Statistical Mechanics of Semantic Compression

Text compression for large language model (LLM) systems is usually framed as token deletion, retrieval, summarization, or exact reconstruction. We study a more aggressive but explicitly lossy setting: compress text into compact codes that an LLM can expand into task-relevant meaning. We call this setting SemanticZip. Unlike lossless compression, SemanticZip does not require byte-identical reconstruction; unlike ordinary summarization, it treats model-based decompression as part of the codec and evaluates whether task-relevant semantic commitments are recovered. This paper is a pilot framework, not a benchmark claim. We formalize LLM-mediated decompression, define a protected/lossy packet architecture, and evaluate six representation regimes over five author-constructed diagnostic cases: structured prose, JSON, CCL-Core, CCL-Min, SemanticZip ASCII, and SemanticZip emoji. An independent decoder LLM reconstructs typed semantic atoms from each compressed representation, and we score Critical Atom Recall, Weighted Atom Recall, precision, and tokenizer gain. In this pilot, structured prose has the highest recoverability, with WAR = 0.956 and 19.1% o200k_base token gain. CCL-Min is the strongest balanced point, with 39.4% token gain and WAR = 0.874. SemanticZip ASCII provides the largest useful compression, with 46.5% token gain and WAR = 0.802, while emoji-heavy SemanticZip performs worse on both compression and recovery. The main contribution is not the claim that these numbers establish a universal frontier. Rather, we introduce a reproducible experimental interface for studying lossy, LLM-decompressible text codes and a design principle: safety-critical and exact commitments should remain protected, while predictable low-risk context may be semantically zipped.

Visual data compression is shifting from human-centered reconstruction to machine-oriented representation coding. In this setting, an image is often mapped to a compact semantic embedding, which is then compressed and transmitted for downstream inference. We propose an adaptive transform-coding method for semantic-feature compression motivated by the conditional rate-distortion function of a Gaussian mixture model. The scheme uses mode-dependent transforms and quantizers selected according to the inferred source component, enabling more efficient coding of heterogeneous feature distributions. Evaluations on features from widely used vision backbones and foundation models show that the proposed method outperforms or is competitive with state-of-the-art neural compression methods while preserving flexibility and interpretability.

Long-context compression is essential for reducing the cost and latency of large language model inference. However, existing methods can fragment important evidence, require additional training or alignment, and often depend on the target model for effective compression. We introduce TopoCompress, a training-free and model-agnostic framework that compresses long contexts by selecting coherent semantic spans. TopoCompress first scores each span using dense and lexical query relevance together with semantic acceleration. It then constructs a hybrid graph that connects spans based on semantic similarity and sequential adjacency, and propagates the query-guided relevance scores over the graph. Across five long-context tasks-HotpotQA, 2WikiMQA, MuSiQue, Qasper, and MultiFieldQA-en-TopoCompress consistently outperforms strong compression baselines. Notably, TopoCompress achieves performance comparable to the strongest baseline while using a 4x smaller compression budget, and provides a 1.41x smaller compression time over the fastest baseline.