Science & Mathematics

Training foundation models at the frontier typically requires large-scale dedicated and centralized clusters with fast interconnects - infrastructure that is prohibitively expensive and generally accessible only to well-resourced organizations. Decentralized training over pooled, geographically distributed GPUs offers an alternative, but introduces substantial heterogeneity in compute, memory, power, and network performance. Existing distributed training systems are primarily designed for clusters with fast, low-latency interconnects and typically use all available GPUs when configuring parallel training. In geo-distributed environments, however, slower devices and weak network links can become bottlenecks, while optimizing solely for throughput overlooks significant energy cost. We present GeoTrain, an automatic parallelism system that jointly optimizes training performance and energy consumption for heterogeneous geo-distributed GPU environments. GeoTrain simultaneously selects GPUs, partitions model layers, and determines pipeline configurations while accounting for heterogeneous compute, memory, power, and network constraints. To efficiently explore this large combinatorial search space, GeoTrain employs an optimized memetic algorithm with specialized genetic operators and local search. Experiments with decoder-only Transformer models on real-world and simulated heterogeneous topologies demonstrate that GeoTrain reduces iteration time and energy consumption by up to $61.4\%$ and $11.7\%$, respectively, over the existing state-of-the-art approaches. It also finds the exact optimum on verifiable instances and scales beyond exact methods as the number of GPUs increases, while exposing favorable energy-time trade-offs, including cases where its time-optimal distributed training plan is both faster and more energy-efficient than the baselines.

Hierarchical world models plan over long horizons by passing predicted states from a coarse model to a lower-level controller. Choosing these states can be expensive: the upper-level planner repeatedly differentiates through candidate macro-action trajectories. We replace this search with a lightweight goal-conditioned network trained through the frozen high-level predictor. The network supplies a conditioning vector, while the predictor generates the next latent waypoint. Training uses hindsight goals and state-prediction losses on offline trajectories, without search-solution targets or macro-action labels. Inference retains an autoregressive high-level rollout, but requires no high-level candidate optimization. We evaluate this approach on the shared-latent HWM checkpoints distributed with H-JEPA, using three backbone seeds and three head initializations per backbone. With a common evaluation protocol, mean success is 70.4% on Cube, 48.7% on Push-T, 100.0% on FourRoom, and 71.1% on Visual AntMaze. The method improves over the corresponding HWM search baseline on three environments and has the same mean on Push-T. Dedicated measurements on an NVIDIA L40S give 1.28-4.39x end-to-end speedups for batched evaluation. Ablations identify state-adaptive conditioning as a consistent contributor, while predictor-mediated subgoals and unrestricted conditions have environment-dependent benefits.

Tokenization-free, pixel-based language models (PLMs) have recently been proposed as an alternative to conventional token-based language models (TLMs), typically motivated by practical considerations, e.g., the flexibility to support new languages or vocabularies. Nevertheless, PLMs also have the potential to serve as infrastructure for computational (psycho)linguistics, where tokenization has been a source of bias in estimating information-theoretic values, such as surprisal, and has pushed the bottom-up visual orthographic features outside the scope. In this study, we first integrate PLMs into the modeling of naturalistic human reading and, in particular, examine their use to estimate next-word predictability, which can also integrate orthographic and parafoveal information. Our results demonstrate that next-word prediction difficulty, computed in pixel space, has strong predictive power for gaze duration and word skipping behavior across various languages. In particular, their advantage is complementary to existing token-level surprisal and entropy estimates. Cross-lingual analyses with script variations also clarify their distinctive visual processing biases, facilitating research into how bottom-up visual information is incrementally integrated into expectation-based reading.

We study fully dynamic $(Δ+1)$-coloring against an adaptive adversary. Behnezhad, Rajaraman, and Wasim (SODA 2025) gave the first algorithm with $\tilde O(n^{8/9})$ amortized update time, later improved to $\tilde O(n^{2/3})$ by Flin and Halldórsson (ICALP 2025). We give a fully dynamic $(Δ+1)$-coloring algorithm with $\tilde O(\sqrt n)$ \textbf{worst-case} update time. Unlike previous algorithms, it avoids sparse-dense decompositions and relies only on elementary data structures, resulting in a short self-contained algorithm and analysis. Moreover, it avoids global recoloring, resulting in a worst-case recourse of $3$.

Image restoration is a fundamental inverse problem that seeks to recover high-quality images from degraded observations. Plug-and-Play (PnP) methods provide a flexible framework for integrating pretrained denoisers into iterative reconstruction, whereas flow matching offers an efficient generative modeling approach based on continuous-time ODE dynamics. Very recently, Martin et al.\ (ICLR, 2025) developed a PnP-Flow method, which integrates the PnP framework with flow matching through a time-dependent denoiser constructed from a pretrained flow matching model.By incorporating a different time schedule and an additional pixel-space projection operator, this paper proposes a novel efficient PnP-Flow algorithm (HP-PnP-Flow) that enjoys rigorous convergence guarantees under mild assumptions, without imposing restrictive conditions on iterates required by the aforementioned work. Numerical experiments on CelebA and AFHQ-Cat demonstrate that the newly proposed HP-PnP-Flow algorithm significantly outperforms PnP-Flow on several restoration tasks such as denoising, deblurring, super-resolution, random inpainting, and box inpainting. Notably, our algorithm achieves comparable or better reconstruction quality with substantially fewer iterations, reducing the iteration count from $500$ to $100$ for deblurring and super-resolution on AFHQ-Cat.

Despite rapid advances in large language models (LLMs), their deployment in the sports and health domain remains high-risk due to the absence of domain-specific evaluation benchmarks. Existing general-purpose benchmarks (e.g., MMLU and HELM) primarily assess broad knowledge and reasoning capabilities, but fail to capture critical domain requirements such as exercise safety, physiological appropriateness, personalization, and actionable coaching quality. This gap is particularly concerning in fitness and health applications, where incorrect or unsafe recommendations can lead to physical harm. To address this limitation, we introduce MoveBench, the first comprehensive benchmarking framework specifically designed for evaluating LLMs in sports and health coaching. The proposed benchmark integrates heterogeneous task formats, including multiple-choice questions (MCQs) and open-ended question answering (OpenQA), grounded in real-world user scenarios and paired with structured rubrics emphasizing safety compliance, scientific validity, and training logic. Through large-scale evaluation of 15 diverse LLMs on 809 questions with 5,012 rubric-level criteria, our results reveal substantial performance variability, particularly in safety awareness, structured program design, and personalization capability, highlighting a critical gap between knowing and doing. Our work establishes a foundational evaluation standard for sports and health LLM applications and provides a reproducible framework for advancing safe, reliable, and context-aware AI-driven coaching systems. Open resources are available at https://github.com/SatoSakula/MoveBench.

In this paper, we study the theoretical computational complexity of counting trees and graphs that are classified positively by a graph neural networks, or said equivalently that satisfy a given formula of modal logic with counting. We also study convergence.

RGBA video generation is essential for creating compositable visual assets in filmmaking, game development, and digital content production. However, generating high-quality RGB appearance alongside temporally coherent transparency remains a significant challenge. Existing text-to-RGBA video methods often entangle RGB and alpha distributions and offer limited control over the precise appearance of a target asset. In addition, incorporating image conditioning typically suffers from the emergence-disappearance effects, which fail existing first-frame or first-and-last-frame conditions due to their fully transparent boundary frames. To address these issues, we present Wan-Alpha++, a unified framework that brings controllable RGBA video generation to both text- and image-to-video diffusion backbones through a shared RGBA latent space, extending our conference version Wan-Alpha from the text-conditioned setting to image-conditioned generation with an interior reference frame. Our method first learns shiftable RGB-alpha distributions while preserving the pretrained RGB prior. Specifically, we introduce a transparency-aware bidirectional diffusion objective to produce distinguishable RGBA latent representations, and a transparency-guided mean sampler that shifts the noise distribution to improve transparency generation and enable spatial controllability. Building upon this RGBA generation prior, we introduce temporal phase reparameterization for image-conditioned effect generation. By cyclically transforming a zero-positive-zero alpha pattern into a positive-zero-positive pattern, it relocates visible content to both temporal boundaries, facilitating effective appearance conditioning with limited RGBA data.

AI systems may miss indirect, culturally situated distress or provide support mismatched to the application context. Existing benchmarks do not jointly address cultural variation, application context, and practitioner disagreement. We introduce VEILED-SH, a benchmark and construction methodology for evaluating single-turn responses to indirect expressions of suicide, self-harm, and distress. Its 10,003 prompts span counselor chat, forum posts, platform search, and triage, drawing on Singapore-grounded sources and public datasets. An expert-validated multi-label taxonomy distinguishes intent, communicative function, and response behavior. Six automated profiles, individually calibrated to three peer-support practitioners and three clinicians, retain separate reference policies for proxy-alignment scoring. Evaluating five systems on a coverage-enriched sample reveals variation in proxy alignment across profile-generated reference policies, even for the same system responses.

We study robust estimation of a Gaussian precision matrix that decomposes as a sparse matrix minus a symmetric, possibly indefinite, low-rank matrix, a structure that arises when latent-variable marginalization is combined with conditioning on linear measurements. The proposed convex estimator replaces the sample covariance by the centered Gaussian measure-transformed (MT) covariance, which preserves the signed graph of the sparse component under the nominal model, and penalizes the low-rank component by the nuclear norm of a congruence transform, an atomic norm that encodes structural side information. Our main result is a primal--dual witness theorem: under restricted invertibility and irrepresentability conditions on the Fisher information, the raw convex optimizer is unique, has no false edges, recovers the signs of all sufficiently strong edges, and has exactly the true rank and inertia. These conditions reduce to the graphical-lasso conditions when the low-rank part is absent, and we verify them from primitive incoherence and near-isotropy assumptions. Over a class on which they hold uniformly, we prove information-theoretic limits for Frobenius estimation, signed graph recovery, and inertia recovery. In particular, inertia recovery requires $N\gtrsim p/ν_{\min}^2$ samples, where $ν_{\min}$ is the smallest nonzero eigenvalue modulus of the low-rank part; the spectral beta-min condition of the witness theorem is necessary up to a $\sqrt{\log p}$ factor; and the Frobenius risk attains the minimax rate up to a factor $\sqrt{μ(1+\min\{d,r\})\log p}$, where $μ$ is the incoherence parameter, $d$ the maximal degree, and $r$ the rank. We further quantify robustness under Huber contamination, with a bias bound that is sharp for the MT functional and vanishes for remote outliers, and give a globally convergent linearized ADMM with closed-form updates.

Formal methods provide a principal approach to obtaining safety guarantees for autonomous agents. Their key bottleneck is their reliance on a formal model (e.g., a Markov decision process) describing the agent-environment interaction. Learning or crafting the model is an error-prone process, which undermines the guarantees offered by formal methods. Robust models account for modelling uncertainty, but may still fail to capture the true environment. This issue can be addressed through \emph{runtime model monitoring}, which aims to raise an alarm when a likely model-environment discrepancy is detected, while keeping the probability of false alarm bounded. Existing approaches impose various assumptions and do not clearly explain the rationale behind their design choices, leaving the broader design space for these monitors somewhat opaque. In this paper, we formalise the design space of monitors for robust stochastic models through the lens of \emph{parameterised sequential betting} algorithms, highlighting the importance of \emph{observation feature} design (choosing what information about the history the monitor uses) and \emph{bet design} (how rich a family of betting rules the monitor can represent). We show that our framework generalizes the existing approaches, and we use its formalization to propose a new \emph{mixture of linear monitors (ML)} design. We prove that these ML monitors achieve an asymptotically optimal detection time within the class of linear monitors, making them a principled choice for our monitoring problem. Our experiments confirm that ML monitors significantly reduce detection times compared to existing monitors and can effectively exploit more complex observation features.

Recent efforts have demonstrated the strong capabilities of Multimodal Large Reasoning Models (MLRMs) in geographic reasoning. By jointly analyzing subtle visual cues, these models can infer the locations of photos, thus enabling doxing even by non-expert adversaries. Existing defense methods struggle to balance the shareability of photos with effective protection, and often fail to sufficiently disrupt the implicit geo-evidence chains embedded in scene semantics. To this end, we propose GeoEdit, an adversarial de-evidencing framework for silent geoprivacy protection via image editing. Specifically, we apply minimal edits to high-risk evidence anchors in the image, thereby disrupting the underlying spatial reasoning chains while preserving overall scene semantics. We identify these anchors by combining structured knowledge with adversarially discovered geographic cues. To further navigate the large editing action space, we adopt a learnable policy to iteratively refine editing decisions, distilling successful trajectories into transferable natural-language insights for consistent and efficient editing. Evaluated on LifePhotoBench, GeoEdit achieves strong protection against 6 mainstream MLRMs, outperforming visual perturbation baselines by over 0.59 in image fidelity.

We study coupon allocation on an online marketplace offering multiple service categories. Issuing coupons requires choosing a vector of category-specific discounts, accounting for both their direct effects and cross-category demand shifts. We present TaQFormer, a treatment-as-query Transformer for this multidimensional treatment setting. Each treatment coordinate is represented as a query token, allowing cross-attention to estimate the response to the full treatment vector. To combine large but policy-biased observational logs with a smaller stream of randomized controlled trial data, we use a two-stage pipeline: observational pretraining learns general outcome patterns, followed by LoRA fine-tuning on RCT data with a request-specific fusion gate. We evaluate the resulting system through the checks required for production, including offline uplift metrics, treatment-parallel serving, latency monitoring, and a 14-day online A/B test. At essentially the same subsidy cost rate, \model increases business value per user by 1.26\% over the production baseline and significantly outperforms both the production baseline and the RCT-only model, while meeting the latency budget. It was subsequently rolled out to all marketplace traffic and has operated at full scale for several months as of October 2026. The deployment illustrates how multidimensional treatment modeling and observational pretraining, combined with adaptation using RCT data, can support effective joint discount decisions in production.

Let $q=p^f$, where $p$ is prime. We prove that every $q$-ary linear code meeting the Griesmer bound, with positive dimension and minimum distance $d\ge1$, is $p^{\max\{0,ν_p(d)-f+1\}}$-divisible, as asserted in Ward's conjecture. Arbitrary projective column multiplicities are allowed. The geometric ingredient is a bound independent of dimension: a nonzero scalar-invariant function $F:\mathbb{F}_q^k\to\mathbb{F}_p$, with $F(0)=0$ and prime-field algebraic degree at most $(f+s)(p-1)$, vanishes identically on at most $p^s(q-1)$ linear hyperplanes when $0\le s

Synchronization between a digital twin (DT) and its physical robot is critical for effective teleoperation, as mismatches directly degrade operator awareness and task performance. Existing synchronization metrics are predominantly time-based and rarely capture the spatial consequences of delayed information during motion. In this paper, we introduce Kinematic Age of Information (K-AoI), a spatio-temporal metric that weights AoI by instantaneous Cartesian velocity, translating temporal staleness into physically meaningful spatial divergence. We implement and evaluate K-AoI on a DT teleoperation testbed comprising a six-degrees-of-freedom (6-DOF) manipulator, a Unity-based twin, and controlled network impairments using tc netem across seven network conditions. Per-sample analysis shows that K-AoI exhibits rank-correlations with AoI at $ρ\leq 0.65$ across all networks, dropping to $ρ= 0.22$ under satellite connections. This shows that K-AoI is not a simple transformation of AoI, but instead captures velocity-dependent degradation effects that time-only metrics cannot resolve. We further analyze AoI tail behavior using Ultra-Low AoI (ULAoI) and find that the commonly assumed Generalized Pareto Distribution (GPD) model is rejected. This reflects the impact of deterministic forwarding and bounded jitter, which violate standard extreme-value assumptions. Overall, K-AoI provides a complementary and physically grounded synchronization metric, linking network delay to task-relevant spatial error in digital-twin teleoperation systems. The dataset and testbed software are publicly available at: https://github.com/luziyaotian/kaoi-testbed.