Abstract

This paper quantifies how far bf16 transformer large language model (LLM) weights—and Q4 K-typed tensors inside GGUF Q4 K M files—can be compressed with no loss of information. Every method is scored under one accounting discipline: a trained profile is billed to its method on each file, each run is checked for a byte-exact roundtrip, and the train/test partition is taken over source models rather than individual tensors. For bf16 weights the marginal-byte ceiling sits at 1:495 (model-level 95% confidence interval [1:487; 1:502]); the strongest method that could be run end-to-end attains 1:499, while the bf16 split coder introduced here reaches 1:488. For Q4 K-typed tensors the marginal-byte ceiling is 1:076 at the tensor-stream level, dropping to 1:041–1:045 once whole GGUF artifacts are scored, because Q4 K M files also carry Q6 K tensors that barely compress (near 1:01); the mixture-CDF coder presented here attains 1:052, whereas a dictionary-trained zstd ends up enlarging the stream once its dictionary is billed per file. Between adjacent same-role weight matrices at bf16 precision no exploitable linear redundancy is found (median Pearson +0:0004 over 250 layer pairs drawn from two Qwen2.5 models). Across 11;942 verified-roundtrip method-evaluations spanning 7;960 distinct benchmark rows, not a single roundtrip failed; the contribution is the comparison protocol itself rather than another compressor. Each ceiling is a compression-ratio bound—hardware independent and confirmed on weights up to 7B parameters (Qwen2.5-7B-Instruct); the single-core x86 (Sapphire Rapids) host constrains only the throughput figures, which are reported for comparability rather than as deployment numbers.

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