Relative Positional Encoding (RPE), which encodes the relative distance between any pair of tokens, is one of the most successful modifications to the original Transformer. As far as we know, theoretical understanding of the RPE-based Transformers is largely unexplored. In this work, we mathematically analyze the power of RPE-based Transformers regarding whether the model is capable of approximating any continuous sequence-to-sequence functions. One may naturally assume the answer is in the affirmative---RPE-based Transformers are universal function approximators. However, we present a negative result by showing there exist continuous sequence-to-sequence functions that RPE-based Transformers cannot approximate no matter how deep and wide the neural network is.

Only one in 20 companies has extensively incorporated AI in offerings or processes. Less than 39% of all companies have an AI strategy in place. According to MIT Sloan Review, the largest companies -- those with at least 100,000 employees -- are the most likely to have an AI strategy, but only half have one. Despite claims that AI is already being subsumed into an array of applications, we're not there yet and won't be in 2018. It is still the early days of adoption, and those companies that are implementing AI now will see the biggest competitive value.

Azeem Azhar is a strategist, product entrepreneur, and analyst living in London. He is the curator of the weekly newsletter Exponential View, from which the following is adapted. This is the first year I am presenting predictions for the coming year. I've received some incredibly helpful comments from readers via Twitter. This has encouraged me to stick my head above the parapet.

Samsung's big phone is back.Meet the Galaxy Note 8 Fans of large phones have been waiting for Samsung's next Galaxy Note since the last one suffered a devastating recall last year. Can the cold vacuum of space crush the'gram?Elon Musk shows off SpaceX's custom space suit on Instagram According to the SpaceX and Tesla boss, this suit is no mere mockup, already tested to "double vacuum pressure." Yes, it's named after'WoW'Inside'Carcraft,' Waymo's virtual world for testing self-driving car AI Google's autonomous vehicle project has logged about three million real-world miles, but a report in The Atlantic opens up its virtual world where 25,000 simulated cars cover 2.5 billion miles every day. Keep an eye on IFASamsung will unveil its next Gear S smartwatch on Aug. 30th After the Galaxy Note 8, Samsung's next big mobile debut is probably a wearable device.

A decade ago, artificial intelligence was something we saw in the movies. Nobody ever imagined AI would become a major part of our lives. Today, there is a huge amount of hype in the world of AI and it is already being seen as a major tool in many fields. Driverless car technology is well advanced and in some countries, notably China, AI research and development is booming. Millions of people use Alexa to turn the lights on or receive targeted online information.

But when I/O kicks off this Wednesday, expect Google's latest artificial intelligence efforts to be what everyone ends up talking about. If you've been paying attention over the last year or so, you've noticed that Google seems especially passionate about AI, injecting it into everything from search results to chat apps to the new Google Assistant for Android phones and the Google Home speaker. CEO Sundar Pichai has sounded especially bullish on the prospects for AI on recent company earnings calls and public interviews. That was just the beginning. Internally, Google sees AI as its next major platform after search and Android -- and it wants to give developers a way to get in early.

It's been a few years since Microsoft's then-CEO Steve Ballmer danced across the stage screaming "DEVELOPERS DEVELOPERS DEVELOPERS," but those are still the three words you'd use to explain this week's Build conference. Like Google's I/O or Apple's WWDC, the annual event is partly a state of the union, partly product unveiling, but mostly a time to bring the developer community together and pitch them on a vision of the future. The conference lasts two days, with keynote addresses starting at 8am on both Wednesday and Thursday. You can watch on Microsoft's site, and you should definitely hang out with us while we liveblog. Microsoft seemingly hasn't left itself much to unveil this time.

The elite movers of the technology industry are about to set the 2017 agenda. The next few weeks will be some of the most exciting in the technosphere. What changes are coming to the operating systems that just about everybody in the world use? What are the next steps in the foundations of machine learning and artificial intelligence? Is there a future for bots?

LAS VEGAS, NV - JANUARY 05: An illuminated sign at the Nvidia booth is seen at CES 2017 at the Las Vegas Convention Center on January 5, 2017 in Las Vegas, Nevada. CES, the world's largest annual consumer technology trade show, runs through January 8 and features 3,800 exhibitors showing off their latest products and services to more than 165,000 attendees. Nvidia Corp. is scheduled to release earnings after Tuesday's close. The stock hit a record high of $120.92/share in February 2017 and is currently trading near $104/share. The stock is prone to big moves after reporting earnings and can easily gap up if the numbers are strong.