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.