This work continues the study of the relationship between sample compression schemes and statistical learning, which has been mostly investigated within the framework of binary classification. We first extend the investigation to multiclass categorization: we prove that in this case learnability is equivalent to compression of logarithmic sample size and that the uniform convergence property implies compression of constant size. We use the compressibility-learnability equivalence to show that (i) for multiclass categorization, PAC and agnostic PAC learnability are equivalent, and (ii) to derive a compactness theorem for learnability. We then consider supervised learning under general loss functions: we show that in this case, in order to maintain the compressibility-learnability equivalence, it is necessary to consider an approximate variant of compression. We use it to show that PAC and agnostic PAC are not equivalent, even when the loss function has only three values.

Optimizing distributed learning systems is an art of balancing between computation and communication. There have been two lines of research that try to deal with slower networks: {\em communication compression} for low bandwidth networks, and {\em decentralization} for high latency networks. In this paper, We explore a natural question: {\em can the combination of both techniques lead to a system that is robust to both bandwidth and latency?} Although the system implication of such combination is trivial, the underlying theoretical principle and algorithm design is challenging: unlike centralized algorithms, simply compressing {\rc exchanged information, even in an unbiased stochastic way, within the decentralized network would accumulate the error and cause divergence.} In this paper, we develop a framework of quantized, decentralized training and propose two different strategies, which we call {\em extrapolation compression} and {\em difference compression}. We analyze both algorithms and prove both converge at the rate of $O(1/\sqrt{nT})$ where $n$ is the number of workers and $T$ is the number of iterations, matching the convergence rate for full precision, centralized training. We validate our algorithms and find that our proposed algorithm outperforms the best of merely decentralized and merely quantized algorithm significantly for networks with {\em both} high latency and low bandwidth.

Somemodelcompression methods have been successfully applied to image classification and detection or language models, but there has been very little work compressing generative adversarial networks(GANs) performing complextasks.

A critical approach for efficiently deploying computationally demanding large language models (LLMs) is Key-V alue (KV) caching.

The application of low-order decomposition results in considerable memory savings while preserving the features essential for learning, and also offers theoretical guarantees to convergence.

To bridge this crucial gap, first, this paper presents a comprehensive benchmark suite to evaluate the out-of-distribution (OOD) performance of image compression methods.

Neural image compression has made a great deal of progress. State-of-the-art models are based on variational autoencoders and are outperforming classical models.