So if I'm understanding this paper correctly, the primary way that these non-local blocks differ from a fully connected net, is that when calculating y_i, you are also able to take into account the input at x_i (not just x_j). Thus, you're able to capture relationships in your image between non-local x_i and x_j, instead of merely local relationships through conv filters. For example, if you ignore x_i in your function and set f(x_i, x_j) W_ij * x_j, then this non-local block essentially approximates a fully connected layer. One thing that confuses me is that it seems like you're throwing away your relative positional data. Is the idea that this relative positional data is already captured through conv nets?

With millions of views published online every day, it can be difficult for Google to rank information correctly within its search engine. Speaking this week, Eric Schmidt, Chairman of Google's parent firm, Alphabet, explained that it is'very difficult' for the search algorithm to weed out the truth in a sea of opposing articles. Thankfully, Schmidt believes the problem should be easy to address by tweaking the algorithm. Speaking this week, Eric Schmidt, Chairman of Google's parent firm, Alphabet, explained that it is'very difficult' for the search algorithm to weed out the truth in a sea of opposing articles Inaccurate results are often down to "Google bombing" used by groups to be ranked highly. These include linking to a fake news site from several other sources and hiding text on a page that is invisible to humans but visible to the search engine's algorithms.

Apple took three years to develop its Siri-powered HomePod smart speaker. According to a new report, the HomePod was originally just a side project at Apple it wasn't really intended to be an Amazon Echo competitor. Sources told Bloomberg that the development of the Apple HomePod began in 2012. At the time, it was merely a side project, which is something that's fairly common within the company. Sources also said that development for the HomePod was canceled and resurrected "several times" because Apple couldn't figure out where it would fit within its current lineup of other products.

Research by Apple computer scientists on how self-driving cars can better spot cyclists and pedestrians while using fewer sensors has been posted online, in what appears to be the company's first publicly disclosed paper on autonomous vehicles. The paper by Yin Zhou and Oncel Tuzel, submitted on 17 November to independent online journal arXiv, is significant because Apple's famed corporate secrecy around future products has been seen as a drawback among artificial intelligence and machine learning researchers. The scientists proposed a new software approach called "VoxelNet" for helping computers detect three-dimensional objects. Academics are used to freely sharing their work with peers at other organisations. Yielding to that dynamic, Apple in July established the Apple Machine Learning Journal for its researchers.

Transformation is a huge component of the Fox show "Gotham," and a lot of its characters has changed - for the better or worse - from Seasons 1 to 4. One of these characters is Solomon Grundy (Drew Powell), who used to be known as the mobster, Butch Gilzean. He had one of the most drastic transformations in the show because he went from being semi-dead to undead. Executive producer Bryan Wynbrandt told Comic Book that his old self and new self will merge and form a completely new character. "I think what you're going to see is a story of duality and of this Frankenstein story when the monster becomes aware that he's a monster," Wynbrandt explained. "How does that person move forward? How can someone move forward knowing, remembering maybe pieces of what they were and now they're this for all intents and purposes a hideous thing?" "So I think what's great is there's really something interesting…that we dive into with Grundy/Butch and you'll see him sort of becoming almost a new version of the character," he continued.

We're one step closer to finding out what a live-action Pokémon film looks like. Legendary Pictures has already nabbed writers for its Detective Pikachu movie (in the form of Guardians of the Galaxy scribe Nicole Perlman and Gravity Falls penman Alex Hirsch), and now it's secured a lead as well. Rising talent Justice Smith -- best known for playing the protagonist on Baz Luhrmann's short-lived Netflix show The Get Down -- has been tapped to star in the film based on the Nintendo 3DS game, according to Variety. Rob Letterman (Monsters vs. Aliens, Goosebumps) is directing. It's unclear at this stage who Smith is playing in the flick -- we're guessing he won't don a yellow onesie for the role of the titular character (although, he could be voicing a CGI Pikachu). Before then, the 22-year-old is on track to gain a lot more exposure, thanks to the upcoming Jurassic World: Fallen Kingdom.

Here at WIRED, we like Sonos speakers. Throughout the last five years, we've reviewed everything from its small Play:1 speaker to its soundbars and recommended every one of them. But it's not cheap to turn your home into a Sonos-powered shrine to sound. Like Apple products, Sonos speakers are built to work with other Sonos speakers, and don't come cheap, starting at $200 for the least expensive, smallest model. But which ones should you buy? Read on for our recommendations.

Correlation matrices are omnipresent in multivariate data analysis. When the number $d$ of variables is large, the sample estimates of correlation matrices are typically noisy and conceal underlying dependence patterns. We consider the case when the variables can be grouped into $K$ clusters with exchangeable dependence; an assumption often made in applications in finance and econometrics. Under this partial exchangeability condition, the corresponding correlation matrix has a block structure and the number of unknown parameters is reduced from $d(d-1)/2$ to at most $K(K+1)/2$. We propose a robust algorithm based on Kendall's rank correlation to identify the clusters without assuming the knowledge of $K$ a priori or anything about the margins except continuity. The corresponding block-structured estimator performs considerably better than the sample Kendall rank correlation matrix when $K < d$. Even in the unstructured case $K = d$, though there is no gain asymptotically, the new estimator can be much more efficient in finite samples. When the data are elliptical, the results extend to linear correlation matrices and their inverses. The procedure is illustrated on financial stock returns.

Peter Cullen and the head of the famous character he voices, Optimus Prime. Peter Cullen and the head of the famous character he voices, Optimus Prime. For a generation of 1980s-reared cartoon-loving television viewers, Peter Cullen's voice as Optimus Prime in movies, TV shows, video games and even toys is instantly recognizable. He has continued to voice the character on and off throughout the years, and returned to Optimus earlier this year in Michael Bay's "Transformers: The Last Knight," which made more than $605 million worldwide this summer. In next year's "Bumblebee," the Transformers spin-off film that recently wrapped filming, Cullen's red, silver and blue Optimus Prime figures in the plot focused on the smaller but ever-popular yellow-and-black Autobot.

The Sonos One is the company's first voice-activated speaker, letting users control their music via Amazon's Alexa assistant. When we reviewed it back in October, editor Nathan Ingraham called it the best-sounding smart speaker you can buy. But when it launched, the Sonos One's voice control features didn't work with Spotify, though Sonos promised it this integration would arrive by December 21. It turns out it's here early; Alexa can now use Spotify to to play your favorite album, artist, playlist or song on the Sonos One. If you have Sonos speakers, but not the Sonos One smart speaker, this news is still relevant to you.