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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
Order Optimal Cascaded Code Distributed Computing With Lo...
Mingming Zhang, Youlong Wu, Minquan Cheng, Dianhua Wu · 2023-07-27 · via cs.IT updates on arXiv.org

Coded distributed computing (CDC), proposed by Li \emph{et al.}, offers significant potential for reducing the communication load in MapReduce computing systems. In cascaded CDC with $K$ nodes, $N$ input files, and $Q$ output functions, each input file will be mapped by $r\geq 1$ nodes and each output function will be computed by $s>1$ nodes such that coding techniques can be applied to generate multicast opportunities. However, a significant limitation of most existing coded distributed computing schemes is their requirement to split the original data into a large number of input files (or output functions) that grows exponentially with $K$, which significantly increases the coding complexity and degrades the system performance. In this paper, we focus on the case of $K/s\in\mathbb{N}$, deliberately designing the strategy of data placement and output functions assignment, such that a low-complexity CDC scheme is achievable. The main advantages of the proposed scheme include: 1) the multicast gains equal to $(r+s-1)(1-1/s)$ and $r+s-1$ which is approximately $r+s-1$ when $s$ is relatively large, and the communication load potentially better than the well-known scheme proposed by Li \emph{et al.}; 2) the proposed scheme requires significantly less input files and output functions; 3) all the operations are implemented over the binary field $\mathbb{F}_2$ with the one-shot fashion (i.e., each node can decode its requested content immediately upon receiving the multicast message during the current time slot). Finally, we derive a new information-theoretic converse bound for the cascaded CDC framework under the proposed strategies of data placement and output functions assignment. We demonstrate that the communication load of the proposed scheme is order optimal within a factor of $2$; and is also approximately optimal when $K$ is sufficiently large for a given $r$.