The completion of low rank matrices from few entries is a task with many practical applications. We consider here two aspects of this problem: detectability, i.e. the ability to estimate the rank r reliably from the fewest possible random entries, and performance in achieving small reconstruction error. We propose a spectral algorithm for these two tasks called MaCBetH (for Matrix Completion with the Bethe Hessian). The rank is estimated as the number of negative eigenvalues of the Bethe Hessian matrix, and the corresponding eigenvectors are used as initial condition for the minimization of the discrepancy between the estimated matrix and the revealed entries. We analyze the performance in a random matrix setting using results from the statistical mechanics of the Hopfield neural network, and show in particular that MaCBetH efficiently detects the rank r of a large n m matrix from C (r)r nm entries, where C ( r) is a constant close to 1. We also evaluate the corresponding root-mean-square error empirically and show that MaCBetH compares favorably to other existing approaches. Matrix completion is the task of inferring the missing entries of a matrix given a subset of known entries. Typically, this is possible because the matrix to be completed has (at least approximately) low rank r . This problem has witnessed a burst of activity, see e.g.

Last week, the Guardian spoke to the team behind Lili, a video game retelling of Macbeth, shown at the Cannes film festival. The headline quote from the piece was "Shakespeare would be writing for games today", which I have heard many times, and does make a lot of sense. Shakespeare worked in the Elizabethan theatre, a period in which plays were considered popularist entertainment hardly worthy of analysis or preservation – just like video games today! The authorities were also concerned about the lewd and violent nature of plays and the effect they may have on the impressionable masses – ditto! But if we agree that a 21st-century Shakespeare would be making games, what sort would he be making?

The Cannes film festival isn't typically associated with video games, but this year it's playing host to an unusual collaboration. Lili is a co-production between the New York-based game studio iNK Stories (creator of 1979 Revolution: Black Friday, about a photojournalist in Iran) and the Royal Shakespeare Company, and it's been turning heads with its eye-catching translocation of Macbeth to modern-day Iran. "It's been such an incredible coup to have it as the first video game experience at Cannes," says iNK Stories co-founder Vassiliki Khonsari. "People have gone in saying, I'm not familiar playing games, so I may just try it out for five minutes. The Cannes festival's Immersive Competition began in 2024, although the lineup doesn't usually feature traditional video games. "VR films and projection mapping is the thrust of it," says iNK Stories' other co-founder, Vassiliki's husband Navid Khonsari. But Lili weaves live-action footage with video game mechanics in a similar way to a game such as Telling Lies or Immortality. Its lead, Zar Amir Ebrahimi, won best actress at Cannes three years ago. Lili focuses on the story of Lady Macbeth, here cast as the ambitious wife of an upwardly mobile officer in the Basij (a paramilitary volunteer militia within the Islamic Revolutionary Guard in Iran). As in the play, she plots a murder to secure her husband's rise. "I think that the narrative of Lady Macbeth is that she's manipulative, and that's exactly what got us interested," says Navid. "The social limitations based on her gender forced her to try to attain whatever leadership role she can," he continues. "If she was a man, she would have been one of the greatest kings that country would have ever experienced, but because she was a woman she had to work within the structure that was there for her.

The completion of low rank matrices from few entries is a task with many practical applications. We consider here two aspects of this problem: detectability, i.e. the ability to estimate the rank r reliably from the fewest possible random entries, and performance in achieving small reconstruction error. We propose a spectral algorithm for these two tasks called MaCBetH (for Matrix Completion with the Bethe Hessian). The rank is estimated as the number of negative eigenvalues of the Bethe Hessian matrix, and the corresponding eigenvectors are used as initial condition for the minimization of the discrepancy between the estimated matrix and the revealed entries. We analyze the performance in a random matrix setting using results from the statistical mechanics of the Hopfield neural network, and show in particular that MaCBetH efficiently detects the rank r of a large n m matrix from C(r)r nm entries, where C(r) is a constant close to 1. We also evaluate the corresponding root-mean-square error empirically and show that MaCBetH compares favorably to other existing approaches. Matrix completion is the task of inferring the missing entries of a matrix given a subset of known entries. Typically, this is possible because the matrix to be completed has (at least approximately) low rank r. This problem has witnessed a burst of activity, see e.g.

Computer users today are demanding greater performance from systems that understand and respond intelligently to human language as input. In the past, researchers proposed and built conceptual analysis systems that attempted to understand language in depth by decomposing a text into structures representing complex combinations of primitive acts, events, and state changes in the world the way people conceive them. However, these systems have traditionally been time-consuming and costly to build and maintain by hand. This paper presents two studies of crowdsourcing a parallel corpus to build conceptual analysis systems through machine learning. In the first study, we found that crowdworkers can view simple English sentences built around specific action words, and build conceptual structures that represent decompositions of the meaning of that action word into simple and complex combinations of conceptual primitives. The conceptual structures created by crowdworkers largely agree with a set of gold standard conceptual structures built by experts, but are often missing parts of the gold standard conceptualization. In the second study, we developed and tested a novel method for improving the corpus through a subsequent round of crowdsourcing; In this "refinement" step, we presented only conceptual structures to a second set of crowdworkers, and found that when crowdworkers could identify the action word in the original sentence based only on the conceptual structure, the conceptual structure was a stronger match to the gold standard structure for that sentence. We also calculated a statistically significant correlation between the number of crowdworkers who identified the original action word for a conceptual structure, and the degree of matching between the conceptual structure and a gold standard conceptual structure. This indicates that crowdsourcing may be used not only to generate the conceptual structures, but also to select only those of the highest quality for a parallel corpus linking them to natural language.

The first time I watched Gargoyles, a Disney cartoon about stone-winged creatures that come alive at night to fight evil, I was enraptured. This was something so dramatically different from anything I'd seen to that point. Thanks to Disney Plus, I had a chance to rewatch the show. My initial response 25 years later: How the hell did this show even get made? That isn't meant as a slight.

Founded in 1990, the Martin Luther King Jr. (MLK) Visiting Professors and Scholars Program honors the life and legacy of Martin Luther King by increasing the presence of, and recognizing the contributions of, underrepresented minority scholars at MIT. MLK Visiting Professors and Scholars enhance their scholarship through intellectual engagement with the MIT community and enrich the cultural, academic, and professional experience of students. Six scholars are visiting MIT this academic year as part of the program. Kasso Okoudjou is returning for a second year as an MLK Visiting Professor in the Department of Mathematics. Originally from Benin, he moved to the United States in 1998 and earned a PhD in mathematics from Georgia Tech. Okoudjou joins MIT from the University of Maryland College Park, where he is a professor.

What is it exactly that makes humans so smart? In his seminal 1950 paper, "Computer Machinery and Intelligence," Alan Turing argued human intelligence was the result of complex symbolic reasoning. Philosopher Marvin Minsky, cofounder of the artificial intelligence lab at the Massachusetts Institute of Technology, also maintained that reasoning--the ability to think in a multiplicity of ways that are hierarchical--was what made humans human. Patrick Henry Winston begged to differ. "I think Turing and Minsky were wrong," he told me in 2017. "We forgive them because they were smart and mathematicians, but like most mathematicians, they thought reasoning is the key, not the byproduct." Winston, a professor of computer science at MIT, and a former director of its AI lab, was convinced the key to human intelligence was storytelling. "My belief is the distinguishing characteristic of humanity is this keystone ability to have descriptions with which we construct stories. I think stories are what make us different from chimpanzees and Neanderthals. And if story-understanding is really where it's at, we can't understand our intelligence until we understand that aspect of it."

There is a head-scratching moment at the beginning of the popular farming simulator video game Stardew Valley, where you wonder, "What now?" Newly installed on your late grandfather's dilapidated farm, you're given no instructions on how to turn the business's fortunes or what to explore in the neighbouring town. This conundrum fills Felix Barrett with glee. As the founder and creative director of British theatre company Punchdrunk, he has spent 19 years turning warehouses into vast worlds that audiences must learn to explore alone. From Woyzeck to Faust, Punchdrunk transforms classic plays into sprawling, interactive experiences. The idea is this: traditional theatre shows are passive affairs where you watch a distant stage from the comfort of a chair - but a Punchdrunk show is active, mysterious, and places you inside a fiction you can touch, smell, and even taste.

Patrick Winston's computer is learning about revenge, ambition, and murder. It knows that victory can make you happy. But it also knows you can't be happy if you're dead. The computer had to learn these things in order to read "Macbeth" -- or, rather, an extremely truncated version of Shakespeare's blood-soaked Scottish tragedy. At just 37 sentences, the rough summary reduces the Bard's immortal poetics to such clunkers as, "Witches had visions and danced" and "Lady Macbeth has bad dreams."