Cholesky
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Related Articles from SNS
Variational Free Energy Pivot Selection for Pivoted Cholesky
arXiv:2606.01821v1 Announce Type: new Abstract: Pivoted Cholesky factorizations construct low-rank approximations of symmetric positive definite matrices by sequentially selecting pivots from the residual diagonal. Classical greedy and randomized rules, such as randomly pivoted Cholesky, target the algebraic trace-norm error of the residual. In many applications, however, the matrix enters a nonlinear matrix functional whose value, not the trace-norm error, determines solution quality, and...
COP-Q: Safety-First Reinforcement Learning for Robot Control via Cholesky-Ordered Projection
arXiv:2606.04749v1 Announce Type: new Abstract: Safe robot control requires maximizing return while satisfying safety constraints. In off-policy safe reinforcement learning, reward and safety Q-values are commonly learned by separate critic ensembles, with uncertainty handled independently for each objective. This objective-wise treatment neglects inter-objective correlation and can lead to overly conservative value estimates, thereby reducing sample efficiency.
Hierarchical Recursive Precision for Accelerating Symmetric Linear Solves on MXUs
Announce Type: replace Abstract: Symmetric positive-definite system solvers based on Cholesky factorization are fundamental to many scientific applications, such as climate modeling. We present a portable, nested recursive mixed-precision solver designed for Matrix Processing Units (MXUs), including NVIDIA Tensor Cores (H200) and AMD Matrix Cores (MI300X), that assigns low-precision FP16 arithmetic to large off-diagonal blocks, while preserving high precision on diagonal blocks to ensure...
Fast Sparse Matrix Permutation for Mesh-Based Direct Solvers
arXiv:2602.00898v2 Announce Type: replace Abstract: We present a fast sparse matrix permutation algorithm tailored to linear systems arising from triangle meshes. Our approach produces nested-dissection-style permutations while significantly reducing permutation runtime overhead. Rather than enforcing strict balance and separator optimality, the algorithm deliberately relaxes these design decisions to favor fast partitioning and efficient elimination-tree construction.
Direct Informed Sampling on Riemannian Manifolds via Loewner Order Lower Bounds
arXiv:2606.02879v1 Announce Type: new Abstract: Informed sampling techniques accelerate sampling-based motion planners by focusing the search on promising regions of the state space, yet most existing methods rely on Euclidean heuristics that become inadmissible under configuration-dependent Riemannian metrics. While scalar eigenvalue bounds restore admissibility by uniformly scaling the Euclidean distance, they discard the directional structure of the metric, producing overly conservative...
GPU-Accelerated Direct Transcription-Based Nonlinear Model Predictive Control
arXiv:2606.04725v1 Announce Type: new Abstract: In this paper, we present a GPU-accelerated framework for nonlinear model predictive control (NMPC) based on direct transcription and second-order interior-point methods. Many real-world systems exhibit nonlinear dynamics that cannot be accurately captured by linear models, motivating the use of NMPC. However, NMPC requires the repeated real-time solution of optimal control problems (OCP), which become computationally demanding large-scale...
WildCat: Near-Linear Attention in Theory and Practice
arXiv:2602.10056v2 Announce Type: replace Abstract: We introduce WildCat, a high-accuracy, low-cost approach to compressing the attention mechanism in neural networks. While attention is a staple of modern network architectures, it is also notoriously expensive to deploy due to resource requirements that scale quadratically with the input sequence length $n$. WildCat avoids these quadratic costs by only attending over a small weighted coreset. Crucially, we select the coreset using a fast...