Understanding is Compression

We have previously shown all understanding or learning are compression, under reasonable assumptions. In principle, better understanding of data should improve data compression. Traditional compression methodologies focus on encoding frequencies or some other computable properties of data. Large language models approximate the uncomputable Solomonoff distribution, opening up a whole new avenue to justify our theory. Under the new uncomputable paradigm, we present LMCompress based on the understanding of data using large models. LMCompress has significantly better lossless compression ratios than all other lossless data compression methods, doubling the compression ratios of JPEG-XL for images, FLAC for audios and H264 for videos, and tripling or quadrupling the compression ratio of bz2 for texts. The better a large model understands the data, the better LMCompress compresses.

Ranking LLMs by compression

We conceptualize the process of understanding as information compression, and propose a method for ranking large language models (LLMs) based on lossless data compression. We demonstrate the equivalence of compression length under arithmetic coding with cumulative negative log probabilities when using a large language model as a prior, that is, the pre-training phase of the model is essentially the process of learning the optimal coding length. At the same time, the evaluation metric compression ratio can be obtained without actual compression, which greatly saves overhead. In this paper, we use five large language models as priors for compression, then compare their performance on challenging natural language processing tasks, including sentence completion, question answering, and coreference resolution. Experimental results show that compression ratio and model performance are positively correlated, so it can be used as a general metric to evaluate large language models.