wikilangs/myv
0
1---2language: myv3language_name: Erzya4language_family: uralic_volgaic5tags:6 - wikilangs7 - nlp8 - tokenizer9 - embeddings10 - n-gram11 - markov12 - wikipedia13 - feature-extraction14 - sentence-similarity15 - tokenization16 - n-grams17 - markov-chain18 - text-mining19 - fasttext20 - babelvec21 - vocabulous22 - vocabulary23 - monolingual24 - family-uralic_volgaic25license: mit26library_name: wikilangs27pipeline_tag: text-generation28datasets:29 - omarkamali/wikipedia-monthly30dataset_info:31 name: wikipedia-monthly32 description: Monthly snapshots of Wikipedia articles across 300+ languages33metrics:34 - name: best_compression_ratio35 type: compression36 value: 4.10437 - name: best_isotropy38 type: isotropy39 value: 0.862840 - name: vocabulary_size41 type: vocab42 value: 043generated: 2026-01-1044---45 46# Erzya - Wikilangs Models47## Comprehensive Research Report & Full Ablation Study48 49This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Erzya** Wikipedia data.50We analyze tokenizers, n-gram models, Markov chains, vocabulary statistics, and word embeddings.51 52## 📋 Repository Contents53 54### Models & Assets55 56- Tokenizers (8k, 16k, 32k, 64k)57- N-gram models (2, 3, 4, 5-gram)58- Markov chains (context of 1, 2, 3, 4 and 5)59- Subword N-gram and Markov chains60- Embeddings in various sizes and dimensions (aligned and unaligned)61- Language Vocabulary62- Language Statistics63 6465 66### Analysis and Evaluation67 68- [1. Tokenizer Evaluation](#1-tokenizer-evaluation)69- [2. N-gram Model Evaluation](#2-n-gram-model-evaluation)70- [3. Markov Chain Evaluation](#3-markov-chain-evaluation)71- [4. Vocabulary Analysis](#4-vocabulary-analysis)72- [5. Word Embeddings Evaluation](#5-word-embeddings-evaluation)73- [6. Morphological Analysis (Experimental)](#6--morphological-analysis-experimental)74- [7. Summary & Recommendations](#7-summary--recommendations)75- [Metrics Glossary](#appendix-metrics-glossary--interpretation-guide)76- [Visualizations Index](#visualizations-index)77 78---79## 1. Tokenizer Evaluation80 8182 8384 8586 8788 89### Results90 91| Vocab Size | Compression | Avg Token Len | UNK Rate | Total Tokens |92|------------|-------------|---------------|----------|--------------|93| **8k** | 3.359x | 3.36 | 0.1174% | 282,726 |94| **16k** | 3.657x | 3.66 | 0.1279% | 259,662 |95| **32k** | 3.923x | 3.93 | 0.1371% | 242,074 |96| **64k** | 4.104x 🏆 | 4.11 | 0.1435% | 231,386 |97 98### Tokenization Examples99 100Below are sample sentences tokenized with each vocabulary size:101 102**Sample 1:** `Киислова () — те велесь Эстэнь Масторсо Вырумаа ёнкссо. Сёрм. Мастор Масторонть ...`103 104| Vocab | Tokens | Count |105|-------|--------|-------|106| 8k | `▁ки ис лова ▁() ▁— ▁те ▁велесь ▁эстэнь ▁масторсо ▁вырумаа ... (+7 more)` | 17 |107| 16k | `▁ки ис лова ▁() ▁— ▁те ▁велесь ▁эстэнь ▁масторсо ▁вырумаа ... (+7 more)` | 17 |108| 32k | `▁ки ис лова ▁() ▁— ▁те ▁велесь ▁эстэнь ▁масторсо ▁вырумаа ... (+7 more)` | 17 |109| 64k | `▁киислова ▁() ▁— ▁те ▁велесь ▁эстэнь ▁масторсо ▁вырумаа ▁ёнкссо . ... (+5 more)` | 15 |110 111**Sample 2:** `Лепамиця лымбамот — лымбиця лыкамось, кона альмезэ аламолгады шканьберть.`112 113| Vocab | Tokens | Count |114|-------|--------|-------|115| 8k | `▁ле па м иця ▁лы мба мот ▁— ▁лы мб ... (+16 more)` | 26 |116| 16k | `▁ле пам иця ▁лы мба мот ▁— ▁лы мб иця ... (+15 more)` | 25 |117| 32k | `▁ле пам иця ▁лы мба мот ▁— ▁лы мб иця ... (+12 more)` | 22 |118| 64k | `▁ле пам иця ▁лы мба мот ▁— ▁лы мб иця ... (+9 more)` | 19 |119 120**Sample 3:** `Мария Гулегина (); чач. Умарьковонь 9 чистэ, Одесса ош, СССР) — морыця (сопрано)...`121 122| Vocab | Tokens | Count |123|-------|--------|-------|124| 8k | `▁мария ▁гу ле г ина ▁(); ▁чач . ▁умарьковонь ▁ ... (+14 more)` | 24 |125| 16k | `▁мария ▁гу ле гина ▁(); ▁чач . ▁умарьковонь ▁ 9 ... (+12 more)` | 22 |126| 32k | `▁мария ▁гу ле гина ▁(); ▁чач . ▁умарьковонь ▁ 9 ... (+12 more)` | 22 |127| 64k | `▁мария ▁гулегина ▁(); ▁чач . ▁умарьковонь ▁ 9 ▁чистэ , ... (+10 more)` | 20 |128 129 130### Key Findings131 132- **Best Compression:** 64k achieves 4.104x compression133- **Lowest UNK Rate:** 8k with 0.1174% unknown tokens134- **Trade-off:** Larger vocabularies improve compression but increase model size135- **Recommendation:** 32k vocabulary provides optimal balance for production use136 137---138## 2. N-gram Model Evaluation139 140141 142143 144145 146### Results147 148| N-gram | Variant | Perplexity | Entropy | Unique N-grams | Top-100 Coverage | Top-1000 Coverage |149|--------|---------|------------|---------|----------------|------------------|-------------------|150| **2-gram** | Word | 5,234 | 12.35 | 13,565 | 19.1% | 50.0% |151| **2-gram** | Subword | 451 🏆 | 8.82 | 4,411 | 55.9% | 96.7% |152| **3-gram** | Word | 5,809 | 12.50 | 17,643 | 20.4% | 49.4% |153| **3-gram** | Subword | 3,849 | 11.91 | 34,647 | 20.1% | 61.1% |154| **4-gram** | Word | 9,800 | 13.26 | 32,090 | 18.1% | 43.0% |155| **4-gram** | Subword | 19,085 | 14.22 | 156,710 | 10.3% | 34.9% |156| **5-gram** | Word | 7,606 | 12.89 | 25,413 | 19.9% | 46.5% |157| **5-gram** | Subword | 51,060 | 15.64 | 321,204 | 6.8% | 24.6% |158 159### Top 5 N-grams by Size160 161**2-grams (Word):**162 163| Rank | N-gram | Count |164|------|--------|-------|165| 1 | `вн истяжо` | 1,572 |166| 2 | `содавикс ломанть` | 1,490 |167| 3 | `ломанть те` | 1,467 |168| 4 | `те велестэнть` | 1,405 |169| 5 | `веленть лемденть` | 1,393 |170 171**3-grams (Word):**172 173| Rank | N-gram | Count |174|------|--------|-------|175| 1 | `содавикс ломанть те` | 1,461 |176| 2 | `ломанть те велестэнть` | 1,405 |177| 3 | `эрицятне раськень состав` | 1,059 |178| 4 | `раськень состав весероссиянь` | 1,054 |179| 5 | `состав весероссиянь перепись` | 1,039 |180 181**4-grams (Word):**182 183| Rank | N-gram | Count |184|------|--------|-------|185| 1 | `содавикс ломанть те велестэнть` | 1,405 |186| 2 | `эрицятне раськень состав весероссиянь` | 1,044 |187| 3 | `раськень состав весероссиянь перепись` | 1,039 |188| 4 | `весероссиянь перепись населения ие` | 1,039 |189| 5 | `состав весероссиянь перепись населения` | 1,039 |190 191**5-grams (Word):**192 193| Rank | N-gram | Count |194|------|--------|-------|195| 1 | `состав весероссиянь перепись населения ие` | 1,039 |196| 2 | `раськень состав весероссиянь перепись населения` | 1,039 |197| 3 | `эрицятне раськень состав весероссиянь перепись` | 1,032 |198| 4 | `содавикс ломанть те велестэнть эрицятне` | 946 |199| 5 | `эрямозо содавикс ломанть те велестэнть` | 917 |200 201**2-grams (Subword):**202 203| Rank | N-gram | Count |204|------|--------|-------|205| 1 | `ь _` | 153,248 |206| 2 | `. _` | 92,452 |207| 3 | `н ь` | 90,818 |208| 4 | `с т` | 68,788 |209| 5 | `, _` | 66,880 |210 211**3-grams (Subword):**212 213| Rank | N-gram | Count |214|------|--------|-------|215| 1 | `н ь _` | 80,150 |216| 2 | `т ь _` | 36,047 |217| 3 | `_ — _` | 29,408 |218| 4 | `о н ь` | 26,266 |219| 5 | `е н ь` | 26,109 |220 221**4-grams (Subword):**222 223| Rank | N-gram | Count |224|------|--------|-------|225| 1 | `о н ь _` | 24,242 |226| 2 | `е н ь _` | 22,554 |227| 3 | `н т ь _` | 20,388 |228| 4 | `_ в е л` | 13,694 |229| 5 | `в е л е` | 12,902 |230 231**5-grams (Subword):**232 233| Rank | N-gram | Count |234|------|--------|-------|235| 1 | `_ в е л е` | 12,574 |236| 2 | `е н т ь _` | 8,208 |237| 3 | `в о н ь _` | 7,157 |238| 4 | `о в о н ь` | 6,844 |239| 5 | `и я н ь _` | 6,197 |240 241 242### Key Findings243 244- **Best Perplexity:** 2-gram (subword) with 451245- **Entropy Trend:** Decreases with larger n-grams (more predictable)246- **Coverage:** Top-1000 patterns cover ~25% of corpus247- **Recommendation:** 4-gram or 5-gram for best predictive performance248 249---250## 3. Markov Chain Evaluation251 252253 254255 256257 258### Results259 260| Context | Variant | Avg Entropy | Perplexity | Branching Factor | Unique Contexts | Predictability |261|---------|---------|-------------|------------|------------------|-----------------|----------------|262| **1** | Word | 0.6530 | 1.572 | 3.67 | 122,977 | 34.7% |263| **1** | Subword | 1.2973 | 2.458 | 11.50 | 833 | 0.0% |264| **2** | Word | 0.1469 | 1.107 | 1.28 | 449,631 | 85.3% |265| **2** | Subword | 1.1429 | 2.208 | 6.92 | 9,577 | 0.0% |266| **3** | Word | 0.0456 | 1.032 | 1.08 | 573,707 | 95.4% |267| **3** | Subword | 0.8768 | 1.836 | 4.15 | 66,234 | 12.3% |268| **4** | Word | 0.0224 🏆 | 1.016 | 1.04 | 613,293 | 97.8% |269| **4** | Subword | 0.6169 | 1.534 | 2.56 | 274,547 | 38.3% |270 271### Generated Text Samples (Word-based)272 273Below are text samples generated from each word-based Markov chain model:274 275**Context Size 1:**276 2771. `ды касы седе ламо м и б в финно угорский прорыв текст биографический фильм без источников`2782. `в суздаль на южния полюс с рус эрзян isbn url consultato il 21 8 чистэ калиновка`2793. `и д в рузанкин н новгород англо хинди русский словарь ок назв а кенерезь лёмзёркссо почодозь`280 281**Context Size 2:**282 2831. `вн истяжо таштамковонь 12 чистэ саран ошсо калмазо апак ёвта секскак велень продештяст истямо сынст ...`2842. `содавикс ломанть те велестэнть веленть эрямозо содавикс ломанть те велестэнть веленть эрямозо содави...`2853. `ломанть те велестэнть эрицятне раськень состав весероссиянь перепись населения ие рузт 56 велеть ошо...`286 287**Context Size 3:**288 2891. `содавикс ломанть те велестэнть веленть эрямозо эрицятне раськень состав весероссиянь перепись населе...`2902. `ломанть те велестэнть эрицятне раськень состав весероссиянь перепись населения ие рузт 93 велеть вел...`2913. `эрицятне раськень состав весероссиянь эрицятнень сёрмадстоманть ие коряс рузт 100 содавикс ломанть т...`292 293**Context Size 4:**294 2951. `содавикс ломанть те велестэнть эрицятне раськень состав весероссиянь перепись населения ие рузт 95 с...`2962. `эрицятне раськень состав весероссиянь перепись населения ие рузт 100 велеть буень велеть`2973. `весероссиянь перепись населения ие печкаст 100 велеть велеть`298 299 300### Generated Text Samples (Subword-based)301 302Below are text samples generated from each subword-based Markov chain model:303 304**Context Size 1:**305 3061. `_вень_кулмиистес`3072. `олияморх_с_мениз`3083. `ав_покрявась_а_к`309 310**Context Size 2:**311 3121. `ь_ких_новияс_эле_`3132. `._валриц_мень_(юу`3143. `нь_эритортаранили`315 316**Context Size 3:**317 3181. `нь_аштемантоликани`3192. `ть_экось_оплангсо_`3203. `_—_ведческие_с_евр`321 322**Context Size 4:**323 3241. `онь_сал,_запись_нас`3252. `ень_ды_уманический_`3263. `нть_эрямонзо_токаль`327 328 329### Key Findings330 331- **Best Predictability:** Context-4 (word) with 97.8% predictability332- **Branching Factor:** Decreases with context size (more deterministic)333- **Memory Trade-off:** Larger contexts require more storage (274,547 contexts)334- **Recommendation:** Context-3 or Context-4 for text generation335 336---337## 4. Vocabulary Analysis338 339340 341342 343344 345### Statistics346 347| Metric | Value |348|--------|-------|349| Vocabulary Size | 47,484 |350| Total Tokens | 705,946 |351| Mean Frequency | 14.87 |352| Median Frequency | 3 |353| Frequency Std Dev | 119.73 |354 355### Most Common Words356 357| Rank | Word | Frequency |358|------|------|-----------|359| 1 | ды | 10,760 |360| 2 | в | 8,187 |361| 3 | и | 6,467 |362| 4 | с | 6,350 |363| 5 | а | 5,547 |364| 6 | те | 5,228 |365| 7 | м | 4,398 |366| 8 | иестэ | 3,988 |367| 9 | ульнесь | 3,596 |368| 10 | ие | 3,563 |369 370### Least Common Words (from vocabulary)371 372| Rank | Word | Frequency |373|------|------|-----------|374| 1 | якшаматянть | 2 |375| 2 | аналогозо | 2 |376| 3 | доминияк | 2 |377| 4 | indeks | 2 |378| 5 | grup | 2 |379| 6 | zawodowych | 2 |380| 7 | muzea | 2 |381| 8 | britishpedia | 2 |382| 9 | osobistości | 2 |383| 10 | bph | 2 |384 385### Zipf's Law Analysis386 387| Metric | Value |388|--------|-------|389| Zipf Coefficient | 1.0126 |390| R² (Goodness of Fit) | 0.996053 |391| Adherence Quality | **excellent** |392 393### Coverage Analysis394 395| Top N Words | Coverage |396|-------------|----------|397| Top 100 | 27.1% |398| Top 1,000 | 55.8% |399| Top 5,000 | 75.1% |400| Top 10,000 | 83.0% |401 402### Key Findings403 404- **Zipf Compliance:** R²=0.9961 indicates excellent adherence to Zipf's law405- **High Frequency Dominance:** Top 100 words cover 27.1% of corpus406- **Long Tail:** 37,484 words needed for remaining 17.0% coverage407 408---409## 5. Word Embeddings Evaluation410 411412 413414 415416 417418 419 420### 5.1 Cross-Lingual Alignment421 422423 424425 426 427### 5.2 Model Comparison428 429| Model | Dimension | Isotropy | Semantic Density | Alignment R@1 | Alignment R@10 |430|-------|-----------|----------|------------------|---------------|----------------|431| **mono_32d** | 32 | 0.8628 🏆 | 0.3405 | N/A | N/A |432| **mono_64d** | 64 | 0.7101 | 0.2786 | N/A | N/A |433| **mono_128d** | 128 | 0.2558 | 0.2702 | N/A | N/A |434| **aligned_32d** | 32 | 0.8628 | 0.3424 | 0.0280 | 0.1300 |435| **aligned_64d** | 64 | 0.7101 | 0.2772 | 0.0360 | 0.1540 |436| **aligned_128d** | 128 | 0.2558 | 0.2675 | 0.0700 | 0.2380 |437 438### Key Findings439 440- **Best Isotropy:** mono_32d with 0.8628 (more uniform distribution)441- **Semantic Density:** Average pairwise similarity of 0.2961. Lower values indicate better semantic separation.442- **Alignment Quality:** Aligned models achieve up to 7.0% R@1 in cross-lingual retrieval.443- **Recommendation:** 128d aligned for best cross-lingual performance444 445---446## 6. Morphological Analysis (Experimental)447 448This 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.449 450### 6.1 Productivity & Complexity451 452| Metric | Value | Interpretation | Recommendation |453|--------|-------|----------------|----------------|454| Productivity Index | **5.000** | High morphological productivity | Reliable analysis |455| Idiomaticity Gap | **0.892** | High formulaic/idiomatic content | - |456 457### 6.2 Affix Inventory (Productive Units)458 459These 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.460 461#### Productive Prefixes462| Prefix | Examples |463|--------|----------|464| `-к` | кемкавтово, кантнить, клавдий |465| `-с` | сайнелень, сабан, скульптуры |466| `-п` | пильгеоскань, политиканьветий, паросто |467| `-ка` | кантнить, казаньсэ, кайсеви |468| `-а` | абус, андонь, англиясо |469| `-т` | тамары, таштоюрьево, туинек |470| `-в` | венстизе, вагриус, венок |471| `-м` | матвеево, монастырень, массрэнь |472 473#### Productive Suffixes474| Suffix | Examples |475|--------|----------|476| `-ь` | пильгеоскань, сайнелень, кантнить |477| `-нь` | пильгеоскань, сайнелень, раввинэнь |478| `-о` | кемкавтово, матвеево, ярмаконзо |479| `-ть` | кантнить, художникенть, эрсить |480| `-а` | задонска, божена, улянка |481| `-е` | венстизе, характеристикатне, европе |482| `-й` | клавдий, политиканьветий, учебной |483| `-сь` | ловомась, куломачись, кельесь |484 485### 6.3 Bound Stems (Lexical Roots)486 487Bound 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.488 489| Stem | Cohesion | Substitutability | Examples |490|------|----------|------------------|----------|491| `ково` | 2.01x | 50 contexts | ковол, беково, ковозо |492| `енть` | 1.92x | 55 contexts | генть, денть, менть |493| `овон` | 2.23x | 30 contexts | човонь, ловонь, ковонь |494| `арка` | 2.00x | 42 contexts | парка, тарка, аркат |495| `риця` | 2.25x | 20 contexts | эриця, триця, мариця |496| `ской` | 1.90x | 34 contexts | арской, южской, ямской |497| `анть` | 1.83x | 38 contexts | канть, панть, манть |498| `вонь` | 2.26x | 18 contexts | орвонь, сёвонь, лувонь |499| `асто` | 1.74x | 44 contexts | тасто, састо, часто |500| `стор` | 1.63x | 48 contexts | сторож, мастор, стороны |501| `ятне` | 1.76x | 33 contexts | цятне, ятнень, атятне |502| `тарк` | 2.14x | 16 contexts | тарка, таркат, тарксо |503 504### 6.4 Affix Compatibility (Co-occurrence)505 506This table shows which prefixes and suffixes most frequently co-occur on the same stems, revealing the 'stacking' rules of the language's morphology.507 508| Prefix | Suffix | Frequency | Examples |509|--------|--------|-----------|----------|510| `-к` | `-ь` | 242 words | компаниянть, кшить |511| `-п` | `-ь` | 182 words | палсь, политикень |512| `-с` | `-ь` | 168 words | семиянь, сельмтнень |513| `-в` | `-ь` | 134 words | вирьавань, вейсветямонь |514| `-т` | `-ь` | 123 words | токалить, термодинамикань |515| `-м` | `-ь` | 118 words | марясть, максоманть |516| `-к` | `-нь` | 117 words | каминь, клеткантень |517| `-а` | `-ь` | 103 words | ашомештень, азребайджанонь |518| `-л` | `-ь` | 94 words | лемдезь, людикинь |519| `-п` | `-нь` | 85 words | политикень, псакань |520 521### 6.5 Recursive Morpheme Segmentation522 523Using **Recursive Hierarchical Substitutability**, we decompose complex words into their constituent morphemes. This approach handles nested affixes (e.g., `prefix-prefix-root-suffix`).524 525| Word | Suggested Split | Confidence | Stem |526|------|-----------------|------------|------|527| инязорава | **`инязор-а-ва`** | 7.5 | `а` |528| материалам | **`материал-а-м`** | 7.5 | `а` |529| пандомась | **`пандо-ма-сь`** | 7.5 | `ма` |530| группанень | **`группа-не-нь`** | 7.5 | `не` |531| экономистов | **`экономи-ст-ов`** | 7.5 | `ст` |532| васеньценть | **`васеньце-н-ть`** | 7.5 | `н` |533| маритьнень | **`марить-не-нь`** | 7.5 | `не` |534| участкась | **`участ-ка-сь`** | 7.5 | `ка` |535| ломаньстэ | **`ломань-ст-э`** | 7.5 | `ст` |536| кемекстись | **`кемекст-и-сь`** | 7.5 | `и` |537| невтемакс | **`невте-ма-кс`** | 7.5 | `ма` |538| чугункасто | **`чугунка-ст-о`** | 7.5 | `ст` |539| велетнесэ | **`велет-не-сэ`** | 7.5 | `не` |540| премиятне | **`премия-т-не`** | 7.5 | `т` |541| медицинань | **`медици-на-нь`** | 7.5 | `на` |542 543### 6.6 Linguistic Interpretation544 545> **Automated Insight:**546The language Erzya shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.547 548> **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.549 550---551## 7. Summary & Recommendations552 553554 555### Production Recommendations556 557| Component | Recommended | Rationale |558|-----------|-------------|-----------|559| Tokenizer | **64k BPE** | Best compression (4.10x) |560| N-gram | **2-gram** | Lowest perplexity (451) |561| Markov | **Context-4** | Highest predictability (97.8%) |562| Embeddings | **100d** | Balanced semantic capture and isotropy |563 564 565---566## Appendix: Metrics Glossary & Interpretation Guide567 568This section provides definitions, intuitions, and guidance for interpreting the metrics used throughout this report.569 570### Tokenizer Metrics571 572**Compression Ratio**573> *Definition:* The ratio of characters to tokens (chars/token). Measures how efficiently the tokenizer represents text.574>575> *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.576>577> *What to seek:* Higher is generally better for efficiency, but extremely high compression may indicate overly aggressive merging that loses morphological information.578 579**Average Token Length (Fertility)**580> *Definition:* Mean number of characters per token produced by the tokenizer.581>582> *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.583>584> *What to seek:* Balance between 2-5 characters for most languages. Arabic/morphologically-rich languages may benefit from slightly longer tokens.585 586**Unknown Token Rate (OOV Rate)**587> *Definition:* Percentage of tokens that map to the unknown/UNK token, indicating words the tokenizer cannot represent.588>589> *Intuition:* Lower OOV means better vocabulary coverage. High OOV indicates the tokenizer encounters many unseen character sequences.590>591> *What to seek:* Below 1% is excellent; below 5% is acceptable. BPE tokenizers typically achieve very low OOV due to subword fallback.592 593### N-gram Model Metrics594 595**Perplexity**596> *Definition:* Measures how "surprised" the model is by test data. Mathematically: 2^(cross-entropy). Lower values indicate better prediction.597>598> *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.599>600> *What to seek:* Lower is better. Perplexity decreases with larger n-grams (more context). Values vary widely by language and corpus size.601 602**Entropy**603> *Definition:* Average information content (in bits) needed to encode the next token given the context. Related to perplexity: perplexity = 2^entropy.604>605> *Intuition:* High entropy means high uncertainty/randomness; low entropy means predictable patterns. Natural language typically has entropy between 1-4 bits per character.606>607> *What to seek:* Lower entropy indicates more predictable text patterns. Entropy should decrease as n-gram size increases.608 609**Coverage (Top-K)**610> *Definition:* Percentage of corpus occurrences explained by the top K most frequent n-grams.611>612> *Intuition:* High coverage with few patterns indicates repetitive/formulaic text; low coverage suggests diverse vocabulary usage.613>614> *What to seek:* Depends on use case. For language modeling, moderate coverage (40-60% with top-1000) is typical for natural text.615 616### Markov Chain Metrics617 618**Average Entropy**619> *Definition:* Mean entropy across all contexts, measuring average uncertainty in next-word prediction.620>621> *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).622>623> *What to seek:* Decreasing entropy with larger context sizes. Very low entropy (<0.1) indicates highly deterministic transitions.624 625**Branching Factor**626> *Definition:* Average number of unique next tokens observed for each context.627>628> *Intuition:* High branching = many possible continuations (flexible but uncertain); low branching = few options (predictable but potentially repetitive).629>630> *What to seek:* Branching factor should decrease with context size. Values near 1.0 indicate nearly deterministic chains.631 632**Predictability**633> *Definition:* Derived metric: (1 - normalized_entropy) × 100%. Indicates how deterministic the model's predictions are.634>635> *Intuition:* 100% predictability means the next word is always certain; 0% means completely random. Real text falls between these extremes.636>637> *What to seek:* Higher predictability for text generation quality, but too high (>98%) may produce repetitive output.638 639### Vocabulary & Zipf's Law Metrics640 641**Zipf's Coefficient**642> *Definition:* The slope of the log-log plot of word frequency vs. rank. Zipf's law predicts this should be approximately -1.643>644> *Intuition:* A coefficient near -1 indicates the corpus follows natural language patterns where a few words are very common and most words are rare.645>646> *What to seek:* Values between -0.8 and -1.2 indicate healthy natural language distribution. Deviations may suggest domain-specific or artificial text.647 648**R² (Coefficient of Determination)**649> *Definition:* Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.650>651> *Intuition:* R² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.652>653> *What to seek:* R² > 0.95 is excellent; > 0.99 indicates near-perfect Zipf adherence typical of large natural corpora.654 655**Vocabulary Coverage**656> *Definition:* Cumulative percentage of corpus tokens accounted for by the top N words.657>658> *Intuition:* Shows how concentrated word usage is. If top-100 words cover 50% of text, the corpus relies heavily on common words.659>660> *What to seek:* Top-100 covering 30-50% is typical. Higher coverage indicates more repetitive text; lower suggests richer vocabulary.661 662### Word Embedding Metrics663 664**Isotropy**665> *Definition:* Measures how uniformly distributed vectors are in the embedding space. Computed as the ratio of minimum to maximum singular values.666>667> *Intuition:* High isotropy (near 1.0) means vectors spread evenly in all directions; low isotropy means vectors cluster in certain directions, reducing expressiveness.668>669> *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.670 671**Average Norm**672> *Definition:* Mean magnitude (L2 norm) of word vectors in the embedding space.673>674> *Intuition:* Indicates the typical "length" of vectors. Consistent norms suggest stable training; high variance may indicate some words are undertrained.675>676> *What to seek:* Relatively consistent norms across models. The absolute value matters less than consistency (low std deviation).677 678**Cosine Similarity**679> *Definition:* Measures angular similarity between vectors, ranging from -1 (opposite) to 1 (identical direction).680>681> *Intuition:* Words with similar meanings should have high cosine similarity. This is the standard metric for semantic relatedness in embeddings.682>683> *What to seek:* Semantically related words should score > 0.5; unrelated words should be near 0. Synonyms often score > 0.7.684 685**t-SNE Visualization**686> *Definition:* t-Distributed Stochastic Neighbor Embedding - a dimensionality reduction technique that preserves local structure for visualization.687>688> *Intuition:* Clusters in t-SNE plots indicate groups of semantically related words. Spread indicates vocabulary diversity; tight clusters suggest semantic coherence.689>690> *What to seek:* Meaningful clusters (e.g., numbers together, verbs together). Avoid over-interpreting distances - t-SNE preserves local, not global, structure.691 692### General Interpretation Guidelines693 6941. **Compare within model families:** Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).6952. **Consider trade-offs:** Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).6963. **Context matters:** Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.6974. **Corpus influence:** All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.6985. **Language-specific patterns:** Morphologically rich languages (like Arabic) may show different optimal ranges than analytic languages.699 700 701### Visualizations Index702 703| Visualization | Description |704|---------------|-------------|705| Tokenizer Compression | Compression ratios by vocabulary size |706| Tokenizer Fertility | Average token length by vocabulary |707| Tokenizer OOV | Unknown token rates |708| Tokenizer Total Tokens | Total tokens by vocabulary |709| N-gram Perplexity | Perplexity by n-gram size |710| N-gram Entropy | Entropy by n-gram size |711| N-gram Coverage | Top pattern coverage |712| N-gram Unique | Unique n-gram counts |713| Markov Entropy | Entropy by context size |714| Markov Branching | Branching factor by context |715| Markov Contexts | Unique context counts |716| Zipf's Law | Frequency-rank distribution with fit |717| Vocab Frequency | Word frequency distribution |718| Top 20 Words | Most frequent words |719| Vocab Coverage | Cumulative coverage curve |720| Embedding Isotropy | Vector space uniformity |721| Embedding Norms | Vector magnitude distribution |722| Embedding Similarity | Word similarity heatmap |723| Nearest Neighbors | Similar words for key terms |724| t-SNE Words | 2D word embedding visualization |725| t-SNE Sentences | 2D sentence embedding visualization |726| Position Encoding | Encoding method comparison |727| Model Sizes | Storage requirements |728| Performance Dashboard | Comprehensive performance overview |729 730---731## About This Project732 733### Data Source734 735Models trained on [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly) - a monthly snapshot of Wikipedia articles across 300+ languages.736 737### Project738 739A project by **[Wikilangs](https://wikilangs.org)** - Open-source NLP models for every Wikipedia language.740 741### Maintainer742 743[Omar Kamali](https://omarkamali.com) - [Omneity Labs](https://omneitylabs.com)744 745### Citation746 747If you use these models in your research, please cite:748 749```bibtex750@misc{wikilangs2025,751 author = {Kamali, Omar},752 title = {Wikilangs: Open NLP Models for Wikipedia Languages},753 year = {2025},754 doi = {10.5281/zenodo.18073153},755 publisher = {Zenodo},756 url = {https://huggingface.co/wikilangs}757 institution = {Omneity Labs}758}759```760 761### License762 763MIT License - Free for academic and commercial use.764 765### Links766 767- 🌐 Website: [wikilangs.org](https://wikilangs.org)768- 🤗 Models: [huggingface.co/wikilangs](https://huggingface.co/wikilangs)769- 📊 Data: [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly)770- 👤 Author: [Omar Kamali](https://huggingface.co/omarkamali)771- 🤝 Sponsor: [Featherless AI](https://featherless.ai)772---773*Generated by Wikilangs Models Pipeline*774 775*Report Date: 2026-01-10 14:15:51*776