Graph transformers (GTs) have shown strong empirical performance, yet current architectures vary widely in their use of attention mechanisms, positional embeddings (PEs), and expressivity. Existing expressivity results are often tied to specific design choices and lack comprehensive empirical validation on large-scale data. This leaves a gap between theory and practice, preventing generalizable insights that exceed particular application domains. Here, we propose the GeneralizedDistance Transformer (GDT), a GT architecture based on standard attention that incorporates many recent advancements for GTs, and we develop a fine-grained understanding of the GDT's representation power in terms of attention and PEs. Through extensive experiments, we identify design choices that consistently perform well across various applications, tasks, and model scales, demonstrating strong performance in a few-shot transfer setting without fine-tuning. Our evaluation covers over eight million graphs with roughly 270M tokens across diverse domains, including image-based object detection, molecular property prediction, code summarization, and out-of-distribution algorithmic reasoning.

Existing NAS methods for semantic segmentation typically apply uniform optimization to all candidate networks (paths) within a one-shot supernet. However, the concurrent existence of both promising and suboptimal paths often results in inefficient weight updates and gradient conflicts. This issue is particularly severe in semantic segmentation due to its complex multi-branch architectures and large search space, which further degrade the supernet's ability to accurately evaluate individual paths and identify high-quality candidates. To address this issue, we propose Dynamic Path Selection (DPS), a selective training strategy that leverages multiple performance proxies to guide path optimization. DPS follows a stagewise paradigm, where each phase emphasizes a different objective: early stages prioritize convergence, the middle stage focuses on expressiveness, and the final stage emphasizes a balanced combination of expressiveness and generalization. At each stage, paths are selected based on these criteria, concentrating optimization efforts on promising paths, thus facilitating targeted and efficient model updates. Additionally, DPS integrates a dynamic stage scheduler and a diversity-driven exploration strategy, which jointly enable adaptive stage transitions and maintain structural diversity among selected paths. Extensive experiments demonstrate that, under the same search space, DPS can discover efficient models with strong generalization and superior performance.

Graph Neural Networks (GNNs) are widely used to compute representations of node pairs for downstream tasks such as link prediction. Yet, theoretical understanding of their expressive power has focused almost entirely on graph-level representations. In this work, we shift the focus to links and provide the first comprehensive study of GNN expressiveness in link representation. We introduce a unifying framework, the kϕ-kρ-mframework, that subsumes existing messagepassing link models and enables formal expressiveness comparisons. Using this framework, we derive a hierarchy of state-of-the-art methods and offer theoretical tools to analyze future architectures. To complement our analysis, we propose a synthetic evaluation protocol comprising the first benchmark specifically designed to assess link-level expressiveness. Finally, we ask: does expressiveness matter in practice? We use a graph symmetry metric that quantifies the difficulty of distinguishing links and show that while expressive models may underperform on standard benchmarks, they significantly outperform simpler ones as symmetry increases, highlighting the need for dataset-aware model selection.

Extensive experiments show that GenColor produces visually compelling results comparable to those of expert colorists and surpasses state-of-the-art methods in both subjective and objective evaluations. We have released the code and dataset.

Efficient long-context modeling remains a critical challenge for natural language processing (NLP), as the time complexity of the predominant Transformer architecture scales quadratically with the sequence length. While state-space models (SSMs) offer alternative sub-quadratic solutions, they struggle to capture longrange dependencies effectively. In this work, we focus on analyzing and improving the long-context modeling capabilities of SSMs. We show that the widely used synthetic task, associative recall, which requires a model to recall a value associated with a single key without context, insufficiently represents the complexities of real-world long-context modeling. To address this limitation, we extend the associative recall to a novel synthetic task, joint recall, which requires a model to recall the value associated with a key given in a specified context. Theoretically, we prove that SSMs do not have the expressiveness to solve multi-query joint recall in sub-quadratic time complexity. To resolve this issue, we propose a solution based on integrating SSMs with Context-Dependent Sparse Attention (CDSA), which has the expressiveness to solve multi-query joint recall with sub-quadratic computation. To bridge the gap between theoretical analysis and real-world applications, we propose locality-sensitive Hashing Attention with sparse Key Selection (HAX), which instantiates the theoretical solution and is further tailored to natural language domains. Extensive experiments on both synthetic and real-world long-context benchmarks show that HAX consistently outperforms SSM baselines and SSMs integrated with context-independent sparse attention (CISA).

The attention mechanism is a core component of the Transformer architecture. Various methods have been developed to compute attention scores, including multihead attention (MHA), multi-query attention, group-query attention and so on. We further analyze the MHA and observe that its performance improves as the number of attention heads increases, provided the hidden size per head remains sufficiently large. Therefore, increasing both the head count and hidden size per head with minimal parameter overhead can lead to significant performance gains at a low cost. Motivated by this insight, we introduce Simulated Attention Score (SAS), which maintains a compact model size while simulating a larger number of attention heads and hidden feature dimension per head. This is achieved by projecting a low-dimensional head representation into a higher-dimensional space, effectively increasing attention capacity without increasing parameter count. Beyond the head representations, we further extend the simulation approach to feature dimension of the key and query embeddings, enhancing expressiveness by mimicking the behavior of a larger model while preserving the original model size. To control the parameter cost, we also propose Parameter-Efficient Attention Aggregation (PEAA). Comprehensive experiments on a variety of datasets and tasks demonstrate the effectiveness of the proposed SAS method, achieving significant improvements over different attention variants.

Message Passing Neural Networks (MPNNs) are the building block of graph foundation models, but fundamentally suffer from oversmoothing and oversquashing. There has recently been a surge of interest in fixing both issues. Existing efforts primarily adopt global approaches, which may be beneficial in some regions but detrimental in others, ultimately leading to the suboptimal expressiveness. In this paper, we begin by revisiting oversquashing through a global measure -- spectral gap $\lambda$ -- and prove that the increase of $\lambda$ leads to gradient vanishing with respect to the input features, thereby undermining the effectiveness of message passing. Motivated by such theoretical insights, we propose a local approach that adaptively adjusts message passing based on local structures. To achieve this, we connect local Riemannian geometry with MPNNs, and establish a novel nonhomogeneous boundary condition to address both oversquashing and oversmoothing. Building on the Robin condition, we design a GBN network with local bottleneck adjustment, coupled with theoretical guarantees. Extensive experiments on homophilic and heterophilic graphs show the expressiveness of GBN. Furthermore, GBN does not exhibit performance degradation even when the network depth exceeds $256$ layers.

Graph Neural Networks (GNNs) are widely used to compute representations of node pairs for downstream tasks such as link prediction. Yet, theoretical understanding of their expressive power has focused almost entirely on graph-level representations. In this work, we shift the focus to links and provide the first comprehensive study of GNN expressiveness in link representation. We introduce a unifying framework, the $k_\phi$-$k_\rho$-$m$ framework, that subsumes existing message-passing link models and enables formal expressiveness comparisons. Using this framework, we derive a hierarchy of state-of-the-art methods and offer theoretical tools to analyze future architectures. To complement our analysis, we propose a synthetic evaluation protocol comprising the first benchmark specifically designed to assess link-level expressiveness. Finally, we ask: does expressiveness matter in practice? We use a graph symmetry metric that quantifies the difficulty of distinguishing links and show that while expressive models may underperform on standard benchmarks, they significantly outperform simpler ones as symmetry increases, highlighting the need for dataset-aware model selection.

Efficient long-context modeling remains a critical challenge for natural language processing (NLP), as the time complexity of the predominant Transformer architecture scales quadratically with the sequence length. While state-space models (SSMs) offer alternative sub-quadratic solutions, they struggle to capture long-range dependencies effectively. In this work, we focus on analyzing and improving the long-context modeling capabilities of SSMs. We show that the widely used synthetic task, associative recall, which requires a model to recall a value associated with a single key without context, insufficiently represents the complexities of real-world long-context modeling. To address this limitation, we extend the associative recall to a novel synthetic task, joint recall, which requires a model to recall the value associated with a key given in a specified context. Theoretically, we prove that SSMs do not have the expressiveness to solve multi-query joint recall in sub-quadratic time complexity. To resolve this issue, we propose a solution based on integrating SSMs with Context-Dependent Sparse Attention (CDSA), which has the expressiveness to solve multi-query joint recall with sub-quadratic computation. To bridge the gap between theoretical analysis and real-world applications, we propose locality-sensitive Hashing Attention with sparse Key Selection (HAX), which instantiates the theoretical solution and is further tailored to natural language domains. Extensive experiments on both synthetic and real-world long-context benchmarks show that HAX consistently outperforms SSM baselines and SSMs integrated with context-independent sparse attention (CISA).

Autonomous spacecraft require rapid, lightweight, and reliable onboard detection of cyber-RF threats. Using the SPARTA attack model, we analyze the latency-accuracy trade-offs of TinyML-compatible classical models -- Random Forest, Logistic Regression, SVM, and MLP -- for detecting uplink jamming, Fake-NR spoofing, payload manipulation, ground-segment compromise, and unauthorized command injection. We present a physics-informed theoretical analysis of each model's computational complexity, VC dimension, Lipschitz continuity, and latency scaling, supported by empirical measurements on adversarial RF spectrograms generated via BandErasure, FakeNR, and NoiseBurst corruption modes. Results show that Logistic Regression achieves microsecond-level inference with only a 1\% accuracy drop relative to Random Forest, making it an effective TinyML baseline for onboard autonomy. The study also identifies opportunities for advancing spacecraft cybersecurity through richer feature encoders and multi-timescale learning architectures, building on recent progress in edge intelligence and trustworthy AI.