What is Iran's Pickaxe Mountain? Six months into the war with Iran, it is worth taking stock of what has actually changed around the Gulf. After Iran's June 2025 missile strike on Al Udeid Air Base in Qatar, I argued that the years ahead would be more perilous for the Gulf and that deeper defence cooperation and integration would eventually become unavoidable. Earlier this month, I wrote here that the Gulf could no longer rely entirely on the old security toolkit and would need to build more of a security ecosystem of its own. So far, events have borne out the broad direction of both arguments.

Why $370bn tech group Palantir pays 1.4 percent tax rate: Report Palantir Technologies, the United States data analytics and artificial intelligence company which has contracts with the country's military and intelligence apparatus, has "engineered its corporate structure" to pay no US federal corporate income tax, according to a new report. The study by the Centre for International Corporate Tax Accountability and Research (CICTAR) comes as Palantir reports soaring revenues, driven partly by government contracts, while it faces continued criticism for providing technology to the Israeli military amid the genocide in Gaza. What does the report show? Earlier this week, Palantir reported second-quarter revenue of $1.94bn, up 93 percent from a year earlier. But despite its rapid growth, CICTAR said its global effective tax rate was just 1.4 percent in 2025.

We consider binary classification restricted to a class of continuous piecewise linear functions whose decision boundaries are (possibly nonconvex) starshaped polyhedral sets, supported on a fixed polyhedral simplicial fan. We investigate the expressivity of these function classes and describe the combinatorial and geometric structure of the loss landscape, most prominently the sublevel sets, for two loss-functions: the 0/1-loss (discrete loss) and a log-likelihood loss function. In particular, we give explicit bounds on the VC dimension of this model, and concretely describe the sublevel sets of the discrete loss as chambers in a hyperplane arrangement. For the log-likelihood loss, we give sufficient conditions for the optimum to be unique, and describe the geometry of the optimum when varying the rate parameter of the underlying exponential probability distribution.

We present a unified framework for automatic multitrack music arrangement that enables a single pre-trained symbolic music model to handle diverse arrangement scenarios, including reinterpretation, simplification, and additive generation. At its core is a segment-level reconstruction objective operating on token-level disentangled content and style, allowing for flexible any-to-any instrumentation transformations at inference time. To support track-wise modeling, we introduce REMI-z, a structured tokenization scheme for multitrack symbolic music that enhances modeling efficiency and effectiveness for both arrangement tasks and unconditional generation. Our method outperforms task-specific state-of-the-art models on representative tasks in different arrangement scenarios--band arrangement, piano reduction, and drum arrangement, in both objective metrics and perceptual evaluations. Taken together, our framework demonstrates strong generality and suggests broader applicability in symbolic music-to-music transformation.1

Our results settle the complexity status regarding these parameters number of dimensions and number of ReLUs if the network is assumed to compute the ReLU case, we show fixed-parameter tractability for the combined parameter four ReLUs (or two linear threshold neurons) with zero training error. Finally, in We also answer a question by Froese et al. [2022, JAIR] proving W[1]-hardness for dimensions, which excludes any polynomial-time algorithm for constant dimension. Khalife and Basu [2022, IPCO] showing that both problems are NP-hard for two eral questions are still open. We answer questions by Arora et al. [2018, ICLR] and complexity of these problems has been studied numerous times in recent years, sevsidering ReLU and linear threshold activation functions.

This paper presents an end-to-end neural architecture based on Diffusion Models for spatial puzzle solving, particularly jigsaw puzzle and room arrangement tasks. In the latter task, for instance, the proposed system takes a set of room layouts as polygonal curves in the top-down view and aligns the room layout pieces by estimating their 2D translations and rotations, akin to solving the jigsaw puzzle of room layouts. A surprising discovery of the paper is that the simple use of a Diffusion Model effectively solves these challenging spatial puzzle tasks as a conditional generation process. To enable learning of an end-to-end neural system, the paper introduces new datasets with ground-truth arrangements: 1) 2DVoronoi jigsaw dataset, a synthetic one where pieces are generated by Voronoi diagram of 2D pointset; and 2) MagicPlan dataset, a real one offered by MagicPlan from its production pipeline, where pieces are room layouts constructed by augmented reality App by real-estate consumers. The qualitative and quantitative evaluations demonstrate that our approach outperforms the competing methods by significant margins in all the tasks. We have provided code and data here.

Federated learning is a distributed learning paradigm where multiple agents, each only with access to local data, jointly learn a global model. There has recently been an explosion of research aiming not only to improve the accuracy rates of federated learning, but also provide certain guarantees around social good properties such as total error. One branch of this research has taken a game-theoretic approach, and in particular, prior work has viewed federated learning as a hedonic game, where error-minimizing players arrange themselves into federating coalitions. This past work proves the existence of stable coalition partitions, but leaves open a wide range of questions, including how far from optimal these stable solutions are. In this work, we motivate and define a notion of optimality given by the average error rates among federating agents (players).

Our information estimator uses only these noisy measurements and a noise model to quantify how well measurements distinguish objects. Many imaging systems produce measurements that humans never see or cannot interpret directly. Your smartphone processes raw sensor data through algorithms before producing the final photo. MRI scanners collect frequency-space measurements that require reconstruction before doctors can view them. Self-driving cars process camera and LiDAR data directly with neural networks.