language: mhr
language_name: Eastern Mari
language_family: uralic_volgaic
tags:
- wikilangs
- nlp
- tokenizer
- embeddings
- n-gram
- markov
- wikipedia
- feature-extraction
- sentence-similarity
- tokenization
- n-grams
- markov-chain
- text-mining
- fasttext
- babelvec
- vocabulous
- vocabulary
- monolingual
- family-uralic_volgaic
license: mit
library_name: wikilangs
pipeline_tag: text-generation
datasets:
- omarkamali/wikipedia-monthly
dataset_info:
name: wikipedia-monthly
description: Monthly snapshots of Wikipedia articles across 300+ languages
metrics:
- name: best_compression_ratio
type: compression
value: 4.335
- name: best_isotropy
type: isotropy
value: 0.8198
- name: vocabulary_size
type: vocab
value: 0
generated: 2026-01-10T00:00:00.000Z
Eastern Mari - Wikilangs Models
Comprehensive Research Report & Full Ablation Study
This repository contains NLP models trained and evaluated by Wikilangs, specifically on Eastern Mari Wikipedia data. We analyze tokenizers, n-gram models, Markov chains, vocabulary statistics, and word embeddings.
📋 Repository Contents
Models & Assets
- Tokenizers (8k, 16k, 32k, 64k)
- N-gram models (2, 3, 4, 5-gram)
- Markov chains (context of 1, 2, 3, 4 and 5)
- Subword N-gram and Markov chains
- Embeddings in various sizes and dimensions (aligned and unaligned)
- Language Vocabulary
- Language Statistics
Analysis and Evaluation
- 1. Tokenizer Evaluation
- 2. N-gram Model Evaluation
- 3. Markov Chain Evaluation
- 4. Vocabulary Analysis
- 5. Word Embeddings Evaluation
- 6. Morphological Analysis (Experimental)
- 7. Summary & Recommendations
- Metrics Glossary
- Visualizations Index
1. Tokenizer Evaluation
Results
| Vocab Size | Compression | Avg Token Len | UNK Rate | Total Tokens |
|---|---|---|---|---|
| 8k | 3.658x | 3.66 | 0.0886% | 476,276 |
| 16k | 3.968x | 3.97 | 0.0961% | 439,027 |
| 32k | 4.189x | 4.19 | 0.1015% | 415,901 |
| 64k | 4.335x 🏆 | 4.34 | 0.1050% | 401,897 |
Tokenization Examples
Below are sample sentences tokenized with each vocabulary size:
Sample 1: Ворзель () — Украиныште Киев велыште Буча кундемыштыже верланыше посёлко. Калыкч...
| Vocab | Tokens | Count |
|---|---|---|
| 8k | ▁вор з ель ▁() ▁— ▁украиныште ▁киев ▁велыште ▁буча ▁кундемыштыже ... (+16 more) |
26 |
| 16k | ▁вор з ель ▁() ▁— ▁украиныште ▁киев ▁велыште ▁буча ▁кундемыштыже ... (+16 more) |
26 |
| 32k | ▁вор з ель ▁() ▁— ▁украиныште ▁киев ▁велыште ▁буча ▁кундемыштыже ... (+16 more) |
26 |
| 64k | ▁ворзель ▁() ▁— ▁украиныште ▁киев ▁велыште ▁буча ▁кундемыштыже ▁верланыше ▁посёлко ... (+14 more) |
24 |
Sample 2: Пункт () — дюймын 1/72 наре ужашыже лийше кӱшычын ӱлык шрифтын висымкугытшо.
| Vocab | Tokens | Count |
|---|---|---|
| 8k | ▁пункт ▁() ▁— ▁д юй мын ▁ 1 / 7 ... (+17 more) |
27 |
| 16k | ▁пункт ▁() ▁— ▁дюй мын ▁ 1 / 7 2 ... (+15 more) |
25 |
| 32k | ▁пункт ▁() ▁— ▁дюй мын ▁ 1 / 7 2 ... (+10 more) |
20 |
| 64k | ▁пункт ▁() ▁— ▁дюймын ▁ 1 / 7 2 ▁наре ... (+8 more) |
18 |
Sample 3: 238 ий — III курымын ийже. Мо лийын Кӧ шочын Кӧ колен курым
| Vocab | Tokens | Count |
|---|---|---|
| 8k | ▁ 2 3 8 ▁ий ▁— ▁iii ▁курымын ▁ийже . ... (+7 more) |
17 |
| 16k | ▁ 2 3 8 ▁ий ▁— ▁iii ▁курымын ▁ийже . ... (+7 more) |
17 |
| 32k | ▁ 2 3 8 ▁ий ▁— ▁iii ▁курымын ▁ийже . ... (+7 more) |
17 |
| 64k | ▁ 2 3 8 ▁ий ▁— ▁iii ▁курымын ▁ийже . ... (+7 more) |
17 |
Key Findings
- Best Compression: 64k achieves 4.335x compression
- Lowest UNK Rate: 8k with 0.0886% 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 | 3,582 | 11.81 | 26,265 | 34.2% | 60.8% |
| 2-gram | Subword | 439 🏆 | 8.78 | 3,878 | 54.6% | 97.4% |
| 3-gram | Word | 4,130 | 12.01 | 36,566 | 34.5% | 60.2% |
| 3-gram | Subword | 3,337 | 11.70 | 33,949 | 19.6% | 64.9% |
| 4-gram | Word | 7,186 | 12.81 | 70,518 | 30.8% | 54.1% |
| 4-gram | Subword | 13,025 | 13.67 | 159,935 | 11.7% | 42.2% |
| 5-gram | Word | 6,518 | 12.67 | 62,229 | 31.1% | 55.2% |
| 5-gram | Subword | 29,667 | 14.86 | 355,981 | 9.8% | 34.7% |
Top 5 N-grams by Size
2-grams (Word):
| Rank | N-gram | Count |
|---|---|---|
| 1 | марий эл |
13,258 |
| 2 | йошкар ола |
10,954 |
| 3 | республики марий |
9,354 |
| 4 | великой отечественной |
6,261 |
| 5 | отечественной войне |
6,227 |
3-grams (Word):
| Rank | N-gram | Count |
|---|---|---|
| 1 | республики марий эл |
9,353 |
| 2 | великой отечественной войне |
6,227 |
| 3 | в великой отечественной |
6,214 |
| 4 | народа в великой |
6,200 |
| 5 | подвиг народа в |
6,199 |
4-grams (Word):
| Rank | N-gram | Count |
|---|---|---|
| 1 | в великой отечественной войне |
6,214 |
| 2 | народа в великой отечественной |
6,200 |
| 3 | документов подвиг народа в |
6,199 |
| 4 | подвиг народа в великой |
6,199 |
| 5 | банк документов подвиг народа |
6,196 |
5-grams (Word):
| Rank | N-gram | Count |
|---|---|---|
| 1 | народа в великой отечественной войне |
6,200 |
| 2 | документов подвиг народа в великой |
6,199 |
| 3 | подвиг народа в великой отечественной |
6,199 |
| 4 | банк документов подвиг народа в |
6,196 |
| 5 | в великой отечественной войне гг |
6,196 |
2-grams (Subword):
| Rank | N-gram | Count |
|---|---|---|
| 1 | . _ |
184,996 |
| 2 | е _ |
147,576 |
| 3 | л а |
134,439 |
| 4 | _ к |
133,534 |
| 5 | а р |
121,950 |
3-grams (Subword):
| Rank | N-gram | Count |
|---|---|---|
| 1 | и й _ |
64,060 |
| 2 | ы н _ |
57,801 |
| 3 | _ м а |
49,403 |
| 4 | м а р |
48,489 |
| 5 | р и й |
42,988 |
4-grams (Subword):
| Rank | N-gram | Count |
|---|---|---|
| 1 | м а р и |
41,511 |
| 2 | _ м а р |
41,069 |
| 3 | а р и й |
40,250 |
| 4 | в л а к |
32,702 |
| 5 | р и й _ |
32,360 |
5-grams (Subword):
| Rank | N-gram | Count |
|---|---|---|
| 1 | м а р и й |
39,931 |
| 2 | _ м а р и |
36,163 |
| 3 | - в л а к |
32,274 |
| 4 | а р и й _ |
30,689 |
| 5 | в л а к _ |
23,835 |
Key Findings
- Best Perplexity: 2-gram (subword) with 439
- Entropy Trend: Decreases with larger n-grams (more predictable)
- Coverage: Top-1000 patterns cover ~35% 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 | 0.8000 | 1.741 | 5.03 | 109,319 | 20.0% |
| 1 | Subword | 1.2025 | 2.301 | 10.94 | 715 | 0.0% |
| 2 | Word | 0.2053 | 1.153 | 1.44 | 547,819 | 79.5% |
| 2 | Subword | 1.1275 | 2.185 | 7.46 | 7,818 | 0.0% |
| 3 | Word | 0.0723 | 1.051 | 1.14 | 786,559 | 92.8% |
| 3 | Subword | 0.9049 | 1.872 | 4.46 | 58,298 | 9.5% |
| 4 | Word | 0.0392 🏆 | 1.028 | 1.08 | 893,046 | 96.1% |
| 4 | Subword | 0.6302 | 1.548 | 2.69 | 260,070 | 37.0% |
Generated Text Samples (Word-based)
Below are text samples generated from each word-based Markov chain model:
Context Size 1:
марий эл юринский район 304 с 123 лашт тыгак ончо тылзын коло ияш туныктен тӱвырам кучылтмашвлак историк влак посёлок боровской российыште вологда вел виче да калабрий регионын рӱдолаже сарман...с 35 ч 1 еҥ ий численность населения городских населенных пунктов звениговский муниципальный район с...
Context Size 2:
марий эл по делам архивов государственный архив республики марий эл республикын йӱдвел кипр турций р...йошкар ола с 125 158 15 ключева м а чап тамга орденын кавалерж кылвер влак хутор балезинареспублики марий эл по делам архивов государственный архив республики марий эл администрация муницип...
Context Size 3:
республики марий эл оршанский район сборник документальных очерков йошкар ола комитет республики мар...великой отечественной войне гг кузнецов михаил сарманаевич i степенян ачамланде сар орден да йошкар ...в великой отечественной войне гг аралымылан степенян чап орден влакын кавалерже ийласе кугу ачамланд...
Context Size 4:
в великой отечественной войне гг заровняев василий фёдорович ийласе кугу ачамланде сарын участникше ...народа в великой отечественной войне гг 11px i степенян ачамланде сар орденын кавалерже ийласе кугу ...документов подвиг народа в великой отечественной войне гг суаплан медальэлектронный банк документов ...
Generated Text Samples (Subword-based)
Below are text samples generated from each subword-based Markov chain model:
Context Size 1:
_165_ушктренынапаск_-штлик_je_йсеше_«стэл:_ичий)
Context Size 2:
._*_matheleptediaе_ке,_эҥеш_марсти_кӧ_кумарий)_jah_
Context Size 3:
ий_элын,_марий_йӱлын_моча_куснен_кун_мари-кушто_дене_в
Context Size 4:
марий-влак_кундемыш_марий_эл,_администарий_эл_по_делам_ар
Key Findings
- Best Predictability: Context-4 (word) with 96.1% predictability
- Branching Factor: Decreases with context size (more deterministic)
- Memory Trade-off: Larger contexts require more storage (260,070 contexts)
- Recommendation: Context-3 or Context-4 for text generation
4. Vocabulary Analysis
Statistics
| Metric | Value |
|---|---|
| Vocabulary Size | 48,490 |
| Total Tokens | 1,425,889 |
| Mean Frequency | 29.41 |
| Median Frequency | 4 |
| Frequency Std Dev | 331.81 |
Most Common Words
| Rank | Word | Frequency |
|---|---|---|
| 1 | марий | 30,639 |
| 2 | влак | 26,643 |
| 3 | с | 22,173 |
| 4 | в | 15,995 |
| 5 | эл | 13,818 |
| 6 | йошкар | 13,689 |
| 7 | ола | 13,467 |
| 8 | ий | 11,834 |
| 9 | ял | 11,645 |
| 10 | и | 11,569 |
Least Common Words (from vocabulary)
| Rank | Word | Frequency |
|---|---|---|
| 1 | слегка | 2 |
| 2 | расстроены | 2 |
| 3 | покачав | 2 |
| 4 | брать | 2 |
| 5 | поглаживая | 2 |
| 6 | настраивать | 2 |
| 7 | взял | 2 |
| 8 | взмахнул | 2 |
| 9 | поплыла | 2 |
| 10 | комнате | 2 |
Zipf's Law Analysis
| Metric | Value |
|---|---|
| Zipf Coefficient | 1.1394 |
| R² (Goodness of Fit) | 0.995171 |
| Adherence Quality | excellent |
Coverage Analysis
| Top N Words | Coverage |
|---|---|
| Top 100 | 36.4% |
| Top 1,000 | 67.2% |
| Top 5,000 | 84.2% |
| Top 10,000 | 90.0% |
Key Findings
- Zipf Compliance: R²=0.9952 indicates excellent adherence to Zipf's law
- High Frequency Dominance: Top 100 words cover 36.4% of corpus
- Long Tail: 38,490 words needed for remaining 10.0% 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 | 0.8198 🏆 | 0.3483 | N/A | N/A |
| mono_64d | 64 | 0.7400 | 0.2927 | N/A | N/A |
| mono_128d | 128 | 0.3509 | 0.2627 | N/A | N/A |
| aligned_32d | 32 | 0.8198 | 0.3439 | 0.0120 | 0.1120 |
| aligned_64d | 64 | 0.7400 | 0.2932 | 0.0280 | 0.1860 |
| aligned_128d | 128 | 0.3509 | 0.2652 | 0.0520 | 0.2340 |
Key Findings
- Best Isotropy: mono_32d with 0.8198 (more uniform distribution)
- Semantic Density: Average pairwise similarity of 0.3010. Lower values indicate better semantic separation.
- Alignment Quality: Aligned models achieve up to 5.2% 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 | 0.590 | 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 |
|---|---|
-к |
кертшылан, кравцов, капитон |
-п |
пургыж, пайгусово, пырысым |
-с |
саксофон, составитель, садретдинов |
-т |
такая, таҥаса, тимофеевский |
-ко |
командирын, кокыте, колмо |
-м |
мурымыж, марийкалыкым, модшын |
-а |
автора, аквалангым, акр |
-в |
вашталтыш, ведра, веткино |
Productive Suffixes
| Suffix | Examples |
|---|---|
-е |
культовые, литературйылме, руэмское |
-н |
кертшылан, капитон, чурийвылышан |
-а |
хайруллина, дата, таҥаса |
-й |
флоренций, тимофеевский, заведующий |
-м |
яким, редакцийжым, марийкалыкым |
-о |
пайгусово, общественно, качейкино |
-ым |
редакцийжым, марийкалыкым, иктешлымашым |
-ий |
флоренций, тимофеевский, заведующий |
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 |
|---|---|---|---|
ндем |
2.44x | 22 contexts | киндем, шындем, тандем |
ланд |
2.03x | 35 contexts | ландау, юланда, мланде |
рлан |
1.84x | 37 contexts | арлан, ерлан, хорлан |
айон |
2.14x | 19 contexts | район, района, районе |
демы |
2.09x | 20 contexts | айдемын, айдемыш, айдемым |
райо |
2.14x | 16 contexts | район, района, районе |
унде |
2.45x | 10 contexts | кундем, кундемна, кундемже |
альн |
1.70x | 25 contexts | дальний, дальние, вокально |
енно |
1.95x | 16 contexts | фенно, именно, военно |
кунд |
2.26x | 9 contexts | кунда, кундем, секунд |
лект |
1.38x | 36 contexts | лекте, лектыш, лектыт |
верл |
2.01x | 8 contexts | верла, верлам, уверла |
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 |
|---|---|---|---|
-к |
-е |
122 words | комнате, каҥашыме |
-п |
-е |
121 words | правление, периодике |
-к |
-н |
109 words | клапан, катян |
-с |
-е |
90 words | савырнымыже, следовательже |
-п |
-н |
71 words | пӧлкажын, пуртыман |
-с |
-н |
69 words | скревын, савырашлан |
-к |
-о |
69 words | колжо, кузьменко |
-т |
-е |
65 words | тиде, тюркское |
-к |
-а |
63 words | куклина, коведяева |
-м |
-н |
60 words | мардежан, музыкан |
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 |
|---|---|---|---|
| автономный | автоном-н-ый |
7.5 | н |
| диалектный | диалект-н-ый |
7.5 | н |
| отвлеченный | отвлечен-н-ый |
7.5 | н |
| министертвын | министерт-в-ын |
7.5 | в |
| всемарийском | в-се-марийском |
7.5 | марийском |
| материалах | материал-а-х |
7.5 | а |
| фильмыште | фильм-ыш-те |
6.0 | фильм |
| биологийын | биолог-ий-ын |
6.0 | биолог |
| тунемыныт | тунем-ын-ыт |
6.0 | тунем |
| комплексыште | комплекс-ыш-те |
6.0 | комплекс |
| абхазийын | абхаз-ий-ын |
6.0 | абхаз |
| каҥашымаш | каҥаш-ым-аш |
6.0 | каҥаш |
| шотландийын | шотланд-ий-ын |
6.0 | шотланд |
| философийже | философ-ий-же |
6.0 | философ |
| вашталтымаш | вашталт-ым-аш |
6.0 | вашталт |
6.6 Linguistic Interpretation
Automated Insight: The language Eastern Mari 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 (4.34x) |
| N-gram | 2-gram | Lowest perplexity (439) |
| Markov | Context-4 | Highest predictability (96.1%) |
| 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) × 100%. Indicates how deterministic the model's predictions are.
Intuition: 100% predictability means the next word is always certain; 0% means completely random. Real text falls between these extremes.
What to seek: Higher predictability for text generation quality, but too high (>98%) may produce repetitive output.
Vocabulary & Zipf's Law Metrics
Zipf's Coefficient
Definition: The slope of the log-log plot of word frequency vs. rank. Zipf's law predicts this should be approximately -1.
Intuition: A coefficient near -1 indicates the corpus follows natural language patterns where a few words are very common and most words are rare.
What to seek: Values between -0.8 and -1.2 indicate healthy natural language distribution. Deviations may suggest domain-specific or artificial text.
R² (Coefficient of Determination)
Definition: Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.
Intuition: R² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.
What to seek: R² > 0.95 is excellent; > 0.99 indicates near-perfect Zipf adherence typical of large natural corpora.
Vocabulary Coverage
Definition: Cumulative percentage of corpus tokens accounted for by the top N words.
Intuition: Shows how concentrated word usage is. If top-100 words cover 50% of text, the corpus relies heavily on common words.
What to seek: Top-100 covering 30-50% is typical. Higher coverage indicates more repetitive text; lower suggests richer vocabulary.
Word Embedding Metrics
Isotropy
Definition: Measures how uniformly distributed vectors are in the embedding space. Computed as the ratio of minimum to maximum singular values.
Intuition: High isotropy (near 1.0) means vectors spread evenly in all directions; low isotropy means vectors cluster in certain directions, reducing expressiveness.
What to seek: Higher isotropy generally indicates better-quality embeddings. Values > 0.1 are reasonable; > 0.3 is good. Lower-dimensional embeddings tend to have higher isotropy.
Average Norm
Definition: Mean magnitude (L2 norm) of word vectors in the embedding space.
Intuition: Indicates the typical "length" of vectors. Consistent norms suggest stable training; high variance may indicate some words are undertrained.
What to seek: Relatively consistent norms across models. The absolute value matters less than consistency (low std deviation).
Cosine Similarity
Definition: Measures angular similarity between vectors, ranging from -1 (opposite) to 1 (identical direction).
Intuition: Words with similar meanings should have high cosine similarity. This is the standard metric for semantic relatedness in embeddings.
What to seek: Semantically related words should score > 0.5; unrelated words should be near 0. Synonyms often score > 0.7.
t-SNE Visualization
Definition: t-Distributed Stochastic Neighbor Embedding - a dimensionality reduction technique that preserves local structure for visualization.
Intuition: Clusters in t-SNE plots indicate groups of semantically related words. Spread indicates vocabulary diversity; tight clusters suggest semantic coherence.
What to seek: Meaningful clusters (e.g., numbers together, verbs together). Avoid over-interpreting distances - t-SNE preserves local, not global, structure.
General Interpretation Guidelines
- 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
- 🌐 Website: wikilangs.org
- 🤗 Models: huggingface.co/wikilangs
- 📊 Data: wikipedia-monthly
- 👤 Author: Omar Kamali
- 🤝 Sponsor: Featherless AI
Generated by Wikilangs Models Pipeline
Report Date: 2026-01-10 11:49:08



















