3D 视觉

We place the attention token on the group: a token is an element $g_i$ of a matrix Lie group $G$ -- a bare transformation, with no feature payload and no external action $ρ(g)$ carrying it. To our knowledge this is the first attention construction whose tokens are bare matrix Lie group elements: their score is the closed-form algebra norm of the relative pose rather than a learned kernel, and it reaches the affine full-frame groups that every irrep- or surjective-exp-based method must exclude. We call it Lie-Algebra Attention. Once tokens are group elements, the rest follows with none of the usual representation-theoretic machinery. The relative geometry of a pair is canonical, $g_i^{-1} g_j$, so the pairwise invariant $w_{ij} = \log(g_i^{-1} g_j)$ is intrinsic rather than designed; equivariance under the diagonal $G$-action is tautological, and the cocycle condition holds automatically. The attention score is the negative squared algebra norm, $s_{ij} = -\|\log(g_i^{-1} g_j)\|_λ^2/τ$: the canonical proximity kernel under a block-weighted Frobenius inner product, with no irreducible representations, spherical harmonics, Clebsch-Gordan products, or learned kernel. The construction applies to any matrix Lie group on a chosen logarithm chart containing the relative poses, including the non-compact non-abelian affine groups with scale and shear that no vector-token attention method reaches: neither the irrep tradition nor surjective-exp methods. Three sequence-completion experiments, on SE(2), SO(3), and Aff(2), bear this out: the closed-form score matches a learned MLP kernel on the same invariant and outperforms it on SE(2), using 50 to 80x fewer score parameters, while a vector-token baseline breaks invariance by five to twelve orders of magnitude.

Robot learning has advanced rapidly in learning control, but learning the physical body of a robot remains much more difficult because jointly searching over design and control creates a very large combinatorial problem. Here, we present a data-driven framework for generating robot hands from human demonstrations. Instead of learning a complex controller together with each candidate design, we generate robot hand designs using the same simple control policy used after fabrication: matching fingertip positions through inverse kinematics. Using more than 4 million frames of human fingertip motion from everyday manipulation, our algorithm optimizes tree-structured robot hands to reproduce desired target motions. The framework produced both a 6-degree-of-freedom (DoF) general-purpose hand and lower-DoF task-specific hands with spatial four-bar mimic joints. To accelerate the search over designs, we trained a reinforcement-learning (RL) actor to propose good hand designs and joint angles, reducing search time from hours to minutes. We fabricated the mechanisms directly as one-piece articulated structures with print-in-place joints. In real-world experiments, the 6-DoF hand achieved highly accurate teleoperated fingertip tracking better than available commercial robot hands, whereas the specialized 3-DoF hands reproduced structured human and synthetic trajectories with reduced mechanical complexity. These results showed that large-scale human motion data can be used not only to train robot controllers but also as a reference for optimizing and generating the physical embodiment of robots.