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

OSCHINA 社区最新新闻
OSCHINA 社区最新新闻
让小产品的独立变现更简单 - ezindie.com
让小产品的独立变现更简单 - ezindie.com
Hugging Face - Blog
Hugging Face - Blog
F
Fortinet All Blogs
G
Google Developers Blog
奇客Solidot–传递最新科技情报
奇客Solidot–传递最新科技情报
V
V2EX
Y
Y Combinator Blog
博客园_首页
Martin Fowler
Martin Fowler
博客园 - 司徒正美
MyScale Blog
MyScale Blog
宝玉的分享
宝玉的分享
B
Blog
有赞技术团队
有赞技术团队
A
About on SuperTechFans
量子位
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
Cyber Security Advisories - MS-ISAC
Cyber Security Advisories - MS-ISAC
酷 壳 – CoolShell
酷 壳 – CoolShell
Apple Machine Learning Research
Apple Machine Learning Research
M
MIT News - Artificial intelligence
阮一峰的网络日志
阮一峰的网络日志
Jina AI
Jina AI

cs.IT updates on arXiv.org

Theoretical Limits of Language Model Alignment $f$-Divergence Regularized RLHF: Two Tales of Sampling and Unified Analyses A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Models When Can Voting Help, Hurt, or Change Course? Exact Structure of Binary Test-Time Aggregation When Semantic Communication Meets Queueing: Cross-Layer Latency and Task Fidelity Optimization Convexity in Disguise: A Theoretical Framework for Nonconvex Low-Rank Matrix Estimation Conditional Diffusion Under Linear Constraints: Langevin Mixing and Information-Theoretic Guarantees Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval Expert Routing for Communication-Efficient MoE via Finite Expert Banks Contextual Memory-Enhanced Source Coding for Low-SNR Communications Realizable Bayes-Consistency for General Metric Losses Leveraging Code Automorphisms for Improved Syndrome-Based Neural Decoding A Hierarchical Sampling Framework for bounding the Generalization Error of Federated Learning Dueling DDQN-Based Adaptive Multi-Objective Handover Optimization for LEO Satellite Networks The Causal Description Gap: Information-Theoretic Separations Across Pearl's Hierarchy Optimization of CV-QKD Under Practical Constraints Benchmarking Wireless Representations: High-Dimensional vs. Compressed Embeddings for Efficiency and Robustness Real-Time Text Transmission via LLM-Based Entropy Coding over Fixed-Rate Channels SwiftChannel: Algorithm-Hardware Co-Design for Deep Learning-Based 5G Channel Estimation Evolving Token Communication with Parametric Memory Network Remote Action Generation: Remote Control with Minimal Communication The (Marginal) Value of a Search Ad: An Online Causal Framework for Repeated Second-price Auctions Stabilizing Private LASSO under Heterogeneous Covariates via Anisotropic Objective Perturbation Linear-Readout Floors and Threshold Recovery in Computation in Superposition Soft Graph Diffusion Transformer for MIMO Detection Hierarchical Federated Learning for Networked AI: From Communication Saving to Architecture-Aware Design Exponential families from a single KL identity MIFair: A Mutual-Information Framework for Intersectionality and Multiclass Fairness Diffusion-OAMP for Joint Image Compression and Wireless Transmission Decoupled Descent: Exact Test Error Tracking Via Approximate Message Passing
Unbounded Donoho-Stark-Elad-Bruckstein-Ricaud-Torrésani U...
K. Mahesh Krishna · 2023-12-01 · via cs.IT updates on arXiv.org

Let $(Ω, μ)$, $(Δ, ν)$ be measure spaces and $p=1$ or $p=\infty$. Let $(\{f_α\}_{α\in Ω}, \{τ_α\}_{α\in Ω})$ and $(\{g_β\}_{β\in Δ}, \{ω_β\}_{β\in Δ})$ be unbounded continuous p-Schauder frames for a Banach space $\mathcal{X}$. Then for every $x \in ( \mathcal{D}(θ_f) \cap\mathcal{D}(θ_g))\setminus\{0\}$, we show that \begin{align}\label{UB} (1) \quad \quad \quad \quad μ(\operatorname{supp}(θ_f x))ν(\operatorname{supp}(θ_g x)) \geq \frac{1}{\left(\displaystyle\sup_{α\in Ω, β\in Δ}|f_α(ω_β)|\right)\left(\displaystyle\sup_{α\in Ω, β\in Δ}|g_β(τ_α)|\right)}, \end{align} where \begin{align*} &θ_f:\mathcal{D}(θ_f) \ni x \mapsto θ_fx \in \mathcal{L}^p(Ω, μ); \quad θ_fx: Ω\ni α\mapsto (θ_fx) (α):= f_α(x) \in \mathbb{K},\\ &θ_g: \mathcal{D}(θ_g) \ni x \mapsto θ_gx \in \mathcal{L}^p(Δ, ν); \quad θ_gx: Δ\ni β\mapsto (θ_gx) (β):= g_β(x) \in \mathbb{K}. \end{align*} We call Inequality (1) as \textbf{Unbounded Donoho-Stark-Elad-Bruckstein-Ricaud-Torrésani Uncertainty Principle}. Along with recent \textbf{Functional Continuous Uncertainty Principle} [arXiv:2308.00312], Inequality (1) also improves Ricaud-Torrésani uncertainty principle [IEEE Trans. Inform. Theory, 2013]. In particular, it improves Elad-Bruckstein uncertainty principle [IEEE Trans. Inform. Theory, 2002] and Donoho-Stark uncertainty principle [SIAM J. Appl. Math., 1989].