Language Models as Zero-shot Lossless Gradient Compressors: Towards General Neural Parameter Prior Models

Despite the widespread use of statistical prior models in various fields, such models for neural network gradients have long been overlooked. The inherent challenge stems from their high-dimensional structures and complex interdependencies, which complicate effective modeling. In this work, we demonstrate the potential of large language models (LLMs) to act as gradient priors in a zero-shot setting. We examine the property by considering lossless gradient compression -- a critical application in distributed learning -- that depends heavily on precise probability modeling. To achieve this, we introduce LM-GC, a novel method that integrates LLMs with arithmetic coding. Our technique converts plain gradients into text-like formats, enhancing token efficiency by up to 38 times compared to their plain representations. We ensure that this data conversion maintains a close alignment with the structure of plain gradients and the symbols commonly recognized by LLMs. Our experiments indicate that LM-GC surpasses existing state-of-the-art lossless compression methods, improving compression rates by 10\% up to 17.2\% across various datasets and architectures. Additionally, our approach shows promising compatibility with lossy compression techniques such as quantization and sparsification. These findings highlight the significant potential of LLMs as a model for effectively handling gradients. We will release the source code upon publication.