Livvi - Wikilangs Models
Comprehensive Research Report & Full Ablation Study
This repository contains NLP models trained and evaluated by Wikilangs, specifically on Livvi 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 | 3.676x | 3.68 | 0.1137% | 182,997 |
| 16k | 4.132x | 4.14 | 0.1278% | 162,798 |
| 32k | 4.545x | 4.55 | 0.1405% | 148,002 |
| 64k | 4.891x π | 4.90 | 0.1512% | 137,524 |
Tokenization Examples
Below are sample sentences tokenized with each vocabulary size:
Sample 1: MidΓ€ rodih sinΓ€ vuon Ken rodihes sinΓ€ vuon Ken kuoli sinΓ€ vuon
| Vocab | Tokens | Count |
|---|---|---|
| 8k | βmidΓ€ βrodih βsinΓ€ βvuon βken βrodihes βsinΓ€ βvuon βken βkuoli ... (+2 more) |
12 |
| 16k | βmidΓ€ βrodih βsinΓ€ βvuon βken βrodihes βsinΓ€ βvuon βken βkuoli ... (+2 more) |
12 |
| 32k | βmidΓ€ βrodih βsinΓ€ βvuon βken βrodihes βsinΓ€ βvuon βken βkuoli ... (+2 more) |
12 |
| 64k | βmidΓ€ βrodih βsinΓ€ βvuon βken βrodihes βsinΓ€ βvuon βken βkuoli ... (+2 more) |
12 |
Sample 2: Merisinikorendo (Orthetrum cancellatum) on sinikorendoloin suguh kuului korendo.
| Vocab | Tokens | Count |
|---|---|---|
| 8k | βmer is in ikor endo β( ort h etr um ... (+16 more) |
26 |
| 16k | βmeris in ikor endo β( orth etr um βc anc ... (+13 more) |
23 |
| 32k | βmeris inikorendo β( orth etr um βcanc ell at um ... (+8 more) |
18 |
| 64k | βmerisinikorendo β( orthetrum βcanc ell at um ) βon βsinikorendoloin ... (+4 more) |
14 |
Sample 3: LieΔehtiedo on tiijollizen tiijon da praktiekallizien metodoin sistiemu, kudaman...
| Vocab | Tokens | Count |
|---|---|---|
| 8k | βlieΔ eht iedo βon βtiij ollizen βtiijon βda βpr akt ... (+25 more) |
35 |
| 16k | βlieΔ eht iedo βon βtiijollizen βtiijon βda βpr akt iek ... (+18 more) |
28 |
| 32k | βlieΔeht iedo βon βtiijollizen βtiijon βda βpraktiek allizien βmet odoin ... (+14 more) |
24 |
| 64k | βlieΔehtiedo βon βtiijollizen βtiijon βda βpraktiek allizien βmetodoin βsistiemu , ... (+11 more) |
21 |
Key Findings
- Best Compression: 64k achieves 4.891x compression
- Lowest UNK Rate: 8k with 0.1137% 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 | 1,811 | 10.82 | 6,046 | 37.0% | 66.9% |
| 2-gram | Subword | 316 π | 8.30 | 2,510 | 62.6% | 98.9% |
| 3-gram | Word | 1,998 | 10.96 | 7,436 | 36.9% | 64.5% |
| 3-gram | Subword | 2,540 | 11.31 | 17,821 | 23.0% | 69.2% |
| 4-gram | Word | 3,746 | 11.87 | 13,217 | 30.5% | 53.2% |
| 4-gram | Subword | 11,661 | 13.51 | 76,149 | 12.6% | 40.3% |
| 5-gram | Word | 3,362 | 11.72 | 10,586 | 29.5% | 54.3% |
| 5-gram | Subword | 30,053 | 14.88 | 156,101 | 9.1% | 29.3% |
Top 5 N-grams by Size
2-grams (Word):
| Rank | N-gram | Count |
|---|---|---|
| 1 | karjalan tazavallan |
1,466 |
| 2 | sinΓ€ vuon |
1,390 |
| 3 | pinduala on |
1,196 |
| 4 | on sijoitannuhes |
1,182 |
| 5 | sinΓ€ piΓ€n |
1,095 |
3-grams (Word):
| Rank | N-gram | Count |
|---|---|---|
| 1 | jΓ€rven pinduala on |
866 |
| 2 | jΓ€rvi kudai on |
858 |
| 3 | sijoitannuhes karjalan tazavallan |
856 |
| 4 | on sijoitannuhes karjalan |
855 |
| 5 | kudai on sijoitannuhes |
854 |
4-grams (Word):
| Rank | N-gram | Count |
|---|---|---|
| 1 | on sijoitannuhes karjalan tazavallan |
852 |
| 2 | kudai on sijoitannuhes karjalan |
841 |
| 3 | jΓ€rvi kudai on sijoitannuhes |
836 |
| 4 | metrii korgiembi meren pindua |
673 |
| 5 | km jΓ€rven pindu on |
663 |
5-grams (Word):
| Rank | N-gram | Count |
|---|---|---|
| 1 | kudai on sijoitannuhes karjalan tazavallan |
841 |
| 2 | jΓ€rvi kudai on sijoitannuhes karjalan |
829 |
| 3 | kylΓ€kunnan alovehel jΓ€rven pinduala on |
614 |
| 4 | on jΓ€rvi kudai on sijoitannuhes |
586 |
| 5 | rodih sinΓ€ vuon ken rodihes |
449 |
2-grams (Subword):
| Rank | N-gram | Count |
|---|---|---|
| 1 | n _ |
79,897 |
| 2 | _ k |
51,186 |
| 3 | a n |
42,849 |
| 4 | e n |
40,303 |
| 5 | i n |
36,766 |
3-grams (Subword):
| Rank | N-gram | Count |
|---|---|---|
| 1 | e n _ |
22,649 |
| 2 | a n _ |
21,951 |
| 3 | o n _ |
19,963 |
| 4 | _ o n |
15,790 |
| 5 | n _ k |
13,751 |
4-grams (Subword):
| Rank | N-gram | Count |
|---|---|---|
| 1 | _ o n _ |
15,313 |
| 2 | _ d a _ |
9,605 |
| 3 | j Γ€ r v |
7,803 |
| 4 | n _ p i |
6,425 |
| 5 | l a n _ |
6,288 |
5-grams (Subword):
| Rank | N-gram | Count |
|---|---|---|
| 1 | j Γ€ r v e |
5,611 |
| 2 | k a r j a |
5,267 |
| 3 | a r j a l |
5,260 |
| 4 | r j a l a |
5,139 |
| 5 | _ k a r j |
4,787 |
Key Findings
- Best Perplexity: 2-gram (subword) with 316
- Entropy Trend: Decreases with larger n-grams (more predictable)
- Coverage: Top-1000 patterns cover ~29% 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 | 0.6069 | 1.523 | 3.28 | 65,772 | 39.3% |
| 1 | Subword | 1.2495 | 2.378 | 9.89 | 551 | 0.0% |
| 2 | Word | 0.1460 | 1.106 | 1.28 | 214,521 | 85.4% |
| 2 | Subword | 1.1250 | 2.181 | 6.23 | 5,449 | 0.0% |
| 3 | Word | 0.0462 | 1.033 | 1.08 | 272,135 | 95.4% |
| 3 | Subword | 0.8604 | 1.815 | 3.88 | 33,912 | 14.0% |
| 4 | Word | 0.0237 π | 1.017 | 1.04 | 289,944 | 97.6% |
| 4 | Subword | 0.6016 | 1.517 | 2.47 | 131,456 | 39.8% |
Generated Text Samples (Word-based)
Below are text samples generated from each word-based Markov chain model:
Context Size 1:
on enzimΓ€ine on sijoitannuhes karjalan tazavallas kondupohjan piirin kylΓ€ on voimattomuksii l ubov t...da ruadajien pos olku sumajΓ€rvi on 324 782 neliΓΆkilometrii vottovaara Π³ ΡΠ½ΠΊΠΎ ΠΌΡΠ·ΡΠΊΠ°Π½ΡΠ° ΠΏΠ΅ΡΠ΅Π²ΠΎΠ΄Π°Π½ Π»ΡΠ°...karjalan tazavallas kondupohjan piirin ven an keeli kiili maakeeli on vokali aa eΓ€ diftongas oa ua
Context Size 2:
karjalan tazavallan mujejΓ€rven piirin lendieran kylΓ€kundah kuului kylΓ€ sen kauti menΓΆy ven an rajal ...sinΓ€ vuon 28 sulakuudu fredrik i ruoΔΔilaine kunigas ken kuoli sinΓ€ piΓ€n ken rodihes sinΓ€ vuon kenpinduala on 616 km rahvahan lugumiΓ€ry on 387 489 196 v hengie 4 2 km jΓ€rven pindu
Context Size 3:
jΓ€rven pinduala on 1 1 km jΓ€rvenpindu on 144 7 metrin korgevuol merenpinnalpΓ€i jΓ€rven lahtespΓ€i vezi...jΓ€rvi kudai on sijoitannuhes karjalan tazavallan puudogan piirin krivcoin kylΓ€kunnan alovehel jΓ€rven...sijoitannuhes karjalan tazavallan kemin piirin viΓ€rΓ€nkosken kylΓ€kunnan alovehel jΓ€rven pinduala on 2...
Context Size 4:
on sijoitannuhes karjalan tazavallan kalevalan piirin jyΕ‘kyjΓ€rven kylΓ€kunnan alovehel jΓ€rven pindual...kudai on sijoitannuhes karjalan tazavallan suojΓ€rven piirin alovehel jΓ€rven pinduala on 1 2 km jΓ€rve...jΓ€rvi kudai on sijoitannuhes karjalan tazavallan kalevalan piirin jyΕ‘kyjΓ€rven kylΓ€kunnan alovehele j...
Generated Text Samples (Subword-based)
Below are text samples generated from each subword-based Markov chain model:
Context Size 1:
_tervarie_gagiΓ€ri_ramezi_kka_puual_hin_vvlielojo
Context Size 2:
n_dah._yhterii._β_kajua_se_supuolian_li_j_jΓ€rvosten
Context Size 3:
en_prot_oli_volliΕΎan_kmΒ²,_valien_erion_da_tuurimilaine
Context Size 4:
_on_voi_ollah_pΓ€ivi_da_syΓΆjy_torianskojΓ€rvi_on_mugah_enim
Key Findings
- Best Predictability: Context-4 (word) with 97.6% predictability
- Branching Factor: Decreases with context size (more deterministic)
- Memory Trade-off: Larger contexts require more storage (131,456 contexts)
- Recommendation: Context-3 or Context-4 for text generation
4. Vocabulary Analysis
Statistics
| Metric | Value |
|---|---|
| Vocabulary Size | 23,754 |
| Total Tokens | 323,407 |
| Mean Frequency | 13.61 |
| Median Frequency | 3 |
| Frequency Std Dev | 137.09 |
Most Common Words
| Rank | Word | Frequency |
|---|---|---|
| 1 | on | 15,359 |
| 2 | da | 9,616 |
| 3 | karjalan | 3,323 |
| 4 | kudai | 2,669 |
| 5 | oli | 2,573 |
| 6 | sinΓ€ | 2,491 |
| 7 | se | 2,234 |
| 8 | km | 1,949 |
| 9 | jΓ€rven | 1,937 |
| 10 | vuvvennu | 1,694 |
Least Common Words (from vocabulary)
| Rank | Word | Frequency |
|---|---|---|
| 1 | alovehella | 2 |
| 2 | kivijogi | 2 |
| 3 | hurstinesiivet | 2 |
| 4 | tankoin | 2 |
| 5 | kaunokirjallisuuden | 2 |
| 6 | kirjailijaliiton | 2 |
| 7 | viΔΔajogi | 2 |
| 8 | viΔΔajΓ€rvi | 2 |
| 9 | nuokkijΓ€rveh | 2 |
| 10 | crottetan | 2 |
Zipf's Law Analysis
| Metric | Value |
|---|---|
| Zipf Coefficient | 1.0015 |
| RΒ² (Goodness of Fit) | 0.996450 |
| Adherence Quality | excellent |
Coverage Analysis
| Top N Words | Coverage |
|---|---|
| Top 100 | 34.5% |
| Top 1,000 | 62.9% |
| Top 5,000 | 81.9% |
| Top 10,000 | 89.9% |
Key Findings
- Zipf Compliance: RΒ²=0.9965 indicates excellent adherence to Zipf's law
- High Frequency Dominance: Top 100 words cover 34.5% of corpus
- Long Tail: 13,754 words needed for remaining 10.1% 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 | 0.6898 | 0.3579 | N/A | N/A |
| mono_64d | 64 | 0.2488 | 0.3561 | N/A | N/A |
| mono_128d | 128 | 0.0385 | 0.3444 | N/A | N/A |
| aligned_32d | 32 | 0.6898 π | 0.3597 | 0.0160 | 0.1400 |
| aligned_64d | 64 | 0.2488 | 0.3454 | 0.0300 | 0.2300 |
| aligned_128d | 128 | 0.0385 | 0.3507 | 0.0540 | 0.2620 |
Key Findings
- Best Isotropy: aligned_32d with 0.6898 (more uniform distribution)
- Semantic Density: Average pairwise similarity of 0.3524. Lower values indicate better semantic separation.
- Alignment Quality: Aligned models achieve up to 5.4% 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 | 0.855 | 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 |
|---|---|
-k |
kΓ€yttΓ€mine, kuduo, kΓ€skys |
-s |
suojoki, suolattomas, sundsvall |
-p |
poliittizen, poikkevuksennu, pohjazii |
-m |
mauri, majakovskii, muan |
-t |
toinegi, tulenisku, tunnetuimat |
-a |
ajatus, azerbaidΕΎuananke, atlantiekan |
-l |
lΓ€hte, luodehpuoles, laulava |
-ka |
kazahstananke, kaitajΓ€rven, kaukozen |
Productive Suffixes
| Suffix | Examples |
|---|---|
-n |
filippinoin, jevroupan, poliittizen |
-i |
suojoki, toinegi, nimesgi |
-en |
poliittizen, kuulujien, Ε‘veitsarien |
-s |
jΓ€iΔΓ€s, ajatus, estimates |
-u |
vuodizennu, poikkevuksennu, ohjattu |
-an |
jevroupan, dunan, muan |
-h |
niih, jiΓ€nnyh, kΓ€skiettih |
-e |
lΓ€hte, kΓ€yttΓ€mine, azerbaidΕΎuananke |
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 |
|---|---|---|---|
jΓ€rv |
1.86x | 57 contexts | jΓ€rvi, jΓ€rves, jΓ€rven |
jala |
1.92x | 27 contexts | jalat, jalal, karjala |
ttih |
2.02x | 22 contexts | ruuttih, ruattih, piettih |
Γ€rve |
1.92x | 17 contexts | Γ€rven, jΓ€rves, jΓ€rven |
iiri |
1.88x | 16 contexts | hiiri, piiri, piiril |
kiel |
1.61x | 25 contexts | kiely, kieli, kieleh |
kirj |
1.73x | 15 contexts | kirju, kirja, kirjah |
uvve |
1.52x | 20 contexts | uvvel, uvves, uvvet |
piir |
1.79x | 10 contexts | piiri, piiril, piirit |
rjal |
1.72x | 10 contexts | karjal, karjalu, karjala |
pind |
2.05x | 6 contexts | pindu, pindua, pindah |
indu |
1.31x | 20 contexts | pindu, rindu, uindu |
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 |
|---|---|---|---|
-k |
-n |
240 words | konsulan, klassifikatsien |
-p |
-n |
139 words | plankan, persienlahten |
-k |
-i |
124 words | kiΓ€ndi, kirjoi |
-s |
-n |
120 words | suolusmΓ€en, saiman |
-k |
-h |
117 words | kΓ€yttΓΆh, korpijΓ€rveh |
-m |
-n |
109 words | modernismin, mjanmaran |
-k |
-en |
103 words | klassifikatsien, karibien |
-t |
-n |
98 words | tarton, tradition |
-p |
-i |
96 words | pahanluadii, piirrettylΓΆi |
-k |
-u |
92 words | kandiduattu, kirjalliΕΎushistourikku |
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 |
|---|---|---|---|
| filosoufies | filosouf-i-es |
7.5 | i |
| tevollizuon | tevolliz-u-on |
7.5 | u |
| jΓ€rvenalah | jΓ€rven-al-ah |
7.5 | al |
| neitronat | neitro-n-at |
7.5 | n |
| sekretarinnu | sekretarin-n-u |
7.5 | n |
| iΔepiΓ€nneh | iΔepiΓ€n-n-eh |
7.5 | n |
| lΓΆydΓ€jΓ€nny | lΓΆydΓ€jΓ€n-n-y |
7.5 | n |
| loppienuh | loppien-u-h |
7.5 | u |
| suvialovehil | su-vi-alovehil |
7.5 | alovehil |
| kaΕΎirodukunnan | kaΕΎirodukun-n-an |
7.5 | n |
| tundietun | tundie-tu-n |
7.5 | tu |
| suojΓ€rvessah | suojΓ€rves-s-ah |
7.5 | s |
| kiΓ€nnΓΆksien | kiΓ€nnΓΆks-i-en |
7.5 | i |
| piΓ€likΓΆnny | piΓ€likΓΆn-n-y |
7.5 | n |
| kaivandukoneh | kaivanduko-n-eh |
7.5 | n |
6.6 Linguistic Interpretation
Automated Insight: The language Livvi 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 (4.89x) |
| N-gram | 2-gram | Lowest perplexity (316) |
| Markov | Context-4 | Highest predictability (97.6%) |
| 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: 2026-01-10 16:33:55



















