arXiv:2606. 26399v1 Announce Type: new Abstract: We study certain extremal problems in combinatorial geometry that ask about configurations of points in an $n \times n$ grid that satisfy strict, global geometric constraints.
We study certain extremal problems in combinatorial geometry that ask about configurations of points in an $n \times n$ grid that satisfy strict, global geometric constraints. Classical exact solvers suffer from combinatorial explosion for these types of problems, and standard reinforcement learning and transformer-based models struggle with the sparse reward "validity cliff" and quadratic token-consumption limits.
arXiv:2609.18379v1 Announce Type: new Abstract: Square jigsaw reassembly requires recovering the spatial arrangement of shuffled fragments from their visual content and pairwise relationships. While...
arXiv:2609.39339v1 Announce Type: cross Abstract: Matching problems are ubiquitous in data science as they enable the alignment of structured objects and distributions. While existing solvers are oft...
arXiv:2609.00713v1 Announce Type: new Abstract: Estimation of the absolute pose of an object is an essential task for various robotic applications. Recently, incorporating gravity direction as prior...
arXiv:2607. 08538v1 Announce Type: cross Abstract: Suppose we observe two sets of $n$ Gaussian vectors in $\mathbb{R}^d$, with the promise that, after applying a permutation of $[n]$ and a rotation of $\mathbb{R}^d$, the two sets are $\rho$-correlated.
arXiv:2604. 04050v2 Announce Type: replace-cross Abstract: Flow-matching methods for 3D shape assembly learn point-wise velocity fields that transport parts toward assembled configurations, yet they receive no explicit guidance about which cross-part interactions should drive the motion.
ThinQuant introduces efficient rotation learning for low‑bit weight and activation quantization of large language models by reducing calibration data through a geometric selection of activations and solving a lower‑dimensional optimization problem via an ADMM algorithm. The method achieves comparable or better quantization performance with dramatically fewer calibration points, completing rotation calibration for Llama‑3‑70B in under 12 minutes and for Llama‑3.1‑405B in just over 2 hours on a single GPU. ThinQuant outperforms existing gradient‑free approaches such as DartQuant and gradient‑based SpinQuant in both speed and perplexity metrics on WikiText‑2.
The paper introduces GMPCR, a non‑learning spectral consistency‑guided framework for multiview point cloud registration in low‑overlap scenes. GMPCR refines initial correspondences into a second‑order compatibility structure, uses spectral analysis to filter unreliable matches and select informative scan pairs, and then applies maximal‑clique hypothesis generation for robust relative transformations. The resulting sparse pose graph is further refined with an adaptive history‑aware synchronization scheme, and a recovery mechanism allows previously down‑weighted edges to regain confidence, achieving high registration recalls on benchmark datasets while reducing computational cost.
Vision Foundation Models (VFMs) have significantly advanced dense feature matching, yet severe in-plane rotation remains a critical challenge. Existing solutions face a fundamental dilemma: data-driven methods require inefficient parameter scaling to implicitly learn rotations, whereas strictly equivariant networks lack the semantic capacity of modern VFMs.
The paper introduces EGGroW, efficient algorithms for computing geodesic Gromov-Wasserstein distances using entropic Sinkhorn-like methods, GenusSink techniques, and random features. It addresses the cubic time complexity of traditional GWD calculations on dense intra-space distance matrices, enabling scalable comparisons of probabilistic distributions on general geodesic manifolds and graph shortest‑path distances. The authors demonstrate EGGroW’s effectiveness in downstream tasks such as 3D pose estimation and partial 3D template recovery, showing accurate results where Euclidean‑based methods fail while maintaining a light computational footprint.
TokenMatch is a transformer-based model that estimates 3D shape correspondences by adaptively tokenising meshes into curvature-guided patches. Trained only on the BeCoS partial-to-partial dataset, it generalises to full-shape matching without retraining, using self‑ and cross‑attention to learn patch‑ and point‑level relations. Evaluated on CP2P, PSMAL, BeCoS, FAUST, SCAPE, and SHREC'19, TokenMatch consistently outperforms existing methods in mean geodesic error and intersection‑over‑union while achieving sub‑second inference speeds.