Tootfinder

Series D, Episode 11 - Orbit
PINDER: Checkmate, Egrorian!
EGRORIAN: How dare you!
PINDER: Checkmate... checkmate...
EGRORIAN: [To game board] Recall the last six moves. [Computer replays a sequence of moves]
PINDER: [Sighing] Oh...
https://blake.torpidity.net/m/411/160

Learning to Build Shapes by Extrusion
Thor Vestergaard Christiansen, Karran Pandey, Alba Reinders, Karan Singh, Morten Rieger Hannemose, J. Andreas B{\ae}rentzen
https://arxiv.org/abs/2601.22858 https://arxiv.org/pdf/2601.22858 https://arxiv.org/html/2601.22858
arXiv:2601.22858v1 Announce Type: new
Abstract: We introduce Text Encoded Extrusion (TEE), a text-based representation that expresses mesh construction as sequences of face extrusions rather than polygon lists, and a method for generating 3D meshes from TEE using a large language model (LLM). By learning extrusion sequences that assemble a mesh, similar to the way artists create meshes, our approach naturally supports arbitrary output face counts and produces manifold meshes by design, in contrast to recent transformer-based models. The learnt extrusion sequences can also be applied to existing meshes - enabling editing in addition to generation. To train our model, we decompose a library of quadrilateral meshes with non-self-intersecting face loops into constituent loops, which can be viewed as their building blocks, and finetune an LLM on the steps for reassembling the meshes by performing a sequence of extrusions. We demonstrate that our representation enables reconstruction, novel shape synthesis, and the addition of new features to existing meshes.
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Polyharmonic Cascade
Yuriy N. Bakhvalov
https://arxiv.org/abs/2512.17671 https://arxiv.org/pdf/2512.17671 https://arxiv.org/html/2512.17671
arXiv:2512.17671v1 Announce Type: new
Abstract: This paper presents a deep machine learning architecture, the "polyharmonic cascade" -- a sequence of packages of polyharmonic splines, where each layer is rigorously derived from the theory of random functions and the principles of indifference. This makes it possible to approximate nonlinear functions of arbitrary complexity while preserving global smoothness and a probabilistic interpretation. For the polyharmonic cascade, a training method alternative to gradient descent is proposed: instead of directly optimizing the coefficients, one solves a single global linear system on each batch with respect to the function values at fixed "constellations" of nodes. This yields synchronized updates of all layers, preserves the probabilistic interpretation of individual layers and theoretical consistency with the original model, and scales well: all computations reduce to 2D matrix operations efficiently executed on a GPU. Fast learning without overfitting on MNIST is demonstrated.
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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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