The trustworthiness of AI decision-making systems is increasingly important. A key feature of such systems is the ability to provide recommendations for how an individual may reverse a negative decision, a problem known as algorithmic recourse. Existing approaches treat recourse outcomes as counterfactuals of a fixed unit, ignoring that real-world recourse involves repeated decisions on the same individual under possibly different latent conditions. We develop a causal framework that models recourse as a process over pre- and post-intervention outcomes, allowing for partial stability and resampling of latent variables. We introduce post-recourse stability conditions that enable reasoning about recourse from observational data alone, and develop a copula-based algorithm for inferring the effects of recourse under these conditions. For settings where paired observations of the same individual before and after intervention are available (called recourse data), we develop methods for inferring copula parameters and performing goodness-of-fit testing. When the copula model is rejected, we provide a distribution-free algorithm for learning recourse effects directly from recourse data. We demonstrate the value of the proposed methods on real and semi-synthetic datasets.

Neural operators provide a framework for learning solution operators of partial differential equations (PDEs), enabling efficient surrogate modeling for complex systems. While universal approximation results are now well understood, approximation analysis specific to nonlinear reaction-diffusion systems remains limited. In this paper, we study neural operators applied to the solution mapping from initial conditions to time-dependent solutions of a generalized Gierer-Meinhardt reaction-diffusion system, a prototypical model of nonlinear pattern formation. Our main results establish explicit approximation error bounds in terms of network depth, width, and spectral rank by exploiting the Laplacian spectral representation of the Green's function underlying the PDE. We show that the required parameter complexity grows at most polynomially with respect to the target accuracy, demonstrating that Laplacian eigenfunction-based neural operator architectures alleviate the curse of parametric complexity encountered in generic operator learning. Numerical experiments on the Gierer-Meinhardt system support the theoretical findings.

Hang gliding Lookout Mountain: What it's really like to be aero-towed 1,700 feet above Georgia Paige Spiranac and her mom stun the internet, Lane Kiffin's incredible shot at Ole Miss & the NFL did it again Maggie Sajak appears at Savannah Bananas game as Jackson Olson's girlfriend, e-bike near death & MEAT! Pulling a gun on your sister's boyfriend and telling him to strip is one way to make family events awkward Paige Spiranac hits bombs at Truist pro-am after years of being shunned, fighter jets interrupt golf & MEAT! Spencer Pratt is'channeling the frustration' of LA voters, 'Ruthless' co-host says'High degree of coordination': Calif mayor admits to being secret Chinese agent Trump predicts'a lot of good things' will happen in China, predicts'golden age of America' after Iran conflict ends Trump says Iran ceasefire on'massive life support' amid Middle East tensions Iran ceasefire on'massive life support' as Trump weighs military options Graham calls out China link to Iran, questions Pakistan's role in negotiations Caine accuses Iran of holding'world's economy hostage' with Strait of Hormuz actions'Fox & Friends' hosts learn backyard camping tips from Scouting America OutKick UCF graduates clobber commencement speaker with boos after she says AI is the'next Industrial Revolution' Gloria Caulfield addressed graduates from UCF's College of Arts and Humanities and the Nicholson School of Communication It's almost the end of the school year, which means it's graduation season, a time where commencement speakers across the nation will be giving boilerplate advice to hungover students. However, one speaker at the University of Central Florida, my alma mater -- Go Knights, Charge On! -- had a rough day at the podium thanks to a comment she made about artificial intelligence . According to Orlando Weekly, UCF held a graduation ceremony for the school's College of Arts and Humanities and the Nicholson School of Communication and Media last week, and the commencement speaker was vice president of strategic alliances for Tavistock Development Company, Gloria Caulfield.

Teen builds'Bionic Underwater Robotic Turtle' to detect ecological threats High schooler Evan Budz's award-winning invention can identify coral bleaching, invasive species, and microplastics without disturbing marine ecosystems. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. Canadian high school student Evan Budz poses with his award-winning bionic turtle. Breakthroughs, discoveries, and DIY tips sent six days a week. Fifteen-year-old Evan Budz was on a camping trip when he saw a snapping turtle that would become the impetus for an award-winning invention .

Things to Do in L.A. Tap to enable a layout that focuses on the article. Inside LAUSD's alleged $22-million money-laundering scheme, 'the largest' in district history This is read by an automated voice. Please report any issues or inconsistencies here . Los Angeles Unified is seeking to recover $22 million from a contractor after alleging that a former district manager steered lucrative IT contracts to the company in exchange for kickbacks. Peng and Sampath have denied wrongdoing.

Universities have become generic, one professor and former dean argues. In the A.I. era, students may demand something they can't get elsewhere. Last week, I asked whether, as a forty-six-year-old father of two, I should keep contributing to my children's college funds, or if perhaps some combination of anti-establishment fervor, A.I., and a shifting economy could save me some money. I don't have a particularly good answer yet, at least not one good enough to inspire the purchase of a midlife-crisis car, my son's and daughter's futures be damned. But, after wrestling with that query in Part 1 of what will be a series of articles, I think there may be a better one to ask. The question is not, I think, "How will A.I. change higher education?" I wanted to talk with someone who stood outside the polite consensus which holds that college as we know it will survive, if only because, as I wrote last week, humans will always want to differentiate their children from other people's children.

A central challenge in dynamic network analysis is to represent temporal evolution in a way that is both geometrically meaningful and statistically identifiable. One approach embeds a sequence of network snapshots as trajectories in a Euclidean space and relates these trajectories to node embeddings. In multilayer and unfolded spectral constructions, however, node embeddings and their underlying latent positions are identifiable only up to general linear transformations. Although this ambiguity preserves edge probabilities, it can distort geometry and invalidate distance based temporal comparisons at both the trajectory and node-levels. We develop Multiscale Euclidean Network Trajectories (MENT), a framework for multiscale temporal trajectories based on second-moment geometry. By imposing an isotropic normalization on the anchor latent positions, we reduce the relevant ambiguity to orthogonal transformations and prevent distortion of the second-moment geometry. In this canonical representation, we define a trace variation distance and mode-wise variation distances along orthogonal directions, and use multidimensional scaling to obtain low-dimensional trajectories of time points at both global and mode-wise levels. The resulting trajectories support interpretation and inference. They admit mode-wise decompositions, support attribution of global and mode-wise temporal changes to nodes, and enable change point detection through 1D trajectories. We prove consistency of the proposed unfolded spectral embedding and of the induced temporal trajectories. Experiments on two synthetic and two real dynamic networks illustrate stable and interpretable recovery of temporal structure and show strong performance against existing change point detection baselines.

The Gromov-Wasserstein (GW) problem provides a framework for aligning heterogeneous datasets by matching their intrinsic geometry, but its statistical and computational scaling remains an issue for high-dimensional problems. Slicing techniques offer an appealing route to scalability, but, unlike Wasserstein distances, GW problems do not generally admit closed-form solutions in one-dimension. We resolve this problem for the GW problem with inner product cost (IGW), propose a sliced IGW distance that enjoys a natural rotational invariance property, and comprehensively study its structural and computational properties. Numerical experiments validating our theory are presented, followed by applications to heterogeneous clustering of text data and language model representation comparison.

We introduce a use of the \(M\)-cover (or \(M\)-layer) transform for machine learning. The method replicates a model \(M\) times, but instead of coupling the copies through parameter averaging or an explicit attractive force, as in replicated SGD or Elastic SGD, it rewires the contexts in which local learning messages are computed. Each local loss is evaluated on a routed model whose parameters are drawn from different copies according to permutations sampled from a structured mixing kernel \(Q\). Training then uses the original local update rule, while the resulting learning messages are redistributed across the copies through these routed computational paths. Thus \(Q\) defines a topology for message transport and controls the long-loop structure of the lifted factor graph. We formulate this construction for perceptrons, committee machines, and multilayer perceptrons, showing that the same principle applies from discrete models to differentiable neural networks. The resulting framework provides a mechanism for improving generalization through structured message sharing rather than replica collapse or parameter-space coupling.

Generative models are powerful tools for sampling from a learned distribution $\mathcal{P}(Y \mid X)$, and inverse-design methods invert this map to find an input $x$ that produces a desired point output $y^*$. However, many design goals are naturally distributional rather than pointwise, incorporating the inherent uncertainty of $Y$ and targeting a specific form for it, a task not addressed by standard inverse design. To address this issue we introduce Conditional Distribution Matching (CDM), a new inverse-design problem class in generative modeling: given a joint distribution $\mathcal{P}(X, Y)$ and a target distribution $\mathcal{G}(Y)$, find an input $x^*$ whose induced conditional distribution $\mathcal{P}(Y \mid X = x^*)$ matches $\mathcal{G}$. We formally define two variants: Conditional Distribution Matching Sampling (CDMS) and Conditional Distribution Matching Optimization (CDMO). To solve these problems, we propose MLGD-F (Matching-Loss Guided Diffusion with a Fast inner sampler), a plug-and-play inference-time algorithm that combines a pretrained score-based diffusion model with a pretrained fast conditional sampler, requiring no additional training or fine-tuning. By leveraging single-step conditional sampling, MLGD-F enables tractable gradient computation, making the estimation of $\mathcal{P}(Y \mid X)$ both memory-efficient and computationally lightweight. We validate MLGD-F on synthetic benchmarks, structured image transformations, and generative editing optimization, demonstrating reliable recovery of inputs whose conditional distributions match diverse user-specified targets, including discrete mixtures and continuous low-rank supports.