February 2026

arXiv:2602.09028v1 Announce Type: new Abstract: This paper reformulates Fermat’s Last Theorem as an embedding problem of information-geometric structures. We reinterpret the Fermat equation as an $n$-th moment constraint, constructing a statistical manifold $mathcal{M}_n$ of generalized normal distributions via the Maximum Entropy Principle. By Chentsov’s Theorem, the natural metric is the Fisher information metric ($L^2$); however, the global structure is governed by the $L^n$ moment constraint. This reveals a discrepancy between the local quadratic metric and the global $L^n$ […]

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arXiv:2602.09027v1 Announce Type: new Abstract: Bitcoin derives a verifiable temporal order from probabilistic block discovery and cumulative proof-of-work rather than from a trusted global clock. We show that block arrivals exhibit stable exponential behavior across difficulty epochs, and that the proof-of-work process maintains a high-entropy search state that collapses discretely upon the discovery of a valid block. This entropy-based interpretation provides a mechanistic account of Bitcoin’s non-continuous temporal structure. In a distributed network, however, entropy collapse is not […]

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While single-agent legged locomotion has witnessed remarkable progress, individual robots remain fundamentally constrained by physical actuation limits. To transcend these boundaries, we introduce Co-jump, a cooperative task where two quadrupedal robots synchronize to execute jumps far beyond their solo capabilities. We tackle the high-impulse contact dynamics of this task under a decentralized setting, achieving synchronization without explicit communication or pre-specified motion primitives. Our framework leverages Multi-Agent Proximal Policy Optimization (MAPPO) enhanced by a progressive curriculum strategy, which effectively […]

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Graph Domain Adaptation (GDA) aims to bridge distribution shifts between domains by transferring knowledge from well-labeled source graphs to given unlabeled target graphs. One promising recent approach addresses graph transfer by discretizing the adaptation process, typically through the construction of intermediate graphs or stepwise alignment procedures. However, such discrete strategies often fail in real-world scenarios, where graph structures evolve continuously and nonlinearly, making it difficult for fixed-step alignment to approximate the actual transformation process. To address these limitations, […]

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The proliferation of ride-hailing services has fundamentally transformed urban mobility patterns, making accurate ride-hailing forecasting crucial for optimizing passenger experience and urban transportation efficiency. However, ride-hailing forecasting faces significant challenges due to geospatial heterogeneity and high susceptibility to external events. This paper proposes MVGR-Net(Multi-View Geospatial Representation Learning), a novel framework that addresses these challenges through a two-stage approach. In the pretraining stage, we learn comprehensive geospatial representations by integrating Points-of-Interest and temporal mobility patterns to capture regional characteristics […]

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We investigate the geometric structure of learning dynamics in overparameterized transformer models through carefully controlled modular arithmetic tasks. Our primary finding is that despite operating in high-dimensional parameter spaces ($d=128$), transformer training trajectories rapidly collapse onto low-dimensional execution manifolds of dimension $3$–$4$. This dimensional collapse is robust across random seeds and moderate task difficulties, though the orientation of the manifold in parameter space varies between runs. We demonstrate that this geometric structure underlies several empirically observed phenomena: (1) […]

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We investigate the geometric structure of learning dynamics in overparameterized transformer models through carefully controlled modular arithmetic tasks. Our primary finding is that despite operating in high-dimensional parameter spaces ($d=128$), transformer training trajectories rapidly collapse onto low-dimensional execution manifolds of dimension $3$–$4$. This dimensional collapse is robust across random seeds and moderate task difficulties, though the orientation of the manifold in parameter space varies between runs. We demonstrate that this geometric structure underlies several empirically observed phenomena: (1) […]

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Graph Domain Adaptation (GDA) transfers knowledge from labeled source graphs to unlabeled target graphs but is challenged by complex, multi-faceted distributional shifts. Existing methods attempt to reduce distributional shifts by aligning manually selected graph elements (e.g., node attributes or structural statistics), which typically require manually designed graph filters to extract relevant features before alignment. However, such approaches are inflexible: they rely on scenario-specific heuristics, and struggle when dominant discrepancies vary across transfer scenarios. To address these limitations, we […]

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GPU memory errors are a critical threat to deep learning (DL) frameworks, leading to crashes or even security issues. We introduce GPU-Fuzz, a fuzzer locating these issues efficiently by modeling operator parameters as formal constraints. GPU-Fuzz utilizes a constraint solver to generate test cases that systematically probe error-prone boundary conditions in GPU kernels. Applied to PyTorch, TensorFlow, and PaddlePaddle, we uncovered 13 unknown bugs, demonstrating the effectiveness of GPU-Fuzz in finding memory errors.

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