Lezgian - Wikilangs Models
Comprehensive Research Report & Full Ablation Study
This repository contains NLP models trained and evaluated by Wikilangs, specifically on Lezgian 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 | 3.556x | 3.56 | 0.2939% | 478,366 |
| 16k | 3.921x | 3.92 | 0.3241% | 433,830 |
| 32k | 4.233x | 4.24 | 0.3498% | 401,922 |
| 64k | 4.461x π | 4.46 | 0.3687% | 381,358 |
Tokenization Examples
Below are sample sentences tokenized with each vocabulary size:
Sample 1: ΠΠ΅ΡΠ΅ΡΠΏΠ°ΡΠ°Π½ Π³ΡΠΈΡΠ±ΠΎΠΊ (Π»Π°Ρ. Raphicerus sharpei) β Π°Π½ΡΠΈΠ»ΠΎΠΏΠ°ΡΡ Ρ
Π·Π°Π½Π΄ΠΈΠ· ΡΠ°Π»ΡΠΊΡ ΡΠΈΡ Π³ΡΠ°...
| Vocab | Tokens | Count |
|---|---|---|
| 8k | βΠΊΠ΅ΡΠ΅ΡΠΏΠ°ΡΠ°Π½ βΠ³Ρ ΠΈΡ Π±ΠΎΠΊ β( Π»Π°Ρ . βr aph ic ... (+14 more) |
24 |
| 16k | βΠΊΠ΅ΡΠ΅ΡΠΏΠ°ΡΠ°Π½ βΠ³Ρ ΠΈΡΠ±ΠΎΠΊ β( Π»Π°Ρ . βraphicerus βsh ar p ... (+10 more) |
20 |
| 32k | βΠΊΠ΅ΡΠ΅ΡΠΏΠ°ΡΠ°Π½ βΠ³ΡΠΈΡΠ±ΠΎΠΊ β( Π»Π°Ρ . βraphicerus βsharpei ) ββ βΠ°Π½ΡΠΈΠ»ΠΎΠΏΠ°ΡΡ ... (+6 more) |
16 |
| 64k | βΠΊΠ΅ΡΠ΅ΡΠΏΠ°ΡΠ°Π½ βΠ³ΡΠΈΡΠ±ΠΎΠΊ β( Π»Π°Ρ . βraphicerus βsharpei ) ββ βΠ°Π½ΡΠΈΠ»ΠΎΠΏΠ°ΡΡ ... (+6 more) |
16 |
Sample 2: ΠΠΈΠ»ΠΎΠ²Π°ΜΡΡ-ΡΡΡ (ΠΊΠΡβ
Ρ) β Π³ΡΠ°ΡΠΈΠ» Π²Π° Ρ ΠΊΠ°ΡΠ΄ΠΈΠΊ ΠΊΡΡΡΠ½Π²Π°ΠΉ ΡΠ½Π΅ΡΠ³ΠΈΡΠ΄ΠΈΠ½ ΠΊΡΠ°Π΄Π°Ρ, Π³ΡΠ°ΠΊΣΠ½ΠΈ ΠΊ...
| Vocab | Tokens | Count |
|---|---|---|
| 8k | βΠΊΠΈΠ» ΠΎΠ²Π° Μ Ρ Ρ - Ρ ΡΡ β( ΠΊ ... (+30 more) |
40 |
| 16k | βΠΊΠΈΠ» ΠΎΠ²Π° ΜΡ Ρ - Ρ ΡΡ β( ΠΊΠ² Ρ ... (+26 more) |
36 |
| 32k | βΠΊΠΈΠ» ΠΎΠ²Π° ΜΡ Ρ - ΡΡΡ β( ΠΊΠ² Ρ β
... (+23 more) |
33 |
| 64k | βΠΊΠΈΠ» ΠΎΠ²Π° ΜΡ Ρ - ΡΡΡ β( ΠΊΠ²Ρ β
Ρ ... (+22 more) |
32 |
Sample 3: ΠΉΠΈΡ (ΡΠ° Π°Π³ΡΠ·ΡΡΠ½ΠΈ ΠΈΡΠΈΠ΄Π²ΠΈΡΠ½ΠΈ ΡΡ
ΡΣΡΡΠ½ΠΈΡΣΠΈΠΊΡΡΠ΄Π»Π°Π³ΡΠ°ΠΉ ΠΉΠΈΡ) β ΡΠΈ ΡΡΠ°Π΄ΠΈΠ½ ΠΉΠΈΡ. XVIII Π²ΠΈΡ...
| Vocab | Tokens | Count |
|---|---|---|
| 8k | βΠΉΠΈΡ β( ΡΠ° βΠ°Π³ΡΠ·ΡΡΠ½ΠΈ βΠΈΡΠΈΠ΄Π²ΠΈΡΠ½ΠΈ βΡΡ
ΡΣΡΡΠ½ΠΈΡΣ ΠΈΠΊΡΡΠ΄Π»Π°Π³ΡΠ°ΠΉ βΠΉΠΈΡ ) ββ ... (+20 more) |
30 |
| 16k | βΠΉΠΈΡ β( ΡΠ° βΠ°Π³ΡΠ·ΡΡΠ½ΠΈ βΠΈΡΠΈΠ΄Π²ΠΈΡΠ½ΠΈ βΡΡ
ΡΣΡΡΠ½ΠΈΡΣ ΠΈΠΊΡΡΠ΄Π»Π°Π³ΡΠ°ΠΉ βΠΉΠΈΡ ) ββ ... (+20 more) |
30 |
| 32k | βΠΉΠΈΡ β( ΡΠ° βΠ°Π³ΡΠ·ΡΡΠ½ΠΈ βΠΈΡΠΈΠ΄Π²ΠΈΡΠ½ΠΈ βΡΡ
ΡΣΡΡΠ½ΠΈΡΣ ΠΈΠΊΡΡΠ΄Π»Π°Π³ΡΠ°ΠΉ βΠΉΠΈΡ ) ββ ... (+20 more) |
30 |
| 64k | βΠΉΠΈΡ β( ΡΠ° βΠ°Π³ΡΠ·ΡΡΠ½ΠΈ βΠΈΡΠΈΠ΄Π²ΠΈΡΠ½ΠΈ βΡΡ
ΡΣΡΡΠ½ΠΈΡΣ ΠΈΠΊΡΡΠ΄Π»Π°Π³ΡΠ°ΠΉ βΠΉΠΈΡ ) ββ ... (+20 more) |
30 |
Key Findings
- Best Compression: 64k achieves 4.461x compression
- Lowest UNK Rate: 8k with 0.2939% 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 | 4,869 | 12.25 | 13,465 | 20.5% | 52.1% |
| 2-gram | Subword | 378 π | 8.56 | 3,725 | 59.9% | 97.5% |
| 3-gram | Word | 4,928 | 12.27 | 15,118 | 20.8% | 53.1% |
| 3-gram | Subword | 2,980 | 11.54 | 29,246 | 23.8% | 66.3% |
| 4-gram | Word | 9,550 | 13.22 | 29,848 | 17.0% | 43.5% |
| 4-gram | Subword | 13,090 | 13.68 | 130,341 | 12.8% | 40.9% |
| 5-gram | Word | 8,440 | 13.04 | 24,720 | 17.7% | 44.1% |
| 5-gram | Subword | 32,189 | 14.97 | 259,667 | 8.8% | 30.4% |
Top 5 N-grams by Size
2-grams (Word):
| Rank | N-gram | Count |
|---|---|---|
| 1 | Π±Π°ΡΠ½Π°Ρ ΡΠ»ΡΡΣΡΠ½Π°Ρ |
1,967 |
| 2 | Π΄Π°Π³ΡΡΡΡΠ°Π½ ΡΠ΅ΡΠΏΡΠ±Π»ΠΈΠΊΠ°Π΄ΠΈΠ½ |
1,527 |
| 3 | ΡΠ°ΠΉΠΎΠ½Π΄Π° Π°Π²Π°ΠΉ |
1,079 |
| 4 | ΡΠ°ΠΉΠΎΠ½Π΄ΠΈΠ½ Ρ
ΡΡΡΠ΅Ρ |
977 |
| 5 | ΠΌΡΡΡΡΠΌΠ°Π½Π°Ρ Ρ |
936 |
3-grams (Word):
| Rank | N-gram | Count |
|---|---|---|
| 1 | Π½Π° 1 ΡΠ½Π²Π°ΡΡ |
911 |
| 2 | ΡΡΠ½ΠΈ ΠΌΡΡΡΡΠΌΠ°Π½Π°Ρ Ρ |
815 |
| 3 | ΠΏΠΎ ΠΌΡΠ½ΠΈΡΠΈΠΏΠ°Π»ΡΠ½ΡΠΌ ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡΠΌ |
767 |
| 4 | 1 ΡΠ½Π²Π°ΡΡ Π³ |
765 |
| 5 | ΠΌΡΠ½ΠΈΡΠΈΠΏΠ°Π»ΡΠ½ΡΠΌ ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡΠΌ Π½Π° |
741 |
4-grams (Word):
| Rank | N-gram | Count |
|---|---|---|
| 1 | Π½Π° 1 ΡΠ½Π²Π°ΡΡ Π³ |
765 |
| 2 | ΠΏΠΎ ΠΌΡΠ½ΠΈΡΠΈΠΏΠ°Π»ΡΠ½ΡΠΌ ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡΠΌ Π½Π° |
741 |
| 3 | ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡΠΌ Π½Π° 1 ΡΠ½Π²Π°ΡΡ |
740 |
| 4 | ΠΌΡΠ½ΠΈΡΠΈΠΏΠ°Π»ΡΠ½ΡΠΌ ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡΠΌ Π½Π° 1 |
740 |
| 5 | ΡΠΎΡΡΠΈΠΉΡΠΊΠΎΠΉ ΡΠ΅Π΄Π΅ΡΠ°ΡΠΈΠΈ ΠΏΠΎ ΠΌΡΠ½ΠΈΡΠΈΠΏΠ°Π»ΡΠ½ΡΠΌ |
582 |
5-grams (Word):
| Rank | N-gram | Count |
|---|---|---|
| 1 | ΠΏΠΎ ΠΌΡΠ½ΠΈΡΠΈΠΏΠ°Π»ΡΠ½ΡΠΌ ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡΠΌ Π½Π° 1 |
740 |
| 2 | ΠΌΡΠ½ΠΈΡΠΈΠΏΠ°Π»ΡΠ½ΡΠΌ ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡΠΌ Π½Π° 1 ΡΠ½Π²Π°ΡΡ |
740 |
| 3 | ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡΠΌ Π½Π° 1 ΡΠ½Π²Π°ΡΡ Π³ |
707 |
| 4 | ΡΠΎΡΡΠΈΠΉΡΠΊΠΎΠΉ ΡΠ΅Π΄Π΅ΡΠ°ΡΠΈΠΈ ΠΏΠΎ ΠΌΡΠ½ΠΈΡΠΈΠΏΠ°Π»ΡΠ½ΡΠΌ ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡΠΌ |
582 |
| 5 | Π½Π°ΡΠ΅Π»Π΅Π½ΠΈΡ ΡΠΎΡΡΠΈΠΉΡΠΊΠΎΠΉ ΡΠ΅Π΄Π΅ΡΠ°ΡΠΈΠΈ ΠΏΠΎ ΠΌΡΠ½ΠΈΡΠΈΠΏΠ°Π»ΡΠ½ΡΠΌ |
582 |
2-grams (Subword):
| Rank | N-gram | Count |
|---|---|---|
| 1 | Π½ _ |
118,436 |
| 2 | ΠΈ Π½ |
101,992 |
| 3 | Π΄ ΠΈ |
90,630 |
| 4 | Π² Π° |
85,472 |
| 5 | Π° ΠΉ |
84,832 |
3-grams (Subword):
| Rank | N-gram | Count |
|---|---|---|
| 1 | ΠΈ Π½ _ |
77,249 |
| 2 | Π΄ ΠΈ Π½ |
55,033 |
| 3 | Π° ΠΉ _ |
41,524 |
| 4 | Π° Ρ _ |
27,897 |
| 5 | Π° Π½ _ |
27,614 |
4-grams (Subword):
| Rank | N-gram | Count |
|---|---|---|
| 1 | Π΄ ΠΈ Π½ _ |
50,137 |
| 2 | Ρ
Ρ Ρ Ρ |
18,492 |
| 3 | _ Ρ
Ρ Ρ |
17,463 |
| 4 | _ ΠΉ ΠΈ Ρ |
16,780 |
| 5 | Π² Π° ΠΉ _ |
14,217 |
5-grams (Subword):
| Rank | N-gram | Count |
|---|---|---|
| 1 | _ Ρ
Ρ Ρ Ρ |
16,863 |
| 2 | Ρ Π° ΠΉ ΠΎ Π½ |
10,265 |
| 3 | _ Ρ Π° ΠΉ ΠΎ |
10,222 |
| 4 | Π½ Π΄ ΠΈ Π½ _ |
9,537 |
| 5 | _ ΠΉ ΠΈ Ρ Π° |
8,563 |
Key Findings
- Best Perplexity: 2-gram (subword) with 378
- Entropy Trend: Decreases with larger n-grams (more predictable)
- Coverage: Top-1000 patterns cover ~30% 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 | 0.7069 | 1.632 | 4.39 | 95,463 | 29.3% |
| 1 | Subword | 0.9092 | 1.878 | 7.01 | 1,497 | 9.1% |
| 2 | Word | 0.1745 | 1.129 | 1.35 | 418,311 | 82.5% |
| 2 | Subword | 0.9040 | 1.871 | 5.60 | 10,485 | 9.6% |
| 3 | Word | 0.0504 | 1.036 | 1.09 | 565,039 | 95.0% |
| 3 | Subword | 0.8361 | 1.785 | 3.99 | 58,647 | 16.4% |
| 4 | Word | 0.0209 π | 1.015 | 1.04 | 611,226 | 97.9% |
| 4 | Subword | 0.6051 | 1.521 | 2.51 | 234,119 | 39.5% |
Generated Text Samples (Word-based)
Below are text samples generated from each word-based Markov chain model:
Context Size 1:
Π²Π° ΠΏΡΠΎΠΌΡΡΠ»Π΅Π½Π½ΠΎΡΡΠ΄ΠΈΠ½ ΠΈΠ½ΡΡΠΈΡΡΡ Ρ ΠΉΠΈΡΠ°Π½ ΡΡ ΠΈΡΠ΄Π° ΡΡΠ°Π½ΡΡΠ· ΡΣΠ°Π»Π°ΡΠ°Π» ΠΌΠ°Π½ΠΈΡΡ ΡΠ³ΡΡΠ½ΠΈΠ½ ΡΡΠ²Π°Ρ ΠΊΠ²Π°Π· ΠΏΠΎΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΈΠ΅...Ρ Π΄ΠΎΠ΄ΡΠ°Ρ ΡΣΠ²Π°Ρ Π²Π°Π½ Π°Π²Π°ΠΉ Ρ ΡΡΡ Π²ΠΈΡΠΈ ΡΠ°Π½Π°Π» ΠΈΡΠ»Π΅ΠΌΠΈΡ ΠΆΠ΅Π·Π²Π°ΠΉ ΠΎΡΠ΄ΠΆΠΎΠ½ΠΈΠΊΠΈΠ΄Π·Π΅Π΄ΠΈΠ½ ΡΣΠ²Π°ΡΡΠ½ΠΈΡ Ρ Π³Π°Π»Π°ΠΉ ΠΌΠ°ΠΊΡΠ°ΠΌΠ°ΡΠ΄ΠΈΠ½Π½...ΡΠΈΡ ΡΠ° ΡΠΈΠ»ΠΈΠ½ Π²ΠΈΠ½Π΅ Π°Π»Π° Π³Π°Π΄Π°ΡΣΠΈΠΉΠΈΡ ΡΡΡΡΡΠ½ ΠΌΡΠ³ΡΠ»Π΅ΠΉΡΠΈΠ½ ΡΣΠ²Π°ΡΠ°Ρ Π°Π»ΠΈΠΌΠ²ΠΈΠ»ΠΈΠ½ Π΄Π΅ΡΠ΅ΠΆΠ°Π΄ΠΈΠ½ ΠΌΠ΅ΠΊΡΠ΅Π±Π°Ρ ΠΊΣΠ²Π°Π»Π°Ρ Π·Π°Π²Π°ΠΉ ...
Context Size 2:
Π±Π°ΡΠ½Π°Ρ ΡΠ»ΡΡΣΡΠ½Π°Ρ ΠΏΠΎΡΠ΅Π»Π΅Π½ΠΈΠ΅ ΡΠ΅Π»ΠΎ ΡΡΠ°Π³ ΠΊΠ°Π·ΠΌΠ°Π»ΡΡ ΡΠ°ΠΉΠΎΠ½Π΄ΠΈΠ½ Ρ ΡΡΡΡΡΠ½ΡΠΎΠ²Π΅ΡΠ°Ρ Π²Π° Π°Π±ΡΡΡΠΊ Π°ΠΊΠ°ΡΠ·Π°Π²Π°ΠΉ Ρ ΡΡΡΠ΅Ρ ΠΈΡΠΏ...Π΄Π°Π³ΡΡΡΡΠ°Π½ ΡΠ΅ΡΠΏΡΠ±Π»ΠΈΠΊΠ°Π΄ΠΈΠ½ Π³ΡΡΠΊΡΠΌΠ°ΡΠ΄ΠΈΠ½ ΡΣΠ°Π» Π°Π²Π° ΡΠΌΡΠΌΠΈ ΡΠ° ΡΣΠ°Π» ΠΊΡΠ°Π±ΡΠ»Π½Π°ΡΠΈΡ Π³ΡΠ° Π° ΡΠΊΡΡΠ· Π°ΠΌ ΠΌΠΎΡΠΊΠ²Π°Π΄ΠΈΠ½ Π±Π°Π±Ρ...ΡΠ°ΠΉΠΎΠ½Π΄Π° Π°Π²Π°ΠΉ ΡΡΠ½Π²Π°ΠΉ Ρ ΡΡΡ Π±ΡΠ³ΡΠ΄Π° ΡΠ΅ΠΏΠ΅ ΡΣΠ²Π°Ρ ΡΡΠΈΠ³Π½Π°Π²Π°ΠΉ ΡΡ ΡΠΈ Π°ΡΠ°Π± ΡΣΠ°Π»Π°Π» ΠΊΡ ΡΠ΅Π½Π²Π°ΠΉ ΡΡΠ΅ΡΡΠΈΠ½ ΠΊΣΠ²Π°ΡΣΠ°Π» ΡΠ· Ρ...
Context Size 3:
Π½Π° 1 ΡΠ½Π²Π°ΡΡ Π³ 2 475 33 ΡΠΈΡΠ»Π΅Π½Π½ΠΎΡΡΡ ΠΏΠΎΡΡΠΎΡΠ½Π½ΠΎΠ³ΠΎ Π½Π°ΡΠ΅Π»Π΅Π½ΠΈΡ ΡΠΎΡΡΠΈΠΉΡΠΊΠΎΠΉ ΡΠ΅Π΄Π΅ΡΠ°ΡΠΈΠΈ ΠΏΠΎ ΠΌΡΠ½ΠΈΡΠΈΠΏΠ°Π»ΡΠ½ΡΠΌ ΠΎΠ±ΡΠ°Π·...ΡΡΠ½ΠΈ ΠΌΡΡΡΡΠΌΠ°Π½Π°Ρ Ρ ΠΉΠΈΡΠ°Π½ ΡΡΡΡΠ°Ρ ΠΈΠΌΠΏΠ΅ΡΠΈΡΠ΄ΠΈΠ½ Π°Π³ΡΠ°Π»ΠΈΡΡ ΡΠΈΡΠ³ΡΠ΄ΠΈΠ· ΠΊΡΠ°ΡΡΠ½ΠΈΠ½ Π½Π΅ΡΠΈΠΆΠ°Π΄Π° ΡΡΠ»ΠΊΠ²Π΅Π΄Π° ΠΊΡΠΈΡΠΈΡΣΠ°Ρ Π°Π²Π°...ΠΏΠΎ ΠΌΡΠ½ΠΈΡΠΈΠΏΠ°Π»ΡΠ½ΡΠΌ ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡΠΌ Π½Π° 1 ΡΠ½Π²Π°ΡΡ Π³ ΠΉΠΈΡΠ°Π½ Π°Π³ΡΠ°Π»ΠΈΡΡ ΡΠΈΡΠ³ΡΡΠΈΠ· ΠΊΡΠ°ΡΡΠ½ΠΈΠ½ Π½Π΅ΡΠΈΠΆΠ°ΡΠΈΠ· ΠΊΠΈΠ»ΠΈΠ³Π½Π° Ρ ΡΡΡΠ΅...
Context Size 4:
Π½Π° 1 ΡΠ½Π²Π°ΡΡ Π³ ΠΉΠΈΡΠ°Π½ Π°Π³ΡΠ°Π»ΠΈΡΡ ΡΠΈΡΠ³ΡΡΠΈΠ· ΠΊΡΠ°ΡΡΠ½ΠΈΠ½ Π½Π΅ΡΠΈΠΆΠ°ΠΉΡΠΈΠ· ΠΊΠΈΠ»ΠΈΠ³Π½Π° Ρ ΡΡΡΠ΅ 472 ΠΊΠ°ΡΠ΄ΠΈ ΡΡΡΠΌΡΡΡ ΠΈΠΉΠΈΠ·Π²Π°ΠΉΠ½Π°Ρ...ΠΏΠΎ ΠΌΡΠ½ΠΈΡΠΈΠΏΠ°Π»ΡΠ½ΡΠΌ ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡΠΌ Π½Π° 1 ΡΠ½Π²Π°ΡΡ Π³ 32 113 33 ΡΠΈΡΠ»Π΅Π½Π½ΠΎΡΡΡ ΠΏΠΎΡΡΠΎΡΠ½Π½ΠΎΠ³ΠΎ Π½Π°ΡΠ΅Π»Π΅Π½ΠΈΡ ΡΠ΅ΡΠΏΡΠ±Π»ΠΈΠΊΠΈ Π΄...ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡΠΌ Π½Π° 1 ΡΠ½Π²Π°ΡΡ Π³ 54 786 35 ΡΠΈΡΠ»Π΅Π½Π½ΠΎΡΡΡ ΠΏΠΎΡΡΠΎΡΠ½Π½ΠΎΠ³ΠΎ Π½Π°ΡΠ΅Π»Π΅Π½ΠΈΡ ΡΠΎΡΡΠΈΠΉΡΠΊΠΎΠΉ ΡΠ΅Π΄Π΅ΡΠ°ΡΠΈΠΈ ΠΏΠΎ ΠΌΡΠ½ΠΈΡ...
Generated Text Samples (Subword-based)
Below are text samples generated from each subword-based Markov chain model:
Context Size 1:
_ΠΏΡ_ΡΠΈΡΡ_Π°ΠΉΡΠ°._ΠΈΠ°Π³Π΅ΠΌΠ΅Π½_Π²ΠΊΡΠ΅ΡΠ°Π³Π°Π³ΠΈΡΠΏΠ°Ρ_Π°ΡΠ΅Π½_ΠΉΠ½_ΡΡ
Context Size 2:
Π½_Β«ΡΡ_ΡΡΠ°_ΡΣΠ΅ΡΠ΄ΠΈ_ΠΈΠ½_ΠΏΠ°Π½ΡΠ΅ΡΠΈΡΠ°Ρ_Π°ΡΠ²Π΄ΠΈ_Π°Π²ΡΠ·_ΠΊΡΡΡΡΠ΄Π°ΡΠ°
Context Size 3:
ΠΈΠ½_ΠΈΠ±ΡΠΈΠ½_Π΄ΠΈΠ΄Π΅Π»Π΅Π½ΠΎ_Π΄ΠΈΠ½_Ρ Π°Π»ΠΊΡ_ΡΠΈΠΏΠΏΠ°Π΄ΠΈΠ½Π°ΠΉ_Ρ Π°Π»ΠΊΣ_ΠΌΡΠ½ΠΈΡΠΈΠΏΠ°Π»
Context Size 4:
Π΄ΠΈΠ½_ΠΏΠ΅ΡΠ΅ΡΡΠ°_Π°Π·Π΅ΡΠ±Π°ΠΉΡ ΡΡΡΠ΅Ρ_Ρ._Π°Π΄Π°Π½_ΠΊΠ΅ΡΠΏ_Ρ ΡΡΡΡΡΠ½_Π°Π³ΡΠ°Π»ΠΈΡΡ_Π΄
Key Findings
- Best Predictability: Context-4 (word) with 97.9% predictability
- Branching Factor: Decreases with context size (more deterministic)
- Memory Trade-off: Larger contexts require more storage (234,119 contexts)
- Recommendation: Context-3 or Context-4 for text generation
4. Vocabulary Analysis
Statistics
| Metric | Value |
|---|---|
| Vocabulary Size | 36,658 |
| Total Tokens | 697,569 |
| Mean Frequency | 19.03 |
| Median Frequency | 3 |
| Frequency Std Dev | 143.41 |
Most Common Words
| Rank | Word | Frequency |
|---|---|---|
| 1 | Π²Π° | 11,171 |
| 2 | Ρ | 10,219 |
| 3 | ΡΠΈΡ | 5,987 |
| 4 | Π°Π²Π°ΠΉ | 5,477 |
| 5 | ΠΉΠΈΡΠ°Π½ | 5,251 |
| 6 | ΡΠ°ΠΉΠΎΠ½Π΄ΠΈΠ½ | 4,964 |
| 7 | ΠΉΠΈΡΡΠ· | 4,832 |
| 8 | Ρ ΡΡΡ | 4,422 |
| 9 | ΠΈ | 3,952 |
| 10 | Π°Π³ΡΠ°Π»ΠΈΡΡ | 3,896 |
Least Common Words (from vocabulary)
| Rank | Word | Frequency |
|---|---|---|
| 1 | ΡΡ | 2 |
| 2 | ΡΠ»ΠΊΡΡΡΡΠ½ | 2 |
| 3 | ΠΊΡΠΌΠ΅ΠΊΠ΄ΠΈΠ½ | 2 |
| 4 | ΡΠΎΠ»ΡΠ΅ΡΠΈΠ½ΠΎ | 2 |
| 5 | ΡΠΎΠ»ΡΠ΅ΡΠΈΠ½ΠΎΠ΄ΠΈΠΊΠ°ΠΉ | 2 |
| 6 | Ρ ΠΊΠΈΠ½Π°Ρ | 2 |
| 7 | ΣΣΣ | 2 |
| 8 | ΡΡΠΊΣΡΡΠΈΠ· | 2 |
| 9 | ΡΡΠΈΠ½ | 2 |
| 10 | ΠΊΡΠ°Π½Π°Π²Π΄ΠΈΠ½ | 2 |
Zipf's Law Analysis
| Metric | Value |
|---|---|
| Zipf Coefficient | 1.0501 |
| RΒ² (Goodness of Fit) | 0.994687 |
| Adherence Quality | excellent |
Coverage Analysis
| Top N Words | Coverage |
|---|---|
| Top 100 | 28.8% |
| Top 1,000 | 60.5% |
| Top 5,000 | 80.5% |
| Top 10,000 | 88.1% |
Key Findings
- Zipf Compliance: RΒ²=0.9947 indicates excellent adherence to Zipf's law
- High Frequency Dominance: Top 100 words cover 28.8% of corpus
- Long Tail: 26,658 words needed for remaining 11.9% 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 | 0.8458 | 0.3324 | N/A | N/A |
| mono_64d | 64 | 0.7103 | 0.2681 | N/A | N/A |
| mono_128d | 128 | 0.3532 | 0.2524 | N/A | N/A |
| aligned_32d | 32 | 0.8458 π | 0.3332 | 0.0120 | 0.1080 |
| aligned_64d | 64 | 0.7103 | 0.2750 | 0.0260 | 0.1320 |
| aligned_128d | 128 | 0.3532 | 0.2570 | 0.0300 | 0.1680 |
Key Findings
- Best Isotropy: aligned_32d with 0.8458 (more uniform distribution)
- Semantic Density: Average pairwise similarity of 0.2863. Lower values indicate better semantic separation.
- Alignment Quality: Aligned models achieve up to 3.0% 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 | 0.451 | 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 |
|---|---|
-ΠΊ |
ΠΊΠΈΡΠΈΠ²ΠΈΡΡ, ΠΊΠΎΠ»Π»Π΅ΠΊΡΠΈΠ²Π΄ΠΈ, ΠΊΡΠ°ΡΠ½ΠΎΡΡΡΠΊΠΎΠ³ΠΎ |
-Π° |
Π°ΡΠΏΠΈΡΠ°Π½Ρ, Π°Π²Π°Ρ ΡΠ·Π°Π²Π°ΠΉ, Π°ΡΡΡΠΌ |
-Ρ |
ΡΠΌΠΎΠΌΠΏΠΊ, ΡΠ΅Π»Π΅Π²ΠΊΠΈΠ΄ΡΠΈΠ½, ΡΠΈΠ΄Π°Π½Ρ |
-ΠΌ |
ΠΌΡΠ΅Π½ΡΠΊ, ΠΌΠ°Π΄ΡΠΈΠ΄Π΄Π°, ΠΌΠΈΡΠ·Π΅Π±ΡΡΠ°ΠΉ |
-Π³ |
Π³ΡΠ°ΠΏΡΡΡΠΈΡ Ρ, Π³ΡΠ°Π΄Π°Ρ Ρ, Π³ΠΎΡΠΎΠ΄Π΅ |
-Ρ |
ΡΠ΅Ρ Π½ΠΈΡΠ΅ΡΠΊΠΈΠΉ, ΡΡΡΠΊΠΌΠ΅Π½Π°Ρ, ΡΠ°Ρ ΡΠΈΡΠΊΠ°ΡΠ²ΠΈΠ»ΠΈΠ· |
-ΠΌΠ° |
ΠΌΠ°Π΄ΡΠΈΠ΄Π΄Π°, ΠΌΠ°Π³ΡΠ°ΡΠ°ΠΌΠ΄Ρ ΡΡΡΡΡΠ½, ΠΌΠ°Π»ΡΠΌΠ΄Π°ΠΉ |
-ΠΊΠ° |
ΠΊΠ°Π½Π²ΠΎΠ½Π΄ΠΎ, ΠΊΠ°ΠΉΡΠ°Π³ΠΈ, ΠΊΠ°ΠΌΠ΅Ρ |
Productive Suffixes
| Suffix | Examples |
|---|---|
-ΠΈΠ½ |
Ρ ΡΡΠ°ΡΠΈΠ½, Π΅ΡΠ΅Π²Π°Π½Π΄ΠΈΠ½, ΡΠ΅Π»Π΅Π²ΠΊΠΈΠ΄ΡΠΈΠ½ |
-Π½ |
Ρ ΡΡΠ°ΡΠΈΠ½, Π΅ΡΠ΅Π²Π°Π½Π΄ΠΈΠ½, ΡΠ°Π³ΡΠ°Π½ |
-Π° |
ΠΌΠ°Π΄ΡΠΈΠ΄Π΄Π°, ΡΠ°ΡΠ°ΡΠ°, Ρ ΡΠ°Π½Π²Π° |
-ΠΈ |
ΡΠΎΡΡΠΈΠΈ, ΠΊΠΎΠ»Π»Π΅ΠΊΡΠΈΠ²Π΄ΠΈ, Π³Π²Π°ΡΠ΄ΠΈΡΠ΄ΠΈ |
-ΠΉ |
ΡΠ³ΡΠ»ΠΈΠΉΡΠΈΠ»Π°ΠΉ, ΡΠ΅Ρ Π½ΠΈΡΠ΅ΡΠΊΠΈΠΉ, Π°Π²Π°Ρ ΡΠ·Π°Π²Π°ΠΉ |
-Π°ΠΉ |
ΡΠ³ΡΠ»ΠΈΠΉΡΠΈΠ»Π°ΠΉ, Π°Π²Π°Ρ ΡΠ·Π°Π²Π°ΠΉ, Π»Π΅ΠΆΠ±Π΅ΡΠ²ΠΈΠ»Π΅Π»Π°ΠΉ |
-Ρ |
ΡΡΡΠΊΠΌΠ΅Π½Π°Ρ, ΠΊΠΈΡΠΈΠ²ΠΈΡΡ, ΡΡΡΠΊΡΠ²Π°Π»Π°Ρ |
-Π°Ρ |
ΡΡΡΠΊΠΌΠ΅Π½Π°Ρ, ΡΡΡΠΊΡΠ²Π°Π»Π°Ρ, Π±ΠΈΠ·Π½Π΅ΡΠΌΠ΅Π½Π°Ρ |
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 |
|---|---|---|---|
ΠΈΡΠ΄ΠΈ |
2.07x | 37 contexts | ΡΠ½ΠΈΡΠ΄ΠΈ, Π΄Π°Π½ΠΈΡΠ΄ΠΈ, Π°ΡΠΌΠΈΡΠ΄ΠΈ |
Π°Π΄ΠΈΠ½ |
1.72x | 58 contexts | ΠΌΠ°Π΄ΠΈΠ½Π°, ΡΠΊΠ°Π΄ΠΈΠ½, ΡΡΠ°Π΄ΠΈΠ½ |
Π°Π»Π΄ΠΈ |
1.74x | 50 contexts | Π΄Π°Π»Π΄ΠΈ, ΡΣΠ°Π»Π΄ΠΈ, ΠΈΠ΄Π°Π»Π΄ΠΈ |
Π°ΠΉΠΎΠ½ |
2.02x | 28 contexts | ΡΠ°ΠΉΠΎΠ½, ΡΠ°ΠΉΠΎΠ½Ρ, ΡΠ°ΠΉΠΎΠ½Π° |
ΡΡΡΠ΅ |
1.65x | 44 contexts | Π³ΡΡΡΠ΅, ΡΡΡΠ΅Ρ, Ρ ΡΡΡΠ΅ |
Π΅Π³ΡΠ΅ |
1.78x | 33 contexts | Π·Π΅Π³ΡΠ΅, Π²Π΅Π³ΡΠ΅ΠΉ, ΡΠ΅Π³ΡΠ΅Ρ |
ΡΡΡΡ |
2.06x | 20 contexts | Ρ ΡΡΡΡΡ, ΠΊΡΡΡΡΡ, Ρ ΡΡΡΡΡΠΊ |
Π½Π΄ΠΈΠ½ |
1.78x | 30 contexts | Π΄ΠΈΠ½Π΄ΠΈΠ½, ΠΈΠΎΠ½Π΄ΠΈΠ½, ΡΠΎΠ½Π΄ΠΈΠ½ |
ΡΠ°ΠΉΠΎ |
2.10x | 17 contexts | ΡΠ°ΠΉΠΎΠ½, ΡΠ°ΠΉΠΎΠ½Ρ, ΡΠ°ΠΉΠΎΠ½Π° |
Π·Π°Π²Π° |
1.63x | 39 contexts | Π·Π°Π²Π°Π», ΡΠ·Π°Π²Π°, Π·Π°Π²Π°ΠΉ |
Π°Π³ΡΠ° |
1.52x | 48 contexts | Π°Π³ΡΠ°Π½, Π±Π°Π³ΡΠ°, ΡΠ°Π³ΡΠ° |
ΠΉΠΎΠ½Π΄ |
2.24x | 10 contexts | ΡΠ°ΠΉΠΎΠ½Π΄Π°, ΡΠ°ΠΉΠΎΠ½Π΄ΠΈ, ΡΠ°ΠΉΠΎΠ½Π΄Π°Π» |
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 |
|---|---|---|---|
-ΠΊ |
-Π½ |
194 words | ΠΊΣΠ²Π°ΡΠ΅ΡΠΈΠ½, ΠΊΡΠ°ΠΊΡΠ°Π½Π²ΠΈΠ»ΠΈΠ½ |
-ΠΊ |
-ΠΈΠ½ |
141 words | ΠΊΣΠ²Π°ΡΠ΅ΡΠΈΠ½, ΠΊΡΠ°ΠΊΡΠ°Π½Π²ΠΈΠ»ΠΈΠ½ |
-ΠΊ |
-ΠΉ |
121 words | ΠΊΡΠ°ΡΠΈΠ²Π°ΠΉ, ΠΊΡ ΡΠΈΡΠ°Π³ΡΠΈΠΊΠ°ΠΉ |
-Π³ |
-Π½ |
119 words | Π³ΡΠ°Π΄ΡΡΠ΄ΠΈΠ½, Π³ΡΠΈΠΊΠ°ΡΡΠ΄ΠΈΠ½ |
-Π° |
-Π½ |
117 words | Π°Π»ΠΈΠΌΠ΄ΠΈΠ½, Π°ΡΡΡΠ°Ρ Π°Π½ |
-ΠΌ |
-Π½ |
114 words | ΠΌΡΡΠ³ΡΡΡΠ΄ΠΈΠ½, ΠΌΡΡΠΆΡΡΠ³ΡΠ°ΡΡΠ΅ΡΠ°Π½ |
-ΠΊ |
-Ρ |
112 words | ΠΊΡΠ°ΠΉΠ΄Π°ΡΡ, ΠΊΡΠ°Ρ |
-ΠΊ |
-Π° |
112 words | ΠΊΠ°Π½Π΄Π°, ΠΊΡΡΡΠ΅Π΄Π° |
-ΠΊ |
-ΠΈ |
107 words | ΠΊΠΎΠ½ΡΡΠΈΡΡΡΠΈΠΈ, ΠΊΡΠΈΡΠΈΡΣΠ²ΠΈ |
-ΠΊ |
-Π°ΠΉ |
101 words | ΠΊΡΠ°ΡΠΈΠ²Π°ΠΉ, ΠΊΡ ΡΠΈΡΠ°Π³ΡΠΈΠΊΠ°ΠΉ |
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 |
|---|---|---|---|
| ΠΏΠΎΠ»ΠΊΠΎΠ²Π½ΠΈΠΊ | ΠΏΠΎΠ»ΠΊΠΎΠ²-Π½-ΠΈΠΊ |
7.5 | Π½ |
| ΡΠ΅ΠΊΡΠ΅ΡΠΈΡ Ρ | ΡΠ΅ΠΊΡΠ΅Ρ-ΠΈ-Ρ
Ρ |
7.5 | ΠΈ |
| ΡΡΠ·Π±Π΅ΠΊΠΈΡΡΠ°Π½Π΄Π° | ΡΡΠ·Π±Π΅ΠΊΠΈΡΡΠ°-Π½-Π΄Π° |
7.5 | Π½ |
| ΡΡΡΡ ΠΊΣΡΡΡΡΠ½ΠΈΠ½ | ΡΡΡΡ
ΠΊΣΡΡΡΡ-Π½-ΠΈΠ½ |
7.5 | Π½ |
| Π±ΠΈΠ·Π½Π΅ΡΠΌΠ΅Π½Π°Ρ | Π±ΠΈΠ·Π½Π΅ΡΠΌΠ΅-Π½-Π°Ρ |
7.5 | Π½ |
| ΠΊΡΡΡΠ°Π³ΡΡΠΈΠ½ | ΠΊΡΡΡΠ°Π³Ρ-Ρ-ΠΈΠ½ |
7.5 | Ρ |
| Π΄Π°Π²Π°ΠΌΠ°ΡΠ΄Π° | Π΄Π°Π²Π°ΠΌ-Π°Ρ-Π΄Π° |
7.5 | Π°Ρ |
| ΡΠΏΡΠ°ΠΆΠ½Π΅Π½ΠΈΡ | ΡΠΏΡΠ°ΠΆΠ½Π΅-Π½-ΠΈΡ |
7.5 | Π½ |
| ΡΡΡΠ±ΠΎΠ»ΠΊΠ°ΡΡ | ΡΡΡΠ±ΠΎΠ»ΠΊ-Π°-ΡΡ |
7.5 | Π° |
| ΡΣΠ²Π°ΡΠ°ΡΠΈΠΊ | ΡΣΠ²Π°Ρ-Π°Ρ-ΠΈΠΊ |
7.5 | Π°Ρ |
| Π°Π»Π°ΠΊΡΡΠ½ΠΈΠ½ | Π°Π»Π°ΠΊΡΡ-Π½-ΠΈΠ½ |
7.5 | Π½ |
| ΠΎΠΊΡΡΠ±ΡΡΠ΄ΠΈΠ»Π°ΠΉ | ΠΎΠΊΡΡΠ±ΡΡΠ΄ΠΈ-Π»-Π°ΠΉ |
7.5 | Π» |
| ΡΡΡΡ ΠΊΣΡΡΡΠ½Π° | ΡΡΡΡ
ΠΊΣΡΡΡ-Π½-Π° |
7.5 | Π½ |
| ΠΎΠ±ΡΠ΅ΡΡΠ²Π΅Π½Π½Π°Ρ | ΠΎΠ±ΡΠ΅ΡΡΠ²Π΅Π½-Π½-Π°Ρ |
7.5 | Π½ |
| ΡΡΡΠΊΣΡΡΡΠ΄Π°Π»Π΄ΠΈ | ΡΡΡΠΊΣΡΡΡΠ΄-Π°Π»-Π΄ΠΈ |
7.5 | Π°Π» |
6.6 Linguistic Interpretation
Automated Insight: The language Lezgian 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 (4.46x) |
| N-gram | 2-gram | Lowest perplexity (378) |
| Markov | Context-4 | Highest predictability (97.9%) |
| 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 10:28:15



















