arXiv:2604.01878v1 Announce Type: cross Abstract: Spectral graph contrastive learning has emerged as a unified paradigm for handling both homophilic and heterophilic graphs by leveraging high-frequency components. However, we identify a fundamental spectral dilemma: while high-frequency signals are indispensable for encoding heterophily, our theoretical analysis proves they exhibit significantly higher variance under spectrally concentrated perturbations. We derive a regret lower bound showing that existing global (node-agnostic) spectral fusion is provably sub-optimal: on mixed graphs with separated node-wise frequency preferences, any global fusion strategy incurs non-vanishing regret relative to a node-wise oracle. To escape this bound, we propose ASPECT, a framework that resolves this dilemma through a reliability-aware spectral gating mechanism. Formulated as a minimax game, ASPECT employs a node-wise gate that dynamically re-weights frequency channels based on their stability against a purpose-built adversary, which explicitly targets spectral energy distributions via a Rayleigh quotient penalty. This design forces the encoder to learn representations that are both structurally discriminative and spectrally robust. Empirical results show that ASPECT achieves new state-of-the-art performance on 8 out of 9 benchmarks, effectively decoupling meaningful structural heterophily from incidental noise.

arXiv:2509.14980v2 Announce Type: replace-cross Abstract: Mobile manipulation requires the coordinated control of a mobile base and a robotic arm while simultaneously perceiving both global scene context and fine-grained object details. Existing single-view approaches often fail in unstructured environments due to limited fields of view, exploration, and generalization abilities. Moreover, classical controllers, although stable, struggle with efficiency and manipulability near singularities. To address these challenges, we propose M4Diffuser, a hybrid framework that integrates a Multi-View Diffusion Policy with a novel Reduced and Manipulability-aware QP (ReM-QP) controller for mobile manipulation. The diffusion policy leverages proprioceptive states and complementary camera perspectives with both close-range object details and global scene context to generate task-relevant end-effector goals in the world frame. These high-level goals are then executed by the ReM-QP controller, which eliminates slack variables for computational efficiency and incorporates manipulability-aware preferences for robustness near singularities. Comprehensive experiments in simulation and real-world environments show that M4Diffuser achieves 7 to 56 percent higher success rates and reduces collisions by 3 to 31 percent over baselines. Our approach demonstrates robust performance for smooth whole-body coordination, and strong generalization to unseen tasks, paving the way for reliable mobile manipulation in unstructured environments. Details of the demo and supplemental material are available on our project website https://sites.google.com/view/m4diffuser.

arXiv:2602.13498v2 Announce Type: replace-cross Abstract: Muon-style optimizers leverage Newton-Schulz (NS) iterations to orthogonalize updates, yielding update geometries that often outperform Adam-series methods. However, this orthogonalization discards magnitude information, rendering training sensitive to step-size hyperparameters and vulnerable to high-energy bursts. To mitigate this, we introduce TrasMuon (\textbf{T}rust \textbf{R}egion \textbf{A}daptive \textbf{S}caling \textbf{Muon}). TrasMuon preserves the near-isometric geometry of Muon while stabilizing magnitudes through (i) global RMS calibration and (ii) energy-based trust-region clipping. We demonstrate that while reintroducing adaptive scaling improves optimization efficiency, it typically exacerbates instability due to high-energy outliers. TrasMuon addresses this by defining a trust region based on relative energy ratios, confining updates to a stable zone. Empirical experiments on vision and language models demonstrate that TrasMuon converges faster than baselines. Furthermore, experiments without warmup stages confirm TrasMuon's superior stability and robustness.

arXiv:2603.05565v2 Announce Type: replace-cross Abstract: Generative AI compresses within-task skill differences while shifting economic value toward concentrated complementary assets, creating an apparent paradox: the technology that equalizes individual performance may widen aggregate inequality. We formalize this tension in a task-based model with endogenous education, employer screening, and heterogeneous firms. The model yields two regimes whose boundary depends on AI's technology structure (proprietary vs. commodity) and labor market institutions (rent-sharing elasticity, asset concentration). A scenario analysis via Method of Simulated Moments, matching six empirical targets, disciplines the model's quantitative magnitudes; a sensitivity decomposition reveals that the five non-$\Delta$Gini moments identify mechanism rates but not the aggregate sign, which at the calibrated parameters is pinned by $m_6$ and $\xi$, while AI's technology structure ($\eta_1$ vs. $\eta_0$) independently crosses the boundary. The contribution is the mechanism -- not a verdict on the sign. Occupation-level regressions using BLS OEWS data (2019--2023) illustrate why such data cannot test the model's task-level predictions. The predictions are testable with within-occupation, within-task panel data that do not yet exist at scale.

arXiv:2603.04277v1 Announce Type: cross Abstract: Autonomous aerial robots operating in GPS-denied or communication-degraded environments frequently lose access to camera metadata and telemetry, leaving onboard perception systems unable to recover the absolute metric scale of the scene. As LLM/VLM-based planners are increasingly adopted as high-level agents for embodied systems, their ability to reason about physical dimensions becomes safety-critical -- yet our experiments show that five state-of-the-art VLMs suffer from spatial scale hallucinations, with median area estimation errors exceeding 50%. We propose VANGUARD, a lightweight, deterministic Geometric Perception Skill designed as a callable tool that any LLM-based agent can invoke to recover Ground Sample Distance (GSD) from ubiquitous environmental anchors: small vehicles detected via oriented bounding boxes, whose modal pixel length is robustly estimated through kernel density estimation and converted to GSD using a pre-calibrated reference length. The tool returns both a GSD estimate and a composite confidence score, enabling the calling agent to autonomously decide whether to trust the measurement or fall back to alternative strategies. On the DOTA~v1.5 benchmark, VANGUARD achieves 6.87% median GSD error on 306~images. Integrated with SAM-based segmentation for downstream area measurement, the pipeline yields 19.7% median error on a 100-entry benchmark -- with 2.6x lower category dependence and 4x fewer catastrophic failures than the best VLM baseline -- demonstrating that equipping agents with deterministic geometric tools is essential for safe autonomous spatial reasoning.

arXiv:2602.13498v1 Announce Type: cross Abstract: Muon-style optimizers leverage Newton-Schulz (NS) iterations to orthogonalize updates, yielding update geometries that often outperform Adam-series methods. However, this orthogonalization discards magnitude information, rendering training sensitive to step-size hyperparameters and vulnerable to high-energy bursts. To mitigate this, we introduce TrasMuon (\textbf{T}rust \textbf{R}egion \textbf{A}daptive \textbf{S}caling \textbf{Muon}). TrasMuon preserves the near-isometric geometry of Muon while stabilizing magnitudes through (i) global RMS calibration and (ii) energy-based trust-region clipping. We demonstrate that while reintroducing adaptive scaling improves optimization efficiency, it typically exacerbates instability due to high-energy outliers. TrasMuon addresses this by defining a trust region based on relative energy ratios, confining updates to a stable zone. Empirical experiments on vision and language models demonstrate that TrasMuon converges faster than baselines. Furthermore, experiments without warmup stages confirm TrasMuon's superior stability and robustness.

arXiv:2410.15756v3 Announce Type: replace-cross Abstract: Ensuring correctness is crucial for code generation. Formal verification offers a definitive assurance of correctness, but demands substantial human effort in proof construction and hence raises a pressing need for automation. The primary obstacle lies in the severe lack of data-there is much fewer proofs than code snippets for Large Language Models (LLMs) to train upon. In this paper, we introduce SAFE, a framework that overcomes the lack of human-written proofs to enable automated proof generation of Rust code. SAFE establishes a self-evolving cycle where data synthesis and fine-tuning collaborate to enhance the model capability, leveraging the definitive power of a symbolic verifier in telling correct proofs from incorrect ones. SAFE also re-purposes the large number of synthesized incorrect proofs to train the self-debugging capability of the fine-tuned models, empowering them to fix incorrect proofs based on the verifier's feedback. SAFE demonstrates superior efficiency and precision compared to GPT-4o. Through tens of thousands of synthesized proofs and the self-debugging mechanism, we improve the capability of open-source models, initially unacquainted with formal verification, to automatically write proofs for Rust code. This advancement leads to a significant improvement in performance, achieving a 52.52% accuracy rate in a benchmark crafted by human experts, a significant leap over GPT-4o's performance of 14.39%.