The editors, previous to accepting. If it doesn't run out of the box and reproduce the result, it doesn't get published.
Then the paper needs to be replicated a few times by independent research teams to be considered valid. This is the step we are probably missing in AI. Any published paper (and even unpublished, on arxiv) are considered valid and by the community but sometimes cannot be replicated.
They obviously meant the reviewers. Not everyone is intimately familiar with academic terminology.
Maybe a solution would be a platform, like a CI for machine learning where authors would send their codes, and the CI would run it for them, and make the results public. Then everyone could check the code and results, reviewers included.
To me, getting the right people to review the paper is more important than reproducible code.
There's also a big difference between accepting a paper and judging if it is good. At a top conference like NIPS, lots of good papers will get rejected. That's the nature of being a top conference in a hot field. It's similar to a high school valedictorian not getting into Harvard: it's not a judgement that they are a bad student. But when you're an elite thing, and lots of people want in, you end up looking for reasons to reject rather than accept. You will end up rejecting good papers/students in such a case. NIPS, or NeurIPS now, is a particularly interesting example, as a colleague recently told me that they just got 12,000 submissions this year.
There's also an issue in computer science papers where people may not like your paper based on personal taste. They may not be convinced you're solving a real problem, and if your paper involves a new artifact, the design of it. I refer to these as "your baby is ugly" reviews. They don't think you're wrong, they just don't like it.
I think people's time is a bigger thing than the wrong people. One problem, I think, is that we tend to compete for these once-a-year conferences, causing an enormous time crunch for reviewers. VLDB has a great model where they do rolling acceptance throughout the year, accepting a few papers every month, even though the conference happens once a year (http://vldb.org/2019/?submission-guidelines). I believe this is the best hybrid between the typical CS conference system, and the more common journal system in the rest of science and engineering.
A better solution imo is to improve openreview.net process somehow, so that I'm motivated to go there, find papers relevant to my research (ideally get notified when such papers are posted for review), and leave a review (and perhaps vote on other reviews just like we do here on HN, or do something else to influence the acceptance decision). Obviously there should be methods to prevent abuse: moderators, reputations of reviewers, restricting reviewers to those with specific publications (e.g. based on keywords), etc. Btw, code reproducibility could be used to give some weight in such public review process.
That's not how the VLDB process works. What they did was establish a PVLDB journal which has a monthly deadline, and it accepts 5-12 papers a month. The papers are public on the website a few months after acceptance. (See: https://vldb.org/pvldb/vol12.html) The VLDB conference is then all of the papers that appeared in PVLDB in the past year.
I would be in favor of exploring your model as well, but I also see the hybrid model developed by VLDB as superior to the standard conference submission and review process.
Are you sure you have thought this through?
This was a major topic at NIPS 2017, yet doesn't seem to be important enough to address.
It would be a big change, but this is actually possible, and it would make things easier for everyone down the line.
Anyhow, I think Qworg has a point in that the editors do have responsibility for what they accept. It's true that referees do not have the resources to reproduce results: I for instance have limited time on the shared high-performance computing resources we have, so I'm not going to use it on someone else's paper. However, as another commenter says, this could be paid for. A journal could potentially "sell" this as a competitive advantage: papers in this journal were actually reproduced, by paid staff who are neither editors nor referees, people paid in currency that can be exchanged for goods (not academic currency).