Importance of publications if one decides to go industry after PhD? If a PhD student (hard sciences like math, physics) decides to work in industry after graduation, are publications important?

For transition to industry, what are the most important factors to take note of during one's PhD?

Thanks for any advice.
Publications demonstrate several things such as:


Ability to conduct, complete, and document work
Ability to communicate clearly
Interest in broadening the field's knowledge
Interest in staying aware of the "state-of-the-art"


All of these are good attributes to demonstrate with a publication record.  Continuing to publish in industry is also valuable, but it is seldom "publish or perish."  

Regarding important factors: use elements of your Ph.D. to demonstrate that you can work independently to solve difficult problems.  A strong work ethic and ability to solve problems are key traits that employers are looking for.