Why Momentum Works

Thanks for pointing that out! We fixed the diagram bug in firefox. There's still bad performance for ~30s after page load -- we're looking into why that's happening -- but after that the page seems to work well.

Re: Why Momentum Works

#5

Post by poppingtonic » Tue, Apr 04, 2017, 5:28 PM UTC

I'm really loving the choice of articles, especially since you're just getting started.

Edit: I'm referring to the journal, not the author.

Re: Why Momentum Works

#6

Post by xapata » Tue, Apr 04, 2017, 5:34 PM UTC

> The added inertia acts both as a smoother and an accelerator

    momentum = mass * velocity

    force = mass * acceleration

    momentum = (force / acceleration) * velocity

So, it looks to me like momentum is inversely related to acceleration. It doesn't seem right to call momentum an "accelerator".

Re: Why Momentum Works

#7

Post by amelius » Tue, Apr 04, 2017, 5:38 PM UTC

Curious, has this method been used for solving linear systems? How would it perform e.g. against conjugate gradient?

And how would it perform for non-positive-definite systems?

Re: Why Momentum Works

#8

Post by mcthorogood » Tue, Apr 04, 2017, 5:40 PM UTC

simplynot wrote: post #2

But simply not on Firefox

The site killed my Firefox on Ubuntu.

Re: Why Momentum Works

#9

Post by colah3 » Tue, Apr 04, 2017, 5:43 PM UTC

xapata wrote: post #6

> The added inertia acts both as a smoother and an accelerator momentum = mass * velocity force = mass * acceleration momentum = (force / acceleration) * velocity So, it looks to me like momentum is inversely related to acceleration. It doesn't seem right to call momentum an "accelerator".

Hi! This article is about momentum in the mathematical field of optimization. Acceleration also refers to a phenomenon in optimization. While there are deep connections to their physical analogues, they aren't aren't quite the same thing.

If you want to make your analogy work, the momentum algorithm adds mass to an object. In terms of literal acceleration at any point in time it is neutral, but the added mass causes you to get through difficult areas much faster.

That said, much of this article is moving away from that physical analogy. :)

Re: Why Momentum Works

#10

Post by gabrielgoh » Tue, Apr 04, 2017, 5:48 PM UTC

amelius wrote: post #7

Curious, has this method been used for solving linear systems? How would it perform e.g. against conjugate gradient? And how would it perform for non-positive-definite systems?

Author here - yes! It can be used to solve symmetric PSD Systems, as the solution of Ax = b is also the minimizer of 0.5*x'Ax - b'x. Conjugate gradient can be seen as a special form of momentum with adaptive alphas and betas