Model-based clustering integrated with variable selection is a powerful tool for uncovering latent structures within complex data. However, its effectiveness is often hindered by challenges such as identifying relevant variables that define heterogeneous subgroups and handling data that are missing not at random, a prevalent issue in fields like transcriptomics. While several notable methods have been proposed to address these problems, they typically tackle each issue in isolation, thereby limiting their flexibility and adaptability. This paper introduces a unified framework designed to address these challenges simultaneously. Our approach incorporates a data-driven penalty matrix into penalized clustering to enable more flexible variable selection, along with a mechanism that explicitly models the relationship between missingness and latent class membership. We demonstrate that, under certain regularity conditions, the proposed framework achieves both asymptotic consistency and selection consistency, even in the presence of missing data. This unified strategy significantly enhances the capability and efficiency of model-based clustering, advancing methodologies for identifying informative variables that define homogeneous subgroups in the presence of complex missing data patterns. The performance of the framework, including its computational efficiency, is evaluated through simulations and demonstrated using both synthetic and real-world transcriptomic datasets.

Air pollution was responsible for 2.6 million deaths across South Asia in 2021 alone, with brick manufacturing contributing significantly to this burden. In particular, the Indo-Gangetic Plain; a densely populated and highly polluted region spanning northern India, Pakistan, Bangladesh, and parts of Afghanistan sees brick kilns contributing 8-14% of ambient air pollution. Traditional monitoring approaches, such as field surveys and manual annotation using tools like Google Earth Pro, are time and labor-intensive. Prior ML-based efforts for automated detection have relied on costly high-resolution commercial imagery and non-public datasets, limiting reproducibility and scalability. In this work, we introduce SENTINELKILNDB, a publicly available, hand-validated benchmark of 62,671 brick kilns spanning threekiln types Fixed Chimney Bull's Trench Kiln (FCBK), Circular FCBK (CFCBK), and Zigzag kilns - annotated with oriented bounding boxes (OBBs) across 2.8 million km2 using free and globally accessible Sentinel-2 imagery. We benchmark state-of-the-art oriented object detection models and evaluate generalization across in-region, out-of-region, and super-resolution settings. SENTINELKILNDB enables rigorous evaluation of geospatial generalization and robustness for low-resolution object detection, and provides a new testbed for ML models addressing real-world environmental and remote sensing challenges at a continental scale. Datasets and code are available in SentinelKilnDB Dataset and SentinelKilnDB Bench-mark, under the Creative Commons Attribution-NonCommercial 4.0 International License.

Designing algorithms for solving high-dimensional Bayesian inverse problems directly in infinite dimensional function spaces - where such problems are naturally formulated - is crucial to ensure stability and convergence as the discretization of the underlying problem is refined. In this paper, we contribute to this line of work by analyzing a widely used sampler for linear inverse problems: Langevin dynamics driven by score based generative models (SGMs) acting as priors, formulated directly in function space. Building on the theoretical framework for SGMs in Hilbert spaces, we give a rigorous definition of this sampler in the infinite-dimensional setting and derive, for the first time, error estimates that explicitly depend on the approximation error of the score. As a consequence, we obtain sufficient conditions for global convergence in Kullback-Leibler divergence on the underlying function space. Preventing numerical instabilities requires preconditioning of the Langevin algorithm and we prove the existence and form of an optimal preconditioner. The preconditioner depends on both the score error and the forward operator and guarantees a uniform convergence rate across all posterior modes. Our analysis applies to both Gaussian and a general class of non Gaussian priors. Finally, we present examples that illustrate and validate our theoretical findings.

Recent advances in language modeling have demonstrated the effectiveness of State Space Models (SSMs) for efficient sequence modeling. While hybrid architectures such as Samba and the decoder-decoder architecture, YOCO, have shown promising performance gains over Transformers, prior works have not investigated the efficiency potential of representation sharing between SSM layers. In this paper, we introduce the Gated Memory Unit (GMU), a simple yet effective mechanism for efficient memory sharing across layers. We apply it to create SambaY, a decoder-hybrid-decoder architecture that incorporates GMUs in the cross-decoder to share memory readout states from a Samba-based self-decoder. SambaY significantly enhances decoding efficiency, preserves linear pre-filling time complexity, and boosts long-context performance, all while eliminating the need for explicit positional encoding. Through extensive scaling experiments, we demonstrate that our model exhibits a significantly lower irreducible loss compared to a strong YOCO baseline, indicating superior performance scalability under large-scale compute regimes. Our largest model enhanced with Differential Attention, Phi4-mini-Flash-Reasoning, achieves significantly better performance than Phi4-mini-Reasoning on reasoning tasks such as Math500, AIME24/25, and GPQA Diamond without any reinforcement learning, while delivering up to 10 higher decoding throughput on 2K-length prompts with 32K generation length under the vLLM inference framework.

Zeroth-order Optimization (ZO) has received wide attention in machine learning, especially when computing full gradient is expensive or even impossible. Recently, ZO has emerged as an important paradigm for memory-efficient fine-tuning of large language models (LLMs), circumventing the memory overhead of backpropagation. However, existing ZO gradient estimators exhibit dimension-dependent variance scaling as $\Theta(d)$, leading to dimension-dependent convergence rates without further assumptions on the objective function, which is prohibitive for large-scale LLM parameters.

The rest of Dyson's promised 2026 vacuum lineup is here, from the new Dyson V16 Piston Animal to an updated version of the favored Dyson V8 Cyclone. Dyson's vacuum lineup had a new look planned for this year . Some of the vacuums have already arrived, like the Dyson PencilVac and Dyson Spot+Scrub robot vacuum, but others we've still been waiting to see. That wait is over as of this month, as Dyson has finally dropped the rest of its anticipated models. Dyson now has three new cordless vacuums you can shop, plus one with a Submarine head variant: the Dyson V16 Piston Animal ($980) and Dyson V16 Piston Animal Submarine ($1,100), the Dyson V10 Konical ($500), and the Dyson V8 Cyclone ($400) .

Training reasoning language models (LMs) with reinforcement learning (RL) for one-hot correctness inherently relies on the LM being able to explore and solve its task with some chance at initialization. Furthermore, a key use case of reasoning LMs is to act as teachers for distilling new students and cold-starting future RL iterations rather than being deployed themselves. From these considerations, we introduce a new framework that avoids RL's exploration challenge by training a new class of Reinforcement-Learned Teachers (RLTs) focused on yielding the most effective downstream distillation. RLTs are prompted with both the question and solution to each problem, and tasked to simply connect-the-dots with detailed explanations tailored for their students. We train RLTs with dense rewards obtained by feeding each explanation to the student and testing its understanding of the problem's solution. In practice, the raw outputs of a 7B RLT provide higher final performance on competition and graduate-level tasks than existing distillation and cold-starting pipelines that collect and postprocess the reasoning traces of orders of magnitude larger LMs. Furthermore, RLTs maintain their effectiveness when training larger students and when applied zero-shot to out-of-distribution tasks, unlocking new levels of efficiency and re-usability for the RL reasoning framework.

Despite progress in language model (LM) capabilities, evaluations have thus far focused on models' performance on tasks that humans have previously solved, including in programming (SWE-Bench) and mathematics (FrontierMath). We therefore propose testing models' ability to design and implement algorithms in an open-ended benchmark: We task LMs with writing code that efficiently solves computationally challenging problems in computer science, physics, and mathematics. Our AlgoTune benchmark consists of 120 tasks collected from domain experts and a framework for validating and timing LM-synthesized solution code, which is compared to reference implementations from popular open-source packages.In addition, we develop a baseline LM agent, AlgoTuner, and evaluate its performance across a suite of frontier models.AlgoTuner achieves an average 1.58x speedup against reference solvers, including methods from packages such as SciPy, scikit-learn and CVXPY.However, we find that current models fail to discover algorithmic innovations, instead preferring surface-level optimizations. We hope that AlgoTune catalyzes the development of LM agents exhibiting creative problem solving beyond state-of-the-art human performance.

Multi-view 3D reconstruction remains a core challenge in computer vision. Recent methods, such as DUSt3R and its successors, directly regress pointmaps from image pairs without relying on known scene geometry or camera parameters. However, the performance of these models is constrained by the diversity and scale of available training data. In this work, we introduce Puzzles, a data augmentation strategy that synthesizes an unbounded volume of high-quality, posed video-depth data from just a single image or video clip. By simulating diverse camera trajectories and realistic scene geometry through targeted image transformations, Puzzles significantly enhances data variety. Extensive experiments show that integrating Puzzles into existing video based 3D reconstruction pipelines consistently boosts performance, all without modifying the underlying network architecture. Notably, models trained on only 10% of the original data, augmented with Puzzles, achieve accuracy comparable to those trained on the full dataset.

Recent efficient sequence modeling methods, such as Gated DeltaNet, TTT, and RWKV-7, have achieved performance improvements by supervising the recurrent memory management through the Delta learning rule. Unlike previous state-space models (e.g., Mamba) and gated linear attentions (e.g., GLA), these models introduce interactions between the recurrent state and the key vector, resulting in a bilinear recursive structure. In this paper, we first introduce the concept of Bilinear RNNs with a comprehensive analysis on the advantages and limitations of these models. Then based on the closed-loop control theory, we propose a novel Bilinear RNN variant named Comba, which adopts a scalar-plus-low-rank state transition, with both state feedback and output feedback corrections. We also implement a hardware-efficient chunk-wise parallel kernel in Triton and train models with 340M/1.3B