Erzya - Wikilangs Models
Comprehensive Research Report & Full Ablation Study
This repository contains NLP models trained and evaluated by Wikilangs, specifically on Erzya 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 | 3.359x | 3.36 | 0.1174% | 282,726 |
| 16k | 3.657x | 3.66 | 0.1279% | 259,662 |
| 32k | 3.923x | 3.93 | 0.1371% | 242,074 |
| 64k | 4.104x π | 4.11 | 0.1435% | 231,386 |
Tokenization Examples
Below are sample sentences tokenized with each vocabulary size:
Sample 1: ΠΠΈΠΈΡΠ»ΠΎΠ²Π° () β ΡΠ΅ Π²Π΅Π»Π΅ΡΡ ΠΡΡΡΠ½Ρ ΠΠ°ΡΡΠΎΡΡΠΎ ΠΡΡΡΠΌΠ°Π° ΡΠ½ΠΊΡΡΠΎ. Π‘ΡΡΠΌ. ΠΠ°ΡΡΠΎΡ ΠΠ°ΡΡΠΎΡΠΎΠ½ΡΡ ...
| Vocab | Tokens | Count |
|---|---|---|
| 8k | βΠΊΠΈ ΠΈΡ Π»ΠΎΠ²Π° β() ββ βΡΠ΅ βΠ²Π΅Π»Π΅ΡΡ βΡΡΡΡΠ½Ρ βΠΌΠ°ΡΡΠΎΡΡΠΎ βΠ²ΡΡΡΠΌΠ°Π° ... (+7 more) |
17 |
| 16k | βΠΊΠΈ ΠΈΡ Π»ΠΎΠ²Π° β() ββ βΡΠ΅ βΠ²Π΅Π»Π΅ΡΡ βΡΡΡΡΠ½Ρ βΠΌΠ°ΡΡΠΎΡΡΠΎ βΠ²ΡΡΡΠΌΠ°Π° ... (+7 more) |
17 |
| 32k | βΠΊΠΈ ΠΈΡ Π»ΠΎΠ²Π° β() ββ βΡΠ΅ βΠ²Π΅Π»Π΅ΡΡ βΡΡΡΡΠ½Ρ βΠΌΠ°ΡΡΠΎΡΡΠΎ βΠ²ΡΡΡΠΌΠ°Π° ... (+7 more) |
17 |
| 64k | βΠΊΠΈΠΈΡΠ»ΠΎΠ²Π° β() ββ βΡΠ΅ βΠ²Π΅Π»Π΅ΡΡ βΡΡΡΡΠ½Ρ βΠΌΠ°ΡΡΠΎΡΡΠΎ βΠ²ΡΡΡΠΌΠ°Π° βΡΠ½ΠΊΡΡΠΎ . ... (+5 more) |
15 |
Sample 2: ΠΠ΅ΠΏΠ°ΠΌΠΈΡΡ Π»ΡΠΌΠ±Π°ΠΌΠΎΡ β Π»ΡΠΌΠ±ΠΈΡΡ Π»ΡΠΊΠ°ΠΌΠΎΡΡ, ΠΊΠΎΠ½Π° Π°Π»ΡΠΌΠ΅Π·Ρ Π°Π»Π°ΠΌΠΎΠ»Π³Π°Π΄Ρ ΡΠΊΠ°Π½ΡΠ±Π΅ΡΡΡ.
| Vocab | Tokens | Count |
|---|---|---|
| 8k | βΠ»Π΅ ΠΏΠ° ΠΌ ΠΈΡΡ βΠ»Ρ ΠΌΠ±Π° ΠΌΠΎΡ ββ βΠ»Ρ ΠΌΠ± ... (+16 more) |
26 |
| 16k | βΠ»Π΅ ΠΏΠ°ΠΌ ΠΈΡΡ βΠ»Ρ ΠΌΠ±Π° ΠΌΠΎΡ ββ βΠ»Ρ ΠΌΠ± ΠΈΡΡ ... (+15 more) |
25 |
| 32k | βΠ»Π΅ ΠΏΠ°ΠΌ ΠΈΡΡ βΠ»Ρ ΠΌΠ±Π° ΠΌΠΎΡ ββ βΠ»Ρ ΠΌΠ± ΠΈΡΡ ... (+12 more) |
22 |
| 64k | βΠ»Π΅ ΠΏΠ°ΠΌ ΠΈΡΡ βΠ»Ρ ΠΌΠ±Π° ΠΌΠΎΡ ββ βΠ»Ρ ΠΌΠ± ΠΈΡΡ ... (+9 more) |
19 |
Sample 3: ΠΠ°ΡΠΈΡ ΠΡΠ»Π΅Π³ΠΈΠ½Π° (); ΡΠ°Ρ. Π£ΠΌΠ°ΡΡΠΊΠΎΠ²ΠΎΠ½Ρ 9 ΡΠΈΡΡΡ, ΠΠ΄Π΅ΡΡΠ° ΠΎΡ, Π‘Π‘Π‘Π ) β ΠΌΠΎΡΡΡΡ (ΡΠΎΠΏΡΠ°Π½ΠΎ)...
| Vocab | Tokens | Count |
|---|---|---|
| 8k | βΠΌΠ°ΡΠΈΡ βΠ³Ρ Π»Π΅ Π³ ΠΈΠ½Π° β(); βΡΠ°Ρ . βΡΠΌΠ°ΡΡΠΊΠΎΠ²ΠΎΠ½Ρ β ... (+14 more) |
24 |
| 16k | βΠΌΠ°ΡΠΈΡ βΠ³Ρ Π»Π΅ Π³ΠΈΠ½Π° β(); βΡΠ°Ρ . βΡΠΌΠ°ΡΡΠΊΠΎΠ²ΠΎΠ½Ρ β 9 ... (+12 more) |
22 |
| 32k | βΠΌΠ°ΡΠΈΡ βΠ³Ρ Π»Π΅ Π³ΠΈΠ½Π° β(); βΡΠ°Ρ . βΡΠΌΠ°ΡΡΠΊΠΎΠ²ΠΎΠ½Ρ β 9 ... (+12 more) |
22 |
| 64k | βΠΌΠ°ΡΠΈΡ βΠ³ΡΠ»Π΅Π³ΠΈΠ½Π° β(); βΡΠ°Ρ . βΡΠΌΠ°ΡΡΠΊΠΎΠ²ΠΎΠ½Ρ β 9 βΡΠΈΡΡΡ , ... (+10 more) |
20 |
Key Findings
- Best Compression: 64k achieves 4.104x compression
- Lowest UNK Rate: 8k with 0.1174% 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 | 5,234 | 12.35 | 13,565 | 19.1% | 50.0% |
| 2-gram | Subword | 451 π | 8.82 | 4,411 | 55.9% | 96.7% |
| 3-gram | Word | 5,809 | 12.50 | 17,643 | 20.4% | 49.4% |
| 3-gram | Subword | 3,849 | 11.91 | 34,647 | 20.1% | 61.1% |
| 4-gram | Word | 9,800 | 13.26 | 32,090 | 18.1% | 43.0% |
| 4-gram | Subword | 19,085 | 14.22 | 156,710 | 10.3% | 34.9% |
| 5-gram | Word | 7,606 | 12.89 | 25,413 | 19.9% | 46.5% |
| 5-gram | Subword | 51,060 | 15.64 | 321,204 | 6.8% | 24.6% |
Top 5 N-grams by Size
2-grams (Word):
| Rank | N-gram | Count |
|---|---|---|
| 1 | Π²Π½ ΠΈΡΡΡΠΆΠΎ |
1,572 |
| 2 | ΡΠΎΠ΄Π°Π²ΠΈΠΊΡ Π»ΠΎΠΌΠ°Π½ΡΡ |
1,490 |
| 3 | Π»ΠΎΠΌΠ°Π½ΡΡ ΡΠ΅ |
1,467 |
| 4 | ΡΠ΅ Π²Π΅Π»Π΅ΡΡΡΠ½ΡΡ |
1,405 |
| 5 | Π²Π΅Π»Π΅Π½ΡΡ Π»Π΅ΠΌΠ΄Π΅Π½ΡΡ |
1,393 |
3-grams (Word):
| Rank | N-gram | Count |
|---|---|---|
| 1 | ΡΠΎΠ΄Π°Π²ΠΈΠΊΡ Π»ΠΎΠΌΠ°Π½ΡΡ ΡΠ΅ |
1,461 |
| 2 | Π»ΠΎΠΌΠ°Π½ΡΡ ΡΠ΅ Π²Π΅Π»Π΅ΡΡΡΠ½ΡΡ |
1,405 |
| 3 | ΡΡΠΈΡΡΡΠ½Π΅ ΡΠ°ΡΡΠΊΠ΅Π½Ρ ΡΠΎΡΡΠ°Π² |
1,059 |
| 4 | ΡΠ°ΡΡΠΊΠ΅Π½Ρ ΡΠΎΡΡΠ°Π² Π²Π΅ΡΠ΅ΡΠΎΡΡΠΈΡΠ½Ρ |
1,054 |
| 5 | ΡΠΎΡΡΠ°Π² Π²Π΅ΡΠ΅ΡΠΎΡΡΠΈΡΠ½Ρ ΠΏΠ΅ΡΠ΅ΠΏΠΈΡΡ |
1,039 |
4-grams (Word):
| Rank | N-gram | Count |
|---|---|---|
| 1 | ΡΠΎΠ΄Π°Π²ΠΈΠΊΡ Π»ΠΎΠΌΠ°Π½ΡΡ ΡΠ΅ Π²Π΅Π»Π΅ΡΡΡΠ½ΡΡ |
1,405 |
| 2 | ΡΡΠΈΡΡΡΠ½Π΅ ΡΠ°ΡΡΠΊΠ΅Π½Ρ ΡΠΎΡΡΠ°Π² Π²Π΅ΡΠ΅ΡΠΎΡΡΠΈΡΠ½Ρ |
1,044 |
| 3 | ΡΠ°ΡΡΠΊΠ΅Π½Ρ ΡΠΎΡΡΠ°Π² Π²Π΅ΡΠ΅ΡΠΎΡΡΠΈΡΠ½Ρ ΠΏΠ΅ΡΠ΅ΠΏΠΈΡΡ |
1,039 |
| 4 | Π²Π΅ΡΠ΅ΡΠΎΡΡΠΈΡΠ½Ρ ΠΏΠ΅ΡΠ΅ΠΏΠΈΡΡ Π½Π°ΡΠ΅Π»Π΅Π½ΠΈΡ ΠΈΠ΅ |
1,039 |
| 5 | ΡΠΎΡΡΠ°Π² Π²Π΅ΡΠ΅ΡΠΎΡΡΠΈΡΠ½Ρ ΠΏΠ΅ΡΠ΅ΠΏΠΈΡΡ Π½Π°ΡΠ΅Π»Π΅Π½ΠΈΡ |
1,039 |
5-grams (Word):
| Rank | N-gram | Count |
|---|---|---|
| 1 | ΡΠΎΡΡΠ°Π² Π²Π΅ΡΠ΅ΡΠΎΡΡΠΈΡΠ½Ρ ΠΏΠ΅ΡΠ΅ΠΏΠΈΡΡ Π½Π°ΡΠ΅Π»Π΅Π½ΠΈΡ ΠΈΠ΅ |
1,039 |
| 2 | ΡΠ°ΡΡΠΊΠ΅Π½Ρ ΡΠΎΡΡΠ°Π² Π²Π΅ΡΠ΅ΡΠΎΡΡΠΈΡΠ½Ρ ΠΏΠ΅ΡΠ΅ΠΏΠΈΡΡ Π½Π°ΡΠ΅Π»Π΅Π½ΠΈΡ |
1,039 |
| 3 | ΡΡΠΈΡΡΡΠ½Π΅ ΡΠ°ΡΡΠΊΠ΅Π½Ρ ΡΠΎΡΡΠ°Π² Π²Π΅ΡΠ΅ΡΠΎΡΡΠΈΡΠ½Ρ ΠΏΠ΅ΡΠ΅ΠΏΠΈΡΡ |
1,032 |
| 4 | ΡΠΎΠ΄Π°Π²ΠΈΠΊΡ Π»ΠΎΠΌΠ°Π½ΡΡ ΡΠ΅ Π²Π΅Π»Π΅ΡΡΡΠ½ΡΡ ΡΡΠΈΡΡΡΠ½Π΅ |
946 |
| 5 | ΡΡΡΠΌΠΎΠ·ΠΎ ΡΠΎΠ΄Π°Π²ΠΈΠΊΡ Π»ΠΎΠΌΠ°Π½ΡΡ ΡΠ΅ Π²Π΅Π»Π΅ΡΡΡΠ½ΡΡ |
917 |
2-grams (Subword):
| Rank | N-gram | Count |
|---|---|---|
| 1 | Ρ _ |
153,248 |
| 2 | . _ |
92,452 |
| 3 | Π½ Ρ |
90,818 |
| 4 | Ρ Ρ |
68,788 |
| 5 | , _ |
66,880 |
3-grams (Subword):
| Rank | N-gram | Count |
|---|---|---|
| 1 | Π½ Ρ _ |
80,150 |
| 2 | Ρ Ρ _ |
36,047 |
| 3 | _ β _ |
29,408 |
| 4 | ΠΎ Π½ Ρ |
26,266 |
| 5 | Π΅ Π½ Ρ |
26,109 |
4-grams (Subword):
| Rank | N-gram | Count |
|---|---|---|
| 1 | ΠΎ Π½ Ρ _ |
24,242 |
| 2 | Π΅ Π½ Ρ _ |
22,554 |
| 3 | Π½ Ρ Ρ _ |
20,388 |
| 4 | _ Π² Π΅ Π» |
13,694 |
| 5 | Π² Π΅ Π» Π΅ |
12,902 |
5-grams (Subword):
| Rank | N-gram | Count |
|---|---|---|
| 1 | _ Π² Π΅ Π» Π΅ |
12,574 |
| 2 | Π΅ Π½ Ρ Ρ _ |
8,208 |
| 3 | Π² ΠΎ Π½ Ρ _ |
7,157 |
| 4 | ΠΎ Π² ΠΎ Π½ Ρ |
6,844 |
| 5 | ΠΈ Ρ Π½ Ρ _ |
6,197 |
Key Findings
- Best Perplexity: 2-gram (subword) with 451
- Entropy Trend: Decreases with larger n-grams (more predictable)
- Coverage: Top-1000 patterns cover ~25% 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 | 0.6530 | 1.572 | 3.67 | 122,977 | 34.7% |
| 1 | Subword | 1.2973 | 2.458 | 11.50 | 833 | 0.0% |
| 2 | Word | 0.1469 | 1.107 | 1.28 | 449,631 | 85.3% |
| 2 | Subword | 1.1429 | 2.208 | 6.92 | 9,577 | 0.0% |
| 3 | Word | 0.0456 | 1.032 | 1.08 | 573,707 | 95.4% |
| 3 | Subword | 0.8768 | 1.836 | 4.15 | 66,234 | 12.3% |
| 4 | Word | 0.0224 π | 1.016 | 1.04 | 613,293 | 97.8% |
| 4 | Subword | 0.6169 | 1.534 | 2.56 | 274,547 | 38.3% |
Generated Text Samples (Word-based)
Below are text samples generated from each word-based Markov chain model:
Context Size 1:
Π΄Ρ ΠΊΠ°ΡΡ ΡΠ΅Π΄Π΅ Π»Π°ΠΌΠΎ ΠΌ ΠΈ Π± Π² ΡΠΈΠ½Π½ΠΎ ΡΠ³ΠΎΡΡΠΊΠΈΠΉ ΠΏΡΠΎΡΡΠ² ΡΠ΅ΠΊΡΡ Π±ΠΈΠΎΠ³ΡΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠΉ ΡΠΈΠ»ΡΠΌ Π±Π΅Π· ΠΈΡΡΠΎΡΠ½ΠΈΠΊΠΎΠ²Π² ΡΡΠ·Π΄Π°Π»Ρ Π½Π° ΡΠΆΠ½ΠΈΡ ΠΏΠΎΠ»ΡΡ Ρ ΡΡΡ ΡΡΠ·ΡΠ½ isbn url consultato il 21 8 ΡΠΈΡΡΡ ΠΊΠ°Π»ΠΈΠ½ΠΎΠ²ΠΊΠ°ΠΈ Π΄ Π² ΡΡΠ·Π°Π½ΠΊΠΈΠ½ Π½ Π½ΠΎΠ²Π³ΠΎΡΠΎΠ΄ Π°Π½Π³Π»ΠΎ Ρ ΠΈΠ½Π΄ΠΈ ΡΡΡΡΠΊΠΈΠΉ ΡΠ»ΠΎΠ²Π°ΡΡ ΠΎΠΊ Π½Π°Π·Π² Π° ΠΊΠ΅Π½Π΅ΡΠ΅Π·Ρ Π»ΡΠΌΠ·ΡΡΠΊΡΡΠΎ ΠΏΠΎΡΠΎΠ΄ΠΎΠ·Ρ
Context Size 2:
Π²Π½ ΠΈΡΡΡΠΆΠΎ ΡΠ°ΡΡΠ°ΠΌΠΊΠΎΠ²ΠΎΠ½Ρ 12 ΡΠΈΡΡΡ ΡΠ°ΡΠ°Π½ ΠΎΡΡΠΎ ΠΊΠ°Π»ΠΌΠ°Π·ΠΎ Π°ΠΏΠ°ΠΊ ΡΠ²ΡΠ° ΡΠ΅ΠΊΡΠΊΠ°ΠΊ Π²Π΅Π»Π΅Π½Ρ ΠΏΡΠΎΠ΄Π΅ΡΡΡΡΡ ΠΈΡΡΡΠΌΠΎ ΡΡΠ½ΡΡ ...ΡΠΎΠ΄Π°Π²ΠΈΠΊΡ Π»ΠΎΠΌΠ°Π½ΡΡ ΡΠ΅ Π²Π΅Π»Π΅ΡΡΡΠ½ΡΡ Π²Π΅Π»Π΅Π½ΡΡ ΡΡΡΠΌΠΎΠ·ΠΎ ΡΠΎΠ΄Π°Π²ΠΈΠΊΡ Π»ΠΎΠΌΠ°Π½ΡΡ ΡΠ΅ Π²Π΅Π»Π΅ΡΡΡΠ½ΡΡ Π²Π΅Π»Π΅Π½ΡΡ ΡΡΡΠΌΠΎΠ·ΠΎ ΡΠΎΠ΄Π°Π²ΠΈ...Π»ΠΎΠΌΠ°Π½ΡΡ ΡΠ΅ Π²Π΅Π»Π΅ΡΡΡΠ½ΡΡ ΡΡΠΈΡΡΡΠ½Π΅ ΡΠ°ΡΡΠΊΠ΅Π½Ρ ΡΠΎΡΡΠ°Π² Π²Π΅ΡΠ΅ΡΠΎΡΡΠΈΡΠ½Ρ ΠΏΠ΅ΡΠ΅ΠΏΠΈΡΡ Π½Π°ΡΠ΅Π»Π΅Π½ΠΈΡ ΠΈΠ΅ ΡΡΠ·Ρ 56 Π²Π΅Π»Π΅ΡΡ ΠΎΡΠΎ...
Context Size 3:
ΡΠΎΠ΄Π°Π²ΠΈΠΊΡ Π»ΠΎΠΌΠ°Π½ΡΡ ΡΠ΅ Π²Π΅Π»Π΅ΡΡΡΠ½ΡΡ Π²Π΅Π»Π΅Π½ΡΡ ΡΡΡΠΌΠΎΠ·ΠΎ ΡΡΠΈΡΡΡΠ½Π΅ ΡΠ°ΡΡΠΊΠ΅Π½Ρ ΡΠΎΡΡΠ°Π² Π²Π΅ΡΠ΅ΡΠΎΡΡΠΈΡΠ½Ρ ΠΏΠ΅ΡΠ΅ΠΏΠΈΡΡ Π½Π°ΡΠ΅Π»Π΅...Π»ΠΎΠΌΠ°Π½ΡΡ ΡΠ΅ Π²Π΅Π»Π΅ΡΡΡΠ½ΡΡ ΡΡΠΈΡΡΡΠ½Π΅ ΡΠ°ΡΡΠΊΠ΅Π½Ρ ΡΠΎΡΡΠ°Π² Π²Π΅ΡΠ΅ΡΠΎΡΡΠΈΡΠ½Ρ ΠΏΠ΅ΡΠ΅ΠΏΠΈΡΡ Π½Π°ΡΠ΅Π»Π΅Π½ΠΈΡ ΠΈΠ΅ ΡΡΠ·Ρ 93 Π²Π΅Π»Π΅ΡΡ Π²Π΅Π»...ΡΡΠΈΡΡΡΠ½Π΅ ΡΠ°ΡΡΠΊΠ΅Π½Ρ ΡΠΎΡΡΠ°Π² Π²Π΅ΡΠ΅ΡΠΎΡΡΠΈΡΠ½Ρ ΡΡΠΈΡΡΡΠ½Π΅Π½Ρ ΡΡΡΠΌΠ°Π΄ΡΡΠΎΠΌΠ°Π½ΡΡ ΠΈΠ΅ ΠΊΠΎΡΡΡ ΡΡΠ·Ρ 100 ΡΠΎΠ΄Π°Π²ΠΈΠΊΡ Π»ΠΎΠΌΠ°Π½ΡΡ Ρ...
Context Size 4:
ΡΠΎΠ΄Π°Π²ΠΈΠΊΡ Π»ΠΎΠΌΠ°Π½ΡΡ ΡΠ΅ Π²Π΅Π»Π΅ΡΡΡΠ½ΡΡ ΡΡΠΈΡΡΡΠ½Π΅ ΡΠ°ΡΡΠΊΠ΅Π½Ρ ΡΠΎΡΡΠ°Π² Π²Π΅ΡΠ΅ΡΠΎΡΡΠΈΡΠ½Ρ ΠΏΠ΅ΡΠ΅ΠΏΠΈΡΡ Π½Π°ΡΠ΅Π»Π΅Π½ΠΈΡ ΠΈΠ΅ ΡΡΠ·Ρ 95 Ρ...ΡΡΠΈΡΡΡΠ½Π΅ ΡΠ°ΡΡΠΊΠ΅Π½Ρ ΡΠΎΡΡΠ°Π² Π²Π΅ΡΠ΅ΡΠΎΡΡΠΈΡΠ½Ρ ΠΏΠ΅ΡΠ΅ΠΏΠΈΡΡ Π½Π°ΡΠ΅Π»Π΅Π½ΠΈΡ ΠΈΠ΅ ΡΡΠ·Ρ 100 Π²Π΅Π»Π΅ΡΡ Π±ΡΠ΅Π½Ρ Π²Π΅Π»Π΅ΡΡΠ²Π΅ΡΠ΅ΡΠΎΡΡΠΈΡΠ½Ρ ΠΏΠ΅ΡΠ΅ΠΏΠΈΡΡ Π½Π°ΡΠ΅Π»Π΅Π½ΠΈΡ ΠΈΠ΅ ΠΏΠ΅ΡΠΊΠ°ΡΡ 100 Π²Π΅Π»Π΅ΡΡ Π²Π΅Π»Π΅ΡΡ
Generated Text Samples (Subword-based)
Below are text samples generated from each subword-based Markov chain model:
Context Size 1:
_Π²Π΅Π½Ρ_ΠΊΡΠ»ΠΌΠΈΠΈΡΡΠ΅ΡΠΎΠ»ΠΈΡΠΌΠΎΡΡ _Ρ_ΠΌΠ΅Π½ΠΈΠ·Π°Π²_ΠΏΠΎΠΊΡΡΠ²Π°ΡΡ_Π°_ΠΊ
Context Size 2:
Ρ_ΠΊΠΈΡ _Π½ΠΎΠ²ΠΈΡΡ_ΡΠ»Π΅_._Π²Π°Π»ΡΠΈΡ_ΠΌΠ΅Π½Ρ_(ΡΡΠ½Ρ_ΡΡΠΈΡΠΎΡΡΠ°ΡΠ°Π½ΠΈΠ»ΠΈ
Context Size 3:
Π½Ρ_Π°ΡΡΠ΅ΠΌΠ°Π½ΡΠΎΠ»ΠΈΠΊΠ°Π½ΠΈΡΡ_ΡΠΊΠΎΡΡ_ΠΎΠΏΠ»Π°Π½Π³ΡΠΎ__β_Π²Π΅Π΄ΡΠ΅ΡΠΊΠΈΠ΅_Ρ_Π΅Π²Ρ
Context Size 4:
ΠΎΠ½Ρ_ΡΠ°Π»,_Π·Π°ΠΏΠΈΡΡ_Π½Π°ΡΠ΅Π½Ρ_Π΄Ρ_ΡΠΌΠ°Π½ΠΈΡΠ΅ΡΠΊΠΈΠΉ_Π½ΡΡ_ΡΡΡΠΌΠΎΠ½Π·ΠΎ_ΡΠΎΠΊΠ°Π»Ρ
Key Findings
- Best Predictability: Context-4 (word) with 97.8% predictability
- Branching Factor: Decreases with context size (more deterministic)
- Memory Trade-off: Larger contexts require more storage (274,547 contexts)
- Recommendation: Context-3 or Context-4 for text generation
4. Vocabulary Analysis
Statistics
| Metric | Value |
|---|---|
| Vocabulary Size | 47,484 |
| Total Tokens | 705,946 |
| Mean Frequency | 14.87 |
| Median Frequency | 3 |
| Frequency Std Dev | 119.73 |
Most Common Words
| Rank | Word | Frequency |
|---|---|---|
| 1 | Π΄Ρ | 10,760 |
| 2 | Π² | 8,187 |
| 3 | ΠΈ | 6,467 |
| 4 | Ρ | 6,350 |
| 5 | Π° | 5,547 |
| 6 | ΡΠ΅ | 5,228 |
| 7 | ΠΌ | 4,398 |
| 8 | ΠΈΠ΅ΡΡΡ | 3,988 |
| 9 | ΡΠ»ΡΠ½Π΅ΡΡ | 3,596 |
| 10 | ΠΈΠ΅ | 3,563 |
Least Common Words (from vocabulary)
| Rank | Word | Frequency |
|---|---|---|
| 1 | ΡΠΊΡΠ°ΠΌΠ°ΡΡΠ½ΡΡ | 2 |
| 2 | Π°Π½Π°Π»ΠΎΠ³ΠΎΠ·ΠΎ | 2 |
| 3 | Π΄ΠΎΠΌΠΈΠ½ΠΈΡΠΊ | 2 |
| 4 | indeks | 2 |
| 5 | grup | 2 |
| 6 | zawodowych | 2 |
| 7 | muzea | 2 |
| 8 | britishpedia | 2 |
| 9 | osobistoΕci | 2 |
| 10 | bph | 2 |
Zipf's Law Analysis
| Metric | Value |
|---|---|
| Zipf Coefficient | 1.0126 |
| RΒ² (Goodness of Fit) | 0.996053 |
| Adherence Quality | excellent |
Coverage Analysis
| Top N Words | Coverage |
|---|---|
| Top 100 | 27.1% |
| Top 1,000 | 55.8% |
| Top 5,000 | 75.1% |
| Top 10,000 | 83.0% |
Key Findings
- Zipf Compliance: RΒ²=0.9961 indicates excellent adherence to Zipf's law
- High Frequency Dominance: Top 100 words cover 27.1% of corpus
- Long Tail: 37,484 words needed for remaining 17.0% 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 | 0.8628 π | 0.3405 | N/A | N/A |
| mono_64d | 64 | 0.7101 | 0.2786 | N/A | N/A |
| mono_128d | 128 | 0.2558 | 0.2702 | N/A | N/A |
| aligned_32d | 32 | 0.8628 | 0.3424 | 0.0280 | 0.1300 |
| aligned_64d | 64 | 0.7101 | 0.2772 | 0.0360 | 0.1540 |
| aligned_128d | 128 | 0.2558 | 0.2675 | 0.0700 | 0.2380 |
Key Findings
- Best Isotropy: mono_32d with 0.8628 (more uniform distribution)
- Semantic Density: Average pairwise similarity of 0.2961. Lower values indicate better semantic separation.
- Alignment Quality: Aligned models achieve up to 7.0% 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 | 0.892 | 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 |
ΠΊΠ΅ΠΌΠΊΠ°Π²ΡΠΎΠ²ΠΎ, ΠΊΠ°Π½ΡΠ½ΠΈΡΡ, ΠΊΠ»Π°Π²Π΄ΠΈΠΉ |
-Ρ |
ΡΠ°ΠΉΠ½Π΅Π»Π΅Π½Ρ, ΡΠ°Π±Π°Π½, ΡΠΊΡΠ»ΡΠΏΡΡΡΡ |
-ΠΏ |
ΠΏΠΈΠ»ΡΠ³Π΅ΠΎΡΠΊΠ°Π½Ρ, ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠ°Π½ΡΠ²Π΅ΡΠΈΠΉ, ΠΏΠ°ΡΠΎΡΡΠΎ |
-ΠΊΠ° |
ΠΊΠ°Π½ΡΠ½ΠΈΡΡ, ΠΊΠ°Π·Π°Π½ΡΡΡ, ΠΊΠ°ΠΉΡΠ΅Π²ΠΈ |
-Π° |
Π°Π±ΡΡ, Π°Π½Π΄ΠΎΠ½Ρ, Π°Π½Π³Π»ΠΈΡΡΠΎ |
-Ρ |
ΡΠ°ΠΌΠ°ΡΡ, ΡΠ°ΡΡΠΎΡΡΡΠ΅Π²ΠΎ, ΡΡΠΈΠ½Π΅ΠΊ |
-Π² |
Π²Π΅Π½ΡΡΠΈΠ·Π΅, Π²Π°Π³ΡΠΈΡΡ, Π²Π΅Π½ΠΎΠΊ |
-ΠΌ |
ΠΌΠ°ΡΠ²Π΅Π΅Π²ΠΎ, ΠΌΠΎΠ½Π°ΡΡΡΡΠ΅Π½Ρ, ΠΌΠ°ΡΡΡΡΠ½Ρ |
Productive Suffixes
| Suffix | Examples |
|---|---|
-Ρ |
ΠΏΠΈΠ»ΡΠ³Π΅ΠΎΡΠΊΠ°Π½Ρ, ΡΠ°ΠΉΠ½Π΅Π»Π΅Π½Ρ, ΠΊΠ°Π½ΡΠ½ΠΈΡΡ |
-Π½Ρ |
ΠΏΠΈΠ»ΡΠ³Π΅ΠΎΡΠΊΠ°Π½Ρ, ΡΠ°ΠΉΠ½Π΅Π»Π΅Π½Ρ, ΡΠ°Π²Π²ΠΈΠ½ΡΠ½Ρ |
-ΠΎ |
ΠΊΠ΅ΠΌΠΊΠ°Π²ΡΠΎΠ²ΠΎ, ΠΌΠ°ΡΠ²Π΅Π΅Π²ΠΎ, ΡΡΠΌΠ°ΠΊΠΎΠ½Π·ΠΎ |
-ΡΡ |
ΠΊΠ°Π½ΡΠ½ΠΈΡΡ, Ρ ΡΠ΄ΠΎΠΆΠ½ΠΈΠΊΠ΅Π½ΡΡ, ΡΡΡΠΈΡΡ |
-Π° |
Π·Π°Π΄ΠΎΠ½ΡΠΊΠ°, Π±ΠΎΠΆΠ΅Π½Π°, ΡΠ»ΡΠ½ΠΊΠ° |
-Π΅ |
Π²Π΅Π½ΡΡΠΈΠ·Π΅, Ρ Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊΠ°ΡΠ½Π΅, Π΅Π²ΡΠΎΠΏΠ΅ |
-ΠΉ |
ΠΊΠ»Π°Π²Π΄ΠΈΠΉ, ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠ°Π½ΡΠ²Π΅ΡΠΈΠΉ, ΡΡΠ΅Π±Π½ΠΎΠΉ |
-ΡΡ |
Π»ΠΎΠ²ΠΎΠΌΠ°ΡΡ, ΠΊΡΠ»ΠΎΠΌΠ°ΡΠΈΡΡ, ΠΊΠ΅Π»ΡΠ΅ΡΡ |
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 |
|---|---|---|---|
ΠΊΠΎΠ²ΠΎ |
2.01x | 50 contexts | ΠΊΠΎΠ²ΠΎΠ», Π±Π΅ΠΊΠΎΠ²ΠΎ, ΠΊΠΎΠ²ΠΎΠ·ΠΎ |
Π΅Π½ΡΡ |
1.92x | 55 contexts | Π³Π΅Π½ΡΡ, Π΄Π΅Π½ΡΡ, ΠΌΠ΅Π½ΡΡ |
ΠΎΠ²ΠΎΠ½ |
2.23x | 30 contexts | ΡΠΎΠ²ΠΎΠ½Ρ, Π»ΠΎΠ²ΠΎΠ½Ρ, ΠΊΠΎΠ²ΠΎΠ½Ρ |
Π°ΡΠΊΠ° |
2.00x | 42 contexts | ΠΏΠ°ΡΠΊΠ°, ΡΠ°ΡΠΊΠ°, Π°ΡΠΊΠ°Ρ |
ΡΠΈΡΡ |
2.25x | 20 contexts | ΡΡΠΈΡΡ, ΡΡΠΈΡΡ, ΠΌΠ°ΡΠΈΡΡ |
ΡΠΊΠΎΠΉ |
1.90x | 34 contexts | Π°ΡΡΠΊΠΎΠΉ, ΡΠΆΡΠΊΠΎΠΉ, ΡΠΌΡΠΊΠΎΠΉ |
Π°Π½ΡΡ |
1.83x | 38 contexts | ΠΊΠ°Π½ΡΡ, ΠΏΠ°Π½ΡΡ, ΠΌΠ°Π½ΡΡ |
Π²ΠΎΠ½Ρ |
2.26x | 18 contexts | ΠΎΡΠ²ΠΎΠ½Ρ, ΡΡΠ²ΠΎΠ½Ρ, Π»ΡΠ²ΠΎΠ½Ρ |
Π°ΡΡΠΎ |
1.74x | 44 contexts | ΡΠ°ΡΡΠΎ, ΡΠ°ΡΡΠΎ, ΡΠ°ΡΡΠΎ |
ΡΡΠΎΡ |
1.63x | 48 contexts | ΡΡΠΎΡΠΎΠΆ, ΠΌΠ°ΡΡΠΎΡ, ΡΡΠΎΡΠΎΠ½Ρ |
ΡΡΠ½Π΅ |
1.76x | 33 contexts | ΡΡΡΠ½Π΅, ΡΡΠ½Π΅Π½Ρ, Π°ΡΡΡΠ½Π΅ |
ΡΠ°ΡΠΊ |
2.14x | 16 contexts | ΡΠ°ΡΠΊΠ°, ΡΠ°ΡΠΊΠ°Ρ, ΡΠ°ΡΠΊΡΠΎ |
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 |
-Ρ |
242 words | ΠΊΠΎΠΌΠΏΠ°Π½ΠΈΡΠ½ΡΡ, ΠΊΡΠΈΡΡ |
-ΠΏ |
-Ρ |
182 words | ΠΏΠ°Π»ΡΡ, ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠ΅Π½Ρ |
-Ρ |
-Ρ |
168 words | ΡΠ΅ΠΌΠΈΡΠ½Ρ, ΡΠ΅Π»ΡΠΌΡΠ½Π΅Π½Ρ |
-Π² |
-Ρ |
134 words | Π²ΠΈΡΡΠ°Π²Π°Π½Ρ, Π²Π΅ΠΉΡΠ²Π΅ΡΡΠΌΠΎΠ½Ρ |
-Ρ |
-Ρ |
123 words | ΡΠΎΠΊΠ°Π»ΠΈΡΡ, ΡΠ΅ΡΠΌΠΎΠ΄ΠΈΠ½Π°ΠΌΠΈΠΊΠ°Π½Ρ |
-ΠΌ |
-Ρ |
118 words | ΠΌΠ°ΡΡΡΡΡ, ΠΌΠ°ΠΊΡΠΎΠΌΠ°Π½ΡΡ |
-ΠΊ |
-Π½Ρ |
117 words | ΠΊΠ°ΠΌΠΈΠ½Ρ, ΠΊΠ»Π΅ΡΠΊΠ°Π½ΡΠ΅Π½Ρ |
-Π° |
-Ρ |
103 words | Π°ΡΠΎΠΌΠ΅ΡΡΠ΅Π½Ρ, Π°Π·ΡΠ΅Π±Π°ΠΉΠ΄ΠΆΠ°Π½ΠΎΠ½Ρ |
-Π» |
-Ρ |
94 words | Π»Π΅ΠΌΠ΄Π΅Π·Ρ, Π»ΡΠ΄ΠΈΠΊΠΈΠ½Ρ |
-ΠΏ |
-Π½Ρ |
85 words | ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠ΅Π½Ρ, ΠΏΡΠ°ΠΊΠ°Π½Ρ |
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 |
|---|---|---|---|
| ΠΈΠ½ΡΠ·ΠΎΡΠ°Π²Π° | ΠΈΠ½ΡΠ·ΠΎΡ-Π°-Π²Π° |
7.5 | Π° |
| ΠΌΠ°ΡΠ΅ΡΠΈΠ°Π»Π°ΠΌ | ΠΌΠ°ΡΠ΅ΡΠΈΠ°Π»-Π°-ΠΌ |
7.5 | Π° |
| ΠΏΠ°Π½Π΄ΠΎΠΌΠ°ΡΡ | ΠΏΠ°Π½Π΄ΠΎ-ΠΌΠ°-ΡΡ |
7.5 | ΠΌΠ° |
| Π³ΡΡΠΏΠΏΠ°Π½Π΅Π½Ρ | Π³ΡΡΠΏΠΏΠ°-Π½Π΅-Π½Ρ |
7.5 | Π½Π΅ |
| ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΡΠΎΠ² | ΡΠΊΠΎΠ½ΠΎΠΌΠΈ-ΡΡ-ΠΎΠ² |
7.5 | ΡΡ |
| Π²Π°ΡΠ΅Π½ΡΡΠ΅Π½ΡΡ | Π²Π°ΡΠ΅Π½ΡΡΠ΅-Π½-ΡΡ |
7.5 | Π½ |
| ΠΌΠ°ΡΠΈΡΡΠ½Π΅Π½Ρ | ΠΌΠ°ΡΠΈΡΡ-Π½Π΅-Π½Ρ |
7.5 | Π½Π΅ |
| ΡΡΠ°ΡΡΠΊΠ°ΡΡ | ΡΡΠ°ΡΡ-ΠΊΠ°-ΡΡ |
7.5 | ΠΊΠ° |
| Π»ΠΎΠΌΠ°Π½ΡΡΡΡ | Π»ΠΎΠΌΠ°Π½Ρ-ΡΡ-Ρ |
7.5 | ΡΡ |
| ΠΊΠ΅ΠΌΠ΅ΠΊΡΡΠΈΡΡ | ΠΊΠ΅ΠΌΠ΅ΠΊΡΡ-ΠΈ-ΡΡ |
7.5 | ΠΈ |
| Π½Π΅Π²ΡΠ΅ΠΌΠ°ΠΊΡ | Π½Π΅Π²ΡΠ΅-ΠΌΠ°-ΠΊΡ |
7.5 | ΠΌΠ° |
| ΡΡΠ³ΡΠ½ΠΊΠ°ΡΡΠΎ | ΡΡΠ³ΡΠ½ΠΊΠ°-ΡΡ-ΠΎ |
7.5 | ΡΡ |
| Π²Π΅Π»Π΅ΡΠ½Π΅ΡΡ | Π²Π΅Π»Π΅Ρ-Π½Π΅-ΡΡ |
7.5 | Π½Π΅ |
| ΠΏΡΠ΅ΠΌΠΈΡΡΠ½Π΅ | ΠΏΡΠ΅ΠΌΠΈΡ-Ρ-Π½Π΅ |
7.5 | Ρ |
| ΠΌΠ΅Π΄ΠΈΡΠΈΠ½Π°Π½Ρ | ΠΌΠ΅Π΄ΠΈΡΠΈ-Π½Π°-Π½Ρ |
7.5 | Π½Π° |
6.6 Linguistic Interpretation
Automated Insight: The language Erzya 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 (4.10x) |
| N-gram | 2-gram | Lowest perplexity (451) |
| Markov | Context-4 | Highest predictability (97.8%) |
| 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 14:15:51



















