Danish - Wikilangs Models

Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on Danish 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

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1. Tokenizer Evaluation

Results

Vocab Size	Compression	Avg Token Len	UNK Rate	Total Tokens
8k	3.590x	3.59	0.1227%	1,644,330
16k	3.953x	3.95	0.1351%	1,493,346
32k	4.286x	4.29	0.1465%	1,377,449
64k	4.557x 🏆	4.56	0.1558%	1,295,305

Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

Sample 1: Ole Bornemann henviser til: Oluf Bornemann – dansk-norsk biskop Ole Bornemann (r...

Vocab	Tokens	Count
8k	▁ole ▁bor nem ann ▁henviser ▁til : ▁oluf ▁bor nem ... (+27 more)	37
16k	▁ole ▁bor nemann ▁henviser ▁til : ▁oluf ▁bor nemann ▁– ... (+21 more)	31
32k	▁ole ▁bor nemann ▁henviser ▁til : ▁oluf ▁bor nemann ▁– ... (+20 more)	30
64k	▁ole ▁bornemann ▁henviser ▁til : ▁oluf ▁bornemann ▁– ▁dansk - ... (+16 more)	26

Sample 2: 18. April er en dansk dokumentarfilm fra instrueret af Poul Meyer. Eksterne henv...

Vocab	Tokens	Count
8k	▁ 1 8 . ▁april ▁er ▁en ▁dansk ▁dokumentarfilm ▁fra ... (+11 more)	21
16k	▁ 1 8 . ▁april ▁er ▁en ▁dansk ▁dokumentarfilm ▁fra ... (+11 more)	21
32k	▁ 1 8 . ▁april ▁er ▁en ▁dansk ▁dokumentarfilm ▁fra ... (+11 more)	21
64k	▁ 1 8 . ▁april ▁er ▁en ▁dansk ▁dokumentarfilm ▁fra ... (+11 more)	21

Sample 3: Takeshi Watanabe (født 10. september er en japansk fodboldspiller. Japans fodbol...

Vocab	Tokens	Count
8k	▁tak es hi ▁wat an ab e ▁( født ▁ ... (+12 more)	22
16k	▁tak es hi ▁wat an abe ▁( født ▁ 1 ... (+11 more)	21
32k	▁takes hi ▁wat an abe ▁( født ▁ 1 0 ... (+10 more)	20
64k	▁takes hi ▁watanabe ▁( født ▁ 1 0 . ▁september ... (+8 more)	18

Key Findings

• Best Compression: 64k achieves 4.557x compression
• Lowest UNK Rate: 8k with 0.1227% unknown tokens
• Trade-off: Larger vocabularies improve compression but increase model size
• Recommendation: 32k vocabulary provides optimal balance for production use

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2. N-gram Model Evaluation

Results

N-gram	Variant	Perplexity	Entropy	Unique N-grams	Top-100 Coverage	Top-1000 Coverage
2-gram	Word	205,179	17.65	1,697,331	7.2%	18.6%
2-gram	Subword	291 🏆	8.19	16,676	66.5%	99.0%
3-gram	Word	930,238	19.83	3,294,874	2.7%	7.8%
3-gram	Subword	2,629	11.36	143,880	25.6%	68.8%
4-gram	Word	2,232,256	21.09	5,289,799	1.9%	5.1%
4-gram	Subword	16,827	14.04	898,389	12.2%	36.9%
5-gram	Word	1,710,284	20.71	3,467,271	1.9%	5.4%
5-gram	Subword	78,315	16.26	3,371,746	6.1%	20.8%

Top 5 N-grams by Size

2-grams (Word):

Rank	N-gram	Count
1	er en	214,430
2	eksterne henvisninger	158,401
3	til at	148,332
4	for at	127,680
5	i den	98,315

3-grams (Word):

Rank	N-gram	Count
1	referencer eksterne henvisninger	69,492
2	eksterne henvisninger fra	52,148
3	en del af	36,449
4	fra danmark fra	31,038
5	på grund af	24,747

4-grams (Word):

Rank	N-gram	Count
1	referencer eksterne henvisninger fra	31,041
2	fra danmark fra danmark	18,040
3	eksterne henvisninger fra danmark	13,653
4	eksterne henvisninger fra usa	10,607
5	eksterne henvisninger film fra	8,857

5-grams (Word):

Rank	N-gram	Count
1	referencer eksterne henvisninger fra danmark	8,198
2	referencer eksterne henvisninger fra usa	7,710
3	referencer eksterne henvisninger film fra	6,839
4	fra danmark fra danmark fra	6,792
5	eksterne henvisninger film fra fra	6,671

2-grams (Subword):

Rank	N-gram	Count
1	e r	14,686,017
2	e _	12,413,595
3	e n	11,692,715
4	d e	11,106,628
5	r _	9,958,657

3-grams (Subword):

Rank	N-gram	Count
1	e r _	6,591,787
2	e n _	5,761,673
3	_ d e	4,088,356
4	e t _	3,830,236
5	_ i _	3,324,144

4-grams (Subword):

Rank	N-gram	Count
1	_ o g _	2,559,398
2	_ f o r	1,851,842
3	_ a f _	1,698,296
4	d e n _	1,598,615
5	_ t i l	1,395,426

5-grams (Subword):

Rank	N-gram	Count
1	_ t i l _	1,111,382
2	_ d e n _	1,013,475
3	_ s o m _	926,452
4	_ f r a _	883,398
5	_ f o r _	860,091

Key Findings

• Best Perplexity: 2-gram (subword) with 291
• Entropy Trend: Decreases with larger n-grams (more predictable)
• Coverage: Top-1000 patterns cover ~21% of corpus
• Recommendation: 4-gram or 5-gram for best predictive performance

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3. Markov Chain Evaluation

Results

Context	Variant	Avg Entropy	Perplexity	Branching Factor	Unique Contexts	Predictability
1	Word	0.9282	1.903	11.03	2,011,765	7.2%
1	Subword	1.1734	2.255	7.58	8,958	0.0%
2	Word	0.3698	1.292	2.34	22,156,805	63.0%
2	Subword	0.6816	1.604	4.74	67,792	31.8%
3	Word	0.1562	1.114	1.36	51,659,329	84.4%
3	Subword	0.7837	1.722	4.70	321,234	21.6%
4	Word	0.0627 🏆	1.044	1.11	69,884,622	93.7%
4	Subword	0.7511	1.683	3.88	1,508,279	24.9%

Generated Text Samples (Word-based)

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

Context Size 1:

1. i sverige bernadotte en tidligere premierminister vladimír vašíček tjekkisk eller med langt de flest...
2. og kortlagte dertil uhensigtsmæssige reaktionsmønstre på denne slags rum som et individuelt hold fra...
3. af det eneste gang i lælehe lunden og shimonoseki afstod unionen og sydlige ishav og egyptiske

Context Size 2:

1. er en aristokrat fra oneglia på en figur på fordi de manglede stadig konkrete beviser det objekts
2. eksterne henvisninger fra nederlandene fra flandern og champagne fra reims til danmark og derpaa ble...
3. til at åbne sine egne retoriske færdigheder selvom de ikke mangler det umiddelbares friskhed inspira...

Context Size 3:

1. referencer eksterne henvisninger 05 i vejle i alt var omkring 100 000 lysår og en tykkelse af cirka
2. eksterne henvisninger fra mozambique fra maputo ved sommer ol mestre fra usa sølvmedaljevindere fra ...
3. en del af moskenes kommune i nordland fylke i norge med et underskud på godt én million kroner

Context Size 4:

1. referencer eksterne henvisninger fra storbritannien medaljevindere i gymnastik mestre fra grækenland...
2. fra danmark fra danmark af videnskabernes selskab i dansk biografisk leksikon fra danmark thomas 1 f...
3. eksterne henvisninger fra danmark film fra fra nordisk film dramafilm fra danmark instrueret af augu...

Generated Text Samples (Subword-based)

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

Context Size 1:

1. _het_i_ldshic._k
2. enoge_der_8.a_t.
3. rerliolin,_opon_

Context Size 2:

1. er_ers_kum._ten_e
2. e_asterdyra_et_fo
3. en_i_kitler_være_

Context Size 3:

1. er_randsbog_blev_p
2. en_i_han_ver_guldv
3. _det_af_daktat_og_

Context Size 4:

1. _og_kristia_schlesw
2. _forfattish_music_d
3. _af_storia_italiste

Key Findings

• Best Predictability: Context-4 (word) with 93.7% predictability
• Branching Factor: Decreases with context size (more deterministic)
• Memory Trade-off: Larger contexts require more storage (1,508,279 contexts)
• Recommendation: Context-3 or Context-4 for text generation

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4. Vocabulary Analysis

Statistics

Metric	Value
Vocabulary Size	885,946
Total Tokens	86,775,295
Mean Frequency	97.95
Median Frequency	4
Frequency Std Dev	6460.78

Most Common Words

Rank	Word	Frequency
1	i	3,396,891
2	og	2,568,581
3	af	1,716,528
4	en	1,361,402
5	til	1,134,702
6	er	1,086,363
7	den	1,040,601
8	at	980,457
9	på	948,450
10	som	939,070

Least Common Words (from vocabulary)

Rank	Word	Frequency
1	elektronikinteresserede	2
2	sinoefloden	2
3	deathconsciousness	2
4	folkedanseforeninger	2
5	affranchi	2
6	superfilmen	2
7	kettletoft	2
8	sandays	2
9	crummack	2
10	rousays	2

Zipf's Law Analysis

Metric	Value
Zipf Coefficient	1.0001
R² (Goodness of Fit)	0.998027
Adherence Quality	excellent

Coverage Analysis

Top N Words	Coverage
Top 100	38.2%
Top 1,000	58.1%
Top 5,000	73.3%
Top 10,000	79.5%

Key Findings

• Zipf Compliance: R²=0.9980 indicates excellent adherence to Zipf's law
• High Frequency Dominance: Top 100 words cover 38.2% of corpus
• Long Tail: 875,946 words needed for remaining 20.5% coverage

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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	0.7924 🏆	0.3816	N/A	N/A
mono_64d	64	0.7720	0.3058	N/A	N/A
mono_128d	128	0.7142	0.2314	N/A	N/A
aligned_32d	32	0.7924	0.3910	0.4140	0.7940
aligned_64d	64	0.7720	0.3076	0.6360	0.9000
aligned_128d	128	0.7142	0.2447	0.7560	0.9480

Key Findings

• Best Isotropy: mono_32d with 0.7924 (more uniform distribution)
• Semantic Density: Average pairwise similarity of 0.3104. Lower values indicate better semantic separation.
• Alignment Quality: Aligned models achieve up to 75.6% R@1 in cross-lingual retrieval.
• Recommendation: 128d aligned for best cross-lingual performance

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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	-0.739	Low formulaic 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

Productive Suffixes

Suffix	Examples
-e	uforfalskede, ledocarpaceae, hærgende
-n	fjerntogsperron, flexlinjen, industriudstillingen
-s	bialiks, epicurus, ratios
-r	bredevandsbakker, provinshertugdømmer, linseskyer
-er	bredevandsbakker, provinshertugdømmer, linseskyer
-en	flexlinjen, industriudstillingen, jordbundslæren
-et	affrikeret, polyarkiet, panserkorpset
-ne	heatene, beslutningsevne, skillingsviserne

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
irke	2.09x	181 contexts	birke, virke, dirke
elig	1.65x	256 contexts	helig, selig, zelig
embe	2.00x	89 contexts	tembe, rembe, embed
nger	1.45x	439 contexts	inger, enger, anger
tisk	1.73x	152 contexts	tiske, etisk, tiski
ndel	1.42x	393 contexts	andel, endel, ndele
mber	1.52x	264 contexts	imber, amber, ember
nmar	1.77x	85 contexts	anmary, enmark, donmar
lsen	1.52x	174 contexts	elsen, ólsen, olsen
rste	1.33x	307 contexts	erste, første, fyrste
rden	1.38x	227 contexts	erden, urden, arden
oner	1.34x	260 contexts	zoner, joner, loner

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.

No significant affix co-occurrences detected.

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
profeterne	prof-et-er-ne	7.5	prof
regierende	regi-er-en-de	7.5	regi
kunstkritikeres	kunstkritik-er-es	6.0	kunstkritik
buccaneer	bucca-ne-er	6.0	bucca
udvikleres	udvikl-er-es	6.0	udvikl
håndredskaberne	håndredskab-er-ne	6.0	håndredskab
bolværkerne	bolværk-er-ne	6.0	bolværk
autogenereret	autog-en-er-er-et	6.0	autog
fællesgraven	fællesgrav-en	4.5	fællesgrav
feltflyvepladser	feltflyveplads-er	4.5	feltflyveplads
sangtrioen	sangtrio-en	4.5	sangtrio
teknologiparken	teknologipark-en	4.5	teknologipark
finnmarken	finnmark-en	4.5	finnmark
patriarker	patriark-er	4.5	patriark
synonymordbogen	synonymordbog-en	4.5	synonymordbog

6.6 Linguistic Interpretation

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

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7. Summary & Recommendations

Production Recommendations

Component	Recommended	Rationale
Tokenizer	64k BPE	Best compression (4.56x)
N-gram	2-gram	Lowest perplexity (291)
Markov	Context-4	Highest predictability (93.7%)
Embeddings	100d	Balanced semantic capture and isotropy

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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

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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

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Generated by Wikilangs Models Pipeline

Report Date: 2026-01-08 09:40:43