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Sanskrit - Wikilangs Models

Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on Sanskrit 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

1. Tokenizer Evaluation

Results

Vocab Size	Compression	Avg Token Len	UNK Rate	Total Tokens
8k	3.370x	3.37	0.2913%	717,781
16k	3.776x	3.78	0.3263%	640,751
32k	4.129x	4.13	0.3569%	585,907
64k	4.437x 🏆	4.44	0.3835%	545,247

Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

Sample 1:

सः यादवकुलस्य राजा आसीत्। प्राचीनवंशावली स्टब्स् प्राप्तः भाषानुबन्धः अपूर्णलेखा...

Vocab	Tokens	Count
8k	`▁सः ▁यादवकुलस्य ▁राजा ▁आसीत् । ▁प्राचीनवंशावली ▁स्टब्स् ▁प्राप्तः ▁भाषानुबन्धः ▁अपूर्णलेखाः ... (+6 more)`	16
16k	`▁सः ▁यादवकुलस्य ▁राजा ▁आसीत् । ▁प्राचीनवंशावली ▁स्टब्स् ▁प्राप्तः ▁भाषानुबन्धः ▁अपूर्णलेखाः ... (+6 more)`	16
32k	`▁सः ▁यादवकुलस्य ▁राजा ▁आसीत् । ▁प्राचीनवंशावली ▁स्टब्स् ▁प्राप्तः ▁भाषानुबन्धः ▁अपूर्णलेखाः ... (+6 more)`	16
64k	`▁सः ▁यादवकुलस्य ▁राजा ▁आसीत् । ▁प्राचीनवंशावली ▁स्टब्स् ▁प्राप्तः ▁भाषानुबन्धः ▁अपूर्णलेखाः ... (+6 more)`	16

Sample 2:

सः अयोध्याकुलस्य राजा आसीत्। प्राचीन-वंशावली अयोध्याकुल स्टब्स् अपूर्णलेखाः योजन...

Vocab	Tokens	Count
8k	`▁सः ▁अयोध्याकुलस्य ▁राजा ▁आसीत् । ▁प्राचीन - वंशावली ▁अयोध्याकुल ▁स्टब्स् ... (+3 more)`	13
16k	`▁सः ▁अयोध्याकुलस्य ▁राजा ▁आसीत् । ▁प्राचीन - वंशावली ▁अयोध्याकुल ▁स्टब्स् ... (+3 more)`	13
32k	`▁सः ▁अयोध्याकुलस्य ▁राजा ▁आसीत् । ▁प्राचीन - वंशावली ▁अयोध्याकुल ▁स्टब्स् ... (+3 more)`	13
64k	`▁सः ▁अयोध्याकुलस्य ▁राजा ▁आसीत् । ▁प्राचीन - वंशावली ▁अयोध्याकुल ▁स्टब्स् ... (+3 more)`	13

Sample 3:

स्वर्णगौरीव्रतम् इत्युक्ते गौरीतृतीया एव । तत्र द्रष्टव्यम् । स्टब्स् अपूर्णलेखा...

Vocab	Tokens	Count
8k	`▁स्वर्ण गौ री व्र तम् ▁इत्युक्ते ▁गौरी त ृत ीया ... (+10 more)`	20
16k	`▁स्वर्ण गौ री व्रतम् ▁इत्युक्ते ▁गौरी तृत ीया ▁एव ▁। ... (+7 more)`	17
32k	`▁स्वर्ण गौरी व्रतम् ▁इत्युक्ते ▁गौरी तृत ीया ▁एव ▁। ▁तत्र ... (+6 more)`	16
64k	`▁स्वर्ण गौरी व्रतम् ▁इत्युक्ते ▁गौरी तृतीया ▁एव ▁। ▁तत्र ▁द्रष्टव्यम् ... (+5 more)`	15

Key Findings

Best Compression: 64k achieves 4.437x compression
Lowest UNK Rate: 8k with 0.2913% 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	11,133	13.44	41,507	20.4%	40.2%
2-gram	Subword	4,254 🏆	12.05	77,760	29.2%	59.0%
3-gram	Word	6,057	12.56	36,616	30.9%	49.8%
3-gram	Subword	37,749	15.20	386,589	11.4%	30.0%
4-gram	Word	22,497	14.46	116,572	23.9%	36.9%
4-gram	Subword	171,126	17.38	1,206,214	7.0%	18.9%
5-gram	Word	17,943	14.13	99,332	26.0%	39.2%
5-gram	Subword	336,494	18.36	1,600,156	5.2%	14.8%

Top 5 N-grams by Size

2-grams (Word):

Rank	N-gram	Count
1	`तमे वर्षे`	6,311
2	`अक्तूबर दिसंबर`	5,560
3	`जनवरी मार्च`	5,559
4	`जुलाई सितंबर`	5,558
5	`मार्च अप्रैल`	5,558

3-grams (Word):

Rank	N-gram	Count
1	`जनवरी मार्च अप्रैल`	5,556
2	`मार्च अप्रैल जून`	5,555
3	`सितंबर अक्तूबर दिसंबर`	5,554
4	`जुलाई सितंबर अक्तूबर`	5,554
5	`अप्रैल जून जुलाई`	5,553

4-grams (Word):

Rank	N-gram	Count
1	`जनवरी मार्च अप्रैल जून`	5,555
2	`जुलाई सितंबर अक्तूबर दिसंबर`	5,554
3	`मार्च अप्रैल जून जुलाई`	5,552
4	`अप्रैल जून जुलाई सितंबर`	5,552
5	`जून जुलाई सितंबर अक्तूबर`	5,548

5-grams (Word):

Rank	N-gram	Count
1	`जनवरी मार्च अप्रैल जून जुलाई`	5,552
2	`मार्च अप्रैल जून जुलाई सितंबर`	5,551
3	`अप्रैल जून जुलाई सितंबर अक्तूबर`	5,548
4	`जून जुलाई सितंबर अक्तूबर दिसंबर`	5,548
5	`सम्बद्धाः लेखाः भारतीयकालमानः ज्योतिषशास्त्रम् संस्कृतम्`	1,906

2-grams (Subword):

Rank	N-gram	Count
1	`। _`	304,328
2	`_ अ`	277,099
3	`_ ।`	243,302
4	`स्य _`	179,722
5	`, _`	145,968

3-grams (Subword):

Rank	N-gram	Count
1	`_ । _`	237,833
2	`_ च _`	50,503
3	`। _ अ`	43,595
4	`_ इ ति`	41,470
5	`म् _ अ`	38,861

4-grams (Subword):

Rank	N-gram	Count
1	`_ इ ति _`	36,444
2	`_ । _ अ`	35,818
3	`ति _ । _`	33,422
4	`त् _ । _`	31,074
5	`_ भ व ति`	24,339

5-grams (Subword):

Rank	N-gram	Count
1	`_ भ व ति _`	17,863
2	`_ अ स्ति _ ।`	17,494
3	`अ स्ति _ । _`	17,320
4	`_ आ सी त् _`	13,617
5	`सी त् _ । _`	13,209

Key Findings

Best Perplexity: 2-gram (subword) with 4,254
Entropy Trend: Decreases with larger n-grams (more predictable)
Coverage: Top-1000 patterns cover ~15% 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	0.4713	1.386	3.33	652,534	52.9%
1	Subword	0.8678	1.825	13.92	17,979	13.2%
2	Word	0.1228	1.089	1.26	2,174,445	87.7%
2	Subword	0.7350	1.664	4.87	250,225	26.5%
3	Word	0.0305	1.021	1.05	2,734,909	96.9%
3	Subword	0.5248	1.439	2.74	1,217,332	47.5%
4	Word	0.0099 🏆	1.007	1.02	2,863,051	99.0%
4	Subword	0.3365	1.263	1.79	3,333,052	66.4%

Generated Text Samples (Word-based)

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

Context Size 1:

च दूरं १ वचनम् अत्र शीलतायाः आनन्दः एव मनः चित्तम् मनः शरीर शरीरं किं भविष्यति विभिन्नवि
इति पदसंज्ञाविधायकं सूत्रं त्रिफला एकं मण्डलं मुघल्साम्राज्यस्य अधीनम् अकरोत् विद्यार्थिकालात् एव रा...
अस्ति या हि साऽवस्था औपनिषदास्तु तां विक्रीतवान् अपि दृश्यते १ २ १ वेदघोष माता प्रसाद नैय्यर

Context Size 2:

तमे वर्षे महामहोपाध्याय प्रशस्तिं दत्त्वा सम्मानितवन्तः चतुर्थं कन्नड साहित्य परिषदः अध्यक्षः आसीत् ...
अक्तूबर दिसंबर बाह्य सूत्राणि calendopedia ६८२ ६८२ स्टब्स् अपूर्णलेखाः योजनीयम् योजनीया स्टब्स् अपूर...
जनवरी मार्च अप्रैल जून जुलाई सितंबर अक्तूबर दिसंबर निधनानि जनवरी मार्च अप्रैल जून जुलाई सितंबर अक्तू...

Context Size 3:

जनवरी मार्च अप्रैल जून जुलाई सितंबर अक्तूबर दिसंबर निधनानि जनवरी मार्च अप्रैल जून जुलाई सितंबर अक्तू...
मार्च अप्रैल जून जुलाई सितंबर अक्तूबर दिसंबर अज्ञात तिथीनां घटनाः जन्मानि जनवरी मार्च अप्रैल जून जुल...
सितंबर अक्तूबर दिसंबर बाह्य सूत्राणि calendopedia स्टब्स् अपूर्णलेखाः नावश्यके सम्बद्धाः लेखाः भारती...

Context Size 4:

जनवरी मार्च अप्रैल जून जुलाई सितंबर अक्तूबर दिसंबर बाह्य सूत्राणि calendopedia स्टब्स् अपूर्णलेखाः न...
जुलाई सितंबर अक्तूबर दिसंबर अज्ञात तिथीनां घटनाः जन्मानि जनवरी मार्च अप्रैल जून जुलाई सितंबर अक्तूबर...
अप्रैल जून जुलाई सितंबर अक्तूबर दिसंबर अज्ञात तिथीनां घटनाः जन्मानि जनवरी मार्च अप्रैल जून जुलाई सित...

Generated Text Samples (Subword-based)

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

Context Size 1:

_स्म_वादः_स्था_विताः_‘विषम्_
।_वितुं_पि_इति_व्यव_शिरोम
व_एवत्_ले_()_जैनयत्_

Context Size 2:

।_ततश्च_।_अस्ति_इत्याख्यस्य_के
_अभवति।_मता_एलायाः_१,२
_।_एव_सुमेर_।_वा"_नास्ति

Context Size 3:

_।_अनेकों_उपस्थितिर्भवति_।_स
_च_दृढकार्यनीतिः_आवश्यकम्_उत्त
।_अस्मिन्_नगरे_अरुणाचलप्रदेश

Context Size 4:

_इति_।_पारिजातवृक्षं,_भागवतस्य
_।_अजमेर-रतन-फर्निचर_इष्णु
ति_।_प्रमाभेदात्_त्रिविधाः_प्रधानमन्त्रि

Key Findings

Best Predictability: Context-4 (word) with 99.0% predictability
Branching Factor: Decreases with context size (more deterministic)
Memory Trade-off: Larger contexts require more storage (3,333,052 contexts)
Recommendation: Context-3 or Context-4 for text generation

4. Vocabulary Analysis

Statistics

Metric	Value
Vocabulary Size	183,249
Total Tokens	2,768,645
Mean Frequency	15.11
Median Frequency	3
Frequency Std Dev	241.86

Most Common Words

Rank	Word	Frequency
1	च	52,641
2	इति	38,813
3	अस्ति	30,239
4	भवति	24,354
5	न	20,240
6	आसीत्	18,819
7	अपि	18,333
8	एव	17,673
9	सन्ति	13,702
10	तस्य	13,542

Least Common Words (from vocabulary)

Rank	Word	Frequency
1	एन्क्रिप्शनस्य	2
2	अनधिकृतप्रवेशात्	2
3	क्रिप्टोग्राफी	2
4	अङ्कीयहस्ताक्षरस्य	2
5	गुप्तीकरणं	2
6	बीमयोः	2
7	व्यवहारौ	2
8	जोखिममूल्याङ्कनम्	2
9	संकटेभ्यः	2
10	pmfby	2

Zipf's Law Analysis

Metric	Value
Zipf Coefficient	0.9504
R² (Goodness of Fit)	0.998392
Adherence Quality	excellent

Coverage Analysis

Top N Words	Coverage
Top 100	24.7%
Top 1,000	46.2%
Top 5,000	63.2%
Top 10,000	70.6%

Key Findings

Zipf Compliance: R²=0.9984 indicates excellent adherence to Zipf's law
High Frequency Dominance: Top 100 words cover 24.7% of corpus
Long Tail: 173,249 words needed for remaining 29.4% 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	0.8179	0.3126	N/A	N/A
mono_64d	64	0.8264	0.2265	N/A	N/A
mono_128d	128	0.8039	0.1686	N/A	N/A
aligned_32d	32	0.8179	0.3205	0.0060	0.0740
aligned_64d	64	0.8264 🏆	0.2281	0.0060	0.0840
aligned_128d	128	0.8039	0.1677	0.0120	0.1360

Key Findings

Best Isotropy: aligned_64d with 0.8264 (more uniform distribution)
Semantic Density: Average pairwise similarity of 0.2374. Lower values indicate better semantic separation.
Alignment Quality: Aligned models achieve up to 1.2% 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	1.652	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
`-स`	सम्पन्नमासीदिति, सर्वोत्तमं, स्वप्रशासनम्
`-क`	क्रीतवान्, कृण्वती, कृशः
`-म`	मूलभूतं, मांसाशी, महिषासुरमर्दिनी
`-अ`	अस्वास्थ्यं, अहम्, अथासौ
`-प`	प्रतिपादन, पर्यटनस्य, पीलीभीतनगरम्
`-व`	वाचमुपासते, व्यक्तित्वैक्यं, व्यञ्जनयोः
`-न`	निर्भरति, निष्पाद्यते, निरोद्धव्याः
`-ब`	बाङ्ला, बॉटनिकल, बलूची

Productive Suffixes

Suffix	Examples
`-य`	पर्यटनस्य, गणकयन्त्रस्य, मुख्यभवनस्य
`-न`	प्रतिपादन, भारतसम्राट्त्वेन, एकाग्रीकरणेन
`-ण`	महाभाष्येण, आनन्दवर्धनाचार्येण, कृतिरूपेण
`-व`	मिलित्व, एतेषामेव, सुविदितमेव
`-र`	चचार, हरिदुष्ट्र, कालचक्र
`-च`	वाक्यपदीयकारश्च, मरिच, आश्रमाणाञ्च
`-s`	overlays, metals, properties
`-त`	चालित, स्वीक्रियन्त, अवर्तन्त

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
`tion`	3.78x	25 contexts	notion, nation, motion
`atio`	3.63x	19 contexts	nation, station, nations
`ture`	3.78x	16 contexts	nature, future, futures
`nter`	3.65x	16 contexts	inter, enter, unter
`ment`	3.56x	14 contexts	mental, cement, moment
`ical`	3.83x	6 contexts	radical, logical, ethical
`inte`	3.67x	6 contexts	inter, winter, interna
`comm`	3.65x	4 contexts	common, comment, commons
`enta`	3.56x	3 contexts	mental, dental, oriental

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
`-प`	`-य`	78 words	परिश्रम्य, प्रियदासस्य
`-स`	`-य`	75 words	सारानाथस्य, सम्बोद्ध्य
`-व`	`-य`	67 words	वर्णधर्मस्य, वेङ्कटमाधवस्य
`-अ`	`-य`	66 words	अधर्माय, अपसारणाय
`-क`	`-य`	53 words	कन्नडसाहित्यसम्मेलनस्य, कूपिय
`-म`	`-य`	39 words	महाराजस्य, मान्यखेटस्य
`-न`	`-य`	39 words	निश्चिकाय, निर्गमनाय
`-प`	`-न`	29 words	पूरणेन, प्रतिमानेन
`-ज`	`-य`	26 words	जापानीय, जीवेश्वरभेदस्य
`-स`	`-न`	26 words	स्वप्रयत्नेन, सोमेन

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
उत्पादनेन	`उत्पादने-न`	4.5	`उत्पादने`
upanishads	`upanishad-s`	4.5	`upanishad`
अवस्थितिः	`अव-स्थितिः`	4.5	`स्थितिः`
अशस्त्रम्	`अ-श-स्त्रम्`	4.5	`स्त्रम्`
उपनायकत्वेन	`उप-नायकत्वेन`	4.5	`नायकत्वेन`
आक्षिपन्ति	`आ-क्षिपन्ति`	4.5	`क्षिपन्ति`
भक्तियोगेन	`भक्तियोगे-न`	4.5	`भक्तियोगे`
योगानन्देन	`योगानन्दे-न`	4.5	`योगानन्दे`
उपलभ्यमाने	`उप-लभ्यमाने`	4.5	`लभ्यमाने`
गुजरातराज्येण	`गुजरातराज्ये-ण`	4.5	`गुजरातराज्ये`
उत्तेजकानि	`उ-त-्तेजकानि`	4.5	`्तेजकानि`
अल्पतमाङ्कस्य	`अ-ल-्पतमाङ्कस्य`	4.5	`्पतमाङ्कस्य`
आरम्भकर्तृषु	`आर-म-्भकर्तृषु`	4.5	`्भकर्तृषु`
रक्तपित्ते	`र-क-्तपित्ते`	4.5	`्तपित्ते`
कार्यकरणेन	`कार्यकरणे-न`	4.5	`कार्यकरणे`

6.6 Linguistic Interpretation

Automated Insight: The language Sanskrit 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 (4.44x)
N-gram	2-gram	Lowest perplexity (4,254)
Markov	Context-4	Highest predictability (99.0%)
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

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

Omar Kamali - Omneity Labs

Citation

If you use these models in your research, please cite:

bibtex

@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.

wikilangs/sa

Sanskrit - Wikilangs Models

Comprehensive Research Report & Full Ablation Study

📋 Repository Contents

Models & Assets

Analysis and Evaluation

1. Tokenizer Evaluation

Results

Tokenization Examples

Key Findings

2. N-gram Model Evaluation

Results

Top 5 N-grams by Size

Key Findings

3. Markov Chain Evaluation

Results

Generated Text Samples (Word-based)

Generated Text Samples (Subword-based)

Key Findings

4. Vocabulary Analysis

Statistics

Most Common Words

Least Common Words (from vocabulary)

Zipf's Law Analysis

Coverage Analysis

Key Findings

5. Word Embeddings Evaluation

5.1 Cross-Lingual Alignment

5.2 Model Comparison

Key Findings

6. Morphological Analysis (Experimental)

6.1 Productivity & Complexity

6.2 Affix Inventory (Productive Units)

Productive Prefixes

Productive Suffixes

6.3 Bound Stems (Lexical Roots)

6.4 Affix Compatibility (Co-occurrence)

6.5 Recursive Morpheme Segmentation

6.6 Linguistic Interpretation

7. Summary & Recommendations

Production Recommendations

Appendix: Metrics Glossary & Interpretation Guide

Tokenizer Metrics

N-gram Model Metrics

Markov Chain Metrics

Vocabulary & Zipf's Law Metrics

Word Embedding Metrics

General Interpretation Guidelines

Visualizations Index

About This Project

Data Source

Project

Maintainer

Citation

License

Links

wikilangs/
sa