Enforcing nonlinear inequality constraints in neural networks remains challenging, especially when the output is subject to many coupled constraints. Existing hard constraint methods often impose structural restrictions on the constraint set or introduce substantial computational overhead for large-scale nonlinear problems. Here, we propose DiffSlack, a differentiable projection layer for nonlinear inequality-constrained neural prediction. DiffSlack reformulates inequalities as equalities with learnable slack variables, which are predicted as part of the augmented network output and provide a data-driven warm start for damped Gauss-Newton projection. The projection layer maps raw predictions onto the augmented feasible manifold while preserving end-to-end differentiability. A two-stage curriculum further stabilizes training and improves constraint satisfaction. We evaluate DiffSlack on vehicle path planning with 200 nonlinear inequality constraints from collision avoidance, curvature limits, and waypoint spacing. Compared with existing learning-based baselines, DiffSlack achieves a higher planning success rate and stronger geometric constraint satisfaction under a comparable inference budget. Ablation studies further show that the hard projection layer reduces sensitivity to supervision quality. Closed-loop tracking in CARLA and real-world vehicle experiments confirms the executability of the generated trajectories. These results demonstrate that DiffSlack provides a practical and scalable approach to embedding hard inequality constraints into neural networks for engineering applications.

Diffusion models have demonstrated strong performance in time series modeling due to their ability to progressively capture complex data distributions through iterative denoising. However, existing approaches struggle with frequency-sensitive denoising, high-frequency reconstruction and balancing global trends with local dynamics. To address these limitations, we propose \textbf{HyFAD}, a \textbf{Hy}brid time-frequency \textbf{D}iffusion model with \textbf{F}requency-\textbf{A}ware embedding for time series imputation. Built upon the DDPM paradigm, HyFAD adopts a coupled time-frequency diffusion framework, in which the reverse denoising proceeds sequentially from the time domain to the frequency domain, enabling coarse-to-fine generation. Specifically, the time-domain diffusion process captures low-frequency global trends, while the frequency-domain diffusion process refines high-frequency spectral components. We further introduce a frequency-aware step embedding that exploits the relationship between diffusion steps and spectral components, providing step-dependent spectral guidance and facilitates more accurate band-wise reconstruction. Extensive experiments on multiple benchmark datasets demonstrate that HyFAD achieves state-of-the-art performance. Our source code is available at https://github.com/hongfangao/HyFAD.

Things to Do in L.A. Tap to enable a layout that focuses on the article. O.C. immigration attorneys suspended for filing briefs filled with AI-hallucinated errors The attorneys were fined $2,500 each and suspended from practicing in the U.S. 9th Circuit Court of Appeals for six months. This is read by an automated voice. Please report any issues or inconsistencies here . A pair of Orange County immigration attorneys received temporary suspensions after the court discovered they used generative AI to write briefs that included "multiple nonexistent cases, misattributed quotations, and gross misrepresentations."

Plus: The EU has proposed new legislation to end its Big Tech dependence. Most days in her chambers, Judge Maritza Braswell, a federal magistrate judge in Colorado, sifts through stacks of documents written by people without a lawyer. The number of these filings has more than doubled compared to before 2023. She puts that jump down to AI. But while AI appears to be expanding access to justice, it doesn't seem to be improving people's chances of winning. Judges are starting to question what rights and duties chatbots should have as they stand in for lawyers.

In 2025, the tech journalist invited artificial intelligence to do nearly everything for her, including editing the book she was writing about the experiment. F or a year, Joanna Stern decided to turn herself into a "lab rat" - the object of her own experiment. Throughout 2025, she invited artificial intelligence into "every corner" of her life. She let AI answer her texts, decide what she ate and cooked, mow her lawn, fold her washing, drive her places, parse her mammograms and even, in the darkness of a burner phone, be her lover. The resulting book, I Am Not a Robot: My Year Using AI to Do (Almost) Everything, asks all the big questions, including: what happens when AI can do everything humans can do? And what comes after that?

Non-convex regularizers usually improve the performance of sparse estimation in practice. To prove this fact, we study the conditions of sparse estimations for the sharp concave regularizers which are a general family of non-convex regularizers including many existing regularizers. For the global solutions of the regularized regression, our sparse eigenvalue based conditions are weaker than that of L1-regularization for parameter estimation and sparseness estimation. For the approximate global and approximate stationary (AGAS) solutions, almost the same conditions are also enough. We show that the desired AGAS solutions can be obtained by coordinate descent (CD) based methods. Finally, we perform some experiments to show the performance of CD methods on giving AGAS solutions and the degree of weakness of the estimation conditions required by the sharp concave regularizers. Keywords: Sparse estimation, non-convex regularization, sparse eigenvalue, coordinate descent 1. Introduction High-dimensional estimation concerns the parameter estimation problems in which the dimensions of parameters are comparable to or larger than the sampling size.

Watermarking methods for language models have been studied extensively in the autoregressive setting, where tokens are generated sequentially. These works largely focus on local-context schemes that perturb the next token's distribution as a function of its preceding tokens. In diffusion language models, distributions over many unresolved positions are jointly sampled, allowing additive statistics of the entire sequence to be tractable during generation. We propose a watermark for masked diffusion language models that controls a global, vector-valued sketch representation of the text. Compared to context-dependent watermarking, the sketch formulation decouples detection from the local contexts seen during generation, resulting in an order-agnostic statistic and a watermarking rule which does not manifest as a simple token bias. We analyze the distortion, soundness, and robustness properties of the method.

Differentially private stochastic gradient descent (DP-SGD) injects noise into every updated coordinate, making the injected noise energy scale with the ambient parameter dimension \(d\). We ask when private training can update fewer coordinates without losing the signal needed for optimization. We propose \textsc{TP-TopK} (Two-Phase TopK DP-SGD), a two-phase method for coordinate-sparse private training without public data, in which a private warm-up phase identifies a coordinate support used to guide the main training phase. We give a criterion characterizing when coordinate restriction can be beneficial, show via a nonconvex stationarity bound that under this condition the relevant noise term scales with the active dimension \(k\) rather than the full parameter dimension \(d\), and provide a lower bound on the reliability of warm-up-based coordinate ranking. Experiments on MNIST, FMNIST, and CIFAR-10 show that learned coordinate supports can retain more gradient energy than size-matched random supports, with the largest gains when the active dimension is small and warm-up scores are informative.

Silicon Valley is turning to ethicists to shape the future of AI. Philosophy has long suffered an unfortunate reputation as pedantic and abstruse. In one of the most prominent debates of the 20th century, philosophers spent a great deal of energy arguing over what means. Paul Graham, the legendary tech investor, studied philosophy as a college student, which seemed "an impressively impractical thing to do," as he later wrote. But over time, Graham became disillusioned: "I kept taking philosophy courses and they kept being boring," he explained .

Despite AI's dizzying improvements in mathematical ability, its successes show just how integral human mathematicians are to the scientific process In 1915, Albert Einstein stood before the Prussian Academy of Science and revealed the now-famous equations of his general theory of relativity. Einstein and relativity are synonymous today with genius, but these revelations were initially met with indifference, in part because the maths was too radical for his peers to fully digest. Today, tech firms would have us believe we are on the brink of "superintelligent" artificial intelligence capable of outperforming experts in most domains, producing scientific breakthroughs on a par with Einstein. As Anthropic CEO Dario Amodei put it, we will see " a country of geniuses in a datacenter ". Claims like these are often provided with little evidence, and identifying genius or elevated intelligence is a murky endeavour.