We address the problem of accurate, training-free guidance for conditional generation in trained diffusion models. Existing methods typically rely on point-estimates to approximate the posterior score, often resulting in biased approximations that fail to capture multimodality inherent to the reverse process of diffusion models. We propose a sequential Monte Carlo (SMC) framework that constructs an unbiased estimator of $p_θ(y|x_t)$ by integrating over the full denoising distribution via Monte Carlo approximation. To ensure computational tractability, we incorporate variance-reduction schemes based on Multi-Level Monte Carlo (MLMC). Our approach achieves new state-of-the-art results for training-free guidance on CIFAR-10 class-conditional generation, achieving $95.6\%$ accuracy with $3\times$ lower cost-per-success than baselines. On ImageNet, our algorithm achieves $1.5\times$ cost-per-success advantage over existing methods.

Randomized subspace methods reduce per-iteration cost; however, in nonconvex optimization, most analyses are expectation-based, and high-probability bounds remain scarce even under sub-Gaussian noise. We first prove that randomized subspace SGD (RS-SGD) admits a high-probability convergence bound under sub-Gaussian noise, achieving the same order of oracle complexity as prior in-expectation results. Motivated by the prevalence of heavy-tailed gradients in modern machine learning, we then propose randomized subspace normalized SGD (RS-NSGD), which integrates direction normalization into subspace updates. Assuming the noise has bounded $p$-th moments, we establish both in-expectation and high-probability convergence guarantees, and show that RS-NSGD can achieve better oracle complexity than full-dimensional normalized SGD.

People who are screened for breast cancer by AI-supported radiologists are less likely to develop aggressive cancers before their next screening round than those who are screened by radiologists alone, raising hopes that AI-assisted screening could save lives. "This is the first randomised controlled trial on the use of AI in mammography screening," says Kristina Lång at Lund University in Sweden. The AI-supported approach involves using the software - which has been trained on more than 200,000 mammography scans from 10 countries - to rank the likelihood of cancer being present in mammograms on a scale of 1 to 10, based on visual patterns in the scans. The scans receiving a score of 1 to 9 are then assessed by one experienced radiologist, while scans receiving a score of 10 - indicating cancer is most likely to be present - are assessed by two experienced radiologists. An earlier study found that this approach could detect 29 per cent more cancers than standard screening, where each mammogram is assessed by two radiologists, without increasing the rate of false detections - where a growth is flagged but follow-up tests reveal it isn't actually there or wouldn't go on to cause problems.

The United States National Highway Traffic Safety Administration (NHTSA) said it is opening an investigation after a Waymo self-driving vehicle struck a child near an elementary school in Santa Monica, California, last week, causing minor injuries and renewing concerns about the safety of robotaxis. The car safety agency said on Thursday that the child ran across the street on January 23 from behind a double-parked SUV towards the school and was struck by the Alphabet-unit Waymo autonomous vehicle during normal school drop-off hours. The agency said there were other children, a crossing guard, and several double-parked vehicles in the vicinity. The US Senate Commerce Committee had already scheduled a hearing on self-driving cars for February 4, which will include Waymo Chief Safety Officer Mauricio Pena. The National Transportation Safety Board (NTSB) also said it will investigate the incident.

We'll link all the stories we spoke about today in the show notes. Adriana Tapia produced this episode, Amar Lal at Macro Sound mixed this episode, Matt Giles and Daniel Roman fact-checked this episode, Mark Leyda was our San Francisco studio engineer, Kate Osborn is our executive producer, and Katie Drummond is WIRED's global editorial director.

Microsoft stock has slumped 12 percent as part of a software industry sell-off, stoking fears of whether hefty investments in artificial intelligence will pay off across the sector. The Redmond, Washington-based tech giant is on track Thursday to finish at its worst day since March 2020 and has seen approximately $400bn in valuation wiped out. Capital expenditures grew by 66 percent in the second quarter compared with the same period the year before, reaching a record $37.5bn for the quarter. Meanwhile, Microsoft predicted Azure growth to stay stable in the period from January to March at 37 percent to 38 percent, after slowing in the last three months of 2025, partially due to AI chip capacity constraints. "[Wall Street] wanted to see less cap-ex spending and faster cloud/AI monetisation and coming out of the gates, it's the opposite. We have said this is a multi-year journey, and Redmond needs to focus on its data center buildout with more customers heading down the AI path. It's a balancing act with 2026 the inflection year for AI and MSFT [Microsoft]," Dan Ives, analyst at Wedbush Securities, said in a note provided to Al Jazeera.

US President Donald Trump says Russia's Vladimir Putin has agreed not to attack Ukraine's capital, Kyiv, and other cities and towns for a week due to extraordinary cold weather. Russia has not confirmed any such agreement, but Ukraine's President Volodymyr Zelensky welcomed Trump's announcement and said he expected Russia to keep its promise. Trump did not specify when the pause would begin, but temperatures in the Ukrainian capital are due to plummet from Thursday night and reach -24C (-11F) in the next few days. Russia has intensified attacks on Ukraine's energy infrastructure during the bitter winter, as it has during cold periods since the full-scale invasion began in 2022. Speaking at a televised cabinet meeting in Washington DC, the US president said: I personally asked President Putin not to fire into Kyiv and the various towns for a week, and he agreed to do that.

The noninvasive method is already monitoring over 100 Alaskan brown bears. Breakthroughs, discoveries, and DIY tips sent six days a week. Instead, the desire to survive generally wins out over lingering to admire the predator's sizable claws or snout shape. Knowing this, you'd be forgiven for having difficulty differentiating one bear from another. For many ecologists, monitoring individual animals over long periods of time--even years--is crucial to conservation efforts.

Tottenham may have coasted through to the Champions League last 16, but their Premier League form remains a problem for boss Thomas Frank. I was at their draw with Burnley last week and there are a lot of angry Spurs fans out there, said BBC Sport football expert Chris Sutton. Their domestic results are such a contrast to their record in Europe, and it could be another difficult afternoon for Frank when they face Manchester City on Sunday. Sutton is making predictions for all 380 Premier League games this season, against AI, BBC Sport readers and a variety of guests. His guest for week 24 is boxer Francesca Hennessy, who supports Chelsea . Hennessy faces Ellie Bouttell in a WBC title eliminator on Saturday, live on BBC Two from 20:00 GMT.

Meta wowed Wall Street with improvements in ad targeting fueled by AI alongside huge investment. Big tech earnings so far this week have sent a clear warning: investors are willing to overlook soaring spending on artificial intelligence if it fuels strong growth, but are quick to punish companies that fall short. The contrast was clear in Thursday's stock market reaction to earnings from Microsoft and Meta, highlighting how dramatically the stakes have changed since the launch of ChatGPT started the AI boom more than three years ago. Shares of the Instagram parent surged more than 9% on strong sales, while those of Microsoft slumped 10% after its cloud business failed to impress. "The market appears to be questioning whether these massive capital expenditure hikes will generate sufficient returns," said Jesse Cohen, senior analyst at Investing.com.