous presentation

It's kind of gross so I'll refrain from linking it

Floating-Point Formats and Deep Learning

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