wikilangs/km

Khmer - Wikilangs Models

Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on Khmer 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	3.556x	3.54	0.1756%	741,877
16k	4.063x	4.05	0.2006%	649,413
32k	4.511x	4.49	0.2228%	584,909
64k	4.889x 🏆	4.87	0.2415%	539,636

Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

Sample 1: សាវតារ ភូមិតាបឹបនេះយើងពុំបានជ្រាបច្បាស់ទេ ។ តែយើងបានដឹងថាក្នុងភូមិនេះមានទួលកប់ខ្...

Vocab	Tokens	Count
8k	▁សាវ តារ ▁ភូមិ ត ាប ឹប នេះ យើង ពុំ បាន ... (+24 more)	34
16k	▁សាវ តារ ▁ភូមិ តាប ឹប នេះ យើង ពុំ បាន ជ្រាប ... (+21 more)	31
32k	▁សាវ តារ ▁ភូមិ តាប ឹប នេះ យើង ពុំបាន ជ្រាប ច្បាស់ ... (+17 more)	27
64k	▁សាវតារ ▁ភូមិ តាប ឹប នេះយើង ពុំបាន ជ្រាប ច្បាស់ទេ ▁។ ▁តែ ... (+13 more)	23

Sample 2: ៖ ឃុំស៊ុង ឃុំមានជ័យ ឃុំសំឡូត ឃុំកំពង់ល្ពៅ ឃុំអូរសំរិល ឃុំតាតោក ឃុំតាសាញ សូមមើលផង...

Vocab	Tokens	Count
8k	▁៖ ▁ឃុំ ស៊ ុង ▁ឃុំ មានជ័យ ▁ឃុំ សំ ឡ ូត ... (+18 more)	28
16k	▁៖ ▁ឃុំ ស៊ ុង ▁ឃុំមានជ័យ ▁ឃុំ សំឡូត ▁ឃុំកំពង់ ល ្ពៅ ... (+13 more)	23
32k	▁៖ ▁ឃុំ ស៊ុង ▁ឃុំមានជ័យ ▁ឃុំ សំឡូត ▁ឃុំកំពង់ ល្ពៅ ▁ឃុំអូរ សំរ ... (+10 more)	20
64k	▁៖ ▁ឃុំ ស៊ុង ▁ឃុំមានជ័យ ▁ឃុំ សំឡូត ▁ឃុំកំពង់ល្ពៅ ▁ឃុំអូរ សំរិល ▁ឃុំ ... (+7 more)	17

Sample 3: ម៉ៃឃើលអាចសំដៅលើ៖ ម៉ៃឃើល ហ្វារ៉ាដេយ ម៉ៃឃើល ចាកសាន់ ម៉ៃឃើល វីកឃឺវី

Vocab	Tokens	Count
8k	▁ម៉ ៃ ឃ ើល អាច សំដៅលើ ៖ ▁ម៉ ៃ ឃ ... (+22 more)	32
16k	▁ម៉ៃឃើល អាច សំដៅលើ៖ ▁ម៉ៃឃើល ▁ហ ្វារ ៉ា ដ េយ ▁ម៉ៃឃើល ... (+8 more)	18
32k	▁ម៉ៃឃើល អាចសំដៅលើ៖ ▁ម៉ៃឃើល ▁ហ្វារ ៉ា ដេយ ▁ម៉ៃឃើល ▁ចាក សាន់ ▁ម៉ៃឃើល ... (+4 more)	14
64k	▁ម៉ៃឃើល អាចសំដៅលើ៖ ▁ម៉ៃឃើល ▁ហ្វារ៉ាដេយ ▁ម៉ៃឃើល ▁ចាក សាន់ ▁ម៉ៃឃើល ▁វីក ឃឺ ... (+1 more)	11

Key Findings

• Best Compression: 64k achieves 4.889x compression
• Lowest UNK Rate: 8k with 0.1756% 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	29,102	14.83	72,055	8.9%	24.7%
2-gram	Subword	5,212 🏆	12.35	88,256	22.4%	57.4%
3-gram	Word	53,084	15.70	103,452	6.4%	17.4%
3-gram	Subword	51,695	15.66	499,965	8.2%	24.3%
4-gram	Word	118,314	16.85	213,260	4.3%	12.7%
4-gram	Subword	260,843	17.99	1,609,249	4.4%	12.4%
5-gram	Word	100,822	16.62	180,877	4.2%	13.0%
5-gram	Subword	609,986	19.22	2,327,771	3.0%	8.0%

Top 5 N-grams by Size

2-grams (Word):

Rank	N-gram	Count
1	example example	21,905
2	of the	4,908
3	ត្រូវ បាន	3,687
4	នៅ ក្នុង	3,249
5	ព្រះ អង្គ	2,574

3-grams (Word):

Rank	N-gram	Count
1	example example example	10,790
2	villageភូមិ villageភូមិ villageភូមិ	1,612
3	ត្រូវ បាន គេ	1,169
4	៤៩៣ ប្រ ក	995
5	សាសនា ព្រះពុទ្ធសាសនា វត្ត	640

4-grams (Word):

Rank	N-gram	Count
1	example example example example	1,615
2	villageភូមិ villageភូមិ villageភូមិ villageភូមិ	1,380
3	អនុវិទ្យាល័យ សាសនា ព្រះពុទ្ធសាសនា វត្ត	558
4	បឋមសិក្សា អនុវិទ្យាល័យ សាសនា ព្រះពុទ្ធសាសនា	536
5	អប់រំ បឋមសិក្សា អនុវិទ្យាល័យ សាសនា	535

5-grams (Word):

Rank	N-gram	Count
1	villageភូមិ villageភូមិ villageភូមិ villageភូមិ villageភូមិ	1,151
2	អប់រំ បឋមសិក្សា អនុវិទ្យាល័យ សាសនា ព្រះពុទ្ធសាសនា	535
3	បឋមសិក្សា អនុវិទ្យាល័យ សាសនា ព្រះពុទ្ធសាសនា វត្ត	528
4	e លិច w ត្បូង s	455
5	n កើត e លិច w	454

2-grams (Subword):

Rank	N-gram	Count
1	។ _	199,513
2	បា ន	145,143
3	ង _	128,650
4	កា រ	123,593
5	e _	121,925

3-grams (Subword):

Rank	N-gram	Count
1	_ និ ង	83,168
2	_ ។ _	67,258
3	រ ប ស់	64,716
4	_ ដែ ល	42,564
5	_ t h	39,828

4-grams (Subword):

Rank	N-gram	Count
1	m p l e	34,032
2	p l e _	33,694
3	_ e x a	33,362
4	a m p l	33,310
5	e x a m	33,310

5-grams (Subword):

Rank	N-gram	Count
1	_ e x a m	33,301
2	a m p l e	33,292
3	e x a m p	33,273
4	x a m p l	33,273
5	m p l e _	33,105

Key Findings

• Best Perplexity: 2-gram (subword) with 5,212
• Entropy Trend: Decreases with larger n-grams (more predictable)
• Coverage: Top-1000 patterns cover ~8% 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	0.2782	1.213	2.41	859,644	72.2%
1	Subword	1.0301	2.042	17.81	14,759	0.0%
2	Word	0.1500	1.110	1.34	2,064,587	85.0%
2	Subword	0.6645	1.585	5.47	262,778	33.5%
3	Word	0.0584	1.041	1.09	2,764,478	94.2%
3	Subword	0.4625	1.378	2.82	1,436,052	53.8%
4	Word	0.0205 🏆	1.014	1.03	3,007,497	98.0%
4	Subword	0.3127	1.242	1.86	4,049,871	68.7%

Generated Text Samples (Word-based)

Below are text samples generated from each word-based Markov chain model:

Context Size 1:

1. និង ឡាវ ព្រះឧបជ្ឈាហ៍ ទេពវង្ស សម្តេច ព្រះអភិសិរីសុគន្ធាមហាសង្ឃរាជាធិបតី សម្តេចព្រះមហាសង្ឃរាជ បួរ គ្រី...
2. example example example example ៧ លោកស្រី គាត់ បាន សម្រាប់ និកាយ ហ្សេន តានត្រិក និងដែនដីបរិសុទ្ធ ដែន...
3. the united states union premier league cup នេះក៏ជាការប្រកួតផ្លូវការណ៍ក្រោមការគ្រប់គ្រងរបស់ cambodian...

Context Size 2:

1. example example example ៣ example example ២៧ example example ១១ example example ៧ example example ex...
2. of the mahayana idea that such an attack scenario dynamically shall make use of both the dmt
3. ត្រូវ បាន អភិវឌ្ឍន សម្រាប់ kde 3 បាន ការ តែង តាំង ជា អភិបាល នៃ តំបន់អុីវាណូ ហ្វ្រែនគីវស៍ ក្នុង នាម

Context Size 3:

1. example example example ៤១ example example example ៦ example example example ១២ example example exam...
2. villageភូមិ villageភូមិ villageភូមិ villageភូមិ village ព្រំប្រទល់នៃ ទិសខាងកើត e ខាងត្បូង s ខាងលិច w...
3. ត្រូវ បាន គេ ធ្វើ តេស្ដ នៅ ក្នុង ថ្នាក់ b និង c គឺជារង្វាស់នៃជ្រុងនៃ ត្រីកោណ ដែលមាន ក្រលាផ្ទៃ f និង ...

Context Size 4:

1. example example example example ៣ ស្រី ៨ example example example ៣៣ example example example ៩ exampl...
2. villageភូមិ villageភូមិ villageភូមិ villageភូមិ villageភូមិ villageភូមិ villageភូមិ village ព្រំប្រទ...
3. អនុវិទ្យាល័យ សាសនា ព្រះពុទ្ធសាសនា វត្ត ផ្សារ រមណីដ្ឋាន ឯកសារពិគ្រោះ គណកម្មការជាតិរៀបចំការបោះឆ្នោត ខេ...

Generated Text Samples (Subword-based)

Below are text samples generated from each subword-based Markov chain model:

Context Size 1:

1. _plovon_(ហៅថានេះ​សេចក្តី
2. ​ច្បាប់​ជាជន៍ជា​គួរលាវបាទទួ
3. ង​ថា_មាគរ_ck_និងសែន​

Context Size 2:

1. ។_rel.2_សង្ខិត្តំ។]_(_s
2. បាន​លទ្ធផលស្គាល់ច្បាស់លាស់_។_ស
3. ង_ត្រឡប់​យកមន្រ្តីខុទ្ទកាល័យ_និ

Context Size 3:

1. _និង_កម្រិត។_ផ្លូវថូម៉ាស"_(r
2. _។_នាម៉ឺន​ពិធី​មាំ​ថែមទៀតផង
3. របស់វីតាមីន_atter_leve

Context Size 4:

1. mple_៥០_និងប្រទេសអូស្រ្ដាលី_កេន
2. ple_example_example
3. _example_example_ex

Key Findings

• Best Predictability: Context-4 (word) with 98.0% predictability
• Branching Factor: Decreases with context size (more deterministic)
• Memory Trade-off: Larger contexts require more storage (4,049,871 contexts)
• Recommendation: Context-3 or Context-4 for text generation

---

4. Vocabulary Analysis

Statistics

Metric	Value
Vocabulary Size	168,571
Total Tokens	2,917,143
Mean Frequency	17.31
Median Frequency	3
Frequency Std Dev	265.83

Most Common Words

Rank	Word	Frequency
1	និង	40,023
2	example	33,205
3	the	28,680
4	ជា	28,379
5	បាន	26,100
6	មាន	21,881
7	of	20,677
8	ដែល	18,961
9	នៅ	18,044
10	ក្នុង	16,838

Least Common Words (from vocabulary)

Rank	Word	Frequency
1	កេលីម៉ាន់តាន់	2
2	สทิงพระ	2
3	ទេសបាលតំបន់	2
4	វត្តច័ន្ទ	2
5	និងការអភិវឌ្ឍខ្លួនឯង	2
6	milliontimes	2
7	អក្សរចិនបុរាណ	2
8	នៅលើផ្ទៃខាងក្រោយងងឹត	2
9	វគ្គជម្រុះជុំទី៣	2
10	wagnalls	2

Zipf's Law Analysis

Metric	Value
Zipf Coefficient	1.0175
R² (Goodness of Fit)	0.996035
Adherence Quality	excellent

Coverage Analysis

Top N Words	Coverage
Top 100	27.0%
Top 1,000	51.0%
Top 5,000	68.7%
Top 10,000	75.6%

Key Findings

• Zipf Compliance: R²=0.9960 indicates excellent adherence to Zipf's law
• High Frequency Dominance: Top 100 words cover 27.0% of corpus
• Long Tail: 158,571 words needed for remaining 24.4% 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	0.8684	0.3333	N/A	N/A
mono_64d	64	0.8701 🏆	0.2501	N/A	N/A
mono_128d	128	0.7385	0.2098	N/A	N/A
aligned_32d	32	0.8684	0.3316	0.0940	0.3400
aligned_64d	64	0.8701	0.2521	0.1220	0.4760
aligned_128d	128	0.7385	0.2166	0.2480	0.6260

Key Findings

• Best Isotropy: mono_64d with 0.8701 (more uniform distribution)
• Semantic Density: Average pairwise similarity of 0.2656. Lower values indicate better semantic separation.
• Alignment Quality: Aligned models achieve up to 24.8% R@1 in cross-lingual retrieval.
• Recommendation: 128d aligned for best cross-lingual performance

---

6. Morphological Analysis (Experimental)

This section presents an automated morphological analysis derived from the statistical divergence between word-level and subword-level models. By analyzing where subword predictability spikes and where word-level coverage fails, we can infer linguistic structures without supervised data.

6.1 Productivity & Complexity

Metric	Value	Interpretation	Recommendation
Productivity Index	5.000	High morphological productivity	Reliable analysis
Idiomaticity Gap	0.614	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
-ស	សឧត្តរំ, ស្វាហ៊ីលី, សម្បកក្រៅរុំ
-ប	បានដល់ការទាយគតិរបស់ព្រះសិទ្ធត្ថរាជកុមារ, បឋមជ្ឈានតោ, ប្រាសាទបាក់បែកនៅខាងក្រោយនៃវត្តស្រីមឿងនៅវាំងចន្ទន៍ភាគកណ្ដាល
-ក	ក្រាំងចិន, ក្រមាខ្មែរ, ក្នុងកាលខាងក្រោយ
-អ	អង្គុយក្នុងទីសមគួរហើយ, អេអូនីសេ, អូរាំងអាស្លី
-ន	និងបន្លែ, នៃម៉ាស់សរុបនៃប្រព័ន្ធព្រះអាទិត្យ, និងបរិវារមួយក្រុមបានភៀសទៅជ្រកកោនក្នុងប្រទេសសៀមជាមួយព្រះ
-ម	មានប្រាសាទ, ម្យ៉ាងទៀតសោត, មានឱកាស
-s	supra, sharia, signals
-រ	រមែងសញ្ជប់សញ្ជឹង, រណ្តៅតូច, របស់ព្រះពុទ្ធមួយភាគដែរ

Productive Suffixes

Suffix	Examples
-ង	រមែងសញ្ជប់សញ្ជឹង, ត្បូងពណ៌បៃតង, ដើម្បីនឹង
-យ	អង្គុយក្នុងទីសមគួរហើយ, ធ្វើឱ្យជាស្ថានទីរីករាយ, គ្មានមន្ទីរពេទ្យ
-ន	ក្រាំងចិន, យោន, គឺមិនមាន
-រ	បានដល់ការទាយគតិរបស់ព្រះសិទ្ធត្ថរាជកុមារ, ក្រមាខ្មែរ, របស់ព្រះពុទ្ធមួយភាគដែរ
-ត	គឺមិនមាននិមិត្ត, ម្យ៉ាងទៀតសោត, និងរារាំងការពង្រីកខ្លួនរបស់ចិនបន្តទៅទៀត
-ក	នៃតំបន់ប្រាសាទសំបូរព្រៃគុក, ក្នុងសំដីរបស់អ្នក, និងចក
-ម	ទៅកាន់មនុស្សទាំងអស់ក្នុងសង្គម, ដូចជាកោះត្រល់ជាដើម, ទឹកនោមផ្អែម
-s	nicolas, thoughts, characters

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
ight	2.39x	50 contexts	fight, night, sight
tion	2.28x	46 contexts	option, nation, lotion
ment	2.30x	39 contexts	cement, moment, mental
atio	2.39x	33 contexts	ratio, nation, horatio
nter	2.15x	37 contexts	enter, inter, winter
inte	2.29x	29 contexts	intel, inter, winter
stor	2.31x	27 contexts	story, jstor, storm
ctio	2.40x	23 contexts	action, section, actions
illa	2.19x	27 contexts	illam, villa, silla
ubli	2.35x	19 contexts	dublin, public, publié
pres	2.24x	22 contexts	press, ypres, presse
iver	2.18x	22 contexts	liver, river, waiver

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
-ប	-ន	50 words	បណ្តាញសាកលវិទ្យាល័យអាស៊ាន, បង្ហាញខ្លួន
-ក	-ង	49 words	ការប្រើដំណរក្នុង, ក្រាំងខ្លុង
-ប	-យ	46 words	បានត្រាស់សេចក្តីនេះរួចហើយ, បន្សាយ
-ន	-យ	44 words	និងសម្តែងដោយ, និងបានយសសក្ដិគ្រប់សព្វណាស់ទៅហើយ
-ក	-យ	40 words	កម្លាំងថយ, ក៏ពោលពាក្យ
-ក	-ន	39 words	កៈទឿន, ការឈ្លានពានរបស់ជប៉ុន
-ន	-ង	38 words	និងចៅប្រមាញ់វិងស៊ុង, និងនៅសងខាង
-ន	-រ	37 words	និងវិចិត្រសិល្បៈខេត្តព្រះវិហារ, នាយសមុទ្រ
-ស	-ន	36 words	សីលជាស្ពាន, សារពត័មាន
-ស	-រ	35 words	សុពាហុត្ថេរ, សភិយត្ថេរ

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
abdagases	abdaga-s-es	7.5	s
នៅពីក្រោយខ្នង	នៅពីក្រោយខ្-ន-ង	7.5	ន
tlaxcaltecas	tlaxcalteca-s	4.5	tlaxcalteca
instrumental	instrument-al	4.5	instrument
អន្តរជាតិ	អ-ន-្តរជាតិ	4.5	្តរជាតិ
អបដិក្កូលេ	អ-បដិក្កូលេ	4.5	បដិក្កូលេ
scholarships	scholarship-s	4.5	scholarship
ស្រមោចហែរ	ស្រមោចហែ-រ	4.5	ស្រមោចហែ
replacements	replacement-s	4.5	replacement
ពួកសត្វតែងមាន	ព-ួកសត្វតែងមា-ន	3.0	ួកសត្វតែងមា
grancrest	grancr-es-t	3.0	grancr
ប្រទាញសងខាង	ប្រទាញសងខា-ង	1.5	ប្រទាញសងខា
ក្នុងថ្ងៃនេះបាន	ក្នុងថ្ងៃនេះបា-ន	1.5	ក្នុងថ្ងៃនេះបា
vidyādhara	vidyādhar-a	1.5	vidyādhar
ក្រុមហាម៉ាស់	ក-្រុមហាម៉ាស់	1.5	្រុមហាម៉ាស់

6.6 Linguistic Interpretation

Automated Insight: The language Khmer 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 (4.89x)
N-gram	2-gram	Lowest perplexity (5,212)
Markov	Context-4	Highest predictability (98.0%)
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

1. Compare within model families: Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
2. Consider trade-offs: Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
3. Context matters: Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
4. Corpus influence: All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
5. 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

Omar Kamali - Omneity Labs

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 08:23:26