It was hard to miss 33-year-old model and writer Abena Christine Jon'el's appearance at a recent major fashion show in Ghana. Walking the runway with her prosthetic leg wrapped in a colourful African print her appearance made a big impact. The Ghanaian-American was hoping to make a statement about the visibility of people with disabilities, building on years of work in the US and here in Ghana of speaking out on the issue. At two years old, Abena's life became defined by a challenge most adults would struggle to face. A large tumour had appeared on her right calf, the first sign of a rare, aggressive soft-tissue cancer, rhabdomyosarcoma.

Devastating impact of Minneapolis shooting on Trump is worse than expected: Poll reveals America's crushing verdict... and what he must do next Bodies are STILL in wreckage of private jet that crashed in Maine on Sunday, killing six including powerful lawyer's attorney wife School principal accused of shoplifting from Walmart using'stacking' method at self-checkout Melania's shock role in Trump's showdown with Kristi Noem revealed: MARK HALPERIN's fly-on-wall account of Oval Office meeting... and who is ACTUALLY taking the fall for Alex Pretti shooting I was barely eating but kept gaining weight. Then I discovered the'taboo' cancer doctors NEVER talk about. Now sex will never be the same... don't ignore these signs Harper Beckham, 14, puts on a stylish display in a fluffy coat and vintage Chanel bag in Paris with her family - after Nicola Peltz's heartbreaking comments about sister-in-law Devastating truth about Blind Side actor Quinton Aaron: More to this'than everyone is letting on', friends reveal... as co-star Sandra Bullock'monitors' situation The wild truth about my influencer sons, their psycho dad and how lawsuits nearly left them bankrupt - by Jake and Logan Paul's MOM Trump knifes'little Napoleon' Border Patrol commander over Minnesota mayhem as he declares: 'We'll de-escalate' Lost tomb of the mysterious'cloud people' unearthed after 1,400 years in'discovery of the decade' READ MORE: How AI cops will be used to patrol Britain's streets Scientists have uncovered four entirely new personality types that all ChatGPT users fall into. According to experts from the University of Oxford and the Berlin University Alliance, every chatbot user has a unique personality type, each with their own motivations. Some truly tech-savvy users fall into the category of ' AI enthusiasts'.

Winners will emerge from the Artificial Intelligence (AI) boom, but there will be carnage along the way, the boss of a US tech giant has warned. Chuck Robbins, chairman and chief executive of Cisco Systems, told the BBC the technology will be bigger than the internet, but the current market is probably a bubble and some companies won't make it. Cisco, one of the world's leading technology companies, is behind some of the critical IT infrastructure enabling day-to-day use of AI. Robbins said some jobs will be changed, or even eliminated, by AI, particularly in areas like customer services where companies will need fewer people, but urged workers to embrace, not fear, the technology. His comments follow a series of warnings over the recent surge in investment in AI, with some claiming the sector amounts to a bubble set to burst, rocking markets and bankrupting companies.

Traditional data-driven methods, effective for deterministic systems or stochastic differential equations (SDEs) with Gaussian noise, fail to handle the discontinuous sample paths and heavy-tailed fluctuations characteristic of Lévy processes, particularly when the noise is state-dependent. To bridge this gap, we establish nonlocal Kramers-Moyal formulas, rigorously generalizing the classical Kramers-Moyal relations to SDEs with multiplicative Lévy noise. These formulas provide a direct link between short-time transition probability densities (or sample path statistics) and the underlying SDE coefficients: the drift vector, diffusion matrix, Lévy jump measure kernel, and Lévy noise intensity functions. Leveraging these theoretical foundations, we develop novel data-driven algorithms capable of simultaneously identifying all governing components from data and establish convergence results and error analysis for the algorithms. We validate the framework through extensive numerical experiments on prototypical systems. This work provides a principled and practical toolbox for discovering interpretable SDE models governing complex systems influenced by discontinuous, heavy-tailed, state-dependent fluctuations, with broad applicability in climate science, neuroscience, epidemiology, finance, and biological physics.

We propose an (offline) multi-dimensional distributional reinforcement learning framework (KE-DRL) that leverages Hilbert space mappings to estimate the kernel mean embedding of the multi-dimensional value distribution under a proposed target policy. In our setting, the state-action variables are multi-dimensional and continuous. By mapping probability measures into a reproducing kernel Hilbert space via kernel mean embeddings, our method replaces Wasserstein metrics with an integral probability metric. This enables efficient estimation in multi-dimensional state-action spaces and reward settings, where direct computation of Wasserstein distances is computationally challenging. Theoretically, we establish contraction properties of the distributional Bellman operator under our proposed metric involving the Matern family of kernels and provide uniform convergence guarantees. Simulations and empirical results demonstrate robust off-policy evaluation and recovery of the kernel mean embedding under mild assumptions, namely, Lipschitz continuity and boundedness of the kernels, highlighting the potential of embedding-based approaches in complex real-world decision-making scenarios and risk evaluation.

The deployment of Artificial Intelligence in high-risk domains, such as finance and healthcare, necessitates models that are both fair and transparent. While regulatory frameworks, including the EU's AI Act, mandate bias mitigation, they are deliberately vague about the definition of bias. In line with existing research, we argue that true fairness requires addressing bias at the intersections of protected groups. We propose a unified framework that leverages Mixed-Integer Optimization (MIO) to train intersectionally fair and intrinsically interpretable classifiers. We prove the equivalence of two measures of intersectional fairness (MSD and SPSF) in detecting the most unfair subgroup and empirically demonstrate that our MIO-based algorithm improves performance in finding bias. We train high-performing, interpretable classifiers that bound intersectional bias below an acceptable threshold, offering a robust solution for regulated industries and beyond.

We propose a framework to construct practical kernel-based two-sample tests from the family of $f$-divergences. The test statistic is computed from the witness function of a regularized variational representation of the divergence, which we estimate using kernel methods. The proposed test is adaptive over hyperparameters such as the kernel bandwidth and the regularization parameter. We provide theoretical guarantees for statistical test power across our family of $f$-divergence estimates. While our test covers a variety of $f$-divergences, we bring particular focus to the Hockey-Stick divergence, motivated by its applications to differential privacy auditing and machine unlearning evaluation. For two-sample testing, experiments demonstrate that different $f$-divergences are sensitive to different localized differences, illustrating the importance of leveraging diverse statistics. For machine unlearning, we propose a relative test that distinguishes true unlearning failures from safe distributional variations.

We analyze Muon as originally proposed and used in practice -- using the momentum orthogonalization with a few Newton-Schulz steps. The prior theoretical results replace this key step in Muon with an exact SVD-based polar factor. We prove that Muon with Newton-Schulz converges to a stationary point at the same rate as the SVD-polar idealization, up to a constant factor for a given number $q$ of Newton-Schulz steps. We further analyze this constant factor and prove that it converges to 1 doubly exponentially in $q$ and improves with the degree of the polynomial used in Newton-Schulz for approximating the orthogonalization direction. We also prove that Muon removes the typical square-root-of-rank loss compared to its vector-based counterpart, SGD with momentum. Our results explain why Muon with a few low-degree Newton-Schulz steps matches exact-polar (SVD) behavior at a much faster wall-clock time and explain how much momentum matrix orthogonalization via Newton-Schulz benefits over the vector-based optimizer. Overall, our theory justifies the practical Newton-Schulz design of Muon, narrowing its practice-theory gap.

We study how to fine-tune LLMs using user-edit deployment data consisting of a set of context, an agent's response, and user edits. This deployment data is naturally generated by users in applications such as LLMs-based writing assistants and coding agents. The _natural_ origin of user edits makes it a desired source for adapting and personalizing LLMs. In this setup, there emerges a unification of various feedback types namely preferences, supervised labels, and cost that are typically studied separately in the literature. In this paper, we initiate the theoretical investigation of learning from user edits. We first derive bounds for learning algorithms that learn from each of these feedback types. We prove that these algorithms have different trade-offs depending upon the user, data distribution, and model class. We then propose a simple ensembling procedure to jointly learn from these feedback types. On two domains adapted from Gao et al. 2024, we show our ensembling procedure outperforms these methods that learn from individual feedback. Further, we show that our proposed procedure can robustly adapt to different user-edit distributions at test time.

Recommender systems have become ubiquitous across a wide range of fields, such as ecommerce, media consumption (including movies, books, music, news, etc.), social networks, finance, and many others, due to their effectiveness in identifying relevant items or content among numerous choices [1, 2]. Traditionally, recommender systems, largely based on collaborative filtering techniques, have focused on recommending individual (or "atomic") items, such as movies or books, by understanding users' preferences for these individual items. However, in certain application domains, recommending "composite" items (i.e., combinations of atomic items) represents a very important capability. For illustration, consider a clothing/fashion recommender system, where we want to recommend "outfits" - combinations of tops (t-shirts, shirts, sweaters) and bottoms (pants, skirts, shorts) - to users. In such a case, multiple fashion items in a recommended outfit ideally have to match both functionally and stylistically, which may require domain expertise (e.g., on things like style compatibility) beyond individual preferences. Another key challenge for such recommender systems is that a given user's personal preference for a composite item may not directly translate to the user's personal preferences for the underlying atomic items and vice versa.