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Spatially-informed transformers: Injecting geostatistical covariance biases into self-attention for spatio-temporal forecasting
Yuri Calleo
https://arxiv.org/abs/2512.17696 https://arxiv.org/pdf/2512.17696 https://arxiv.org/html/2512.17696
arXiv:2512.17696v1 Announce Type: new
Abstract: The modeling of high-dimensional spatio-temporal processes presents a fundamental dichotomy between the probabilistic rigor of classical geostatistics and the flexible, high-capacity representations of deep learning. While Gaussian processes offer theoretical consistency and exact uncertainty quantification, their prohibitive computational scaling renders them impractical for massive sensor networks. Conversely, modern transformer architectures excel at sequence modeling but inherently lack a geometric inductive bias, treating spatial sensors as permutation-invariant tokens without a native understanding of distance. In this work, we propose a spatially-informed transformer, a hybrid architecture that injects a geostatistical inductive bias directly into the self-attention mechanism via a learnable covariance kernel. By formally decomposing the attention structure into a stationary physical prior and a non-stationary data-driven residual, we impose a soft topological constraint that favors spatially proximal interactions while retaining the capacity to model complex dynamics. We demonstrate the phenomenon of ``Deep Variography'', where the network successfully recovers the true spatial decay parameters of the underlying process end-to-end via backpropagation. Extensive experiments on synthetic Gaussian random fields and real-world traffic benchmarks confirm that our method outperforms state-of-the-art graph neural networks. Furthermore, rigorous statistical validation confirms that the proposed method delivers not only superior predictive accuracy but also well-calibrated probabilistic forecasts, effectively bridging the gap between physics-aware modeling and data-driven learning.
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CAG-Avatar: Cross-Attention Guided Gaussian Avatars for High-Fidelity Head Reconstruction
Zhe Chang, Haodong Jin, Yan Song, Hui Yu
https://arxiv.org/abs/2601.14844 https://arxiv.org/pdf/2601.14844 https://arxiv.org/html/2601.14844
arXiv:2601.14844v1 Announce Type: new
Abstract: Creating high-fidelity, real-time drivable 3D head avatars is a core challenge in digital animation. While 3D Gaussian Splashing (3D-GS) offers unprecedented rendering speed and quality, current animation techniques often rely on a "one-size-fits-all" global tuning approach, where all Gaussian primitives are uniformly driven by a single expression code. This simplistic approach fails to unravel the distinct dynamics of different facial regions, such as deformable skin versus rigid teeth, leading to significant blurring and distortion artifacts. We introduce Conditionally-Adaptive Gaussian Avatars (CAG-Avatar), a framework that resolves this key limitation. At its core is a Conditionally Adaptive Fusion Module built on cross-attention. This mechanism empowers each 3D Gaussian to act as a query, adaptively extracting relevant driving signals from the global expression code based on its canonical position. This "tailor-made" conditioning strategy drastically enhances the modeling of fine-grained, localized dynamics. Our experiments confirm a significant improvement in reconstruction fidelity, particularly for challenging regions such as teeth, while preserving real-time rendering performance.
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