惯性聚合 高效追踪和阅读你感兴趣的博客、新闻、科技资讯
阅读原文 在惯性聚合中打开

推荐订阅源

B
Blog
量子位
奇客Solidot–传递最新科技情报
奇客Solidot–传递最新科技情报
Last Week in AI
Last Week in AI
酷 壳 – CoolShell
酷 壳 – CoolShell
人人都是产品经理
人人都是产品经理
Jina AI
Jina AI
雷峰网
雷峰网
博客园_首页
WordPress大学
WordPress大学
博客园 - 司徒正美
爱范儿
爱范儿
博客园 - 聂微东
IT之家
IT之家
美团技术团队
钛媒体:引领未来商业与生活新知
钛媒体:引领未来商业与生活新知
博客园 - 三生石上(FineUI控件)
有赞技术团队
有赞技术团队
OSCHINA 社区最新新闻
OSCHINA 社区最新新闻
T
Tailwind CSS Blog
博客园 - Franky
V
V2EX
GbyAI
GbyAI
阮一峰的网络日志
阮一峰的网络日志

math updates on arXiv.org

Coupling-Robust Accuracy in Multiphysics Physics Informed Neural Networks via Kronecker-Preconditioned Optimization Non-normal spectral signatures of instability in neural network training dynamics Optimization of randomized neural networks for transfer operator approximation Selective Ambulance Dispatch Under Contextual Travel-Time Uncertainty LLAMA LIMA: A Living Meta-Analysis on the Effects of Generative AI on Learning Mathematics Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations LLMs as Noisy Channels: A Shannon Perspective on Model Capacity and Scaling Laws On the Stability of Spherical Hellinger-Kantorovich Flows and Their Implications for Differential Privacy Training-Free Looped Transformers Move on Muon : A Hamiltonian probability gradient flow perspective of Muon optimizer Entrywise Error Bounds for Spectral Ranking with Semi-Random Adversaries Asymmetric Scaling Laws from Sparse Features Is Dimensionality a Barrier for Retrieval Models? RA-DCA: A Randomized Active-Set DCA for Directional Stationarity in Max-Structured DC Programs Commutator-Induced Uncertainty in VAEs Weisfeiler-Leman Is Incomplete on Simple Spectrum Graphs, so Canonicalize Them Sparse In-Network Learning via Shortest-Path Backpropagation and Finite-Rate Gating Instance-Optimal Estimation with Multiple LLM Judges on a Budget Entropy Equivalence Testing Expand More, Shrink Less: Shaping Effective-Rank Dynamics for Dense Scaling in Recommendation Any-Dimensional Invariant Universality Operationalizing Individual Fairness via Gradient Descent and Bradley-Terry Models Anytime Training with Schedule-Free Spectral Optimization Diffusion-based Denoising Beats Vanilla Score Matching in Parameter Estimation: A Theoretical Explanation Resilience Characterization of AI-Native Wireless Receivers via Persistent Homology The General Theory of Localization Methods Group-Algebraic Tensors: Provably-optimal Equivariant Learning and Physical Symmetry Discovery General Lower Bounds for Differentially Private Federated Learning with Arbitrary Public-Transcript Interactions PilotWiMAE: Pilot-Native Representation Learning for Wireless Channels Proximal basin hopping: global optimization with guarantees
Pontryagin Maximum Principle in Free Probability Theory
[Submitted on 19 Jun 2026] · 2026-06-23 · via math updates on arXiv.org

View PDF HTML (experimental)

Abstract:Motivated by the classical stochastic maximum principle, random matrices and free stochastic differential equations we, develop an analog maximum principle for control problems driven by non-commutative random variables, e.g. random matrices. We formulate an optimal control problem in the setting of free probability, consisting of the controlled forward equation, a free backward stochastic differential equation. For both, we give global existence theorems. Due to the non-commutative Itô-formula, the definition of the Hamiltonian differs to the commutative case. Our strategy is to stay as close as possible to the commutative case. Finally we formulate and proof the maximum principle in the context of free probability. Several examples show the application of the maximum principle, where explicit solutions can be found.

Submission history

From: Michael Wibmer [view email]
[v1] Fri, 19 Jun 2026 21:55:03 UTC (29 KB)