We consider MaxCut-type semidefinite programs (SDP) which admit a low rank solution. To numerically leverage the low rank hypothesis, a standard algorithmic approach is the Burer-Monteiro factorization, which allows to significantly reduce the dimensionality of the problem at the cost of its convexity. We give a sharp condition on the conditioning of the Laplacian matrix associated with the SDP under which any second-order critical point of the non-convex problem is a global minimizer. By applying our theorem, we improve on recent results about the correctness of the Burer-Monteiro approach on $\mathbb{Z}_2$-synchronization problems.

The concentration of power in a few digital technology companies has become a subject of increasing interest in both academic and non-academic discussions. One of the most noteworthy contributions to the debate is Lina Khan's Amazon's Antitrust Paradox. In this work, Khan contends that Amazon has systematically exerted its dominance in online retail to eliminate competitors and subsequently charge above-market prices. This work contributed to Khan's appointment as the chair of the US Federal Trade Commission (FTC), one of the most influential antitrust organisations. Today, several ongoing antitrust lawsuits in the US and Europe involve major technology companies like Apple, Google/Alphabet, and Facebook/Meta. In the realm of generative AI, we are once again witnessing the same companies taking the lead in technological advancements, leaving little room for others to compete. This article examines the market dominance of these corporations in the technology stack behind generative AI from an antitrust law perspective.

Uber has been ordered to reinstate five British drivers who were struck off from its ride-hailing app by robot technology. The five drivers, backed by the App Drivers & Couriers Union (ADCU) and the campaign group Worker Info Exchange, argued that they had been wrongly accused of fraudulent activity based on mistaken information from Uber's technology, and that the company had failed to provide the drivers with proper evidence to support the allegations. In a judgment published on Wednesday, the district court of Amsterdam – where Uber's European headquarters is located – said the ride-hailing app should reinstate the five British drivers, and one Dutch driver, because the decisions had been "based solely on automated processing, including profiling". The judgment was made by default, as Uber did not attend the hearing; the company said it had been unaware of the legal action until last week. The court said Uber should pay a penalty of €5,000 (£4,300) for each day that it had failed to comply with the order to reinstate the drivers, which was made in February, up to a maximum of €50,000, as well as €100,474 in damages.

As a grad student working on artificial intelligence, Mohamed Abdalla could probably walk into a number of well-paid industry jobs. Instead, he wants to draw attention to how Big Tech's big bucks may be warping the perspective of his field. Abdalla, who is finishing his PhD at the University of Toronto, has coauthored a paper highlighting the number of top AI researchers--including those who study the ethical challenges raised by the technology--who receive funding from tech companies. That can be a particular problem, he says, when corporate AI systems raise ethical issues, such as algorithmic bias, military use, or questions about the fairness and accuracy of face recognition programs. Abdalla found that more than half of tenure-track AI faculty at four prominent universities who disclose their funding sources have received some sort of backing from Big Tech.