Manchester City already hold the record for most consecutive FA Cup semi-finals - eight between 2019 and 2026 - but can they become the first team to reach four finals in a row? That is their target when they play Championship side Southampton at Wembley on Saturday at 17:15 BST, live on BBC One and Radio 5 Live. It will be interesting to see whether City boss Pep Guardiola changes his team up much, said BBC Sport football expert Chris Sutton. They don't play again until they go to Everton on 4 May, so I don't think he will. But, whoever Pep picks, he will be looking for his team to connect again, the way they were playing before they played Burnley . As well as the FA Cup, Sutton is making predictions for all 380 Premier League games this season, against AI, BBC Sport readers and a variety of guests. For all of this weekend's games, he takes on Tottenham fan Alfie Watts, co-host of the Race Across the World: The Detour visual podcast.

We introduce Metric-Aware Principal Component Analysis (MAPCA), a unified framework for scale-invariant representation learning based on the generalised eigenproblem max Tr(W^T Sigma W) subject to W^T M W = I, where M is a symmetric positive definite metric matrix. The choice of M determines the representation geometry. The canonical beta-family M(beta) = Sigma^beta, beta in [0,1], provides continuous spectral bias control between standard PCA (beta=0) and output whitening (beta=1), with condition number kappa(beta) = (lambda_1/lambda_p)^(1-beta) decreasing monotonically to isotropy. The diagonal metric M = D = diag(Sigma) recovers Invariant PCA (IPCA), a method rooted in Frisch (1928) diagonal regression, as a distinct member of the broader framework. We prove that scale invariance holds if and only if the metric transforms as M_tilde = CMC under rescaling C, a condition satisfied exactly by IPCA but not by the general beta-family at intermediate values. Beyond its classical interpretation, MAPCA provides a geometric language that unifies several self-supervised learning objectives. Barlow Twins and ZCA whitening correspond to beta=1 (output whitening); VICReg's variance term corresponds to the diagonal metric. A key finding is that W-MSE, despite being described as a whitening-based method, corresponds to M = Sigma^{-1} (beta = -1), outside the spectral compression range entirely and in the opposite spectral direction to Barlow Twins. This distinction between input and output whitening is invisible at the level of loss functions and becomes precise only within the MAPCA framework.

The residents of Potters Bar are working to protect the "green belt" of farms, forests, and meadows that surround London from the endless demand for AI infrastructure. A short drive from London, the town of Potters Bar is separated from the village of South Mimms by 85 acres of rolling farmland segmented by a scribble of hedgerows. In one of the fields, a lone oak serves as a rest stop along a public footpath. Lately, the tree has become a site of protest, too. A poster tied to its trunk reads: "NO TO DATA CENTRE."

Police told to reinvestigate man's death after suspected blackmail on Grindr Police have been told to reopen their investigation into the death of Scott Gough, who allegedly took his own life after being targeted by a gang of men on the gay dating app Grindr. A police Professional Standards Department (PSD) report found failures in the investigation into the 56-year-old's death, which happened the day after a group of men turned up at his home demanding his car keys. His partner, Cameron Tewson accused the police of marking their own homework after his complaint of homophobia was not upheld. Hertfordshire Police, the investigating force, said it remains committed to ensuring members of the LGBTQ+ community feel supported when approaching the force. The report into the police's actions comes after a BBC investigation found multiple cases of suspected blackmail involving victims targeted on Grindr in Gough's local area, with at least four connected to the same gang, which remains at large.

The home secretary has announced a blueprint for reforming what she called the broken policing model in England and Wales. Shabana Mahmood confirmed the shake-up will create a new National Police Service (NPS) to fight the most complex cross-border crime and could also see the number of local forces in England and Wales cut by around two-thirds. She told the House of Commons she also intends to make better use of technology - including the largest-ever rollout of facial recognition. This government's reforms will ensure we have the right policing in the right place, Mahmood said. I set out reforms that are long overdue and define a new model for policing in this country, with local policing that protects our communities and national policing that protects us all.

A core objective of RoboCup is to promote and advance robotics and AI research through the challenges offered by its various leagues. The ultimate goal of the soccer competition is that, by 2050, a team of fully autonomous humanoid robots will defeat the most recent winner of the FIFA World Cup. To bring this vision closer to reality, the RoboCup Federation has announced several changes to the leagues . We spoke with Alessandra Rossi, a trustee who has been involved in the humanoid soccer league for many years, to learn more. Could you start by introducing yourself and tell us how you've been involved in RoboCup throughout the years, because you've been involved in so many aspects of the competition!

A visitor has called it a miracle no-one was hurt when a section of cliff collapsed on to a beach on Dorset's Jurassic Coast. Suzanne Sears, from Hemel Hempstead in Hertfordshire, was taking a walk near West Bay when she heard a deep cracking noise coming from the cliffs before the rockfall shortly after 16:00 GMT on Tuesday. The Maritime and Coastguard Agency confirmed a rescue team was sent to a report of a cliff fall at West Bay and no one was found to be in distress. A woman was forced to run to safety as the Dorset cliff collapsed on Saturday. The kayakers spotted the creature after hearing it exhaling loudly off Portland Castle beach.

Police accused of'homophobic assumptions' over victims of blackmail on Grindr Police failed to properly investigate allegations that a gang was blackmailing men on the gay dating app Grindr, the BBC can reveal. Our investigation has learned of five cases of suspected blackmail involving victims targeted on Grindr in one area, with at least four of them connected to the same gang, which remains at large. In one instance, a suspected victim killed himself 24 hours after a group of men turned up at his home demanding he hand over his new Range Rover. The Independent Office for Police Conduct (IOPC) watchdog has told Hertfordshire Police - the investigating force - to examine whether homophobic assumptions could have contributed to failures in the investigation. Hertfordshire Police said it was unable to discuss specific points about the case, which has now been reopened, but said it is committed to building and maintaining good working relationships with the LGBTQ+ communities.

Is tracking your adult children OK or should parents learn to let go? Is it caring or overbearing? Many parents are turning to their phones to keep tabs on their adult children - but is this OK (if they agree to it) or is it a sign of mums and dads struggling to let go? Dad-of-two Steven Medway, 53, has his whole family set up on a tracking app and couldn't understand why it was such a divisive subject among fellow parents. He said it became particularly useful when his daughter Martha moved 100 miles away from home for university.