Yibang Li | Searcharxiv

arXiv2026

Wrench-Based Bayesian Pose Estimation via Matrix--Fisher Gaussian Inference

In this paper, a residual-safeguarded local Matrix Fisher--Gaussian (MFG) inference method is developed for wrench-based pose estimation on $\mathrm{SO}(3)\times\mathbb{R}^3$. The force/torque measurements are modeled by a quasi-static contact system in which the predicted wrench depends on the unknown object pose through an implicit equilibrium state. Since the resulting nonlinear likelihood is not globally conjugate to the coupled MFG family, a local Bayesian update is constructed by linearizing the reduced wrench residual and matching the induced Gauss--Newton posterior model to a coupled MFG distribution. It is shown that the reduced residual Jacobian has a Schur-complement form, and that the local quadratic posterior admits a closed-form MFG approximation matching the prescribed local first- and second-order posterior coefficients. The same sensitivity model yields a compensated rotational information score, which characterizes the weakest locally informative attitude direction after translational compensation. A residual-safeguarded recentering algorithm is further introduced to update the linearization point only through candidates that decrease the recomputed whitened wrench residual. In the tested sparse prior-mismatch regimes, the resulting estimator reduces residual merit and pose error relative to single-pass and local baseline variants, and controlled robot experiments provide a proof of concept under calibrated quasi-static conditions.

math.MG↗

arXiv2026

Intrinsic Muon: Spectral Optimization on Riemannian Matrix Manifolds

Muon and related norm-constrained matrix optimizers have become central to large-scale learning problems. They are formulated as a linear maximization oracle (LMO) over an ambient matrix-norm ball in unconstrained Euclidean space. However, these do not generalize cleanly to manifold-valued parameters such as low-rank factorizations, orthogonality constraints, or symmetric positive definite (SPD) matrices. Naively restricting the Muon LMO to the tangent space (i) breaks quotient symmetries and (ii) couples the tangent-space constraint with an ambient norm bound, thereby obstructing closed-form solutions on various manifolds of interest. We resolve both issues with a single observation: every Riemannian metric canonically lifts a unitarily invariant Euclidean norm to an intrinsic norm on each tangent space, and the resulting intrinsic norm constrained LMO is symmetry preserving. Building on this, we introduce intrinsic Muon (iMuon), a unified framework that yields closed-form updates on the fixed-rank, SPD, Stiefel, and Grassmann manifolds for any unitarily invariant norm, including the spectral, Frobenius, and nuclear norms. We establish convergence guarantees for both deterministic and stochastic iMuon with rate constants that depend only on the manifold dimension. Notably, on the fixed-rank manifold this constant depends only on the rank, making the rate independent of factor conditioning and removing the runtime factor-rescaling required by prior work. Experiments on LoRA finetuning of LLMs, image classification, and subspace learning illustrate the efficacy of the proposed approach.

cs.LG↗