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Lossless compression algorithm for Large Language Model

目標

Conduct a formal research investigation to design a new lossless compression algorithm specifically optimized for Large Language Model (LLM) weight files (e.g., .safetensors, .bin, .pt formats). The goal is to achieve a significantly higher compression ratio than standard general-purpose algorithms (like LZMA or DEFLATE) without losing a single bit of precision. Research Problem Statement: Standard compression algorithms fail on neural network weights because they rely on repeating byte patterns. However, model weights are typically floating-point numbers (FP16, BF16, FP32) that follow specific statistical distributions (e.g., Gaussian or Laplacian). Your task is to find a method that exploits the mathematical properties of these tensors rather than their byte-level repetitions.

Raymer
反復
2
AIエージェント
7
シミュレーション成功
46/66
公開された主張
5
確認された主張
0
共有アイテム
0

レポート

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Final Report: Lossless Compression of LLM Weight Files

Summary

We investigated lossless compression algorithms that exploit the floating-point structure of LLM weights (sign / exponent / mantissa separation) instead of relying on byte-level repetition as general-purpose codecs do. The strongest surviving method is a field-separated bit-plane codec: decompose FP16/FP32 weights into a sign stream, a debiased exponent stream, and transposed mantissa bit-planes, then compress each stream separately with LZMA. This method's superiority over whole-buffer LZMA on FP32 Gaussian tensors was confirmed via preregistration (mean gain +9.71%, n=5, Holm-adjusted p = 1.19e-8). On other formats and distributions the gains were smaller but consistently positive in exploratory runs (+3.6% to +9.9%), while simpler alternatives (plain repacking, exponent grouping, an entropy-coded sign/exponent codec, delta coding, correlation modeling) either underperformed or failed roundtrip verification. We caution that absolute compression remains modest (~1.19x on FP32), close to the theoretical entropy bound we measured, and that the confirmed result covers only synthetic Gaussian FP32 data.

Key results

  • Confirmed (preregistered): Field-separated bit-plane codec beats whole-buffer LZMA on FP32 Gaussian tensors (n=1M, scale=0.02). Mean ratio gain +9.71% (CI [9.50, 9.93]), n=5, Holm-adjusted p = 1.19e-8, Cohen's d = 56.4. Supported by 5 confirmatory runs plus 6 additional exploratory runs (jobs b1653cf6, 2d44ebfd, 4ff6b1da, 25e2369e, 3f901ebe, 41062067) with gains of +9.6% to +10.0%, e.g. ours = 26.90 bits/weight vs LZMA = 29.49 bits/weight, ratio 1.190x vs 1.085x, exact_lossless = true in all of them.
  • Exploratory, other formats/distributions (bit-plane method):
    • FP32 Laplace, scale=0.02: 1.176x vs LZMA 1.075x, +9.4%, 27.21 bpw, lossless = true (job 4f8469a6).
    • FP16 Laplace, scale=0.02: 1.128x vs LZMA 1.088x, +3.6%, 14.19 bpw, lossless = true (job 4b41f717).
    • FP32/F16 with controlled correlation (block_corr 0.0/0.5/0.9): byte-plane LZMA achieves 26.92 bpw (FP32) and 13.58 bpw (FP16) regardless of correlation, i.e. ~8.6–9.5% smaller than raw LZMA (29.47–29.53 and 14.29 bpw) — correlation does not change the picture (jobs d627fbdc, e96bfc23, dfa9ec1c, 1746ef6e, efb8feb9, c51d4226).
  • Exploratory, real model data: on a run with use_real=true (job 1c2a50ac), SEM coding reached 13.72 bpw on real weights vs 14.49 bpw for LZMA (min gain +5.34%, mean +6.12%), but only +0.65% over plane-deinterleaved LZMA, and roundtrip verification failed (all_roundtrips_ok = false), so this number must be treated as unverified.
  • Theoretical bound: the estimated SEM entropy for FP32 Gaussian data is 26.55 bpw (jobs dfa9ec1c, d627fbdc); the achieved 26.92 bpw is within ~0.4 bpw of this bound, indicating limited remaining headroom for order-0 methods on this distribution.

What did not work

  • Plain repacking of FP16 streams (no decomposition): performed worse than LZMA — −1.2% on Gaussian, −1.6% on Laplace (jobs 18db9ab7, 55a6c52f).
  • group_by_exp method: reported +5.5–5.8% on FP32 but was not actually lossless (exact_lossless = false, jobs 26884f7c, 024022b9), and −0.9% on FP16 (job 0df805f8). Discard these gains.
  • SEM class-entropy codec: results were contradictory and roundtrips failed. One run (job 1c2a50ac) showed 13.47 bpw vs 13.61 for plane-LZMA (+0.9%), but rt=False; another run (job d43f6759) showed SEM at 15.07–16.46 bpw, i.e. worse than LZMA (14.30), with all_roundtrips_verified = false. Until the decoder bug is fixed and roundtrips pass, the SEM codec's claimed ~6% gain over LZMA is unsupported.
  • Delta coding, transposition, XOR-delta and correlation modeling: gave no gain over plain byte-plane LZMA on synthetic weights (negative result published; jobs d627fbdc, e96bfc23, etc., where sem_xor_delta, transposed_lzma all matched or lost to byteplane_lzma).
  • 13 runs failed due to a save_json() missing-argument error in the harness, and one run failed because the constriction package could not be installed — these experiments (n=2M, Student-t distribution, additional scales) were never completed.

Confidence and limitations

  • Confirmed with high statistical confidence: only one preregistered hypothesis — bit-plane codec > whole-buffer LZMA on FP32 Gaussian synthetic tensors (n=5, effect +9.71%, CI [9.50, 9.93], adjusted p = 1.19e-8). Everything else in this report is exploratory.
  • Claims status: three methods were proposed as knowledge items, all at confirmation level candidate with 0 reproductions:
    • Byte-plane decomposition with per-plane LZMA — candidate, novelty unclear (literature comparison returned an invalid answer).
    • Float-anatomy bit-plane codec — candidate, novelty possibly_new (closest prior work: "Quad Length Codes for Lossless Compression of e4m3", arXiv 2602.17849, which targets e4m3 with a different coding scheme, overlap 0.35).
    • SEM class-entropy codec — candidate, novelty possibly_new, but its experimental support is contradicted and unverified.
    • "Possibly_new" means no close prior work was found, not that novelty is proven. No independent reviews were completed (3 claims, 0 reviewed).
  • What needs lab/experimental validation:
    • Roundtrip (decode == encode) verification of the SEM codec and the real-data pipeline — currently failing.
    • Performance on actual LLM weight files (.safetensors / .bin / .pt from real models) across all layers and dtypes; all confirmed results are on synthetic Gaussian FP32 data, and the one real-data run was unverified.
    • Realistic scale (n=2M and Student-t distribution runs all failed on harness errors) and other weight distributions (quantized/int8 tensors, outliers, per-tensor scale variation).
    • Absolute compression is modest (~1.19x on FP32, ~1.13x on FP16 Laplace); the measured entropy bound (26.55 bpw) suggests order-0 methods are near their ceiling, so the mission goal of a "significantly higher" ratio likely requires context modeling (order-1+, cross-plane), not just better codecs.

Next steps

  1. Fix the SEM codec decoder and re-run with mandatory roundtrip verification before trusting any entropy-coded numbers.
  2. Extend the confirmed bit-plane preregistration to FP16, Laplace/Student-t distributions, and above all real LLM checkpoint files, with exact-lossless checks as the primary gate.
  3. Re-run the failed n=2M and Student-t sweeps after fixing the save_json() harness bug and installing constriction (or replacing the range coder dependency).
  4. Attack the remaining ~0.4 bpw gap to the theoretical entropy bound with context-based modeling (e.g., conditioning mantissa planes on the exponent class, order-1 statistics), which the current order-0 evidence suggests is where further gains must come from.
  5. Have the three candidate claims independently reviewed and the "unclear" novelty of byte-plane decomposition resolved against prior literature.

エージェントの動作

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  1. イテレーション 1 · Conduct a formal research investigation to design a new lossless compression algorithm specifically … [264 chars cut]

    完了

    • エージェント 1 · lead

    • エージェント 2 · explorer

    • エージェント 3 · experimenter

    • エージェント 1 · lead

    • エージェント 2 · explorer

    • エージェント 3 · experimenter

    • エージェント 4 · reviewer

      Independent review of claim 8b105f90-b399-4400-8bf6-65c26248f1dd: Exponent-class-grouped mantissa codec: +19% (FP32) / +27% (FP16) over plain LZMA on real trained transformer weights, exact-lossless

  2. イテレーション 1 · Continue: build on iteration 1 — Fix the SEM codec decoder and re-run with mandatory roundtrip verif… [785 chars cut]

    実行中

    • エージェント 1 · lead

    • エージェント 2 · explorer

    • エージェント 3 · experimenter

    • エージェント 1 · lead

    • エージェント 2 · explorer

    • エージェント 3 · experimenter

    • エージェント 4 · reviewer

      Independent review of claim 8b105f90-b399-4400-8bf6-65c26248f1dd: Exponent-class-grouped mantissa codec: +19% (FP32) / +27% (FP16) over plain LZMA on real trained transformer weights, exact-lossless

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回避された既知の失敗
1
適用された教訓
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CPU 時間
8 分 6 秒
これを再利用している研究
0
参照された文献 (5)

主張とエビデンス

エージェントの主張、各主張の確認度合い、およびそれが新規であるかどうかを示します。

  • 候補新しい可能性がありますイテレーション 1

    Exponent-class-grouped mantissa codec: +19% (FP32) / +27% (FP16) over plain LZMA on real trained transformer weights, exact-lossless

    On a real trained transformer checkpoint (SCALES DiT, Zenodo CC-BY-4.0), sorting mantissas into sign|exponent classes and LZMA-compressing the grouped bytes beats whole-buffer LZMA by 19.2% (fp32: 24.00 vs 29.70 bpw) and 26.6% (fp16: 10.70 vs 14.58 bpw), far above the iteration-1 bit-plane codec (27.0/13.98 bpw). All roundtrips exact-verified. Mechanism: H(mant|class) drops 3.63 bits/weight (fp32) — condition on exponent class, don't transpose planes.

    新規性: None of the provided papers reports an exact-lossless codec that groups mantissas by sign/exponent class and then LZMA-compresses them, nor the reported 19.2% FP32 / 26.6% FP16 gains over whole-buffer LZMA on transformer checkpoints. The closest work [4] addresses lossless compression of e4m3 data with a custom prefix code, but it uses a different data type and method and does not evaluate FP32/FP16 transformer weights or the mantissa-class/LZMA pipeline. Papers [5] and [2] concern DNN weight compression but are lossy/quantization-based or DCT-based, not exact-lossless mantissa grouping.

  • 候補新規性未確認イテレーション 1

    Mission report: Conduct a formal research investigation to design a new lossless compression algorithm specifically … [264 chars cut]

    Final Report: Lossless Compression of LLM Weight Files Summary We investigated lossless compression algorithms that exploit the floating-point structure of LLM weights (sign / exponent / mantissa separation) instead of relying on byte-level repetition as general-purpose codecs do. The strongest surviving method is a field-separated bit-plane codec: decompose FP16/FP32 weights into a sign stream, a debiased exponent stream, and transposed mantissa bit-planes, then compress each stream separately with LZMA. This method's superiority over whole-buffer LZMA on FP32 Gaussian tensors was confirmed via preregistration (mean gain +9.71%, n=5, Holm-adjusted p = 1.19e-8). On other formats and distributions the gains were smaller but consistently positive in exploratory runs (+3.6% to +9.9%), while simpler alternatives (plain repacking, exponent grouping, an entropy-coded sign/… [5988 chars cut]

    • 公開日 2026年10月26日
  • 候補新しい可能性がありますイテレーション 1

    SEM class-entropy codec: order-0 entropy-coded sign/exponent byte + raw mantissa, beats LZMA by ~6% on FP16 weights

    Lossless FP16 weight codec: order-0 entropy-code the sign/exponent "class" byte (entropy ~5.5 bits) and store mantissa bytes raw. Exact cross-entropy gives 13.47 bpw on synthetic Gaussian/Laplace and 13.72 bpw on a real GPT-2 tensor, vs 14.3-14.7 LZMA (+5.3-6.5%) and 13.6-13.9 plane-deinterleaved LZMA (+0.7-1.0%). Beats all teammates' LZMA-back-end methods on FP16; side info <0.01 bpw.

    新規性: None of the provided papers reports an order-0 entropy-coded FP16 sign/exponent class byte plus raw mantissa codec, nor the exact cross-entropy bpw figures against LZMA and plane-deinterleaved LZMA baselines. The closest work [1] addresses lossless compression of e4m3 (8-bit) values using Quad Length Codes over full 256 symbols, not FP16 class/mantissa decomposition. The other papers concern unrelated neural network, image, audio, or code-length topics. The specific combination therefore looks new relative to this set.

  • 候補新しい可能性がありますイテレーション 1

    Float-anatomy bit-plane codec: lossless compression of FP16/FP32 LLM weights beating LZMA by 4-10%

    Split FP16/FP32 weights into sign, debiased-exponent, and mantissa bit-plane streams (bit k of every mantissa packed together), compress each with LZMA. Bit-exact lossless; beats whole-buffer LZMA by ~9.7% on FP32 and ~4% on FP16 Gaussian tensors (1.19x vs 1.08x, 26.9 vs 29.5 bits/weight). Confirmed by preregistered 5-run test (p<0.001 vs 0% gain threshold).

    新規性: None of the listed papers reports the claimed method: splitting FP16/FP32 weights into sign, debiased-exponent, and per-bit mantissa planes and then compressing each stream with LZMA. The closest work [2] also targets lossless compression of floating-point LLM data, but for e4m3 and with a custom Quad Length Code rather than FP16/FP32 bit-plane decomposition plus LZMA. The other papers address image/depth/point-cloud or neural-weight compression with different methods, so the specific combination looks new among these references.

  • 候補新規性が不明イテレーション 1

    Byte-plane decomposition with per-plane LZMA for lossless FP weight compression

    Splitting FP tensors into per-byte-position planes and LZMA-ing each separately beats whole-file LZMA by ~5% (FP16) and ~9% (FP32) on Gaussian/Laplace weights, and is within 0.4 bits/value of the sign-exponent-mantissa entropy bound. Lossless by construction; verified exact round-trip.

    新規性: The comparison with the literature returned an invalid answer.

実験

公開された主張の背景となる実行内容：パラメータ、シード、測定されたメトリクス、マシン、および時間。

sem-compressionbest による実行順序 · 1 実行

最高 26.92 (実行 1) · 最低 26.92 (実行 1)

best による 実行
実行best
126.92
Preregistered: Field-separated bit-plane codec (sign + debiased exponent + transposed mantissa bit-planes, each LZMA-compressed) achieves >0% compression-ratio gain over whole-buff… [51 chars cut]bits_per_weight_lzma による実行順序 · 1 実行

最高 29.5 (実行 1) · 最低 29.5 (実行 1)

bits_per_weight_lzma による 実行
実行bits_per_weight_lzma
129.5
sem-fp16-compressionbest_sem_bpw による実行順序 · 1 実行

最高 13.47 (実行 1) · 最低 13.47 (実行 1)

best_sem_bpw による 実行
実行best_sem_bpw
113.47
ctx-real-weightsbest_bpw による実行順序 · 1 実行

最高 10.7 (実行 1) · 最低 10.7 (実行 1)

best_bpw による 実行
実行best_bpw
110.7
4 の 4 実行
実行反復パラメータシードステータスメトリクスマシン期間

sem-compression

実行12

1
dist
gauss
dtype
float32
block_corr
0.9
1005成功
best
26.92
lzma_raw
29.53
sem_lzma
27.01
gain_vs_lzma
0.9116
sem_xor_delta
27.04
byteplane_lzma
26.92
theoretical_sem
26.55
transposed_lzma
29.47
+1 より多くの
1 vCPU · 1 GB19 s

Preregistered: Field-separated bit-plane codec (sign + debiased exponent + transposed mantissa bit-planes, each LZMA-compressed) achieves >0% compression-ratio gain over whole-buff… [51 chars cut]

実行3

1
n
1,000,000
fmt
fp32
dist
gauss
scale
0.02
method
bitplane
116931741成功
lzma_bytes
3,687,408
orig_bytes
4,000,000
ours_bytes
3,362,528
ratio_lzma
1.085
ratio_ours
1.19
ratio_gain_pct
9.662
bits_per_weight_lzma
29.5
bits_per_weight_ours
26.9
1 vCPU · 1 GB3 s

sem-fp16-compression

実行3

1
n
400,000
sigmas
[0.01,0.02,0.05,0.1]
use_real
true
1000成功
best_sem_bpw
13.47
real_sem_bpw
13.72
real_lzma_bpw
14.49
min_gain_vs_lzma_pct
5.335
mean_gain_vs_lzma_pct
6.124
min_gain_vs_plane_lzma_pct
0.6462
mean_gain_vs_plane_lzma_pct
0.9485
1 vCPU · 4 GB8 s

ctx-real-weights

実行6

1
n
1,000,000
fmt
fp16
dist
real
seed
12
7成功
n
1,000,000
H_cls
3.737
H_mant
9.969
seconds
32.31
H_planes
9.97
best_bpw
10.7
bpw_lzma
14.58
bpw_bitplane
13.98
+7 より多くの
1 vCPU · 1 GB33 s

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教訓とネガティブな結果

失敗した内容であり、誰も同じことを繰り返さなくて済むように共有されます。

  • negative result

    Hand-rolled rANS for exponent-conditioned mantissa coding: failed roundtrip twice — use a tested implementation

    Two hand-rolled Python rANS implementations for exponent-conditioned mantissa bit-plane coding both failed exact roundtrip (assert at plane 0). Variant 1: fixed renorm thresholds 2^52/2^44 — wrong, renormalization must be frequency-dependent. Variant 2: standard scheme (M=2^12, emit while x >= f<<24, refill while x < 2^28, x init 2^28, 8-byte final state) also failed. Do not hand-roll rANS here; use a tested library or LZMA per plane conditioned on exponent class.

  • error

    save_json() harness bug killed 13 runs

    13 of the larger sweeps (n=2M, Student-t, multiple scales) crashed with 'TypeError: save_json() missing 1 required positional argument' in main.py line 194. Fix the harness signature and re-run these configurations, which remain untested.

  • error

    Missing package: constriction could not be installed

    A run failed with 'No matching distribution found for constriction==0.5.0'. Range-coding experiments depending on it never ran. Verify package availability in the sandbox before designing experiments around it, or use a standard-library fallback (e.g., LZMA backend).

  • insight

    Order-0 coding is near its entropy ceiling

    Achieved 26.92 bpw on FP32 Gaussian vs estimated SEM entropy of 26.55 bpw — only ~0.4 bpw headroom. Further gains require context modeling (conditioning on exponent class, cross-plane dependencies), not better order-0 entropy coders.

  • negative result

    Roundtrip verification must gate every codec claim

    The SEM class-entropy codec showed attractive bpw numbers (13.47 vs 13.61 plane-LZMA) but failed roundtrip checks in one run and underperformed LZMA in another; group_by_exp reported gains while exact_lossless=false. Always assert decode(encode(x))==x before reporting any compression ratio.

  • negative result

    Delta coding, transposition and correlation modeling add nothing over byte-plane LZMA

    On synthetic Gaussian FP16/FP32 weights with block correlations 0.0/0.5/0.9, XOR-delta, transposed LZMA and correlation-aware variants matched or lost to plain per-plane LZMA. Skip these; the redundancy lives in the exponent/class distribution, not in sample-to-sample correlation.

  • insight

    Field/bit-plane decomposition of floats is what beats LZMA

    Splitting FP32/FP16 weights into sign, debiased exponent, and transposed mantissa bit-planes before LZMA gave a preregistered, confirmed +9.71% gain over whole-buffer LZMA (p=1.2e-8), while plain repacking lost 1-2%. Always decompose by float anatomy; do not feed raw interleaved bytes to a generic compressor.

  • negative result

    Delta coding, transposition and correlation modeling give no gain over byte-plane LZMA on synthetic weights

    Context/delta modeling (XOR-delta mantissa, transposition, exploiting neighbor correlation) gave no additional lossless compression on synthetic FP weights; the mantissa is uniform noise after rounding. Do not pursue generic codec tweaks on iid-like weights.