Faroese - Wikilangs Models
Comprehensive Research Report & Full Ablation Study
This repository contains NLP models trained and evaluated by Wikilangs, specifically on Faroese Wikipedia data. We analyze tokenizers, n-gram models, Markov chains, vocabulary statistics, and word embeddings.
π 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 | 3.578x | 3.58 | 0.0475% | 501,416 |
| 16k | 3.909x | 3.91 | 0.0518% | 459,065 |
| 32k | 4.191x | 4.19 | 0.0556% | 428,081 |
| 64k | 4.421x π | 4.42 | 0.0586% | 405,872 |
Tokenization Examples
Below are sample sentences tokenized with each vocabulary size:
Sample 1: Nagano er ein bΓ½ur Γ‘ oynni Honshu Γ Japan. Γ vΓ³ru OL-veturleikirnir Γ bΓ½num. ΓvΓ...
| Vocab | Tokens | Count |
|---|---|---|
| 8k | βn ag ano βer βein βbΓ½ur βΓ‘ βoynni βhon sh ... (+35 more) |
45 |
| 16k | βnag ano βer βein βbΓ½ur βΓ‘ βoynni βhon sh u ... (+34 more) |
44 |
| 32k | βnag ano βer βein βbΓ½ur βΓ‘ βoynni βhon shu βΓ ... (+29 more) |
39 |
| 64k | βnag ano βer βein βbΓ½ur βΓ‘ βoynni βhonshu βΓ βjapan ... (+28 more) |
38 |
Sample 2: EslΓΆv er ein bΓ½ur Γ EslΓΆvs kommunu Γ SkΓ₯ne lΓ€n Γ SvΓΈrΓki. BΓ½urin hevur umleiΓ° 17...
| Vocab | Tokens | Count |
|---|---|---|
| 8k | βe sl ΓΆv βer βein βbΓ½ur βΓ βe sl ΓΆv ... (+25 more) |
35 |
| 16k | βe slΓΆv βer βein βbΓ½ur βΓ βe slΓΆv s βkommunu ... (+23 more) |
33 |
| 32k | βeslΓΆv βer βein βbΓ½ur βΓ βeslΓΆv s βkommunu βΓ βskΓ₯ne ... (+21 more) |
31 |
| 64k | βeslΓΆv βer βein βbΓ½ur βΓ βeslΓΆvs βkommunu βΓ βskΓ₯ne βlΓ€n ... (+20 more) |
30 |
Sample 3: Langeskov kommuna (danskt: Langeskov kommune), er ein kommuna Γ Fyns Amt Γ Danma...
| Vocab | Tokens | Count |
|---|---|---|
| 8k | βlang e skov βkommuna β( danskt : βlang e skov ... (+28 more) |
38 |
| 16k | βlang e skov βkommuna β( danskt : βlang e skov ... (+27 more) |
37 |
| 32k | βlange skov βkommuna β( danskt : βlange skov βkommune ), ... (+24 more) |
34 |
| 64k | βlangeskov βkommuna β( danskt : βlangeskov βkommune ), βer βein ... (+21 more) |
31 |
Key Findings
- Best Compression: 64k achieves 4.421x compression
- Lowest UNK Rate: 8k with 0.0475% 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 | 19,074 | 14.22 | 52,510 | 11.9% | 30.1% |
| 2-gram | Subword | 358 π | 8.49 | 4,371 | 60.3% | 98.7% |
| 3-gram | Word | 30,965 | 14.92 | 64,802 | 8.8% | 23.6% |
| 3-gram | Subword | 3,173 | 11.63 | 35,149 | 21.7% | 64.3% |
| 4-gram | Word | 56,491 | 15.79 | 107,657 | 6.7% | 19.4% |
| 4-gram | Subword | 18,109 | 14.14 | 189,262 | 10.5% | 34.3% |
| 5-gram | Word | 37,176 | 15.18 | 74,269 | 7.8% | 23.2% |
| 5-gram | Subword | 64,574 | 15.98 | 496,959 | 6.5% | 21.1% |
Top 5 N-grams by Size
2-grams (Word):
| Rank | N-gram | Count |
|---|---|---|
| 1 | f kr |
17,129 |
| 2 | Γ‘rini f |
6,533 |
| 3 | er ein |
5,079 |
| 4 | Γ fΓΈroyum |
4,019 |
| 5 | ΓΈld f |
2,454 |
3-grams (Word):
| Rank | N-gram | Count |
|---|---|---|
| 1 | Γ‘rini f kr |
6,533 |
| 2 | ΓΈld f kr |
2,454 |
| 3 | hendingar fΓΈΓ°ingar andlΓ‘t |
751 |
| 4 | ein kommuna Γ |
656 |
| 5 | iΓ° byrjaΓ°i Γ‘ |
638 |
4-grams (Word):
| Rank | N-gram | Count |
|---|---|---|
| 1 | iΓ° byrjaΓ°i Γ‘ einum |
636 |
| 2 | er ein kommuna Γ |
621 |
| 3 | f kr hendingar fΓΈΓ°ingar |
548 |
| 4 | kr hendingar fΓΈΓ°ingar andlΓ‘t |
534 |
| 5 | er ein bΓ½ur Γ |
521 |
5-grams (Word):
| Rank | N-gram | Count |
|---|---|---|
| 1 | f kr hendingar fΓΈΓ°ingar andlΓ‘t |
534 |
| 2 | fΓΈΓ°ingar andlΓ‘t ΓΈld f kr |
497 |
| 3 | hendingar fΓΈΓ°ingar andlΓ‘t ΓΈld f |
495 |
| 4 | kr hendingar fΓΈΓ°ingar andlΓ‘t ΓΈld |
493 |
| 5 | kalendaranum eitt vanligt Γ‘r iΓ° |
476 |
2-grams (Subword):
| Rank | N-gram | Count |
|---|---|---|
| 1 | r _ |
290,904 |
| 2 | i n |
229,266 |
| 3 | a r |
218,692 |
| 4 | _ s |
209,679 |
| 5 | a n |
183,340 |
3-grams (Subword):
| Rank | N-gram | Count |
|---|---|---|
| 1 | _ Γ _ |
94,332 |
| 2 | u r _ |
93,257 |
| 3 | u m _ |
92,289 |
| 4 | a r _ |
73,100 |
| 5 | i Γ° _ |
65,495 |
4-grams (Subword):
| Rank | N-gram | Count |
|---|---|---|
| 1 | _ o g _ |
65,054 |
| 2 | _ e r _ |
33,635 |
| 3 | _ a t _ |
28,671 |
| 4 | n u m _ |
27,682 |
| 5 | i n i _ |
26,628 |
5-grams (Subword):
| Rank | N-gram | Count |
|---|---|---|
| 1 | _ s u m _ |
22,835 |
| 2 | _ v i Γ° _ |
20,464 |
| 3 | _ t i l _ |
20,113 |
| 4 | _ f . k r |
17,103 |
| 5 | f . k r . |
17,094 |
Key Findings
- Best Perplexity: 2-gram (subword) with 358
- 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
3. Markov Chain Evaluation
Results
| Context | Variant | Avg Entropy | Perplexity | Branching Factor | Unique Contexts | Predictability |
|---|---|---|---|---|---|---|
| 1 | Word | 0.8217 | 1.767 | 5.75 | 176,129 | 17.8% |
| 1 | Subword | 0.8858 | 1.848 | 6.33 | 2,058 | 11.4% |
| 2 | Word | 0.2659 | 1.202 | 1.65 | 1,010,213 | 73.4% |
| 2 | Subword | 0.8361 | 1.785 | 5.38 | 13,016 | 16.4% |
| 3 | Word | 0.0884 | 1.063 | 1.15 | 1,662,607 | 91.2% |
| 3 | Subword | 0.8358 | 1.785 | 4.43 | 69,978 | 16.4% |
| 4 | Word | 0.0297 π | 1.021 | 1.04 | 1,896,454 | 97.0% |
| 4 | Subword | 0.7103 | 1.636 | 3.08 | 309,872 | 29.0% |
Generated Text Samples (Word-based)
Below are text samples generated from each word-based Markov chain model:
Context Size 1:
Γ Γ hΓΈvuΓ°sstaΓ°arregiΓ³n danmarkar var forkvinna Γ‘ youtube com dΓ½rd harrans deyΓ°ur 30 sesongin av oljuog eru 1 4 5 97 265 maleisia myanmar aung san marino italskt tΓ³naskald d 28er amerikanskur sjΓ³nleikari og tann 44 minuttir ΓΊtgΓ‘vudato 14 f pearl bailey and stonehenge var taΓ°
Context Size 2:
f kr 16 f kr hendingar fΓΈΓ°ingar andlΓ‘t ΓΈld f kr 580 Γ‘rini f kr hendingar fΓΈΓ°ingarΓ‘rini f kr Γ‘rstal 152 f kr Γ‘ratΓggju 390 Γ‘rini f kr 10 Γ‘rini f kr 220er ein kommuna Γ regiΓ³n suΓ°urdanmark Γ danmark lΓ¦rarastarviΓ° gjΓΈrdist lΓvsstarv hansara var hΓΈvuΓ°sat...
Context Size 3:
Γ‘rini f kr 230 f kr 229 f kr 228 f kr 227 f kr 226 f krΓΈld f kr Γ‘ratΓggju 490 Γ‘rini 500 Γ‘rini 510 Γ‘rini 520 Γ‘rini 530 Γ‘rini 540 Γ‘rini 550 Γ‘riniein kommuna Γ gΓ€vleborgs lΓ€n Γ svΓΈrΓki bjuvs kommuna hevur 14 015 ΓbΓΊgvar i riket lΓ€n och kommuner
Context Size 4:
iΓ° byrjaΓ°i Γ‘ einum mΓ‘nadegi hendingar 1 januar vestursΓ‘moa verΓ°ur frΓ¦lst rΓki 8 november lΓΈgtingsval...er ein kommuna Γ keypmannahavns amt Γ danmark hΓΈje taastrup kommuna hevur umleiΓ° 48 695 ΓbΓΊgvar Γ da...f kr hendingar fΓΈΓ°ingar andlΓ‘t ΓΈld f kr
Generated Text Samples (Subword-based)
Below are text samples generated from each subword-based Markov chain model:
Context Size 1:
_nangaterΓ°rn_om.apskand_ΓΊrim_160rnΓΆrn_kl_bΓ½r_och
Context Size 2:
r_vilberΓ°u_(svar_iniziskur_sonakt_ardin,_nast_hav_b
Context Size 3:
_Γ_dagfΓΈroyskilu,_ur_Γ_fΓΈroyingur_tuum_byrgdir_sonerha
Context Size 4:
_og_atli_bayern_lon_er_m.a._Γ_nazithro_at_nΓ‘ttΓΊrutengdum_
Key Findings
- Best Predictability: Context-4 (word) with 97.0% predictability
- Branching Factor: Decreases with context size (more deterministic)
- Memory Trade-off: Larger contexts require more storage (309,872 contexts)
- Recommendation: Context-3 or Context-4 for text generation
4. Vocabulary Analysis
Statistics
| Metric | Value |
|---|---|
| Vocabulary Size | 77,098 |
| Total Tokens | 2,107,707 |
| Mean Frequency | 27.34 |
| Median Frequency | 4 |
| Frequency Std Dev | 537.11 |
Most Common Words
| Rank | Word | Frequency |
|---|---|---|
| 1 | Γ | 96,564 |
| 2 | og | 65,210 |
| 3 | er | 34,690 |
| 4 | at | 28,863 |
| 5 | Γ‘ | 26,503 |
| 6 | sum | 23,040 |
| 7 | av | 21,270 |
| 8 | viΓ° | 21,264 |
| 9 | f | 21,130 |
| 10 | til | 20,883 |
Least Common Words (from vocabulary)
| Rank | Word | Frequency |
|---|---|---|
| 1 | afgΓΈres | 2 |
| 2 | semifinalerne | 2 |
| 3 | straffesparkskonkurrence | 2 |
| 4 | præmiepenge | 2 |
| 5 | udekampe | 2 |
| 6 | amerikanaranum | 2 |
| 7 | squibb | 2 |
| 8 | beregszΓ‘sziovΓ‘ | 2 |
| 9 | brΓΈΓ°rarΓΈrslan | 2 |
| 10 | befg | 2 |
Zipf's Law Analysis
| Metric | Value |
|---|---|
| Zipf Coefficient | 1.0122 |
| RΒ² (Goodness of Fit) | 0.998602 |
| Adherence Quality | excellent |
Coverage Analysis
| Top N Words | Coverage |
|---|---|
| Top 100 | 38.1% |
| Top 1,000 | 61.0% |
| Top 5,000 | 77.8% |
| Top 10,000 | 84.6% |
Key Findings
- Zipf Compliance: RΒ²=0.9986 indicates excellent adherence to Zipf's law
- High Frequency Dominance: Top 100 words cover 38.1% of corpus
- Long Tail: 67,098 words needed for remaining 15.4% 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 | 0.8663 | 0.3394 | N/A | N/A |
| mono_64d | 64 | 0.8701 π | 0.2508 | N/A | N/A |
| mono_128d | 128 | 0.8059 | 0.1852 | N/A | N/A |
| aligned_32d | 32 | 0.8663 | 0.3298 | 0.0720 | 0.3400 |
| aligned_64d | 64 | 0.8701 | 0.2499 | 0.1180 | 0.4260 |
| aligned_128d | 128 | 0.8059 | 0.1896 | 0.1760 | 0.5080 |
Key Findings
- Best Isotropy: mono_64d with 0.8701 (more uniform distribution)
- Semantic Density: Average pairwise similarity of 0.2574. Lower values indicate better semantic separation.
- Alignment Quality: Aligned models achieve up to 17.6% 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 | 0.100 | 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 |
|---|---|
-st |
statsleiΓ°ararnar, stovnum, stillir |
Productive Suffixes
| Suffix | Examples |
|---|---|
-r |
roykir, kippur, rannsΓ³knir |
-n |
hΓ³ttan, alden, tuin |
-um |
homrum, stovnum, sonevndum |
-ar |
statsleiΓ°ararnar, pilar, akrar |
-ur |
kippur, heindrikkur, trΓkantur |
-in |
tuin, mentamÑlarÑðharrin, undirsjóvartunnilin |
-num |
stovnum, skarninum, muslimunum |
-ir |
roykir, rannsΓ³knir, stillir |
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 |
|---|---|---|---|
rini |
2.22x | 35 contexts | Γ‘rini, trini, irini |
ggja |
1.63x | 94 contexts | eggja, oyggja, sΓggja |
ansk |
1.64x | 88 contexts | mansk, dansk, fransk |
ndin |
1.56x | 111 contexts | endin, andin, vandin |
nlei |
1.99x | 36 contexts | gunleif, sunleif, finleif |
aΓ°ur |
1.95x | 30 contexts | jaΓ°ur, maΓ°ur, staΓ°ur |
ngar |
1.61x | 56 contexts | ongar, ingar, ungar |
ndur |
1.59x | 56 contexts | undur, endur, Γ³ndur |
ikar |
1.78x | 36 contexts | bikar, tikari, peikar |
ldur |
1.69x | 43 contexts | aldur, eldur, baldur |
eldu |
1.77x | 30 contexts | eldur, teldu, feldu |
nsku |
1.81x | 27 contexts | ensku, enskur, finsku |
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 |
|---|---|---|---|
-st |
-r |
34 words | studentaskΓΊlanΓ¦mingar, stΓvur |
-st |
-n |
23 words | stormen, stundin |
-st |
-um |
17 words | studioalbum, strandgeiranum |
-st |
-ar |
12 words | studentaskúlanæmingar, stokkar |
-st |
-ni |
11 words | strandafjΓΈllini, strandalondini |
-st |
-ur |
10 words | stΓvur, stΓ³rΓdnaΓ°ur |
-st |
-num |
8 words | strandgeiranum, stættatinginum |
-st |
-ir |
7 words | steroidir, stættir |
-st |
-iΓ° |
6 words | strandaΓΈkiΓ°, stΓ³rbΓ½arΓΈkiΓ° |
-st |
-in |
5 words | stundin, stapin |
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 |
|---|---|---|---|
| prestagarΓ°urin | prestagarΓ°-ur-in |
6.0 | prestagarΓ° |
| harΓ°skapurin | harΓ°skap-ur-in |
6.0 | harΓ°skap |
| handverkarum | handverk-ar-um |
6.0 | handverk |
| mentanini | menta-ni-ni |
6.0 | menta |
| tjΓ³Γ°argarΓ°urin | tjΓ³Γ°argarΓ°-ur-in |
6.0 | tjΓ³Γ°argarΓ° |
| krossfiskurin | krossfisk-ur-in |
6.0 | krossfisk |
| forstaΓ°inum | forstaΓ°i-num |
4.5 | forstaΓ°i |
| fyrrapartin | fyrrapart-in |
4.5 | fyrrapart |
| landslΓΈgum | landslΓΈg-um |
4.5 | landslΓΈg |
| suΓ°uroyarmΓ‘liΓ° | suΓ°uroyarmΓ‘l-iΓ° |
4.5 | suΓ°uroyarmΓ‘l |
| gongustjΓΈrnunum | gongustjΓΈrnu-num |
4.5 | gongustjΓΈrnu |
| sΓ³knarprestin | sΓ³knarprest-in |
4.5 | sΓ³knarprest |
| fjΓ³rΓ°ingar | fjΓ³rΓ°ing-ar |
4.5 | fjΓ³rΓ°ing |
| lastbilar | lastbil-ar |
4.5 | lastbil |
| grundlΓ³gin | grundlΓ³g-in |
4.5 | grundlΓ³g |
6.6 Linguistic Interpretation
Automated Insight: The language Faroese shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.
7. Summary & Recommendations
Production Recommendations
| Component | Recommended | Rationale |
|---|---|---|
| Tokenizer | 64k BPE | Best compression (4.42x) |
| N-gram | 2-gram | Lowest perplexity (358) |
| Markov | Context-4 | Highest predictability (97.0%) |
| 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) Γ 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.
RΒ² (Coefficient of Determination)
Definition: Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.
Intuition: RΒ² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.
What to seek: RΒ² > 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
- Compare within model families: Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
- Consider trade-offs: Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
- Context matters: Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
- Corpus influence: All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
- 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
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
- π Website: wikilangs.org
- π€ Models: huggingface.co/wikilangs
- π Data: wikipedia-monthly
- π€ Author: Omar Kamali
- π€ Sponsor: Featherless AI
Generated by Wikilangs Models Pipeline
Report Date: 2026-01-04 14:57:33



















