In Algorithm 1 we present the memorizing and recalling procedures of the single-layer tPC.Algorithm 1 Memorizing and recalling with single-layer tPC Here we present the proof for Property 1 in the main text, that the single-layer tPC can be viewed as a "whitened" version of the AHN. When applied to the data sequence, it whitens the data such that (i.e., Eq.16 in the main text): These observations are consistent with our numerical results shown in Figure 1. MCAHN has a much larger MSE than that of the tPC because of the entirely wrong recalls. In Figure 1 we also present the online recall results of the models in MovingMNIST, CIFAR10 and UCF101. In Fig 4 we show a natural example of aliased sequences where a movie of a human doing push-ups is memorized and recalled by the model.

We introduce the Cambridge Law Corpus (CLC), a corpus for legal AI research.

As prediction market platforms like Polymarket and Kalshi battle regulators in court, Senate Democrats are urging the CFTC to avoid weighing in, escalating a broader fight over the burgeoning industry. Senator Adam Schiff, a Democrat from California, is leading the group of lawmakers urging the CFTC to stay out of state prediction market lawsuits. A group of 23 Democratic US senators sent a letter Friday to the top federal regulator overseeing prediction markets, urging the agency to avoid weighing in on pending court cases over the legality of offerings on the platforms tied to "sports, war, and other prohibited events." Prediction markets, which sell contracts tied to the outcome of real-world developments, have exploded in popularity over the past year, attracting an increasingly mainstream fanbase eager to wager on everything from geopolitical conflicts to fashion choices to the Super Bowl. As they expanded, the platforms have become a magnet for ethical and legal controversies.

AI researcher says'world is in peril' and quits to study poetry An AI safety researcher has quit US firm Anthropic with a cryptic warning that the world is in peril. In his resignation letter shared on X, Mrinank Sharma told the firm he was leaving amid concerns about AI, bioweapons and the state of the wider world. He said he would instead look to pursue writing and studying poetry, and move back to the UK to become invisible. It comes in the same week that a OpenAI researcher said she had resigned, sharing concerns about the ChatGPT maker's decision to deploy adverts in its chatbot . Anthropic, best known for its Claude chatbot, had released a series of commercials aimed at OpenAI, criticising the company's move to include adverts for some users.

A court filing in a trademark lawsuit reveals OpenAI won't use the name "io" for its AI hardware device, which isn't expected to ship until 2027. OpenAI CEO Sam Altman speaks to members of the press in Sun Valley, Idaho. OpenAI will not use the name " io " for its forthcoming line of AI hardware devices, according to a Monday court filing. The motion is part of a trademark infringement lawsuit filed last year by audio device startup iyO, which sued OpenAI after it acquired famed Apple designer Jony Ive's startup io. Peter Welinder, OpenAI's vice president and general manager, said in the filing that OpenAI had reviewed its product-naming strategy and "decided not to use the name'io' (or'IYO,' or any capitalization of either) in connection with the naming, advertising, marketing, or sale of any artificial intelligence-enabled hardware products."

Landmark cases on social media's impact on children begin this week in US Two lawsuits accusing the world's largest social media companies of harming children begin this week, marking the first legal efforts to hold companies like Meta responsible for the effects their products have on young users. Opening arguments began today in a case brought by New Mexico's attorney general's office, which alleges that Meta failed to protect children from sexually explicit material. A separate case in Los Angeles, which accuses Meta and the Google-owned YouTube of deliberately designing their platforms to be addictive for children, is set to begin later this week. The New Mexico and California lawsuits are the first of a wave of 40 lawsuits filed by state attorneys general around the US against Meta, specifically, that allege that the social media giant is harming the mental health of young Americans. In the opening argument in the New Mexico case, which was first filed in 2023, prosecutors told jurors on Monday that Meta - Facebook and Instagram's parent company - had failed to disclose its platforms' harmful effects on kids.

Apple could unveil Gemini-powered Siri in Feb. Plaintiffs claimed they saw ads based on conversations Google Assistant shouldn't have heard. Google has agreed to a $68 million settlement regarding claims that its voice assistant inappropriately spied on smartphone users. Plaintiffs claimed that the company's Google Assistant platform began listening to them after it misheard conversations that sounded like its wake words. The suit argued that private information that Google Assistant shouldn't have heard was then used to deliver those individuals targeted ads. The preliminary class action settlement was filed on Friday and now awaits approval from U.S. District Judge Beth Labson Freeman.

Google has agreed to pay $68m (£51m) to settle a lawsuit claiming it secretly listened to people's private conversations through their phones. Users accused Google Assistant - a virtual assistant present on many Android devices - of recording private conversations after it was inadvertently triggered on their devices. They claimed the recordings were then shared with advertisers in order to send them targeted advertising. The BBC has contacted Google for comment. But in a filing seeking to settle the case, it denied wrongdoing and said it was seeking to avoid litigation.