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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 Why Self-Supervised Encoders Want to Be Normal Statistical Channel Fingerprint Construction for Massive MIMO: A Unified Tensor Learning Framework Adaptive Transform Coding for Semantic Compression Lightweight Quantum Agent for Edge Systems: Joint PQC and NOMA Resource Allocation Rethinking KV Cache Eviction via a Unified Information-Theoretic Objective Information bottleneck for learning the phase space of dynamics from high-dimensional experimental data MEG-RAG: Quantifying Multi-modal Evidence Grounding for Evidence Selection in RAG Generalising maximum mean discrepancy: kernelised functional Bregman divergences Improving Robustness of Tabular Retrieval via Representational Stability Information-Theoretic Measures in AI: A Practical Decision Guide A Unified Fractional Regularization Framework for Sparse Recovery Shape of Memory: a Geometric Analysis of Machine Unlearning in Second-Order Optimizers The Exact Replica Threshold for Nonlinear Moments of Quantum States Semantic Error Correction and Decoding for Short Block Codes Null-Space Flow Matching for MIMO Channel Estimation in Latency-Constrained Systems Directional Confusions Reveal Divergent Inductive Biases Through Rate-Distortion Geometry in Human and Machine Vision MambaCSP: Hybrid-Attention State Space Models for Hardware-Efficient Channel State Prediction Amortized Vine Copulas for High-Dimensional Density and Information Estimation Decentralized Machine Learning with Centralized Performance Guarantees via Gibbs Algorithms Secure Rate-Distortion-Perception: A Randomized Distributed Function Computation Approach for Realism RateQuant: Optimal Mixed-Precision KV Cache Quantization via Rate-Distortion Theory FB-NLL: A Feature-Based Approach to Tackle Noisy Labels in Personalized Federated Learning Ultrametric OGP - parametric RDT \emph{symmetric} binary perceptron connection Watts-per-Intelligence Part II: Algorithmic Catalysis AirFM-DDA: Air-Interface Foundation Model in the Delay-Doppler-Angle Domain for AI-Native 6G Lossless Compression via Chained Lightweight Neural Predictors with Information Inheritance Regret Tail Characterization of Optimal Bandit Algorithms with Generic Rewards Exploiting Correlations in Federated Learning: Opportunities and Practical Limitations A Synonymous Variational Perspective on the Rate-Distortion-Perception Tradeoff Aerial Multi-Functional RIS in Fluid Antennas-Aided Full-Duplex Networks: A Self-Optimized Hybrid Deep Reinforcement Learning Approach InfoChess: A Game of Adversarial Inference and a Laboratory for Quantifiable Information Control Endogenous Information in Routing Games: Memory-Constrained Equilibria, Recall Braess Paradoxes, and Memory Design Beyond Fixed False Discovery Rates: Post-Hoc Conformal Selection with E-Variables LAWS: Learning from Actual Workloads Symbolically -- A Self-Certifying Parametrized Cache Architecture for Neural Inference, Robotics, and Edge Deployment The AI Telco Engineer: Toward Autonomous Discovery of Wireless Communications Algorithms Sequential KV Cache Compression via Probabilistic Language Tries: Beyond the Per-Vector Shannon Limit Diffusion Denoiser Achievable Analysis for Finite Blocklength Unsourced Random Access Joint Interference Detection and Identification via Adversarial Multi-task Learning Agentic AI-Based Joint Computing and Networking via Mixture of Experts and Large Language Models eOptShrinkQ: Near-Lossless KV Cache Compression Through Optimal Spectral Denoising and Quantization StateSMix: Online Lossless Compression via Mamba State Space Models and Sparse N-gram Context Mixing Polynomial-Time Optimal Group Selection via the Double-Commutator Eigenvalue Problem Algebraic Diversity: Group-Theoretic Spectral Estimation from Single Observations The Root Theorem of Context Engineering Continual Few-shot Adaptation for Synthetic Fingerprint Detection The Geometry of Knowing: From Possibilistic Ignorance to Probabilistic Certainty -- A Measure-Theoretic Framework for Epistemic Convergence A Decision-Theoretic Formalisation of Steganography With Applications to LLM Monitoring On the Rate-Distortion-Complexity Tradeoff for Semantic Communication Binary Flow Matching: Prediction-Loss Space Alignment for Robust Learning A Rational Account of Categorization Based on Information Theory Contextuality from Single-State Ontological Models: An Information-Theoretic Obstruction A Mixture of Experts Vision Transformer for High-Fidelity Surface Code Decoding On the Non-decoupling of Supervised Fine-tuning and Reinforcement Learning in Post-training Energy-Aware Routing to Large Reasoning Models Efficient Vector Symbolic Architectures from Histogram Recovery Forget BIT, It is All about TOKEN: Towards Semantic Information Theory for LLMs What Can Be Recovered Under Sparse Adversarial Corruption? Assumption-Free Theory for Linear Measurements Feedback Lunch: Learned Feedback Codes for Secure Communications On the optimization dynamics of RLVR: Gradient gap and step size thresholds Synthetic Counterfactual Labels for Efficient Conformal Counterfactual Inference Natural Image Classification via Quasi-Cyclic Graph Ensembles and Random-Bond Ising Models at the Nishimori Temperature Multimodal Remote Inference Let's Measure Information Step-by-Step: AI-Based Evaluation Beyond Vibes Best Agent Identification for General Game Playing Optimal Single-Policy Sample Complexity and Transient Coverage for Average-Reward Offline RL MLorc: Momentum Low-rank Compression for Memory Efficient Large Language Model Adaptation Biased Federated Learning under Wireless Heterogeneity MultiTok: Variable-Length Tokenization for Efficient LLMs Adapted from LZW Compression Anomaly Detection from a Tensor Train Perspective Semantic Variational Bayes Based on Semantic Information G Theory for Solving Latent Variables
Matrix-Monotonic Optimization Part II: Multi-Variable Optimization
Chengwen Xing, Shuai Wang, Sheng Chen, Shaodan Ma, H. Vincent Po · 2020-09-24 · via cs.IT updates on arXiv.org

In contrast to Part I of this treatise [1] that focuses on the optimization problems associated with single matrix variables, in this paper, we investigate the application of the matrix-monotonic optimization framework in the optimization problems associated with multiple matrix variables. It is revealed that matrix-monotonic optimization still works even for multiple matrix-variate based optimization problems, provided that certain conditions are satisfied. Using this framework, the optimal structures of the matrix variables can be derived and the associated multiple matrix-variate optimization problems can be substantially simplified. In this paper, several specific examples are given, which are essentially open problems. Firstly, we investigate multi-user multiple-input multiple-output (MU- MIMO) uplink communications under various power constraints. Using the proposed framework, the optimal structures of the precoding matrices at each user under various power constraints can be derived. Secondly, we considered the optimization of the signal compression matrices at each sensor under various power constraints in distributed sensor networks. Finally, we investigate the transceiver optimization for multi-hop amplify-and-forward (AF) MIMO relaying networks with imperfect channel state information (CSI) under various power constraints. At the end of this paper, several simulation results are given to demonstrate the accuracy of the proposed theoretical results.