“Imagine a flock of birds in flight. There’s no leader. No central command. Each bird aligns with its neighbors—matching direction, adjusting speed, maintaining coherence through purely local coordination. The result is global order emerging from local consistency.”

“The article explores how combining separately trained models can create a 'super model' that leverages the best of each individual model.”

“By embedding the Riemannian metric tensor into the automatic differentiation graph, our architecture analytically reconstructs the Laplace-Beltrami operator, decoupling solution complexity from geometric discretization.”

“Our approach relies on a unified formulation of the distance from a point to a hyperplane on the considered spaces.”

“GaMO expands the field of view from existing camera poses, which inherently preserves geometric consistency while providing broader scene coverage.”

“Both uniform attention and trainable attention architectures implement the same algorithm via topologically and geometrically equivalent representations.”

“The paper classifies the irreducible components of V(d,n), gives criteria for the ideal I(d,n) to be prime or a complete intersection, and for the variety V(d,n) to be normal. It also gives near-equivalent conditions for V(d,n) to be factorial.”

“The paper revisits the process of eigenvalue approximation from the perspective of computational spectral geometry.”

“FoundationSLAM achieves superior trajectory accuracy and dense reconstruction quality across multiple challenging datasets, while running in real-time at 18 FPS.”

“The paper shows that non-planar diagrams, specifically MHV diagrams, can be represented by pseudo-positive geometries in the Grassmannian G(2,n).”

“The paper shows that the homeomorphism problem for compact topological n-manifolds is Borel equivalent to equality on natural numbers, while the homeomorphism problem for noncompact topological 2-manifolds is of maximal complexity.”

“The paper shows that commutative Frobenius pseudomonoids in the bicategory of spans are in correspondence with 2-Segal cosymmetric sets.”

“The paper proves that α=-1 is the unique choice achieving optimal energy stability under a specific condition, highlighting its theoretical advantage.”

“Each such variety is irreducible and admits a rational parametrization. The assignment is functorial: algebra quotients correspond to monomial maps among the varieties.”

“The authors report an experimentally accessible protocol for directly measuring the mixed-state topological invariant.”

“The paper proves that for certain values of the circle diameter, the number of touching pairs is less than that from a specific spiral construction, which is conjectured to be extremal.”

“The paper shows that its restricted holonomy group is SU(2), implying universal single-qubit control by closed loops in shape space.”

“The introduction of the 'Darboux family' as a tool for studying r-matrices in four-dimensional indecomposable coboundary Lie bialgebras.”

“The paper shows that changing the gluing edge isomorphisms does not affect the quasi-isometry type of these groups.”

“The droplet-to-slab transition always follows a similar mechanism to its equilibrium counterpart, but the reverse (slab-to-droplet) transition depends on rare non-equilibrium fluctuations.”

“The paper develops a solid geometric framework for the theory by creating isochrons, which are the level sets of the asymptotic phase, using the Graph Transform theorem.”

“Splatwizard provides an easy-to-use framework to implement new 3DGS compression model and utilize state-of-the-art techniques proposed by previous work.”

“An acyclic mcp graph is amenable if and only if a.e. component has at most two nonvanishing ends, while it is nowhere amenable exactly when a.e. component has a nonempty perfect (closed) set of nonvanishing ends.”

“The paper explains that the situation where the T-dual of a toric Kähler geometry is a generalized Kähler geometry involving semi-chiral fields is generic for polycylinders, tori and related geometries.”

“On $\mathscr{M}$-arrangements of conics and lines with ordinary singularities.”

“The discussion revolves around the future of "world models," with researchers offering predictions on breakthroughs in areas like geometric foundation models, self-supervised learning, and the development of 4D/5D/6D AIGC.”

“The paper provides direct experimental evidence of a pseudo-electric field that results in an unusual dynamic strain-induced Hall response.”

“The paper provides a necessary and sufficient condition for the incenter of a given n-simplex with k-rational vertices to be k-rational.”

“Temperature, chemical potential, and pressure arise as conjugate variables of a single information-theoretic functional.”

“The paper identifies the obstruction to the existence of the Prequantum Groupoid as the non-additivity of the integration of the prequantum form on the space of loops.”

“The paper discusses two approaches for extracting the QGT: quasi-QGT and pseudospin tomography.”

“DISF reduces CoM misalignment while maintaining geometric compatibility, translating into higher grasp success in both simulation and real-world execution compared to baselines.”

“The paper determines generalised Chebyshev-like forms for the determinants of gram matrices of contravariant forms for standard modules.”

“The paper analyzes the self-orthogonality in the vicinity of an EP and the Berry phase.”

“The paper proves that any ancient, asymptotically cylindrical flow is non-collapsed, convex, rotationally symmetric, and belongs to one of three canonical families: ancient ovals, the bowl soliton, or the flying wing translating solitons.”

“The paper presents the main ideas and techniques involved in the linear versions of several conjectures, including the Shafarevich conjecture and Kollár's conjecture.”

“The paper proposes 'weighted geometric mean' odds ratios and relative risks, and 'weighted mean' risk differences as transparent summary measures for ordinal outcomes.”

“ViReLoc plans routes between two given ground images.”

“A "pointy" limit set implies asymptotic dependence, offering practical geometric criteria for identifying extremal dependence classes.”

“The results show accurate and robust map merging with low error, and the learned features deliver strong performance in both loop closure detection and relative pose estimation.”

“The analysis reveals how tracking error in the attitude loop influences the position loop, how model uncertainties affect the closed-loop system, and the practical pitfalls of the control architecture.”

“A skew-gentle algebra is τ-tilting finite if and only if it is representation-finite.”

“FIGR improves the base model by 13.12% on AIME 2025 and 11.00% on BeyondAIME, highlighting the effectiveness of figure-guided multimodal reasoning in enhancing the stability and reliability of complex reasoning.”

“The framework reconceptualizes stitching from a two-dimensional warping paradigm to a three-dimensional consistency paradigm.”

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“The paper explains how the hierarchical hull of a pair of points in any colorable hierarchically hyperbolic space is quasi-isometric to a finite CAT(0) cube complex of bounded dimension.”

“Key findings demonstrate that sub-goal decomposition and irrelevant premise filtering critically influence final problem-solving accuracy, whereas Chain-of-Thought prompting unexpectedly degrades performance in some tasks.”

“The paper gives sufficient criteria that guarantee the integrability for the aforementioned generalized structures, formulated in terms of properties of the associated 2-form and connection.”

“HyperGRL delivers superior representation quality and generalization across diverse graph structures, achieving average improvements of 1.49%, 0.86%, and 0.74% over the strongest existing methods, respectively.”