The rise of large language models (LLMs) is revolutionizing information retrieval, question answering, summarization, and code generation tasks. However, in addition to confidently presenting factually inaccurate information at times (known as "hallucinations"), LLMs are also inherently limited by the number of input and output tokens that can be processed at once, making them potentially less effective on tasks that require processing a large set or continuous stream of information. A common approach to reducing the size of data is through lossless or lossy compression. Yet, in some cases it may not be strictly necessary to perfectly recover every detail from the original data, as long as a requisite level of semantic precision or intent is conveyed. This paper presents three contributions to research on LLMs. First, we present the results from experiments exploring the viability of approximate compression using LLMs, focusing specifically on GPT-3.5 and GPT-4 via ChatGPT interfaces. Second, we investigate and quantify the capability of LLMs to compress text and code, as well as to recall and manipulate compressed representations of prompts. Third, we present two novel metrics -- Exact Reconstructive Effectiveness (ERE) and Semantic Reconstruction Effectiveness (SRE) -- that quantify the level of preserved intent between text compressed and decompressed by the LLMs we studied. Our initial results indicate that GPT-4 can effectively compress and reconstruct text while preserving the semantic essence of the original text, providing a path to leverage $\sim$5$\times$ more tokens than present limits allow.
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