Oceania
Coded Computing for Resilient Distributed Computing: A Learning-Theoretic Framework
Coded computing has emerged as a promising framework for tackling significant challenges in large-scale distributed computing, including the presence of slow, faulty, or compromised servers. In this approach, each worker node processes a combination of the data, rather than the raw data itself. The final result then is decoded from the collective outputs of the worker nodes. However, there is a significant gap between current coded computing approaches and the broader landscape of general distributed computing, particularly when it comes to machine learning workloads. To bridge this gap, we propose a novel foundation for coded computing, integrating the principles of learning theory, and developing a framework that seamlessly adapts with machine learning applications. In this framework, the objective is to find the encoder and decoder functions that minimize the loss function, defined as the mean squared error between the estimated and true values. Facilitating the search for the optimum decoding and functions, we show that the loss function can be upper-bounded by the summation of two terms: the generalization error of the decoding function and the training error of the encoding function. Focusing on the second-order Sobolev space, we then derive the optimal encoder and decoder.
Appendix A V ariational Paragraph Embedder A.1 Selection of substitution rate p
Figure 4: Impact of the proportion of injected noise for learning Paragraph Em-beddings on XSum dataset. (Figure 4). The results of the ablation study are presented in Table 5. Embedder in providing clean and denoised reconstructions. In general, it has been observed that generations progress in a coarse-to-fine manner. The early time step, which is close to 1, tends to be less fluent and generic. This was the nicest stay we have ever had. Turtle Bay was a great resort. This was the nicest stay we have ever had.