Nahuatl languages - Wikilangs Models
Comprehensive Research Report & Full Ablation Study
This repository contains NLP models trained and evaluated by Wikilangs, specifically on Nahuatl languages 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 | 3.986x | 4.00 | 0.0238% | 92,310 |
| 16k | 4.334x | 4.35 | 0.0259% | 84,893 |
| 32k | 4.614x | 4.63 | 0.0276% | 79,736 |
| 64k | 4.837x π | 4.85 | 0.0289% | 76,056 |
Tokenization Examples
Below are sample sentences tokenized with each vocabulary size:
Sample 1: Δ«tΕcΔ cΔ xihuitl Δ«pan mΔcuΔ«lpΕhualxihuitl 13 Δ«pan mahtlΔcxihuitl. MochΔ«hualiztli...
| Vocab | Tokens | Count |
|---|---|---|
| 8k | βΔ«tΕcΔ βcΔ βxihuitl βΔ«pan βmΔcuΔ«lpΕhual xihuitl β 1 3 βΔ«pan ... (+7 more) |
17 |
| 16k | βΔ«tΕcΔ βcΔ βxihuitl βΔ«pan βmΔcuΔ«lpΕhual xihuitl β 1 3 βΔ«pan ... (+7 more) |
17 |
| 32k | βΔ«tΕcΔ βcΔ βxihuitl βΔ«pan βmΔcuΔ«lpΕhual xihuitl β 1 3 βΔ«pan ... (+7 more) |
17 |
| 64k | βΔ«tΕcΔ βcΔ βxihuitl βΔ«pan βmΔcuΔ«lpΕhual xihuitl β 1 3 βΔ«pan ... (+7 more) |
17 |
Sample 2: 847 Δ«tΕcΔ cΔ xihuitl Δ«pan mΔcuΔ«lpΕhualxihuitl 9 Δ«pan 840s mahtlΔcxihuitl. MochΔ«h...
| Vocab | Tokens | Count |
|---|---|---|
| 8k | β 8 4 7 βΔ«tΕcΔ βcΔ βxihuitl βΔ«pan βmΔcuΔ«lpΕhual xihuitl ... (+15 more) |
25 |
| 16k | β 8 4 7 βΔ«tΕcΔ βcΔ βxihuitl βΔ«pan βmΔcuΔ«lpΕhual xihuitl ... (+15 more) |
25 |
| 32k | β 8 4 7 βΔ«tΕcΔ βcΔ βxihuitl βΔ«pan βmΔcuΔ«lpΕhual xihuitl ... (+15 more) |
25 |
| 64k | β 8 4 7 βΔ«tΕcΔ βcΔ βxihuitl βΔ«pan βmΔcuΔ«lpΕhual xihuitl ... (+15 more) |
25 |
Sample 3: Δ«tΕcΔ cΔ xihuitl Δ«pan mΔcuΔ«lpΕhualxihuitl 12 Δ«pan mahtlΔcxihuitl. MochΔ«hualiztli...
| Vocab | Tokens | Count |
|---|---|---|
| 8k | βΔ«tΕcΔ βcΔ βxihuitl βΔ«pan βmΔcuΔ«lpΕhual xihuitl β 1 2 βΔ«pan ... (+7 more) |
17 |
| 16k | βΔ«tΕcΔ βcΔ βxihuitl βΔ«pan βmΔcuΔ«lpΕhual xihuitl β 1 2 βΔ«pan ... (+7 more) |
17 |
| 32k | βΔ«tΕcΔ βcΔ βxihuitl βΔ«pan βmΔcuΔ«lpΕhual xihuitl β 1 2 βΔ«pan ... (+7 more) |
17 |
| 64k | βΔ«tΕcΔ βcΔ βxihuitl βΔ«pan βmΔcuΔ«lpΕhual xihuitl β 1 2 βΔ«pan ... (+7 more) |
17 |
Key Findings
- Best Compression: 64k achieves 4.837x compression
- Lowest UNK Rate: 8k with 0.0238% 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 | 582 | 9.18 | 2,574 | 49.8% | 80.2% |
| 2-gram | Subword | 257 π | 8.00 | 1,917 | 69.1% | 99.1% |
| 3-gram | Word | 593 | 9.21 | 3,076 | 50.9% | 78.5% |
| 3-gram | Subword | 1,587 | 10.63 | 12,907 | 37.0% | 75.9% |
| 4-gram | Word | 1,134 | 10.15 | 5,251 | 42.7% | 69.4% |
| 4-gram | Subword | 5,857 | 12.52 | 49,857 | 26.7% | 53.4% |
| 5-gram | Word | 1,235 | 10.27 | 4,148 | 39.7% | 72.1% |
| 5-gram | Subword | 11,633 | 13.51 | 85,697 | 23.3% | 44.3% |
Top 5 N-grams by Size
2-grams (Word):
| Rank | N-gram | Count |
|---|---|---|
| 1 | Δ«tΕcΔ cΔ |
2,347 |
| 2 | Δ«pan mΔcuΔ«lpΕhualxihuitl |
2,077 |
| 3 | cΔ xihuitl |
2,072 |
| 4 | xihuitl Δ«pan |
2,021 |
| 5 | tlΔcatiliztli miquiztli |
1,948 |
3-grams (Word):
| Rank | N-gram | Count |
|---|---|---|
| 1 | cΔ xihuitl Δ«pan |
1,988 |
| 2 | xihuitl Δ«pan mΔcuΔ«lpΕhualxihuitl |
1,968 |
| 3 | Δ«tΕcΔ cΔ xihuitl |
1,960 |
| 4 | mochΔ«hualiztli tlΔcatiliztli miquiztli |
1,881 |
| 5 | mahtlΔcxihuitl mochΔ«hualiztli tlΔcatiliztli |
1,500 |
4-grams (Word):
| Rank | N-gram | Count |
|---|---|---|
| 1 | cΔ xihuitl Δ«pan mΔcuΔ«lpΕhualxihuitl |
1,968 |
| 2 | Δ«tΕcΔ cΔ xihuitl Δ«pan |
1,960 |
| 3 | mahtlΔcxihuitl mochΔ«hualiztli tlΔcatiliztli miquiztli |
1,463 |
| 4 | Δ«pan mahtlΔcxihuitl mochΔ«hualiztli tlΔcatiliztli |
921 |
| 5 | mΔhtlacxihuitl mochΔ«hualiztli tlΔcatiliztli miquiztli |
399 |
5-grams (Word):
| Rank | N-gram | Count |
|---|---|---|
| 1 | Δ«tΕcΔ cΔ xihuitl Δ«pan mΔcuΔ«lpΕhualxihuitl |
1,960 |
| 2 | Δ«pan mahtlΔcxihuitl mochΔ«hualiztli tlΔcatiliztli miquiztli |
884 |
| 3 | cΔ xihuitl Δ«pan mΔcuΔ«lpΕhualxihuitl 15 |
170 |
| 4 | xihuitl Δ«pan mΔcuΔ«lpΕhualxihuitl 15 Δ«pan |
170 |
| 5 | Δ«pan mΔcuΔ«lpΕhualxihuitl 15 Δ«pan mahtlΔcxihuitl |
170 |
2-grams (Subword):
| Rank | N-gram | Count |
|---|---|---|
| 1 | t l |
48,016 |
| 2 | l i |
32,159 |
| 3 | n _ |
26,955 |
| 4 | h u |
25,168 |
| 5 | u i |
22,921 |
3-grams (Subword):
| Rank | N-gram | Count |
|---|---|---|
| 1 | l i _ |
14,715 |
| 2 | t l i |
13,229 |
| 3 | t l a |
12,936 |
| 4 | a n _ |
11,601 |
| 5 | z t l |
11,086 |
4-grams (Subword):
| Rank | N-gram | Count |
|---|---|---|
| 1 | t l i _ |
11,323 |
| 2 | z t l i |
10,901 |
| 3 | i z t l |
10,448 |
| 4 | u i t l |
8,705 |
| 5 | h u i t |
8,526 |
5-grams (Subword):
| Rank | N-gram | Count |
|---|---|---|
| 1 | i z t l i |
10,379 |
| 2 | z t l i _ |
9,771 |
| 3 | h u i t l |
8,254 |
| 4 | l i z t l |
7,810 |
| 5 | i h u i t |
7,378 |
Key Findings
- Best Perplexity: 2-gram (subword) with 257
- Entropy Trend: Decreases with larger n-grams (more predictable)
- Coverage: Top-1000 patterns cover ~44% 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 | 0.5364 | 1.450 | 2.77 | 33,565 | 46.4% |
| 1 | Subword | 1.0165 | 2.023 | 7.61 | 617 | 0.0% |
| 2 | Word | 0.1320 | 1.096 | 1.24 | 92,088 | 86.8% |
| 2 | Subword | 0.9596 | 1.945 | 5.40 | 4,690 | 4.0% |
| 3 | Word | 0.0399 | 1.028 | 1.06 | 112,754 | 96.0% |
| 3 | Subword | 0.8013 | 1.743 | 3.55 | 25,317 | 19.9% |
| 4 | Word | 0.0175 π | 1.012 | 1.03 | 117,889 | 98.3% |
| 4 | Subword | 0.5541 | 1.468 | 2.22 | 89,855 | 44.6% |
Generated Text Samples (Word-based)
Below are text samples generated from each word-based Markov chain model:
Context Size 1:
in ompa yeppa conmottiliani 108 centenas de literatura literature littΓ©rature ΔmatlalcΔyΕtl gramΓ‘tic...Δ«pan 360s mΔhtlacxihuitl mochΔ«hualiztli tlΔcatiliztli miquiztli amoxtlahcuilohqueh xiuhpan Δ«tΕca in ...cΔ xihuitl Δ«pan 900s mahtlΔcxihuitl mochΔ«hualiztli tlΔcatiliztli miquiztli tlamΔcuΔ«lti 5 la vega alt...
Context Size 2:
Δ«tΕcΔ cΔ xihuitl Δ«pan mΔcuΔ«lpΕhualxihuitl 14 Δ«pan mahtlΔcxihuitl mochΔ«hualiztli tlΔcatiliztli miquiz...Δ«pan mΔcuΔ«lpΕhualxihuitl 17 Δ«pan mahtlΔcxihuitl mochΔ«hualiztli tlΔcatiliztli miquiztli tlamahtlΔcti ...cΔ xihuitl Δ«pan mΔcuΔ«lpΕhualxihuitl 1 Δ«pan 50s mΔhtlacxihuitl mochΔ«hualiztli tlΔcatiliztli miquiztli...
Context Size 3:
cΔ xihuitl Δ«pan mΔcuΔ«lpΕhualxihuitl 10 Δ«pan 980s mahtlΔcxihuitl mochΔ«hualiztli tlΔcatiliztli miquizt...xihuitl Δ«pan mΔcuΔ«lpΕhualxihuitl 1 Δ«pan 40s mΔhtlacxihuitl mochΔ«hualiztli tlΔcatiliztli miquiztli tl...Δ«tΕcΔ cΔ xihuitl Δ«pan mΔcuΔ«lpΕhualxihuitl 10 Δ«pan 990s mahtlΔcxihuitl mochΔ«hualiztli tlΔcatiliztli m...
Context Size 4:
cΔ xihuitl Δ«pan mΔcuΔ«lpΕhualxihuitl 18 Δ«pan mahtlΔcxihuitl mochΔ«hualiztli tlΔcatiliztli miquiztli tl...Δ«tΕcΔ cΔ xihuitl Δ«pan mΔcuΔ«lpΕhualxihuitl 6 Δ«pan 550s mahtlΔcxihuitl mochΔ«hualiztli tlΔcatiliztli mi...Δ«pan mahtlΔcxihuitl mochΔ«hualiztli tlΔcatiliztli miquiztli nΕ xiquitta cuΔ«capan
Generated Text Samples (Subword-based)
Below are text samples generated from each subword-based Markov chain model:
Context Size 1:
_xitlΔhΔ«palih._sia,_ztiztliuil_(a_molahcahΔ«lizcΓ΄
Context Size 2:
tlathayotliztli_jliztli_*_*_*_*_*_n_tl_4,40%_san_ma
Context Size 3:
li_tlanΔci_uikaliltli_mammakandrealttlahtoznequichtlat
Context Size 4:
tli_tlacatlahkuitl_ztli._in_tlacatiliziztli_(yΔm_+_pΕhual
Key Findings
- Best Predictability: Context-4 (word) with 98.3% predictability
- Branching Factor: Decreases with context size (more deterministic)
- Memory Trade-off: Larger contexts require more storage (89,855 contexts)
- Recommendation: Context-3 or Context-4 for text generation
4. Vocabulary Analysis
Statistics
| Metric | Value |
|---|---|
| Vocabulary Size | 11,901 |
| Total Tokens | 139,625 |
| Mean Frequency | 11.73 |
| Median Frequency | 3 |
| Frequency Std Dev | 116.70 |
Most Common Words
| Rank | Word | Frequency |
|---|---|---|
| 1 | in | 8,302 |
| 2 | Δ«pan | 5,152 |
| 3 | cΔ | 2,961 |
| 4 | xihuitl | 2,907 |
| 5 | Δ«tΕcΔ | 2,782 |
| 6 | miquiztli | 2,512 |
| 7 | mΔcuΔ«lpΕhualxihuitl | 2,216 |
| 8 | tlΔcatiliztli | 2,123 |
| 9 | mochΔ«hualiztli | 2,005 |
| 10 | mahtlΔcxihuitl | 1,706 |
Least Common Words (from vocabulary)
| Rank | Word | Frequency |
|---|---|---|
| 1 | polanco | 2 |
| 2 | tepochcalli | 2 |
| 3 | tenis | 2 |
| 4 | mapatoltiliztli | 2 |
| 5 | panohco | 2 |
| 6 | ichcacuatitlan | 2 |
| 7 | tepetzintlah | 2 |
| 8 | itlachijchiualis | 2 |
| 9 | vehΓculos | 2 |
| 10 | vehΓculo | 2 |
Zipf's Law Analysis
| Metric | Value |
|---|---|
| Zipf Coefficient | 0.9414 |
| RΒ² (Goodness of Fit) | 0.992093 |
| Adherence Quality | excellent |
Coverage Analysis
| Top N Words | Coverage |
|---|---|
| Top 100 | 46.5% |
| Top 1,000 | 69.8% |
| Top 5,000 | 88.7% |
| Top 10,000 | 97.3% |
Key Findings
- Zipf Compliance: RΒ²=0.9921 indicates excellent adherence to Zipf's law
- High Frequency Dominance: Top 100 words cover 46.5% of corpus
- Long Tail: 1,901 words needed for remaining 2.7% 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 | 0.2842 π | 0.4247 | N/A | N/A |
| mono_64d | 64 | 0.0571 | 0.4200 | N/A | N/A |
| mono_128d | 128 | 0.0070 | 0.4306 | N/A | N/A |
| aligned_32d | 32 | 0.2842 | 0.4337 | 0.0200 | 0.1680 |
| aligned_64d | 64 | 0.0571 | 0.4188 | 0.0260 | 0.2000 |
| aligned_128d | 128 | 0.0070 | 0.4318 | 0.0580 | 0.2360 |
Key Findings
- Best Isotropy: mono_32d with 0.2842 (more uniform distribution)
- Semantic Density: Average pairwise similarity of 0.4266. Lower values indicate better semantic separation.
- Alignment Quality: Aligned models achieve up to 5.8% 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 | 0.627 | 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 |
|---|---|
-t |
texohtic, teyaotlacah, tecpanchantli |
-c |
connor, conihcuΔniliΔ, carochi |
-m |
momotlalistli, motzololoc, marcelo |
-a |
azul, amoxchihualiztli, azz |
-i |
indΓgena, itzcuintli, ixeliuhcayo |
-p |
polΓtica, proceso, peuh |
-te |
texohtic, teyaotlacah, tecpanchantli |
-s |
square, sandoval, sombra |
Productive Suffixes
| Suffix | Examples |
|---|---|
-li |
momotlalistli, tecpanchantli, tubartlahtΕlli |
-i |
momotlalistli, tecpanchantli, omonamicti |
-a |
niquelehuia, sombra, indΓgena |
-tl |
zΔzotepozmalacatl, tepozohtlamalacatl, pipincΔyΕtl |
-l |
sandoval, zΔzotepozmalacatl, tepozohtlamalacatl |
-n |
harrison, Δ«huan, jesutzin |
-o |
oro, dentado, ixeliuhcayo |
-h |
teyaotlacah, quihualquixtih, Εquitzintih |
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 |
|---|---|---|---|
tlac |
1.49x | 22 contexts | itlac, tlacah, tlacat |
iliz |
1.76x | 11 contexts | inemiliz, iyoliliz, Δ«nemiliz |
chΔ«h |
1.76x | 10 contexts | chΔ«hua, mochΔ«hua, chΔ«hualo |
uitl |
1.52x | 14 contexts | xiuitl, tequitl, ilhuitl |
iqui |
1.46x | 14 contexts | iquin, miqui, triqui |
laht |
1.43x | 12 contexts | tlahtΕl, tlahtec, tlahtic |
hΔ«hu |
1.76x | 7 contexts | chΔ«hua, mochΔ«hua, chΔ«hualo |
lizt |
1.88x | 6 contexts | yoliztli, yeliztli, axiliztli |
ztli |
1.65x | 8 contexts | eztli, otztli, meztli |
aliz |
1.63x | 8 contexts | alizΓ©e, ihcaliz, icealiz |
lΔca |
1.55x | 9 contexts | tlΔcah, tlΔcati, otlΔcat |
huit |
1.54x | 9 contexts | huitz, ilhuitl, xiuhuit |
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 |
|---|---|---|---|
-t |
-i |
494 words | tonameyocaquizcopinaloni, tlateΕmahuiztiliztli |
-t |
-li |
377 words | tlateΕmahuiztiliztli, tlakxitoktli |
-t |
-l |
183 words | thumbnail, tlacuΔ«calizpal |
-t |
-tl |
172 words | tepozyΕllΕtl, tlacetilΔ«llahtohcΔyΕtΔcatl |
-c |
-i |
161 words | capuli, cempohualli |
-n |
-i |
119 words | nΕncuahquΔ«zaliztli, neehΔcanΔmictiliztli |
-c |
-l |
117 words | chiucnauhtetl, cacallotl |
-t |
-n |
114 words | tzintzontzan, tomΓn |
-c |
-li |
109 words | capuli, cempohualli |
-n |
-li |
102 words | nΕncuahquΔ«zaliztli, neehΔcanΔmictiliztli |
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 |
|---|---|---|---|
| mΔcuΔ«lxΕchitl | mΔcuΔ«lxΕch-i-tl |
7.5 | i |
| itlahtollaliz | itlahtoll-al-iz |
7.5 | al |
| octacatia | octacat-i-a |
7.5 | i |
| mihcuanih | mihcuan-i-h |
7.5 | i |
| oyuhquimottili | oyuhquimott-i-li |
7.5 | i |
| tlahtolcopa | tlahtol-co-pa |
7.5 | co |
| atlΔntico | atlΔnt-i-co |
7.5 | i |
| tlahcalli | tlahc-al-li |
7.5 | al |
| huehcaΔ«xipcaxitl | huehcaΔ«xipcax-i-tl |
7.5 | i |
| huitztlan | huitz-tl-an |
7.5 | tl |
| cihuΔtlΔn | cihuΔ-tl-Δn |
7.5 | tl |
| chΔlchihuitl | chΔlchihu-i-tl |
7.5 | i |
| desgracia | desgrac-i-a |
7.5 | i |
| quipanahuia | quipanahu-i-a |
7.5 | i |
| tlazoxochitl | tlazoxoch-i-tl |
7.5 | i |
6.6 Linguistic Interpretation
Automated Insight: The language Nahuatl languages 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 (4.84x) |
| N-gram | 2-gram | Lowest perplexity (257) |
| Markov | Context-4 | Highest predictability (98.3%) |
| 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 14:41:15



















