cs.ITFeb 23, 2026

Nacrith: Neural Lossless Compression via Ensemble Context Modeling and High-Precision CDF Coding

Authors: Roberto Tacconelli

Organizations: Independent Researcher

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Abstract

We present Nacrith, a lossless compression system that combines a 135M-parameter transformer language model (SmolLM2-135M) with an ensemble of lightweight online predictors and a 32-bit arithmetic coder, achieving the best compression results among the systems evaluated in this study on natural language text. Beyond the base LLM-plus-arithmetic-coding paradigm, Nacrith introduces several contributions: (1) a CDF precision upgrade from 2^16 to 2^24 that eliminates ~75% of quantization overhead caused by minimum-probability floors in large vocabularies; (2) a token-level N-gram model for fast local predictions; (3) an adaptive log-space bias head correcting per-document LLM errors via online gradient descent; (4) confidence-based LLM skip for accelerating highly predictable tokens; (5) a hybrid binary format (NC06) extending neural compression to arbitrary binary files--to our knowledge a first among LLM-based compressors; (6) a llama cpp inference backend achieving ~7x faster single-token decode than PyTorch; (7) parallel multi-GPU compression across up to 8 workers; and (8) native KV cache sliding window reducing per-slide cost by ~37x. The system requires only ~500 MB of GGUF weights and ~1.2 GB VRAM per worker, running on consumer GPUs. On alice29 (Canterbury Corpus, 152 KB), Nacrith achieves 0.918 bits per byte (bpb)--outperforming gzip by 3.1x, bzip2 by 2.5x, CMIX v21 by 44%, and ts_zip by 20%, while compressing below the 0th-, 1st-, and 2nd-order byte-level Shannon entropy bounds. On enwik8 (100 MB), Nacrith achieves 0.9389 bpb (11.74%), surpassing ts_zip (~1.11 bpb) by 15% and FineZip (1.024 bpb) by 8% despite using a 60x smaller model with no fine-tuning. An out-of-distribution (OOD) evaluation on a document published after the model's training cutoff confirms these gains are not memorization artifacts, achieving 0.723 bpb on unseen text.

Figures & tables

SystemModelParamsWeightsbpb (enwik8)BinaryOpen Source
gzip (DEFLATE)———2.916✓✓
xz (LZMA2)———1.989✓✓
bzip2———2.321✓✓
CMIX v21LSTM + mixing∼\sim 50Min-code1.17✓✓
PAQ8pxContext mixing——∼\sim 1.27 ¶✓✓
NNCP v3Transformer-XLonlinein-output∼\sim 1.19✓—
Table 1: Comparison of lossless compressors on enwik8 (100 MB). All bpb values are for enwik8. †\dagger Model weights excluded from compressed size. ‡\ddagger LoRA adapter stored in compressed output. \lx@sectionsign\lx@sectionsign Visually extracted from the model-size chart (Fig. 3) in [ 6 ] ; the same paper reports 0.664 bpb on enwik9 (1 GB). \lx@paragraphsign\lx@paragraphsign PAQ8px enwik8 figure is for the -12L setting [ 17 ] .
CompressorSize (B)Ratiobpb
Original152,089100.0%8.000
gzip -954,19135.6%2.851
zstd -1949,21532.4%2.589
xz -948,50031.9%2.551
Brotli -q 1146,48730.6%2.445
bzip2 -943,20228.4%2.273
Table 2: Compression results on alice29.txt (152,089 bytes, Canterbury Corpus). All results directly measured. PAQ8px run at -8L (level 8 with LSTM, v211).
FileOrig.Compr.bpb
sample_3k.txt3,072 B263 B0.685
sample_50k.txt51,200 B4,059 B0.634
sample_100k.txt102,863 B9,817 B0.764
alice29.txt152,089 B17,458 B0.918
asyoulik.txt125,179 B20,408 B1.304
Table 3: Nacrith compression across multiple text types. Modern English prose achieves 0.63–0.76 bpb .
MethodSizebits/byte
Original148.5 KB8.000
Shannon 0th-order84.8 KB4.568
Shannon 1st-order63.5 KB3.419
Shannon 2nd-order46.1 KB2.485
gzip -952.9 KB2.851
xz -947.4 KB2.551
Table 4: Shannon entropy bounds vs. actual compressed sizes on alice29.txt (152,089 B). Nacrith compresses 80% below the 0th-order, 73% below the 1st-order, and 63% below the 2nd-order bounds.
SystemParamsalice29enwik8
gzip -9—2.852.916
xz -9—2.551.989
bzip2 -9—2.272.321
Brotli -q 11—2.452.059
zstd -19—2.5892.156
CMIX v21∼\sim 50M1.631.17
Table 5: Bits per byte across systems and scales. “alice29” column shows verified results on alice29.txt (152 KB). All enwik8 classical values directly measured. †\dagger Compression ratio ≈\approx 0.2 visually extracted from the model-size chart (Fig. 3) in [ 6 ] for enwik8; the same paper reports 0.664 bpb on enwik9 (1 GB). ‡\ddagger Weights excluded. ⋆\star No alice29 result. PAQ8px enwik8 figure is for -12L [ 17 ] .
CompressorSize (B)bpb
Original333,7948.000
gzip -991,3482.189
zstd -1979,7091.910
xz -972,5521.739
bzip2 -969,3051.661
Brotli -q 1168,6811.646
Table 6: Out-of-distribution evaluation on text published after SmolLM2’s training cutoff. FineZip uses the same SmolLM2-135M model as Nacrith for a controlled comparison isolating the architecture.
 enwik8 (1 MB)alice29
ConfigbpbΔ\DeltabpbΔ\Delta
A0: LLM + AE1.817—1.861—
A1: + CDF-241.300−- 0.5171.358−- 0.503
A2: + Adaptive head1.285−- 0.0151.341−- 0.017
A3: + N-gram + Skip0.897−- 0.3880.940−- 0.401
A4: Full system0.896−- 0.0010.939−- 0.001
Table 7: Ablation study: incremental feature contributions. Δ\Delta is the bpb reduction from the previous row. All runs use --workers 1 .
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