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Hassan Jaber

Publications and source records attributed to Hassan Jaber.

3 recordsLinked to original sources

EmbodimentSemantic: A Spatial Scene-Graph Dataset and Benchmark for Vision-Language Models on Embodied Manipulation Trajectories

Spatial grounding remains a key limitation of vision-language-action (VLA) systems for robotic manipulation. While current models can recognize objects and follow language instructions, they often lack an explicit representation of how objects are arranged in space, including support, containment, ordering, occlusion, and depth-sensitive relations. We introduce EmbodimentSemantic, a spatial scene-graph dataset and benchmark for evaluating relational grounding in embodied manipulation. EmbodimentSemantic represents scenes as directed object-relation-object triplets, where each triplet specifies a spatial relation between an ordered pair of objects using a fixed set of relations. This representation enables direct evaluation of object binding, relation prediction, and spatial consistency. The dataset includes real-world manipulation observations collected with the low-cost SO101 robot arm, together with generated scene graphs for studying spatial grounding in practical robotic settings. To provide controlled validation, we also introduce a simulator-grounded LIBERO benchmark with over 60K manipulation frames and more than 120K camera-specific scene graphs across paired third-person and wrist views, where ground-truth relations are derived automatically from MuJoCo geometry, world coordinates, camera projections, and visibility constraints. We further test whether scene graphs improve downstream control by injecting them into existing VLA policy prompts. Experiments across open-source and commercial VLMs show that current models often predict plausible relations but struggle with exact depth-aware and viewpoint-dependent spatial structure. EmbodimentSemantic provides a unified framework for diagnosing spatial grounding in VLM perception and testing its utility for VLA manipulation.

cs.RO

Hardy-Sobolev Equations on Compact Riemannian Manifolds

Let (M,g) be a compact Riemannien Manifold of dimension n > 2, x_0 in M a fix and singular point and s in (0,2). We let 2*(s) = 2(n-s)/(n-2) be the critical Hardy-Sobolev exponent. we investigate the existence of positive distributional solutions u in C^0(M) to the critical equation Δ_g u + a(x) u = u^{2*(s)-1}/ d_g(x,x_0)^s in M where Δ_g := - div_g(\nabla) is the Laplace-Beltrami operator, and d_g is the Riemannian distance on (M,g). Via a minimization method in the spirit of Aubin, we prove existence in dimension n > 3 when the potential a is sufficiently below the scalar curvature at x_0. In dimension n = 3, we use a global argument and we prove existence when the mass of the linear operator Δ_g + a is positive at x_0. As a byproduct of our analysis, we compute the best first constant for the related Riemannian Hardy-Sobolev inequality.

math.DG

Optimal Hardy-Sobolev Inequalities on Compact Riemannain Manifolds

Given a compact Riemannian Manifold (M,g) of dimension n > 2, a point x_0 in M and s in (0,2). We let 2*(s) = 2(n-s)/(n-2) be the critical Hardy-Sobolev exponent. The Hardy-Sobolev embedding yields the existence of A,B > 0 such that (\int_M|u|^{2*(s)}dv_g)^{2/2*(s)} \leq A\int_M |\nabla u|_g^2 dv_g +B\int_M u^2 dv_g for all u in H_1^2(M). It has been proved that A\leq K(n,s) and that one can take any value A > K(n,s) in in the above inequality where $K(n,s)$ is the best possible constant in the Euclidean Hardy-Sobolev inequality. In the present manuscript, we prove that one can also take A = K(n,s) in the above inequality.

math.DG