\emph{geometric
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Related Articles from SNS
From Symbolic to Geometric: Enabling Spatial Reasoning in Large Language Models
arXiv:2606.04381v1 Announce Type: new Abstract: Recent large language models (LLMs) often appear to exhibit spatial reasoning ability; however, this capability is largely \emph{symbolic}, arising from pattern matching over spatial language rather than true \emph{geometric} reasoning over space. Because LLMs operate on discrete tokens, they lack native support for continuous spatial representations, explicit geometric computation, and structured spatial operators.
Polynomial Context-Truncation Sensitivity in Autoregressive Language Models: Sequential Wyner-Ziv Bounds for KV Cache Compression
arXiv:2605.25085v2 Announce Type: replace Abstract: We study the rate-distortion limits of online KV cache compression in autoregressive language models, formulating it as sequential Wyner-Ziv source coding on the filtration induced by the model, with the next-step query as decoder side information. Empirically, across four models spanning two families and $0.5$-$3$B parameters, we find that the next-token distribution's sensitivity to context truncation decays \emph{polynomially} rather...
Apple-Peel Unfolding in Three and Four Dimensions: Spiral and Zonal Selection Rules
arXiv:2605.30373v1 Announce Type: new Abstract: Apple-Peel Unfolding is a greedy algorithm that selects the faces (or cells) of a polyhedron (or polytope) one at a time in a spiral order, producing a net analogous to peeling an apple in a single continuous strip. We define two face-selection rules -- RS (Spiral rule: minimum signed determinant, i.e.\ sharpest clockwise turn) and RZ (Zonal rule: maximum coordinate along the peeling axis) -- and systematically evaluate their unfolding success...
MAdam: Metric-Aware Multi-Objective Adam
Announce Type: new Abstract: Multi-objective optimization (MOO) underlies many machine learning problems, yet MOO solvers across the loss-balancing, gradient-balancing, and Pareto-based families almost universally hand their reconciled directions to Adam~\cite{kingma2015adam}. We show this coupling introduces two systematic gaps between the solver's intent and the optimizer's execution. The first is a \emph{weighting mismatch}: Adam's second-moment denominator entangles the time-varying...
DisFlow: Scene Flow from Distance Field for Object Pose, Velocity Tracking, and Dynamic Object Reconstruction
Announce Type: new Abstract: We present \emph{DisFlow}, a novel framework for online scene flow estimation from distance field that enables \emph{6DoF dynamic object pose estimation}, \emph{motion tracking}, and \emph{surface reconstruction}. The scene is represented by Gaussian Process Implicit Surfaces (GPIS), with surface normals serving as derivative constraints, enabling accurate signed distance computations near the surface and gradient queries with uncertainty. With this...
Functional Attention: From Pairwise Affinities to Functional Correspondences
arXiv:2605.31559v1 Announce Type: new Abstract: Learning mappings between infinite-dimensional function spaces, or operator learning, is essential for many machine learning applications. Although transformer-based operators are popular, they often rely on token-wise attention. These methods treat continuous fields as discrete tokens and usually ignore the global functional structure.
Understanding Quantization-Aware Training: Gradients at Quantized Weights Bias to the Low-Loss Basin
arXiv:2606.09012v1 Announce Type: new Abstract: Post-training quantization (PTQ) converts a trained full-precision model into low-bit weights without task-level retraining, while quantization-aware training (QAT) incorporates quantization into the training loop. Although PTQ is efficient and often accurate at moderate bitwidths, it can fail sharply at aggressive bitwidths; QAT is more expensive but can often recover the lost accuracy. We propose a unified geometric framework that explains...
The price of incrementality in k-center clustering
arXiv:2606.08713v1 Announce Type: new Abstract: The $k$-center problem is one of the best-studied and most intuitive clustering formulations. It asks, given a set of $n$ points in a metric space, for $k$ of the points to be designated as cluster centers, so that the maximum distance of an input point to its nearest center is minimized.
When Detectors Forget Forensics: Blocking Semantic Shortcuts for Generalizable AI-Generated Image Detection
arXiv:2603.09242v2 Announce Type: replace Abstract: The growing realism of generative models has blurred the boundary between real and synthetic content, posing significant challenges to reliable AI-generated image detection. Although large-scale pre-trained Vision Foundation Models have advanced detection capability, their generalization to images from unseen generation pipelines remains inadequate. In this paper, we identify, for the first time, a key failure mechanism, termed...
ReciNet: Reciprocal Space-Aware Long-Range Modeling for Crystalline Property Prediction
Announce Type: replace Abstract: Predicting properties of crystals from their structures is a fundamental yet challenging task in materials science. Unlike molecules, crystal structures exhibit infinite periodic arrangements of atoms, requiring methods capable of capturing both local and global information effectively. However, current works fall short of capturing long-range interactions within periodic structures.