wikilangs/lmo

Lombard - Wikilangs Models

Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on Lombard Wikipedia data. We analyze tokenizers, n-gram models, Markov chains, vocabulary statistics, and word embeddings.

📋 Repository Contents

Models & Assets

• Tokenizers (8k, 16k, 32k, 64k)
• N-gram models (2, 3, 4, 5-gram)
• Markov chains (context of 1, 2, 3, 4 and 5)
• Subword N-gram and Markov chains
• Embeddings in various sizes and dimensions (aligned and unaligned)
• Language Vocabulary
• Language Statistics

Analysis and Evaluation

• 1. Tokenizer Evaluation
• 2. N-gram Model Evaluation
• 3. Markov Chain Evaluation
• 4. Vocabulary Analysis
• 5. Word Embeddings Evaluation
• 6. Morphological Analysis (Experimental)
• 7. Summary & Recommendations
• Metrics Glossary
• Visualizations Index

---

1. Tokenizer Evaluation

Results

Vocab Size	Compression	Avg Token Len	UNK Rate	Total Tokens
8k	2.899x	2.90	0.1988%	276,191
16k	3.111x	3.11	0.2133%	257,402
32k	3.306x	3.31	0.2267%	242,211
64k	3.475x 🏆	3.48	0.2382%	230,431

Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

Sample 1: a l'è un comun de la Cechia, part de la Moravia de Sota e del distret de Hodonín...

Vocab	Tokens	Count
8k	▁a ▁l ' è ▁un ▁comun ▁de ▁la ▁cechia , ... (+18 more)	28
16k	▁a ▁l ' è ▁un ▁comun ▁de ▁la ▁cechia , ... (+16 more)	26
32k	▁a ▁l ' è ▁un ▁comun ▁de ▁la ▁cechia , ... (+16 more)	26
64k	▁a ▁l ' è ▁un ▁comun ▁de ▁la ▁cechia , ... (+16 more)	26

Sample 2: El 872 a l'è 'n ann del secol quell de noeuv. Cossa l'è sucedud Chi l'è che l'è ...

Vocab	Tokens	Count
8k	▁el ▁ 8 7 2 ▁a ▁l ' è ▁' ... (+33 more)	43
16k	▁el ▁ 8 7 2 ▁a ▁l ' è ▁' ... (+33 more)	43
32k	▁el ▁ 8 7 2 ▁a ▁l ' è ▁' ... (+33 more)	43
64k	▁el ▁ 8 7 2 ▁a ▁l ' è ▁' ... (+33 more)	43

Sample 3: Superfice: 6.334 km² Popolazzion (ISTAT 606.413 ab. Densità: 96 ab./km² Numer de...

Vocab	Tokens	Count
8k	▁superfice : ▁ 6 . 3 3 4 ▁km 2 ... (+50 more)	60
16k	▁superfice : ▁ 6 . 3 3 4 ▁km 2 ... (+49 more)	59
32k	▁superfice : ▁ 6 . 3 3 4 ▁km 2 ... (+48 more)	58
64k	▁superfice : ▁ 6 . 3 3 4 ▁km 2 ... (+48 more)	58

Key Findings

• Best Compression: 64k achieves 3.475x compression
• Lowest UNK Rate: 8k with 0.1988% unknown tokens
• Trade-off: Larger vocabularies improve compression but increase model size
• Recommendation: 32k vocabulary provides optimal balance for production use

---

2. N-gram Model Evaluation

Results

N-gram	Variant	Perplexity	Entropy	Unique N-grams	Top-100 Coverage	Top-1000 Coverage
2-gram	Word	7,760	12.92	122,388	29.0%	53.4%
2-gram	Subword	268 🏆	8.07	6,535	68.2%	98.7%
3-gram	Word	14,354	13.81	199,723	22.6%	48.6%
3-gram	Subword	2,089	11.03	52,666	30.7%	72.9%
4-gram	Word	20,963	14.36	321,119	20.2%	45.6%
4-gram	Subword	10,897	13.41	280,505	17.5%	44.7%
5-gram	Word	15,543	13.92	228,095	20.6%	47.3%
5-gram	Subword	37,324	15.19	760,735	11.8%	32.7%

Top 5 N-grams by Size

2-grams (Word):

Rank	N-gram	Count
1	l è	175,964
2	de la	121,062
3	a l	80,762
4	alter proget	33,969
5	de l	33,487

3-grams (Word):

Rank	N-gram	Count
1	a l è	71,526
2	l è un	32,278
3	è un comun	23,691
4	l è n	19,224
5	el g ha	18,949

4-grams (Word):

Rank	N-gram	Count
1	a l è un	30,858
2	l è un comun	23,691
3	è un comun de	15,254
4	un comun de la	15,236
5	l è n cümü	14,678

5-grams (Word):

Rank	N-gram	Count
1	a l è un comun	23,684
2	l è un comun de	15,254
3	è un comun de la	15,236
4	cont una popolazzion de abitant	13,027
5	una popolazzion de abitant riferiment	12,935

2-grams (Subword):

Rank	N-gram	Count
1	a _	1,432,799
2	_ d	1,057,415
3	e _	1,006,725
4	d e	886,199
5	_ l	709,001

3-grams (Subword):

Rank	N-gram	Count
1	_ d e	789,525
2	d e _	528,733
3	e l _	383,347
4	l a _	338,250
5	_ l a	295,669

4-grams (Subword):

Rank	N-gram	Count
1	_ d e _	515,677
2	_ l a _	273,207
3	_ d e l	205,525
4	d e l _	203,248
5	d e _ l	169,714

5-grams (Subword):

Rank	N-gram	Count
1	_ d e l _	198,355
2	_ d e _ l	168,983
3	_ l ' è _	164,316
4	e _ l a _	145,472
5	d e _ l a	122,850

Key Findings

• Best Perplexity: 2-gram (subword) with 268
• Entropy Trend: Decreases with larger n-grams (more predictable)
• Coverage: Top-1000 patterns cover ~33% of corpus
• Recommendation: 4-gram or 5-gram for best predictive performance

---

3. Markov Chain Evaluation

Results

Context	Variant	Avg Entropy	Perplexity	Branching Factor	Unique Contexts	Predictability
1	Word	0.8496	1.802	5.71	320,846	15.0%
1	Subword	0.9820	1.975	7.44	2,274	1.8%
2	Word	0.3082	1.238	1.84	1,817,237	69.2%
2	Subword	0.9539	1.937	6.24	16,914	4.6%
3	Word	0.1317	1.096	1.27	3,319,649	86.8%
3	Subword	0.8409	1.791	4.52	105,502	15.9%
4	Word	0.0581 🏆	1.041	1.10	4,172,728	94.2%
4	Subword	0.7003	1.625	3.13	476,503	30.0%

Generated Text Samples (Word-based)

Below are text samples generated from each word-based Markov chain model:

Context Size 1:

1. de bourg en fransés arrondissements e in del comun del regn d abitant riferiment lista di
2. l è staa fat tort che la u s cieta del dipartimènt de 215 alter proget
3. la stiria waidhofen an und freude ich dich dass dese en g ha na popolasiù de

Context Size 2:

1. l è de 4 23 test immanuel casto musega keen horror vacui feat romina falconi che a
2. de la serie a l éra csì trascüra e csì da póch che federìco i el re
3. a l è iniziàa in del pleistocene poeu soeu poeu giò 3 milion de alber qe l

Context Size 3:

1. a l è un comun di isole balear cont una popolazzion de abitant riferiment hacienda es alter proget
2. l è un paes de l asia del pakistan
3. è un comun del distret de hradec králové e del distret de jura nord vaudois in del canton

Context Size 4:

1. a l è un cumün svizzer del canton türgovia la süperfiss del teritori del cumün l è de 2
2. l è un comun del distret de prešov in la region de trnava ligam de foeura sit ofizzial alter
3. è un comun de la provincia de noara giamò in del el tö part a una manifestaziun ligada ai

Generated Text Samples (Subword-based)

Below are text samples generated from each subword-based Markov chain model:

Context Size 1:

1. _sò_denal'ètetom
2. a_str_mü_dinteme
3. essöva_gàn_m_d,_

Context Size 2:

1. a_giù_doregia_l'è
2. _denaa_a_de_abeci
3. e_imèntù_del_noli

Context Size 3:

1. _de_15_mederàl_bib
2. de_altèsa_movincia
3. el_gh'era,_elegh_u

Context Size 4:

1. _de_l'onda_dentan_d
2. _la_red_hd_-_gattag
3. _del_cannon._person

Key Findings

• Best Predictability: Context-4 (word) with 94.2% predictability
• Branching Factor: Decreases with context size (more deterministic)
• Memory Trade-off: Larger contexts require more storage (476,503 contexts)
• Recommendation: Context-3 or Context-4 for text generation

---

4. Vocabulary Analysis

Statistics

Metric	Value
Vocabulary Size	144,217
Total Tokens	7,040,353
Mean Frequency	48.82
Median Frequency	4
Frequency Std Dev	2201.90

Most Common Words

Rank	Word	Frequency
1	de	519,158
2	l	332,263
3	la	287,692
4	del	200,975
5	è	195,911
6	a	181,605
7	el	167,836
8	e	158,973
9	in	125,242
10	che	81,914

Least Common Words (from vocabulary)

Rank	Word	Frequency
1	platamone	2
2	ludvik	2
3	zorzut	2
4	alojz	2
5	gradnik	2
6	böhmstetten	2
7	monegasche	2
8	diaconești	2
9	chichinsci	2
10	şerbănești	2

Zipf's Law Analysis

Metric	Value
Zipf Coefficient	1.0675
R² (Goodness of Fit)	0.999638
Adherence Quality	excellent

Coverage Analysis

Top N Words	Coverage
Top 100	54.0%
Top 1,000	72.1%
Top 5,000	82.9%
Top 10,000	87.3%

Key Findings

• Zipf Compliance: R²=0.9996 indicates excellent adherence to Zipf's law
• High Frequency Dominance: Top 100 words cover 54.0% of corpus
• Long Tail: 134,217 words needed for remaining 12.7% coverage

---

5. Word Embeddings Evaluation

5.1 Cross-Lingual Alignment

5.2 Model Comparison

Model	Dimension	Isotropy	Semantic Density	Alignment R@1	Alignment R@10
mono_32d	32	0.8136	0.3373	N/A	N/A
mono_64d	64	0.7985	0.2665	N/A	N/A
mono_128d	128	0.7531	0.2072	N/A	N/A
aligned_32d	32	0.8136 🏆	0.3393	0.0920	0.3580
aligned_64d	64	0.7985	0.2646	0.1660	0.5380
aligned_128d	128	0.7531	0.2006	0.2320	0.5780

Key Findings

• Best Isotropy: aligned_32d with 0.8136 (more uniform distribution)
• Semantic Density: Average pairwise similarity of 0.2693. Lower values indicate better semantic separation.
• Alignment Quality: Aligned models achieve up to 23.2% R@1 in cross-lingual retrieval.
• Recommendation: 128d aligned for best cross-lingual performance

---

6. Morphological Analysis (Experimental)

This section presents an automated morphological analysis derived from the statistical divergence between word-level and subword-level models. By analyzing where subword predictability spikes and where word-level coverage fails, we can infer linguistic structures without supervised data.

6.1 Productivity & Complexity

Metric	Value	Interpretation	Recommendation
Productivity Index	5.000	High morphological productivity	Reliable analysis
Idiomaticity Gap	0.446	High formulaic/idiomatic content	-

6.2 Affix Inventory (Productive Units)

These are the most productive prefixes and suffixes identified by sampling the vocabulary for global substitutability patterns. A unit is considered an affix if stripping it leaves a valid stem that appears in other contexts.

Productive Prefixes

Prefix	Examples
-s	suldà, sedimm, serraj
-a	alfanumerich, antiege, apinac
-c	capitana, centralizzazzion, concentrich
-p	percepìd, pròssima, pizzà
-ca	capitana, cabardes, cambo
-b	beve, broeulla, buildings
-m	mésage, mysteries, mia
-d	dificila, dàl, dreits

Productive Suffixes

Suffix	Examples
-a	capitana, ghiffa, vallinfreda
-n	granon, repulsion, eisenbahn
-e	beve, antiege, häme
-i	liebenbergii, percassi, kiuruvesi
-o	riuso, malvito, quagliuzzo
-s	vachères, mysteries, mauvais
-t	nètt, tunet, fònoisolant
-on	granon, repulsion, centralizzazzion

6.3 Bound Stems (Lexical Roots)

Bound stems are high-frequency subword units that are semantically cohesive but rarely appear as standalone words. These often correspond to the 'core' of a word that requires inflection or derivation to be valid.

Stem	Cohesion	Substitutability	Examples
zzio	2.50x	36 contexts	azzion, lazzio, dozzion
rovi	2.01x	57 contexts	rovin, rovid, trovi
itan	1.73x	84 contexts	titan, ritan, gaitan
stre	1.63x	106 contexts	èstre, stret, strel
lter	1.80x	61 contexts	òlter, älter, olter
ifer	1.85x	49 contexts	cifer, zifer, riferì
inci	1.56x	98 contexts	vinci, incis, incin
perf	1.94x	39 contexts	perfet, perfid, perfèt
popo	2.31x	21 contexts	popoi, popoj, popov
istr	1.57x	93 contexts	istra, nistra, distro
omun	2.09x	29 contexts	comun, comune, comunn
tret	2.23x	23 contexts	stret, trets, strett

6.4 Affix Compatibility (Co-occurrence)

This table shows which prefixes and suffixes most frequently co-occur on the same stems, revealing the 'stacking' rules of the language's morphology.

Prefix	Suffix	Frequency	Examples
-c	-a	182 words	consideràda, calabiana
-s	-a	140 words	satyagraha, südtirulesa
-p	-a	135 words	porta, provenienza
-a	-a	96 words	apiifolia, ajaa
-c	-o	79 words	collecchio, cosimo
-c	-e	77 words	cadore, cunoniaceae
-s	-n	74 words	stagion, stallikon
-c	-n	74 words	cardinalin, cunserven
-d	-a	71 words	diavolezza, dulia
-b	-a	64 words	bicicleta, balaustra

6.5 Recursive Morpheme Segmentation

Using Recursive Hierarchical Substitutability, we decompose complex words into their constituent morphemes. This approach handles nested affixes (e.g., prefix-prefix-root-suffix).

Word	Suggested Split	Confidence	Stem
independentisem	independentis-e-m	7.5	e
büsserach	büsser-a-ch	7.5	a
desvilupar	desvilup-a-r	7.5	a
sudcorean	sudco-re-an	7.5	re
ingrendient	ingrendi-e-nt	7.5	e
desgrazzia	de-s-grazzia	7.5	grazzia
monterrei	monterr-e-i	7.5	e
beutelsbach	beutelsb-a-ch	7.5	a
pianzanda	pianza-n-da	7.5	n
compagnii	compagn-i-i	7.5	i
marchesan	marches-a-n	7.5	a
scrivania	scriva-n-ia	7.5	n
recustrüii	recustrü-i-i	7.5	i
principiar	princip-ia-r	6.0	princip
modernitaa	moderni-ta-a	6.0	moderni

6.6 Linguistic Interpretation

Automated Insight: The language Lombard shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.

Note on Idiomaticity: The high Idiomaticity Gap suggests a large number of frequent multi-word expressions or formulaic sequences that are statistically distinct from their component parts.

---

7. Summary & Recommendations

Production Recommendations

Component	Recommended	Rationale
Tokenizer	64k BPE	Best compression (3.47x)
N-gram	2-gram	Lowest perplexity (268)
Markov	Context-4	Highest predictability (94.2%)
Embeddings	100d	Balanced semantic capture and isotropy

---

Appendix: Metrics Glossary & Interpretation Guide

This section provides definitions, intuitions, and guidance for interpreting the metrics used throughout this report.

Tokenizer Metrics

Compression Ratio

Definition: The ratio of characters to tokens (chars/token). Measures how efficiently the tokenizer represents text.

Intuition: Higher compression means fewer tokens needed to represent the same text, reducing sequence lengths for downstream models. A 3x compression means ~3 characters per token on average.

What to seek: Higher is generally better for efficiency, but extremely high compression may indicate overly aggressive merging that loses morphological information.

Average Token Length (Fertility)

Definition: Mean number of characters per token produced by the tokenizer.

Intuition: Reflects the granularity of tokenization. Longer tokens capture more context but may struggle with rare words; shorter tokens are more flexible but increase sequence length.

What to seek: Balance between 2-5 characters for most languages. Arabic/morphologically-rich languages may benefit from slightly longer tokens.

Unknown Token Rate (OOV Rate)

Definition: Percentage of tokens that map to the unknown/UNK token, indicating words the tokenizer cannot represent.

Intuition: Lower OOV means better vocabulary coverage. High OOV indicates the tokenizer encounters many unseen character sequences.

What to seek: Below 1% is excellent; below 5% is acceptable. BPE tokenizers typically achieve very low OOV due to subword fallback.

N-gram Model Metrics

Perplexity

Definition: Measures how "surprised" the model is by test data. Mathematically: 2^(cross-entropy). Lower values indicate better prediction.

Intuition: If perplexity is 100, the model is as uncertain as if choosing uniformly among 100 options at each step. A perplexity of 10 means effectively choosing among 10 equally likely options.

What to seek: Lower is better. Perplexity decreases with larger n-grams (more context). Values vary widely by language and corpus size.

Entropy

Definition: Average information content (in bits) needed to encode the next token given the context. Related to perplexity: perplexity = 2^entropy.

Intuition: High entropy means high uncertainty/randomness; low entropy means predictable patterns. Natural language typically has entropy between 1-4 bits per character.

What to seek: Lower entropy indicates more predictable text patterns. Entropy should decrease as n-gram size increases.

Coverage (Top-K)

Definition: Percentage of corpus occurrences explained by the top K most frequent n-grams.

Intuition: High coverage with few patterns indicates repetitive/formulaic text; low coverage suggests diverse vocabulary usage.

What to seek: Depends on use case. For language modeling, moderate coverage (40-60% with top-1000) is typical for natural text.

Markov Chain Metrics

Average Entropy

Definition: Mean entropy across all contexts, measuring average uncertainty in next-word prediction.

Intuition: Lower entropy means the model is more confident about what comes next. Context-1 has high entropy (many possible next words); Context-4 has low entropy (few likely continuations).

What to seek: Decreasing entropy with larger context sizes. Very low entropy (<0.1) indicates highly deterministic transitions.

Branching Factor

Definition: Average number of unique next tokens observed for each context.

Intuition: High branching = many possible continuations (flexible but uncertain); low branching = few options (predictable but potentially repetitive).

What to seek: Branching factor should decrease with context size. Values near 1.0 indicate nearly deterministic chains.

Predictability

Definition: Derived metric: (1 - normalized_entropy) × 100%. Indicates how deterministic the model's predictions are.

Intuition: 100% predictability means the next word is always certain; 0% means completely random. Real text falls between these extremes.

What to seek: Higher predictability for text generation quality, but too high (>98%) may produce repetitive output.

Vocabulary & Zipf's Law Metrics

Zipf's Coefficient

Definition: The slope of the log-log plot of word frequency vs. rank. Zipf's law predicts this should be approximately -1.

Intuition: A coefficient near -1 indicates the corpus follows natural language patterns where a few words are very common and most words are rare.

What to seek: Values between -0.8 and -1.2 indicate healthy natural language distribution. Deviations may suggest domain-specific or artificial text.

R² (Coefficient of Determination)

Definition: Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.

Intuition: R² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.

What to seek: R² > 0.95 is excellent; > 0.99 indicates near-perfect Zipf adherence typical of large natural corpora.

Vocabulary Coverage

Definition: Cumulative percentage of corpus tokens accounted for by the top N words.

Intuition: Shows how concentrated word usage is. If top-100 words cover 50% of text, the corpus relies heavily on common words.

What to seek: Top-100 covering 30-50% is typical. Higher coverage indicates more repetitive text; lower suggests richer vocabulary.

Word Embedding Metrics

Isotropy

Definition: Measures how uniformly distributed vectors are in the embedding space. Computed as the ratio of minimum to maximum singular values.

Intuition: High isotropy (near 1.0) means vectors spread evenly in all directions; low isotropy means vectors cluster in certain directions, reducing expressiveness.

What to seek: Higher isotropy generally indicates better-quality embeddings. Values > 0.1 are reasonable; > 0.3 is good. Lower-dimensional embeddings tend to have higher isotropy.

Average Norm

Definition: Mean magnitude (L2 norm) of word vectors in the embedding space.

Intuition: Indicates the typical "length" of vectors. Consistent norms suggest stable training; high variance may indicate some words are undertrained.

What to seek: Relatively consistent norms across models. The absolute value matters less than consistency (low std deviation).

Cosine Similarity

Definition: Measures angular similarity between vectors, ranging from -1 (opposite) to 1 (identical direction).

Intuition: Words with similar meanings should have high cosine similarity. This is the standard metric for semantic relatedness in embeddings.

What to seek: Semantically related words should score > 0.5; unrelated words should be near 0. Synonyms often score > 0.7.

t-SNE Visualization

Definition: t-Distributed Stochastic Neighbor Embedding - a dimensionality reduction technique that preserves local structure for visualization.

Intuition: Clusters in t-SNE plots indicate groups of semantically related words. Spread indicates vocabulary diversity; tight clusters suggest semantic coherence.

What to seek: Meaningful clusters (e.g., numbers together, verbs together). Avoid over-interpreting distances - t-SNE preserves local, not global, structure.

General Interpretation Guidelines

1. Compare within model families: Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
2. Consider trade-offs: Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
3. Context matters: Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
4. Corpus influence: All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
5. Language-specific patterns: Morphologically rich languages (like Arabic) may show different optimal ranges than analytic languages.

Visualizations Index

Visualization	Description
Tokenizer Compression	Compression ratios by vocabulary size
Tokenizer Fertility	Average token length by vocabulary
Tokenizer OOV	Unknown token rates
Tokenizer Total Tokens	Total tokens by vocabulary
N-gram Perplexity	Perplexity by n-gram size
N-gram Entropy	Entropy by n-gram size
N-gram Coverage	Top pattern coverage
N-gram Unique	Unique n-gram counts
Markov Entropy	Entropy by context size
Markov Branching	Branching factor by context
Markov Contexts	Unique context counts
Zipf's Law	Frequency-rank distribution with fit
Vocab Frequency	Word frequency distribution
Top 20 Words	Most frequent words
Vocab Coverage	Cumulative coverage curve
Embedding Isotropy	Vector space uniformity
Embedding Norms	Vector magnitude distribution
Embedding Similarity	Word similarity heatmap
Nearest Neighbors	Similar words for key terms
t-SNE Words	2D word embedding visualization
t-SNE Sentences	2D sentence embedding visualization
Position Encoding	Encoding method comparison
Model Sizes	Storage requirements
Performance Dashboard	Comprehensive performance overview

---

About This Project

Data Source

Models trained on wikipedia-monthly - a monthly snapshot of Wikipedia articles across 300+ languages.

Project

A project by Wikilangs - Open-source NLP models for every Wikipedia language.

Maintainer

Omar Kamali - Omneity Labs

Citation

If you use these models in your research, please cite:

@misc{wikilangs2025,
  author = {Kamali, Omar},
  title = {Wikilangs: Open NLP Models for Wikipedia Languages},
  year = {2025},
  doi = {10.5281/zenodo.18073153},
  publisher = {Zenodo},
  url = {https://huggingface.co/wikilangs}
  institution = {Omneity Labs}
}

License

MIT License - Free for academic and commercial use.

Links

• 🌐 Website: wikilangs.org
• 🤗 Models: huggingface.co/wikilangs
• 📊 Data: wikipedia-monthly
• 👤 Author: Omar Kamali
• 🤝 Sponsor: Featherless AI

---

Generated by Wikilangs Models Pipeline

Report Date: 2026-01-10 11:37:13