Feature attributions are post-training analysis methods that assess how various input features of a machine learning model contribute to an output prediction. Their interpretation is straightforward when features act independently, but becomes less direct when the predictive model involves interactions such as multiplicative relationships or joint feature contributions. In this work, we propose a general theory of higher-order feature attribution, which we develop on the foundation of Integrated Gradients (IG). This work extends existing frameworks in the literature on explainable AI. When using IG as the method of feature attribution, we discover natural connections to statistics and topological signal processing. We provide several theoretical results that establish the theory, and we validate our theory on a few examples.

Monitoring greenhouse gas emissions and evaluating national inventories require efficient, scalable, and reliable inference methods. Top-down approaches, combined with recent advances in satellite observations, provide new opportunities to evaluate emissions at continental and global scales. However, transport models used in these methods remain a key source of uncertainty: they are computationally expensive to run at scale, and their uncertainty is difficult to characterise. Artificial intelligence offers a dual opportunity to accelerate transport simulations and to quantify their associated uncertainty. We present an ensemble-based pipeline for estimating atmospheric transport "footprints", greenhouse gas mole fraction measurements, and their uncertainties using a graph neural network emulator of a Lagrangian Particle Dispersion Model (LPDM). The approach is demonstrated with GOSAT (Greenhouse Gases Observing Satellite) observations for Brazil in 2016. The emulator achieved a ~1000x speed-up over the NAME LPDM, while reproducing large-scale footprint structures. Ensembles were calculated to quantify absolute and relative uncertainty, revealing spatial correlations with prediction error. The results show that ensemble spread highlights low-confidence spatial and temporal predictions for both atmospheric transport footprints and methane mole fractions. While demonstrated here for an LPDM emulator, the approach could be applied more generally to atmospheric transport models, supporting uncertainty-aware greenhouse gas inversion systems and improving the robustness of satellite-based emissions monitoring. With further development, ensemble-based emulators could also help explore systematic LPDM errors, offering a computationally efficient pathway towards a more comprehensive uncertainty budget in greenhouse gas flux estimates.

Dolly Parton's sister asks for prayers for music icon, 79, amid mystery health battle Bloodcurdling videos shows girl aged 12 subway surfing days before she and friend, 13, died during 3.10am stunt Trump's mass deportation effort removed staggering amount of migrants from US in first year of term: 'Just the beginning' Mom-of-two hospitalized, her son left suicidal and their dog dead... after a simple mistake turns $500K home into a death trap Popular actress shocks fans with'unrecognizable' appearance after suffering heartbreaking tragedy Selena Gomez's'disgusting' habit on her wedding day exposed by eagle-eyed fans despite star's efforts to hide it Charlie Kirk leaked text confirms he was livid about'bullying' Jewish donors: 'I'm leaving pro-Israel cause' She's accused of'murder-for-hire' plot against her famous TV star husband. Now there's a shock twist in the case... and she's forced to stare her demons in the face Man is arrested on terror charges over disturbing Halloween display of fake body bags with town official's titles Space agency breaks silence on'foreign' interstellar object soaring past Mars: 'A rare visitor' 'Disneyland of grocery stores' reveals items most hit by tariffs and the fan favorite it STOPPED buying from China Space agency breaks silence on'foreign' interstellar object soaring past Mars: 'A rare visitor' READ MORE: Mysterious interstellar visitor spotted above Mars appears as'massive cylindrical craft' The European Space Agency (ESA) has finally shared new details about the mysterious interstellar visitor days after its closest approach to Mars . The object, dubbed 3I/ATLAS, came within 18.6 million miles of the Red Planet on October 3, and while NASA quickly uploaded images captured by its Perseverance rover on the Martian surface, ESA had remained quiet until now . The ESA's ExoMars Trace Gas Orbiter (TGO) captured images of the object, appearing as a tiny, blurry white dot in a series of images. The object's icy nucleus and its surrounding halo of gas and dust, called a coma, could not be distinguished separately, but the faint glow was clearly visible against the blackness of space.

Dolly Parton's sister asks for prayers for music icon, 79, amid mystery health battle Charlie Kirk leaked text confirms he was livid about'bullying' Jewish donors: 'I'm leaving pro-Israel cause' Mom-of-two hospitalized, her son left suicidal and their dog dead... after a simple mistake turns $500K home into a death trap Trump's mass deportation effort removed staggering amount of migrants from US in first year of term: 'Just the beginning' Man is arrested on terror charges over disturbing Halloween display of fake body bags with town official's titles Selena Gomez's'disgusting' habit on her wedding day exposed by eagle-eyed fans despite star's efforts to hide it Popular actress shocks fans with'unrecognizable' appearance after suffering heartbreaking tragedy She's accused of'murder-for-hire' plot against her famous TV star husband. Now there's a shock twist in the case... and she's forced to stare her demons in the face Bloodcurdling videos shows girl aged 12 subway surfing days before she and friend, 13, died during 3.10am stunt'Kissing Trump's a**': President mocks Canada's obsequious PM as he begs for tariff relief Keith Urban's guitarist Maggie once vowed to'never' date a tour mate... as she's accused of charming Nicole Kidman's ex Hollywood's favorite muscle car primed for return as America's No.1 automaker files secret paperwork Do you have one of these gathering dust in your attic? It was only a couple of decades ago that homes and offices were filled with answering machines and BlackBerry phones. And although they've been obsolete for years, they're now among the retro gadgets that could make you a fortune. Brits are sitting on a hidden goldmine of old forgotten tech devices that may be gathering dust in the attic, according to a new report from Gumtree.

Charlie Kirk leaked text confirms he was livid about'bullying' Jewish donors: 'I'm leaving pro-Israel cause' White House insider who says WAR with Venezuela is inevitable... as Trump's lethal options are laid out I've seen the real Victoria Beckham... her actions gave me PTSD, she shunned me and even banned me from glancing in her direction. Jimmy Kimmel's audience boom comes crashing down as he loses 71% of viewers in one week'Kissing Trump's a**': President mocks Canada's obsequious PM as he begs for tariff relief World's most invasive predator terrorizing East Coast is delicious and should be eaten to stop its spread, experts say I've had enough of the arrogant and entitled fat brigade. Bloodcurdling videos shows girl aged 12 subway surfing days before she and friend, 13, died during 3.10am stunt Another blow for Prince Harry as African country cuts ties with his'disrespectful' charity Friends fear for new CBS News boss Bari Weiss, claiming her wife thinks she sold out... and her new job will'consume her life' Keith Urban's guitarist Maggie once vowed to'never' date a tour mate... as she's accused of charming Nicole Kidman's ex Hollywood's favorite muscle car primed for return as America's No.1 automaker files secret paperwork AMANDA PLATELL: I never thought I'd feel sorry for Harry. There's one thing he'd do anything to defend... and now Meghan's trampled all over it Ben Affleck's VERY familiar whispers to Jennifer Lopez on the red carpet revealed... as their romantic new era sends fans into overdrive Jimmy Kimmel continues anti-Trump rants and says he's more popular with Americans than the president Brits have been left in awe after spotting what is believed to be a'meteor' glowing through the night sky. Lucky stargazers in Northfields and West Ealing, west London, have reported seeing a blue-ish green blob race through the city's sky tonight.

Tesla unveiled more affordable versions of its best-selling Model Y SUV and its Model 3 sedan at $39,990 and $36,990, respectively, as the electric vehicle (EV) manufacturer seeks to reverse falling sales and waning market share amid rising competition. The EV maker announced its new models on Tuesday. Late last year, Musk said the vehicle would be priced below the "key threshold" of $30,000, including US EV tax credits. In the United States, prices effectively rose by $7,500 at the end of last month, when the EV tax credit ended. That helped goose quarterly sales to a record, but expectations are that they will slow down for the rest of the year, unless the affordable car comes to the rescue.

'Kissing Trump's a**': President mocks Canada's obsequious PM as he begs for tariff relief World's most invasive predator terrorizing East Coast is delicious and should be eaten to stop its spread, experts say Clash of the White House titans: Two of Trump's most powerful lieutenants go to WAR with each other - after vicious leak sent shockwaves AMANDA PLATELL: I never thought I'd feel sorry for Harry. There's one thing he'd do anything to defend... and now Meghan's trampled all over it White House insider who says WAR with Venezuela is inevitable... as Trump's lethal options are laid out Jimmy Kimmel's audience boom comes crashing down as he loses 71% of viewers in one week Lynn put her strange symptoms down to being a busy mum. AOC hit by shockingly crude sex insult by White House after she mocked'TINY' Stephen Miller Friends fear for new CBS News boss Bari Weiss, claiming her wife thinks she sold out... and her new job will'consume her life' Biden ordered CIA cover-up of his'corrupt' business ties to Ukraine, astonishing secret files show We've lost FOURTEEN stone on weight-loss jabs... and it's changed our lives in ways you'd NEVER expect. Jerry Jones slapped with fine by NFL for making rude gesture to fans... but Cowboys owner gives baffling excuse And a humiliating lifeline: Backroom secrets of Taylor Swift and Blake Lively... after hit new song Inside the rise of'kidfluencers' and the hidden toll of turning childhood into million-dollar content A US Air Force jet designed to collect intelligence on enemy radar systems was spotted making circles over Russia, following rising tensions with Moscow . Flight tracking data showed the RC-135U'Combat Sent' taking off from England early Tuesday, flying over the Baltic states and looping around Kaliningrad, the Russian exclave between Poland and Lithuania, before returning to the UK.

AI toys are all the rage in China--and now they're appearing on shelves in the US too Competition is heating up, with Mattel and OpenAI expected to launch a product for kids this year. Kids have always played with and talked to stuffed animals. But now their toys can talk back, thanks to a wave of companies that are fitting children's playthings with chatbots and voice assistants. It's a trend that has particularly taken off in China: A recent report by the Shenzhen Toy Industry Association and JD.com predicts that the sector will surpass ¥100 billion ($14 billion) by 2030, growing faster than almost any other branch of consumer AI. According to the Chinese corporation registration database Qichamao, there are over 1,500 AI toy companies operating in China as of October 2025. One of the latest entrants to the market is a toy called BubblePal, a device the size of a Ping-Pong ball that clips onto a child's favorite stuffed animal and makes it "talk."

AOC hit by shockingly crude sex insult by White House after she mocked'TINY' Stephen Miller Biden ordered CIA cover-up of his'corrupt' business ties to Ukraine, astonishing secret files show NYC girls aged 12 and 13 meet tragic end after going subway surfing across Williamsburg Bridge at 3.10am ERIC TRUMP: The darkest day in my dad's marriage to Melania... before the ugly truth was exposed More girls are starting their periods younger than ever before - scientists think they've finally found what's causing it Taylor Swift reveals truth behind raunchy song about Travis Kelce's manhood Meghan is accused of'giggling as model stumbles on the catwalk': More Paris Fashion Week disasters emerge, including awkward moment with Kristin Scott Thomas The TRUTH to the doting mother who slaughtered her children and husband told by those she'd been quietly tormenting for years The troubled background of delivery man stabbed by Mark Sanchez... as he launches million-dollar lawsuit and sparks civil war at Fox Revealed: Which slimming jab REALLY works best. The doctors' ultimate expert guide on which to pick, how to save money, beat every side effect... and what you need to know about the'golden dose' I haven't heard that name in so long' Ominous warning for humanity as birds suddenly adopt'unsettling' behavior And a humiliating lifeline: Backroom secrets of Taylor Swift and Blake Lively... after hit new song Bottled water contains dangerous levels of microplastics that lodge in vital organs and raise cancer risk', scientists warn Sea level rise could plunge 100 MILLION buildings underwater, warn scientists - so, is your home at risk? Rising sea levels could plunge more than 100 million buildings underwater by 2100, scientists have warned. The experts in Canada estimated how many buildings in Africa, Southeast Asia and Central and South America would be flooded by different sea level changes. Their assessment found that sea level rises of just 1.6 feet (0.5 metres) would flood three million buildings in the global south alone.

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