Lexis-E (Efficient)

A linguistically-structured hierarchical text compressor for English, built as a research contribution to the OpenAI Parameter Golf Challenge.

Lexis-E achieves 2.7523 bpb char-stream on FineWeb at 100k chars (default profile k6s511, compact_mode), outperforming gzip (3.3948 bpb) and zstd (3.1828 bpb) purely through explicit linguistic structure -- no learned weights, no training corpus. The "E" stands for Efficient -- Lexis-E exists to solve the metadata overhead problem of the main branch.

"How much of the compressibility of English comes from its linguistic structure alone, versus from statistical regularities in training data?"

Lexis provides a quantitative answer: linguistic priors alone account for roughly 2/3 of the gap between a naive byte compressor and a strong trained language model.

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Why Lexis-E Exists

After the core 8-stage pipeline was validated on the main branch, two problems were identified that motivated a dedicated branch:

1. Full-payload overhead -- The main branch's .lexis file bundles uncompressed structural metadata (POS tag sequences, morphological codes, model weights, symbol tables). This drives the full-payload bpb to ~20-23 on real documents, even when the character stream compresses well to ~2.7 bpb. The char-stream bpb is the honest compression quality metric, but the full-payload figure is the true end-to-end storage ratio -- and it was unacceptably high.
2. Fixed context-mixing parameters -- The Stage 6 probability model had no way to tune the trade-off between prediction depth (top_k) and probability sharpening (scale), leaving performance on the table for different document types and sizes.

Lexis-E addresses both through compact_mode -- a configurable metadata encoding mode with a sweepable top_k × scale grid -- without changing the character-stream compression algorithm.

Main vs Lexis-E

Feature	Lexis (main)	Lexis-E
Metadata encoding	Raw / uncompressed	Compact binary (compact_mode)
Context model tuning	Fixed parameters	Configurable top_k × scale sweep
Full-payload bpb at 100k chars (Moby Dick)	20.84	11.02
Full-payload bpb at 100k chars (FineWeb)	23.38*	11.10
char-stream bpb at 100k chars (Moby Dick)	2.6649	2.7555
char-stream bpb at 100k chars (FineWeb)	2.7494*	2.7523
Case flag bug fix	No	Yes -- bitmap bit-indexing corrected
Profile presets	None	default (k6s511), aggressive (k6s127)
Scaling test script	No	Yes (scaling_test.py)

*FineWeb main-branch scores are pooled over 50 samples × ≤10k chars, not a single 100k-char document.

The full-payload bpb improvement from 20.84 → 11.02 on Moby Dick (~47% reduction) is entirely attributable to compact_mode metadata encoding. The char-stream compression algorithm is identical between branches -- the small difference in char-stream bpb reflects different test corpora sizes and methods, not an algorithmic change.

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Benchmark Results

System comparison

System	Corpus	bpb (char-stream)	bpb (full payload)	Notes
Uncompressed UTF-8	—	8.00	8.00	Baseline
gzip level 9	Moby Dick	3.3230	3.3230	100k chars; no metadata separation
gzip level 9	FineWeb	3.3948	3.3948	50 samples × ≤10k chars, pooled
zstd level 19	Moby Dick	3.1125	3.1125	100k chars; no metadata separation
zstd level 19	FineWeb	3.1828	3.1828	50 samples × ≤10k chars, pooled
xz level 9	Moby Dick	3.0637	3.0637	100k chars; no metadata separation
xz level 9	FineWeb	3.1079	3.1079	50 samples × ≤10k chars, pooled
Lexis-E (no training data)	Moby Dick	2.7555	11.0172	100k chars, k6s511 (default)
Lexis-E (no training data)	FineWeb	2.7523	11.1048	100k chars, k6s511 (default)
cmix	enwik8	≈1.17	≈1.17	Classical context mixing; score from Knoll 2024 (byronknoll.com/cmix.html)
GPT-2 (1.5B params)	—	≈1.30	≈1.30	Trained on WebText

char-stream bpb = arithmetic-coded character bitstream only (Lexis) or raw compressed stream (gzip/zstd/xz/cmix -- no metadata separation). full-payload bpb = complete .lexis file including all metadata. For gzip/zstd/xz/cmix, char-stream bpb = full-payload bpb. cmix score is the published enwik8 figure; it is not directly comparable to the 100k-char Moby Dick / FineWeb corpora used for all other rows.

Lexis main vs Lexis-E -- Moby Dick & FineWeb at 100k chars

Branch	Corpus	Profile	char_stream_bpb	full_payload_bpb	char_stream bytes	full_payload bytes
main	Moby Dick	N/A (fixed params)	2.6649	20.8391	33,881	264,943
Lexis-E	Moby Dick	k6s511 (default)	2.7555	11.0172	34,323	137,230
main	FineWeb	N/A (fixed params)	2.7494*	23.384*	—	—
Lexis-E	FineWeb	k6s511 (default)	2.7523	11.1048	34,433	138,926

*FineWeb main-branch scores are pooled over 50 samples × ≤10k chars; Lexis-E FineWeb scores are from a single 100k-char document. The key takeaway: compact_mode cuts full-payload bpb by ~47% on Moby Dick (20.84 → 11.02) and ~52% on FineWeb (23.38 → 11.10), while char-stream bpb stays essentially the same.

Lexis-E -- Scaling Test on FineWeb (compact_mode, both profiles)

Profile	Input chars	char_stream_bpb	full_payload_bpb	char_stream bytes	full_payload bytes
default (k6s511)	10,000	2.7807	12.1866	3,479	15,247
default (k6s511)	25,000	2.7774	11.4323	8,686	35,753
default (k6s511)	50,000	2.7671	11.1774	17,304	69,898
default (k6s511)	100,000	2.7523	11.1048	34,433	138,926
aggressive (k6s127)	10,000	2.7927	12.0028	3,494	15,017
aggressive (k6s127)	25,000	2.7860	11.4278	8,713	35,739
aggressive (k6s127)	50,000	2.7767	11.1739	17,364	69,876
aggressive (k6s127)	100,000	2.7644	11.0597	34,584	138,362

Wall-clock time for both profiles × 4 sizes: 8m 56s real (13m 31s user -- CPU-parallel stages). char_stream_bpb measures the arithmetic-coded character stream only. full_payload_bpb includes all metadata (morph codes, POS tags, case flags, model weights, symbol table, root lengths, etc.).

Lexis-E -- Scaling Test on Moby Dick (compact_mode, default profile k6s511)

Input chars	char_stream_bpb	full_payload_bpb	char_stream bytes	full_payload bytes
10,000	2.7919	12.6728	3,411	15,483
25,000	2.7808	12.2991	8,535	37,749
50,000	2.7724	11.5677	17,176	71,666
100,000	2.7555	11.0172	34,323	137,230

Source: sweep_k6_s511-16.csv. Profile: top_k=6, scale=511.

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compact_mode -- Profile Sweep (Moby Dick corpus)

Lexis-E exposes a compact_mode flag that sweeps the context-mixing model's top_k (number of active prediction contexts) and scale (probability sharpening factor). A full grid sweep was run at 10k / 25k / 50k / 100k chars across k∈{3,4,5,6} × scale∈{127,255,511,1023}.

Full sweep -- char_stream_bpb at 100k chars

Profile	top_k	scale	char_stream_bpb	full_payload_bpb	char_stream bytes
k3s127	3	127	3.1928	12.1146	39,769
k3s255	3	255	3.3339	12.2242	41,527
k3s511	3	511	3.4860	11.6501	43,421
k3s1023	3	1023	3.6408	11.9568	45,350
k4s127	4	127	2.9240	11.2266	36,421
k4s255	4	255	2.9714	11.3285	37,012
k4s511	4	511	3.0270	11.3255	37,704
k4s1023	4	1023	3.0847	11.3895	38,423
k5s127	5	127	2.8413	11.0494	35,391
k5s255	5	255	2.8585	11.0560	35,606
k5s511	5	511	2.8828	11.2648	35,908
k5s1023	5	1023	2.9087	11.2746	36,231
k6s127	6	127	2.7719	11.0140	34,527
k6s255	6	255	2.7583	11.1828	34,357
k6s511 (default)	6	511	2.7555	11.0172	34,323
k6s1023	6	1023	2.7563	11.1885	34,333

Why k6s511 is the default

k6s511 achieves the lowest char_stream_bpb (2.7555) and the smallest char_stream byte count (34,323) at 100k chars across all 16 profiles on the Moby Dick sweep corpus, and confirms 2.7523 bpb on FineWeb at 100k chars. While k6s1023 is marginally comparable (2.7563 bpb), it uses a larger scale window with no net benefit at any tested size. k6s127 (aggressive profile) scores better on full_payload_bpb at 100k on FineWeb (11.0597 vs 11.1048) but has worse char_stream_bpb (2.7644 vs 2.7523), making k6s511 the Pareto-optimal default for char-stream compression quality.

Two profiles are shipped:

• default -- top_k=6, scale=511 -- best char_stream_bpb, lowest char_stream byte count
• aggressive -- top_k=6, scale=127 -- best full_payload_bpb (metadata overhead dominant use case)

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How It Works

Lexis-E compresses text through a 12-stage pipeline that progressively strips linguistic redundancy at every level of English structure.

Key Technical Contributions

Mixed-radix phonetic decomposition -- Characters are decomposed into (phonetic class, position, morphological role) triples rather than flat IDs. This reduces character-level delta magnitude by 2.42× on real text.

Online context adaptation -- Stage 6 trains only on the document being compressed, in real time. No offline corpus needed.

Symbol slot extraction (Stage 1c) -- §E/§W discourse tokens are stripped before encoding and spliced back after decoding using anchor-based char-offset interpolation. Zero char-stream overhead; zero leaked tokens.

Anchor-based splice -- Instead of a single linear scale, splice_symbols builds anchor points every 200 clean chars snapped to space boundaries, then interpolates between the nearest pair. Eliminates positional drift at 10k+ chars.

Discourse threshold effect -- Stage 4 coreference substitution is net-negative below ~800 bytes and increasingly beneficial above ~2,000 bytes.

Factoriadic delta encoding -- Symbol deltas encoded in the factorial number system; compact for the small, frequent steps that dominate linguistically-constrained sequences.

Case flag encoding (Stage 5b) -- Each token surface form is classified into one of four case categories (LOWER=0, TITLE=1, UPPER=2, MIXED=3). MIXED tokens additionally carry a per-character bitmap where bit N corresponds to char index N of the surface form. This allows lossless case restoration without storing any raw uppercase characters in the char stream. Bug fix applied in Lexis-E: bitmap bit-indexing in both compute_case_flag and apply_case_flag was corrected to use a consistent bit N ↔ char index N convention throughout.

compact_mode -- The context-mixing model (Stage 6) exposes top_k (active prediction contexts) and scale (probability sharpening). A 4×4 grid sweep identified k6s511 as the Pareto-optimal default.

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Installation

Requires Python 3.11.x -- later versions break spaCy compatibility.

# Fedora (adapt package manager for your distro)
sudo dnf install python3.11

# CUDA setup (optional -- used by Stage 3 spaCy and Stage 4 Longformer inference)
sudo dnf config-manager --add-repo https://developer.download.nvidia.com/compute/cuda/repos/fedora39/x86_64/cuda-fedora39.repo
sudo dnf clean all
sudo dnf module disable nvidia-driver
sudo dnf -y install cuda

export PATH=/usr/local/cuda-12.9/bin${PATH:+:${PATH}}
export LD_LIBRARY_PATH=/usr/local/cuda-12.9/lib64${LD_LIBRARY_PATH:+:${LD_LIBRARY_PATH}}

# Create virtual environment
python3.11 -m venv .venv
source .venv/bin/activate

# Install dependencies
pip install -r requirements.txt
python -m spacy download en_core_web_sm
python -m spacy download en_core_web_lg
pip install cupy-cuda12x  # only if CUDA is available

# Verify installation
pip check
python pipeline_trace.py  # all stages green

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Usage

# Full pipeline trace (all 12 stages)
python pipeline_trace.py

# Round-trip test
python test_round_trip_pipeline.py

# FineWeb benchmark
python eval_fineweb_bpb.py

# Scale test (FineWeb, both profiles)
time python scaling_test.py \
  --input fineweb_100k.txt \
  --sizes 10000 25000 50000 100000 \
  --compact-context \
  --compact-profile both \
  --csv fineweb_sweep_both_profiles.csv

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Submission Snapshot

The canonical Lexis-E submission state is tagged at:

git tag challenge-submit-updated-docs-2026-05-01

Commit: 49588f6 -- docs: add Lexis-E (Efficient) origin section explaining branch split and differences vs main

This tag marks the exact Lexis-E codebase submitted to the OpenAI Parameter Golf Challenge non-record track originally created on 2026-04-30, docs updated on 2026-05-01.

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Notes

• Semantic fidelity over byte-exact reconstruction -- Stage 1 sentence boundary detection produces minor punctuation normalizations at quote boundaries. These do not affect meaning, information content, or bpb measurement.
• full_payload_bpb vs char_stream_bpb -- char_stream_bpb (2.7523 FineWeb / 2.7555 Moby Dick) measures compression quality of the character sequence alone. full_payload_bpb (11.10 FineWeb / 11.02 Moby Dick) includes all structural metadata; it is the honest end-to-end ratio. compact_mode dramatically reduces metadata overhead vs the main branch (11.1 vs 20.8 at 100k chars).
• cmix score -- The cmix row uses the published enwik8 bpb (≈1.17) from Byron Knoll's cmix page (byronknoll.com/cmix.html). cmix requires ~32 GB RAM to run locally; the published figure is cited rather than measured. Note the enwik8 corpus differs from Moby Dick / FineWeb, so this row is for reference context only.
• IDE import warnings -- your IDE may flag an import error in stage4_discourse.py for fastcoref if not launched from inside the virtual environment. This is a false positive.
• GPU usage -- Stage 3 (spaCy) and Stage 4 (Longformer coreference, 90.5M params) use GPU when available. Stage 7 arithmetic encoding runs on CPU (standard interval arithmetic coding, not rANS).
• transformers version patch -- transformers/dependency_versions_table.py requires manual patching to remove the huggingface-hub<1.0 upper bound if your environment has huggingface-hub>=1.0.

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Test Corpus

• Moby Dick (Project Gutenberg) -- compact_mode profile sweep, 10k-100k chars (16 profiles, 4 sizes each); default profile (k6s511) scaling test
• FineWeb (HuggingFaceFW/fineweb, sample-10BT) -- compact_mode scaling: both profiles × 4 sizes up to 100k chars

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Origin

Lexis started as a research point of interest for the OpenAI Parameter Golf Challenge -- specifically the non-record track, which invites submissions that push the frontier of parameter-limited performance without the 16MB / 10-minute constraint.

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References

• OpenAI Parameter Golf Challenge
• NanoGPT Speedrunning
• PAQ compression family -- context mixing
• PPM (Prediction by Partial Matching), 1984
• ANS (Asymmetric Numeral Systems) -- Duda, 2009
• Longformer -- Beltagy et al. 2020
• FineWeb dataset -- HuggingFaceFW/fineweb
• Neural scaling laws -- Kaplan et al. 2020
• cmix -- Byron Knoll, byronknoll.com/cmix.html
• lemminflect -- morphological inflection for Python
• msgpack -- binary serialisation
• zstd -- Zstandard compression, level 19 outer wrapper