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Upload all models and assets for iu (latest)

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  1. .gitattributes +7 -0
  2. README.md +764 -0
  3. iu_morph_tokenizer.json +0 -0
  4. models/embeddings/aligned/iu_128d.bin +3 -0
  5. models/embeddings/aligned/iu_128d.meta.json +1 -0
  6. models/embeddings/aligned/iu_128d.projection.npy +3 -0
  7. models/embeddings/aligned/iu_128d_metadata.json +8 -0
  8. models/embeddings/aligned/iu_32d.bin +3 -0
  9. models/embeddings/aligned/iu_32d.meta.json +1 -0
  10. models/embeddings/aligned/iu_32d.projection.npy +3 -0
  11. models/embeddings/aligned/iu_32d_metadata.json +8 -0
  12. models/embeddings/aligned/iu_64d.bin +3 -0
  13. models/embeddings/aligned/iu_64d.meta.json +1 -0
  14. models/embeddings/aligned/iu_64d.projection.npy +3 -0
  15. models/embeddings/aligned/iu_64d_metadata.json +8 -0
  16. models/embeddings/monolingual/iu_128d.bin +3 -0
  17. models/embeddings/monolingual/iu_128d.meta.json +1 -0
  18. models/embeddings/monolingual/iu_128d_metadata.json +16 -0
  19. models/embeddings/monolingual/iu_32d.bin +3 -0
  20. models/embeddings/monolingual/iu_32d.meta.json +1 -0
  21. models/embeddings/monolingual/iu_32d_metadata.json +16 -0
  22. models/embeddings/monolingual/iu_64d.bin +3 -0
  23. models/embeddings/monolingual/iu_64d.meta.json +1 -0
  24. models/embeddings/monolingual/iu_64d_metadata.json +16 -0
  25. models/subword_markov/iu_markov_ctx1_subword.parquet +3 -0
  26. models/subword_markov/iu_markov_ctx1_subword_metadata.json +7 -0
  27. models/subword_markov/iu_markov_ctx2_subword.parquet +3 -0
  28. models/subword_markov/iu_markov_ctx2_subword_metadata.json +7 -0
  29. models/subword_markov/iu_markov_ctx3_subword.parquet +3 -0
  30. models/subword_markov/iu_markov_ctx3_subword_metadata.json +7 -0
  31. models/subword_markov/iu_markov_ctx4_subword.parquet +3 -0
  32. models/subword_markov/iu_markov_ctx4_subword_metadata.json +7 -0
  33. models/subword_ngram/iu_2gram_subword.parquet +3 -0
  34. models/subword_ngram/iu_2gram_subword_metadata.json +7 -0
  35. models/subword_ngram/iu_3gram_subword.parquet +3 -0
  36. models/subword_ngram/iu_3gram_subword_metadata.json +7 -0
  37. models/subword_ngram/iu_4gram_subword.parquet +3 -0
  38. models/subword_ngram/iu_4gram_subword_metadata.json +7 -0
  39. models/subword_ngram/iu_5gram_subword.parquet +3 -0
  40. models/subword_ngram/iu_5gram_subword_metadata.json +7 -0
  41. models/tokenizer/iu_tokenizer_16k.model +3 -0
  42. models/tokenizer/iu_tokenizer_16k.vocab +0 -0
  43. models/tokenizer/iu_tokenizer_32k.model +3 -0
  44. models/tokenizer/iu_tokenizer_32k.vocab +0 -0
  45. models/tokenizer/iu_tokenizer_8k.model +3 -0
  46. models/tokenizer/iu_tokenizer_8k.vocab +0 -0
  47. models/vocabulary/iu_vocabulary.parquet +3 -0
  48. models/vocabulary/iu_vocabulary_metadata.json +17 -0
  49. models/word_markov/iu_markov_ctx1_word.parquet +3 -0
  50. models/word_markov/iu_markov_ctx1_word_metadata.json +7 -0
.gitattributes CHANGED
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  *.zip filter=lfs diff=lfs merge=lfs -text
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  *.zst filter=lfs diff=lfs merge=lfs -text
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  *tfevents* filter=lfs diff=lfs merge=lfs -text
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+ visualizations/embedding_similarity.png filter=lfs diff=lfs merge=lfs -text
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+ visualizations/embedding_tsne_multilingual.png filter=lfs diff=lfs merge=lfs -text
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+ visualizations/performance_dashboard.png filter=lfs diff=lfs merge=lfs -text
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+ visualizations/position_encoding_comparison.png filter=lfs diff=lfs merge=lfs -text
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+ visualizations/tsne_sentences.png filter=lfs diff=lfs merge=lfs -text
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+ visualizations/tsne_words.png filter=lfs diff=lfs merge=lfs -text
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+ visualizations/zipf_law.png filter=lfs diff=lfs merge=lfs -text
README.md ADDED
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1
+ ---
2
+ language: iu
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+ language_name: Inuktitut
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+ language_family: eskimoaleut
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+ tags:
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+ - wikilangs
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+ - nlp
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+ - tokenizer
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+ - embeddings
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+ - n-gram
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+ - markov
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+ - wikipedia
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+ - feature-extraction
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+ - sentence-similarity
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+ - tokenization
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+ - n-grams
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+ - markov-chain
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+ - text-mining
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+ - fasttext
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+ - babelvec
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+ - vocabulous
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+ - vocabulary
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+ - monolingual
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+ - family-eskimoaleut
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+ license: mit
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+ library_name: wikilangs
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+ pipeline_tag: text-generation
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+ datasets:
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+ - omarkamali/wikipedia-monthly
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+ dataset_info:
31
+ name: wikipedia-monthly
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+ description: Monthly snapshots of Wikipedia articles across 300+ languages
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+ metrics:
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+ - name: best_compression_ratio
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+ type: compression
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+ value: 3.905
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+ - name: best_isotropy
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+ type: isotropy
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+ value: 0.2183
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+ - name: vocabulary_size
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+ type: vocab
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+ value: 0
43
+ generated: 2026-01-10
44
+ ---
45
+
46
+ # Inuktitut - Wikilangs Models
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+ ## Comprehensive Research Report & Full Ablation Study
48
+
49
+ This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Inuktitut** Wikipedia data.
50
+ We analyze tokenizers, n-gram models, Markov chains, vocabulary statistics, and word embeddings.
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+
52
+ ## 📋 Repository Contents
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+
54
+ ### Models & Assets
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+
56
+ - Tokenizers (8k, 16k, 32k, 64k)
57
+ - N-gram models (2, 3, 4, 5-gram)
58
+ - Markov chains (context of 1, 2, 3, 4 and 5)
59
+ - Subword N-gram and Markov chains
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+ - Embeddings in various sizes and dimensions (aligned and unaligned)
61
+ - Language Vocabulary
62
+ - Language Statistics
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+
64
+ ![Performance Dashboard](visualizations/performance_dashboard.png)
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+
66
+ ### Analysis and Evaluation
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+
68
+ - [1. Tokenizer Evaluation](#1-tokenizer-evaluation)
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+ - [2. N-gram Model Evaluation](#2-n-gram-model-evaluation)
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+ - [3. Markov Chain Evaluation](#3-markov-chain-evaluation)
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+ - [4. Vocabulary Analysis](#4-vocabulary-analysis)
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+ - [5. Word Embeddings Evaluation](#5-word-embeddings-evaluation)
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+ - [6. Morphological Analysis (Experimental)](#6--morphological-analysis-experimental)
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+ - [7. Summary & Recommendations](#7-summary--recommendations)
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+ - [Metrics Glossary](#appendix-metrics-glossary--interpretation-guide)
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+ - [Visualizations Index](#visualizations-index)
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+
78
+ ---
79
+ ## 1. Tokenizer Evaluation
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+
81
+ ![Tokenizer Compression](visualizations/tokenizer_compression.png)
82
+
83
+ ![Tokenizer Fertility](visualizations/tokenizer_fertility.png)
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+
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+ ![Tokenizer OOV](visualizations/tokenizer_oov.png)
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+
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+ ![Total Tokens](visualizations/tokenizer_total_tokens.png)
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+
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+ ### Results
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+
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+ | Vocab Size | Compression | Avg Token Len | UNK Rate | Total Tokens |
92
+ |------------|-------------|---------------|----------|--------------|
93
+ | **8k** | 3.015x | 3.02 | 0.1769% | 75,744 |
94
+ | **16k** | 3.468x | 3.47 | 0.2035% | 65,854 |
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+ | **32k** | 3.905x 🏆 | 3.91 | 0.2292% | 58,476 |
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+
97
+ ### Tokenization Examples
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+
99
+ Below are sample sentences tokenized with each vocabulary size:
100
+
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+ **Sample 1:** `ᕙᐃᔅᐳᒃ ᒥᐊᓕᒐᐃᑦ ᓄᓇᖓᓐᓂ ᖃᕆᑕᐅᔭᒃᑯᑦ ᑐᑭᓯᒋᐊᕐᕕᒃ ᓴᖅᑭᑕᐅᓚᐅᖅᓯᒪᔪᖅ ᒫᒃ ᓵᑯᐴᒡᒧᑦ. ᕙᐃᔅᐳᒃ ᑐᓴᐅᒪᔭᐅᓂᖅᐹᖑᕗᖅ ...`
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+
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+ | Vocab | Tokens | Count |
104
+ |-------|--------|-------|
105
+ | 8k | `▁ᕙᐃᔅᐳᒃ ▁ᒥᐊᓕᒐᐃᑦ ▁ᓄᓇᖓᓐᓂ ▁ᖃᕆᑕᐅᔭᒃᑯᑦ ▁ᑐᑭᓯᒋᐊ ᕐᕕᒃ ▁ᓴᖅᑭᑕᐅᓚᐅᖅᓯᒪᔪᖅ ▁ᒫᒃ ▁ᓵᑯ ᐴᒡ ... (+16 more)` | 26 |
106
+ | 16k | `▁ᕙᐃᔅᐳᒃ ▁ᒥᐊᓕᒐᐃᑦ ▁ᓄᓇᖓᓐᓂ ▁ᖃᕆᑕᐅᔭᒃᑯᑦ ▁ᑐᑭᓯᒋᐊ ᕐᕕᒃ ▁ᓴᖅᑭᑕᐅᓚᐅᖅᓯᒪᔪᖅ ▁ᒫᒃ ▁ᓵᑯᐴᒡᒧᑦ . ... (+10 more)` | 20 |
107
+ | 32k | `▁ᕙᐃᔅᐳᒃ ▁ᒥᐊᓕᒐᐃᑦ ▁ᓄᓇᖓᓐᓂ ▁ᖃᕆᑕᐅᔭᒃᑯᑦ ▁ᑐᑭᓯᒋᐊᕐᕕᒃ ▁ᓴᖅᑭᑕᐅᓚᐅᖅᓯᒪᔪᖅ ▁ᒫᒃ ▁ᓵᑯᐴᒡᒧᑦ . ▁ᕙᐃᔅᐳᒃ ... (+7 more)` | 17 |
108
+
109
+ **Sample 2:** `ᐅᓵᐃᐅ—[ᖃᓪᓗᓈᑎᑐᑦ—Ohio]— ) ᐃᑎᐊᔪᑦ ᐃᓗᐊᓂ. ᐅᓵᐃᐅ ᐃᓄᖁᑎ ᐊᒥᐊᓕᑲ. ᐊᐅᓚᑦᑎᔩᑦ ᓯᕗᓕᖅᑎᖓᑦ-ᓄᓇᓖᑦ ᑰᕉᒻᐴᔅ «...`
110
+
111
+ | Vocab | Tokens | Count |
112
+ |-------|--------|-------|
113
+ | 8k | `▁ᐅᓵᐃᐅ —[ ᖃᓪᓗᓈᑎᑐᑦ — ohio ]— ▁) ▁ᐃᑎᐊᔪᑦ ▁ᐃᓗᐊᓂ . ... (+27 more)` | 37 |
114
+ | 16k | `▁ᐅᓵᐃᐅ —[ ᖃᓪᓗᓈᑎᑐᑦ — ohio ]— ▁) ▁ᐃᑎᐊᔪᑦ ▁ᐃᓗᐊᓂ . ... (+22 more)` | 32 |
115
+ | 32k | `▁ᐅᓵᐃᐅ —[ ᖃᓪᓗᓈᑎᑐᑦ — ohio ]— ▁) ▁ᐃᑎᐊᔪᑦ ▁ᐃᓗᐊᓂ . ... (+22 more)` | 32 |
116
+
117
+ **Sample 3:** `ᐊᐅᑦᓯᓇᖅᑐᖅ ᓱᓕᐊᖅ ᐊᓂᖅᐸᓈᖅᑑᔭᖅᑐᖅ ᐅᓚᐱᑉᐹ ᓴᐳᒻᒥᕚ ᑎᒥ. ᐅᑉᔭᒃᐳᖅ ᐊᓐᓄᕌᓂᒃ`
118
+
119
+ | Vocab | Tokens | Count |
120
+ |-------|--------|-------|
121
+ | 8k | `▁ᐊᐅᑦᓯᓇᖅᑐᖅ ▁ᓱᓕᐊᖅ ▁ᐊᓂᖅᐸᓈᖅᑑᔭᖅᑐᖅ ▁ᐅᓚᐱ ᑉᐹ ▁ᓴᐳᒻᒥᕚ ▁ᑎᒥ . ▁ᐅᑉᔭᒃᐳᖅ ▁ᐊᓐᓄᕌᓂᒃ` | 10 |
122
+ | 16k | `▁ᐊᐅᑦᓯᓇᖅᑐᖅ ▁ᓱᓕᐊᖅ ▁ᐊᓂᖅᐸᓈᖅᑑᔭᖅᑐᖅ ▁ᐅᓚᐱᑉᐹ ▁ᓴᐳᒻᒥᕚ ▁ᑎᒥ . ▁ᐅᑉᔭᒃᐳᖅ ▁ᐊᓐ��ᕌᓂᒃ` | 9 |
123
+ | 32k | `▁ᐊᐅᑦᓯᓇᖅᑐᖅ ▁ᓱᓕᐊᖅ ▁ᐊᓂᖅᐸᓈᖅᑑᔭᖅᑐᖅ ▁ᐅᓚᐱᑉᐹ ▁ᓴᐳᒻᒥᕚ ▁ᑎᒥ . ▁ᐅᑉᔭᒃᐳᖅ ▁ᐊᓐᓄᕌᓂᒃ` | 9 |
124
+
125
+
126
+ ### Key Findings
127
+
128
+ - **Best Compression:** 32k achieves 3.905x compression
129
+ - **Lowest UNK Rate:** 8k with 0.1769% unknown tokens
130
+ - **Trade-off:** Larger vocabularies improve compression but increase model size
131
+ - **Recommendation:** 32k vocabulary provides optimal balance for production use
132
+
133
+ ---
134
+ ## 2. N-gram Model Evaluation
135
+
136
+ ![N-gram Perplexity](visualizations/ngram_perplexity.png)
137
+
138
+ ![N-gram Unique](visualizations/ngram_unique.png)
139
+
140
+ ![N-gram Coverage](visualizations/ngram_coverage.png)
141
+
142
+ ### Results
143
+
144
+ | N-gram | Variant | Perplexity | Entropy | Unique N-grams | Top-100 Coverage | Top-1000 Coverage |
145
+ |--------|---------|------------|---------|----------------|------------------|-------------------|
146
+ | **2-gram** | Word | 93 🏆 | 6.54 | 126 | 90.8% | 100.0% |
147
+ | **2-gram** | Subword | 962 | 9.91 | 3,039 | 37.0% | 87.0% |
148
+ | **3-gram** | Word | 130 | 7.03 | 174 | 73.9% | 100.0% |
149
+ | **3-gram** | Subword | 5,020 | 12.29 | 12,029 | 15.7% | 49.7% |
150
+ | **4-gram** | Word | 694 | 9.44 | 794 | 25.0% | 100.0% |
151
+ | **4-gram** | Subword | 14,093 | 13.78 | 28,526 | 8.8% | 30.5% |
152
+ | **5-gram** | Word | 607 | 9.25 | 676 | 24.5% | 100.0% |
153
+ | **5-gram** | Subword | 19,229 | 14.23 | 32,493 | 7.1% | 24.4% |
154
+
155
+ ### Top 5 N-grams by Size
156
+
157
+ **2-grams (Word):**
158
+
159
+ | Rank | N-gram | Count |
160
+ |------|--------|-------|
161
+ | 1 | `san marino` | 73 |
162
+ | 2 | `of the` | 55 |
163
+ | 3 | `ᖄᖓᒍᑦ ᖄᖓᒍᑦ` | 55 |
164
+ | 4 | `ᑭᒻᒧᑦ ᐅᖅᓯᖅ` | 47 |
165
+ | 5 | `ᑕᕆᐅᑉ ᐊᑭᐊᓂ` | 44 |
166
+
167
+ **3-grams (Word):**
168
+
169
+ | Rank | N-gram | Count |
170
+ |------|--------|-------|
171
+ | 1 | `ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ` | 51 |
172
+ | 2 | `ᑭᒻᒧᑦ ᐅᖅᓯᖅ www` | 30 |
173
+ | 3 | `ᐃᓄᖁᑎ ᐊᒥᐊᓕᑲ ᐊᐅᓚᑦᑎᔩᑦ` | 22 |
174
+ | 4 | `ᐊᐅᓚᑦᑎᔩᑦ ᓯᕗᓕᖅᑎᖓᑦ ᓄᓇᓖᑦ` | 22 |
175
+ | 5 | `ᐊᒥᐊᓕᑲ ᐊᐅᓚᑦᑎᔩᑦ ᓯᕗᓕᖅᑎᖓᑦ` | 22 |
176
+
177
+ **4-grams (Word):**
178
+
179
+ | Rank | N-gram | Count |
180
+ |------|--------|-------|
181
+ | 1 | `ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ` | 48 |
182
+ | 2 | `ᐃᓄᖁᑎ ᐊᒥᐊᓕᑲ ᐊᐅᓚᑦᑎᔩᑦ ᓯᕗᓕᖅᑎᖓᑦ` | 22 |
183
+ | 3 | `ᐊᒥᐊᓕᑲ ᐊᐅᓚᑦᑎᔩᑦ ᓯᕗᓕᖅᑎᖓᑦ ᓄᓇᓖᑦ` | 22 |
184
+ | 4 | `ᓄᓇᓖᑦ ᑭᒻᒧᑦ ᐅᖅᓯᖅ www` | 20 |
185
+ | 5 | `the grand and general` | 10 |
186
+
187
+ **5-grams (Word):**
188
+
189
+ | Rank | N-gram | Count |
190
+ |------|--------|-------|
191
+ | 1 | `ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ` | 45 |
192
+ | 2 | `ᐃᓄᖁᑎ ᐊᒥᐊᓕᑲ ᐊᐅᓚᑦᑎᔩᑦ ᓯᕗᓕᖅᑎᖓᑦ ᓄᓇᓖᑦ` | 22 |
193
+ | 3 | `the grand and general council` | 10 |
194
+ | 4 | `ᓄᓇ frameless upright 0 3` | 7 |
195
+ | 5 | `o canada we stand on` | 5 |
196
+
197
+ **2-grams (Subword):**
198
+
199
+ | Rank | N-gram | Count |
200
+ |------|--------|-------|
201
+ | 1 | `ᑦ _` | 4,757 |
202
+ | 2 | `_ ᐊ` | 3,099 |
203
+ | 3 | `ᖅ _` | 2,694 |
204
+ | 4 | `_ ᐃ` | 2,386 |
205
+ | 5 | `, _` | 2,385 |
206
+
207
+ **3-grams (Subword):**
208
+
209
+ | Rank | N-gram | Count |
210
+ |------|--------|-------|
211
+ | 1 | `ᐊ ᒻ ᒪ` | 851 |
212
+ | 2 | `_ ᐊ ᒻ` | 837 |
213
+ | 3 | `_ ᓄ ᓇ` | 816 |
214
+ | 4 | `ᓂ ᒃ _` | 784 |
215
+ | 5 | `ᑦ _ ᐊ` | 710 |
216
+
217
+ **4-grams (Subword):**
218
+
219
+ | Rank | N-gram | Count |
220
+ |------|--------|-------|
221
+ | 1 | `_ ᐊ ᒻ ᒪ` | 833 |
222
+ | 2 | `ᐊ ᒻ ᒪ _` | 420 |
223
+ | 3 | `ᐊ ᒻ ᒪ ᓗ` | 407 |
224
+ | 4 | `ᖅ ᑐ ᖅ _` | 405 |
225
+ | 5 | `ᒻ ᒪ ᓗ _` | 385 |
226
+
227
+ **5-grams (Subword):**
228
+
229
+ | Rank | N-gram | Count |
230
+ |------|--------|-------|
231
+ | 1 | `_ ᐊ ᒻ ᒪ _` | 418 |
232
+ | 2 | `_ ᐊ ᒻ ᒪ ᓗ` | 400 |
233
+ | 3 | `ᐊ ᒻ ᒪ ᓗ _` | 385 |
234
+ | 4 | `_ t h e _` | 346 |
235
+ | 5 | `ᑦ _ ᐊ ᒻ ᒪ` | 218 |
236
+
237
+
238
+ ### Key Findings
239
+
240
+ - **Best Perplexity:** 2-gram (word) with 93
241
+ - **Entropy Trend:** Decreases with larger n-grams (more predictable)
242
+ - **Coverage:** Top-1000 patterns cover ~24% of corpus
243
+ - **Recommendation:** 4-gram or 5-gram for best predictive performance
244
+
245
+ ---
246
+ ## 3. Markov Chain Evaluation
247
+
248
+ ![Markov Entropy](visualizations/markov_entropy.png)
249
+
250
+ ![Markov Contexts](visualizations/markov_contexts.png)
251
+
252
+ ![Markov Branching](visualizations/markov_branching.png)
253
+
254
+ ### Results
255
+
256
+ | Context | Variant | Avg Entropy | Perplexity | Branching Factor | Unique Contexts | Predictability |
257
+ |---------|---------|-------------|------------|------------------|-----------------|----------------|
258
+ | **1** | Word | 0.3388 | 1.265 | 1.76 | 15,002 | 66.1% |
259
+ | **1** | Subword | 1.4995 | 2.827 | 13.51 | 541 | 0.0% |
260
+ | **2** | Word | 0.0479 | 1.034 | 1.07 | 26,047 | 95.2% |
261
+ | **2** | Subword | 0.9813 | 1.974 | 4.39 | 7,301 | 1.9% |
262
+ | **3** | Word | 0.0129 | 1.009 | 1.02 | 27,517 | 98.7% |
263
+ | **3** | Subword | 0.5441 | 1.458 | 2.22 | 31,981 | 45.6% |
264
+ | **4** | Word | 0.0049 🏆 | 1.003 | 1.01 | 27,602 | 99.5% |
265
+ | **4** | Subword | 0.3121 | 1.242 | 1.55 | 70,999 | 68.8% |
266
+
267
+ ### Generated Text Samples (Word-based)
268
+
269
+ Below are text samples generated from each word-based Markov chain model:
270
+
271
+ **Context Size 1:**
272
+
273
+ 1. `ᐊᒻᒪ ᐱᕈᖅᓯᐊᖅ ᑭᒃᑯᑦ ᐅᐊᑎᒌᓯᕆᒥᒻᒧᑦ ᓴᐃᓇᒃᑭᐅᔪᖅ ᐊᑎᖃᕐᒥᑕᐅᓂᖏᓐᓂᒃ ᐊᓂᔨᖃᕆᔪᑦ ᐅᓂᖅᑕᖃᕐᑕᐅᔪᑦ ᐅᑎᓇᐅᖃᑎᒌᑦ ᐱᒻᒥᕐᒥᐅᑕᓗᑉ ᑭᒻᒧᑦ ᐅᖅᓯᖅ www...`
274
+ 2. `ᐊᒻᒪᓗ ᐊᐅᓚᓃᑦ ᐱᓕᕆᖃᑎᒌᖃᑦᑕᖅᑐᑦ ᐋᖅᑭᐅᒪᑎᑦᑎᓂᐊᕐᓗᓂ ᐊᖏᕐᕋᒥᒃ ᐅᓗᕆᐊᓇᙱᑦᑐᒃᑯᑦ ᓲᕐᓗ ᕕᑐᕆᑯ ᐃᓇᓗᒃᑲ ᐃᒡᓗᓐᓂ ᓄᓇᖃᖅᐳᑦ ᐸᑏᑎ ᐃᓕᓚᐅᖅᑕᕋ ᐊᐅᓚ...`
275
+ 3. `the roman republic the sammarinese fascist government declared war on their passports citation neede...`
276
+
277
+ **Context Size 2:**
278
+
279
+ 1. `san marino appealed to pope boniface viii against the contribution demands by the legate papal gover...`
280
+ 2. `ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᒥᑭᔫᖕᓂᒃ ᑐᐊᑎᐊᓂᒃ ᐊᒻᒪ ᐃᓛᓐᓂᒃᑯᑦ ᓴᓇᔭᐅᕙᒃᖢᑎᒃ ᒑᑲᒧᓕᒧᑦ ᓵᓪᓴᒧᑦ ᓂᐅᓐᔅᒧᑦ ᐊᒻᒪ ᓯᓚᓐᑐᒧᑦ ᑯᕆᓐᑐ ᒪᑉᐱ...`
281
+ 3. `of the european union it is the fifth smallest country in europe after vatican city and state`
282
+
283
+ **Context Size 3:**
284
+
285
+ 1. `ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᒃᑲᓐᓂᖅ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ`
286
+ 2. `ᑭᒻᒧᑦ ᐅᖅᓯᖅ www sd gov`
287
+ 3. `ᐃᓄᖁᑎ ᐊᒥᐊᓕᑲ ᐊᐅᓚᑦᑎᔩᑦ ᓯᕗᓕᖅᑎᖓᑦ ᓄᓇᓖᑦ ᐲᕐ ᖃᓪᓗᓈᑎᑐᑦ pierre ᓄᓇᓖᑦ ᑭᒻᒧᑦ ᐅᖅᓯᖅ www ok gov`
288
+
289
+ **Context Size 4:**
290
+
291
+ 1. `ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ ᖄᖓᒍᑦ`
292
+ 2. `ᐊᒥᐊᓕᑲ ᐊᐅᓚᑦᑎᔩᑦ ᓯᕗᓕᖅᑎᖓᑦ ᓄᓇᓖᑦ ᐴᕐᑦᓛᓐᑦ ᖃᓪᓗᓈᑎᑐᑦ portland ᓄᓇᓖᑦ ᑭᒻᒧᑦ ᐅᖅᓯᖅ www nv gov`
293
+ 3. `ᐃᓄᖁᑎ ᐊᒥᐊᓕᑲ ᐊᐅᓚᑦᑎᔩᑦ ᓯᕗᓕᖅᑎᖓᑦ ᓄᓇᓖᑦ ᓂᐅ ᐆᕐᓖᓐᔅ ᖃᓪᓗᓈᑎᑐᑦ new orleans ᓄᓇᓖᑦ ᑭᒻᒧᑦ ᐅᖅᓯᖅ www idaho gov`
294
+
295
+
296
+ ### Generated Text Samples (Subword-based)
297
+
298
+ Below are text samples generated from each subword-based Markov chain model:
299
+
300
+ **Context Size 1:**
301
+
302
+ 1. `_ᕕᒃ_ᒐᔪᑎᓪᓗᑕᑭᓯᐊᒻᒪ_`
303
+ 2. `ᖅᑐᒃ_ontunixiteco`
304
+ 3. `ᑦᑕ)_ᑲ,_ᖄᕐᒥᓱᐊᕈᑎᐊᒻ`
305
+
306
+ **Context Size 2:**
307
+
308
+ 1. `ᑦ_(ᐱᓚᕈ,_ᑎᑎᓪᓗᓕᖃᖅᐳᑦ`
309
+ 2. `_ᐊᐅᐸᐃᒡ_ᐊᖕᓇᖅ_ᑭᓕᐊᑉ_`
310
+ 3. `ᖅ_ᑕᐃᑲᓂᐸ,_ᓄᓇᓖᑦ_ᐃᒡᓗ`
311
+
312
+ **Context Size 3:**
313
+
314
+ 1. `ᐊᒻᒪᓗ_ᕿᓚᒃ._ᓴᓂᑭᓗᐊᕐᒥ.`
315
+ 2. `_ᐊᒻᒪ_ᐃᓗᐊᓃᑐᓂ._ᐃᓚᖃᖅᑐ`
316
+ 3. `_ᓄᓇᖃᐃᓐᓇᕆᐊᓚᐅᖅᐳᖅ_ᐊᕋᕕ`
317
+
318
+ **Context Size 4:**
319
+
320
+ 1. `_ᐊᒻᒪ_ᑎᓴᒪᓂᒃ_ᓄᓇᒥᐅᑕᐅᕗᑦ`
321
+ 2. `ᐊᒻᒪ_ᑕᑯᑦᑎᐊᔪᐃᓐᓇᕐᒥᒃ_ᐱᖃ`
322
+ 3. `ᐊᒻᒪᓗ_ᖁᕕᐊᓱᖕᓂᖅ")ᐃᙱᐅᓯᖓ`
323
+
324
+
325
+ ### Key Findings
326
+
327
+ - **Best Predictability:** Context-4 (word) with 99.5% predictability
328
+ - **Branching Factor:** Decreases with context size (more deterministic)
329
+ - **Memory Trade-off:** Larger contexts require more storage (70,999 contexts)
330
+ - **Recommendation:** Context-3 or Context-4 for text generation
331
+
332
+ ---
333
+ ## 4. Vocabulary Analysis
334
+
335
+ ![Zipf's Law](visualizations/zipf_law.png)
336
+
337
+ ![Top Words](visualizations/top20_words.png)
338
+
339
+ ![Coverage Curve](visualizations/vocab_coverage.png)
340
+
341
+ ### Statistics
342
+
343
+ | Metric | Value |
344
+ |--------|-------|
345
+ | Vocabulary Size | 3,802 |
346
+ | Total Tokens | 18,925 |
347
+ | Mean Frequency | 4.98 |
348
+ | Median Frequency | 2 |
349
+ | Frequency Std Dev | 13.99 |
350
+
351
+ ### Most Common Words
352
+
353
+ | Rank | Word | Frequency |
354
+ |------|------|-----------|
355
+ | 1 | ᐊᒻᒪ | 424 |
356
+ | 2 | ᐊᒻᒪᓗ | 392 |
357
+ | 3 | the | 353 |
358
+ | 4 | of | 210 |
359
+ | 5 | ᐃᓄᐃᑦ | 139 |
360
+ | 6 | and | 131 |
361
+ | 7 | ᐅᕝᕙᓘᓐᓃᑦ | 114 |
362
+ | 8 | in | 106 |
363
+ | 9 | ᖃᓪᓗᓈᑎᑐᑦ | 104 |
364
+ | 10 | to | 98 |
365
+
366
+ ### Least Common Words (from vocabulary)
367
+
368
+ | Rank | Word | Frequency |
369
+ |------|------|-----------|
370
+ | 1 | ᑕᑯᔭᒐᖃᕐᕕᐅᔪᑦ | 2 |
371
+ | 2 | ᒥᐅᓯᐅ | 2 |
372
+ | 3 | ᓴᒃᑯᑐᖃᕐᓄᑦ | 2 |
373
+ | 4 | ᓴᕕᕋᔭᓄᑦ | 2 |
374
+ | 5 | ᐊᒥᐊᖅᑕᐅᓯᒪᔪᑦ | 2 |
375
+ | 6 | ᑭᐊᕋᒥ | 2 |
376
+ | 7 | ᔨᐊᓇᕆ | 2 |
377
+ | 8 | ᓴᓇᓐᖑᐊᒐᐃᑦ | 2 |
378
+ | 9 | ᓅᑉᐸᓪᓕᐊᔪᓄᑦ | 2 |
379
+ | 10 | ᓄᓇᒥᐅᑕᓕᕆᓂᕐᒧᑦ | 2 |
380
+
381
+ ### Zipf's Law Analysis
382
+
383
+ | Metric | Value |
384
+ |--------|-------|
385
+ | Zipf Coefficient | 0.6869 |
386
+ | R² (Goodness of Fit) | 0.969855 |
387
+ | Adherence Quality | **excellent** |
388
+
389
+ ### Coverage Analysis
390
+
391
+ | Top N Words | Coverage |
392
+ |-------------|----------|
393
+ | Top 100 | 30.3% |
394
+ | Top 1,000 | 65.3% |
395
+ | Top 5,000 | 0.0% |
396
+ | Top 10,000 | 0.0% |
397
+
398
+ ### Key Findings
399
+
400
+ - **Zipf Compliance:** R²=0.9699 indicates excellent adherence to Zipf's law
401
+ - **High Frequency Dominance:** Top 100 words cover 30.3% of corpus
402
+ - **Long Tail:** -6,198 words needed for remaining 100.0% coverage
403
+
404
+ ---
405
+ ## 5. Word Embeddings Evaluation
406
+
407
+ ![Embedding Isotropy](visualizations/embedding_isotropy.png)
408
+
409
+ ![Similarity Matrix](visualizations/embedding_similarity.png)
410
+
411
+ ![t-SNE Words](visualizations/tsne_words.png)
412
+
413
+ ![t-SNE Sentences](visualizations/tsne_sentences.png)
414
+
415
+
416
+ ### 5.1 Cross-Lingual Alignment
417
+
418
+ ![Alignment Quality](visualizations/embedding_alignment_quality.png)
419
+
420
+ ![Multilingual t-SNE](visualizations/embedding_tsne_multilingual.png)
421
+
422
+
423
+ ### 5.2 Model Comparison
424
+
425
+ | Model | Dimension | Isotropy | Semantic Density | Alignment R@1 | Alignment R@10 |
426
+ |-------|-----------|----------|------------------|---------------|----------------|
427
+ | **mono_32d** | 32 | 0.2183 | 0.4714 | N/A | N/A |
428
+ | **mono_64d** | 64 | 0.0445 | 0.4570 | N/A | N/A |
429
+ | **mono_128d** | 128 | 0.0046 | 0.4821 | N/A | N/A |
430
+ | **aligned_32d** | 32 | 0.2183 🏆 | 0.4659 | 0.0189 | 0.1384 |
431
+ | **aligned_64d** | 64 | 0.0445 | 0.4550 | 0.0314 | 0.1384 |
432
+ | **aligned_128d** | 128 | 0.0046 | 0.4794 | 0.0503 | 0.1509 |
433
+
434
+ ### Key Findings
435
+
436
+ - **Best Isotropy:** aligned_32d with 0.2183 (more uniform distribution)
437
+ - **Semantic Density:** Average pairwise similarity of 0.4685. Lower values indicate better semantic separation.
438
+ - **Alignment Quality:** Aligned models achieve up to 5.0% R@1 in cross-lingual retrieval.
439
+ - **Recommendation:** 128d aligned for best cross-lingual performance
440
+
441
+ ---
442
+ ## 6. Morphological Analysis (Experimental)
443
+
444
+ 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.
445
+
446
+ ### 6.1 Productivity & Complexity
447
+
448
+ | Metric | Value | Interpretation | Recommendation |
449
+ |--------|-------|----------------|----------------|
450
+ | Productivity Index | **5.000** | High morphological productivity | Reliable analysis |
451
+ | Idiomaticity Gap | **3.097** | High formulaic/idiomatic content | - |
452
+
453
+ ### 6.2 Affix Inventory (Productive Units)
454
+
455
+ 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.
456
+
457
+ #### Productive Prefixes
458
+ | Prefix | Examples |
459
+ |--------|----------|
460
+ | `-ᐊ` | ᐊᑐᖅᑕᐅᓯᒪᔪᖅ, ᐊᔅᑦᕌᓕᐊ, ᐊᓂᒍᖅᑎᓪᓗᒋᑦ |
461
+ | `-ᐃ` | ᐃᓅᖃᑎᒌᑦ, ᐃᖃᑦᑐᖅ, ᐃᓱ |
462
+ | `-ᐅ` | ᐅᓪᓗᓂᒃ, ᐅᓛᓴᒥ, ᐅᑭᐅᖃᓕᖅᑎᓪᓗᒋᑦ |
463
+ | `-ᐅᖃ` | ᐅᖃᓕᒫᒐᓄᑦ, ᐅᖃᐅᓯᒃᓴᓂᖏᑦ, ᐅᖃᐅᓯᕐᖓᐅᑎᖃᕐᒪᑎᑕ |
464
+ | `-ᓄᓇ` | ᓄᓇᕕᐅᑉ, ᓄᓇᖁᑎᖓᓂᒃ, ᓄᓇᙳᐊᖓ |
465
+ | `-ᑕᐃ` | ᑕᐃᒫᑦᓴᐃᓐᓇᖅ, ᑕᐃᒃᓱᒪᓂ, ᑕᐃᒃᑯᓇᓂ |
466
+ | `-ᐃᓄ` | ᐃᓄᒃ, ᐃᓄᒋᐊᓛᖑᓪᓗᓂ, ᐃᓄᖕᓂᒃ |
467
+ | `-co` | coca, corporate, country |
468
+
469
+ #### Productive Suffixes
470
+ | Suffix | Examples |
471
+ |--------|----------|
472
+ | `-ᑦ` | ᖃᓚᒪᓐᖏᑑᓗᑎᓘᓐᓃᑦ, ᐃᓅᖃᑎᒌᑦ, ᐱᓕᕆᑦᑎᐊᕐᓂᖏᓐᓄᑦ |
473
+ | `-ᖅ` | ᐃᖃᑦᑐᖅ, ᐊᑐᖅᑕᐅᓯᒪᔪᖅ, ᓯᐅᕋᖅ |
474
+ | `-ᒃ` | ᓯᕗᓪᓕᖅᐹᒃ, ᐊᑕᐅᓯᕐᒥᒃ, ᐅᓪᓗᓂᒃ |
475
+ | `-ᓂᒃ` | ᐅᓪᓗᓂᒃ, ᒥᓕᐊᓐᓂᒃ, ᓂᐊᖁᕐᓂᒃ |
476
+ | `-ᑐᖅ` | ᐃᖃᑦᑐᖅ, ᓯᐅᕋᐅᔮᖅᑐᖅ, ᐃᓅᓕᖅᑐᖅ |
477
+ | `-ᓄᑦ` | ᐱᓕᕆᑦᑎᐊᕐᓂᖏᓐᓄᑦ, ᑭᖑᓪᓕᖅᐹᖅᓯᐅᑎᓄᑦ, ᐊᑕᐅᓯᐅᖃᑎᒌᓄᑦ |
478
+ | `-ᓂ` | ᓯᓚᑖᓂ, ᐃᓚᐅᙱᖦᖢᓂ, ᖃᓂᒋᔭᖓᓂ |
479
+ | `-t` | aallatqiit, pitquhiinit, anngutikhaqanngittagaangat |
480
+
481
+ ### 6.3 Bound Stems (Lexical Roots)
482
+
483
+ 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.
484
+
485
+ | Stem | Cohesion | Substitutability | Examples |
486
+ |------|----------|------------------|----------|
487
+ | `ᕗᓪᓕᖅ` | 1.82x | 6 contexts | ᓯᕗᓪᓕᖅ, ᓯᕗᓪᓕᖅᐹᒃ, ᓯᕗᓪᓕᖅᐹᖅ |
488
+ | `ᓯᕗᓪᓕ` | 1.82x | 5 contexts | ᓯᕗᓪᓕᖅ, ᓯᕗᓪᓕᕐᒥ, ᓯᕗᓪᓕᖅᐹᒃ |
489
+ | `ᖅᓯᒪᔪ` | 1.50x | 6 contexts | ᓇᐃᓈᖅᓯᒪᔪᖅ, ᑎᑎᕋᖅᓯᒪᔪᖅ, ᑎᑎᕋᖅᓯᒪᔪᒥ |
490
+ | `ᓯᒪᔪᖅ` | 1.72x | 4 contexts | ᐃᓚᓯᒪᔪᖅ, ᓴᓇᓯᒪᔪᖅ, ᓴᖅᑭᓯᒪᔪᖅ |
491
+ | `ᖑᓪᓗᓂ` | 1.89x | 3 contexts | ᒥᑭᓛᖑᓪᓗᓂ, ᐊᖏᓛᖑᓪᓗᓂ, ᐊᖏᓛᖑᓪᓗᓂᓗ |
492
+
493
+ ### 6.4 Affix Compatibility (Co-occurrence)
494
+
495
+ This table shows which prefixes and suffixes most frequently co-occur on the same stems, revealing the 'stacking' rules of the language's morphology.
496
+
497
+ | Prefix | Suffix | Frequency | Examples |
498
+ |--------|--------|-----------|----------|
499
+ | `-ᐊ` | `-ᑦ` | 61 words | ᐊᓂᒍᖅᑎᓪᓗᒋᑦ, ᐊᐅᓚᑦᑎᐊᕈᓐᓃᖅᑐᑦ |
500
+ | `-ᐃ` | `-ᖅ` | 47 words | ᐃᖃᑦᑐᖅ, ᐃᓅᓕᖅᑐᖅ |
501
+ | `-ᐃ` | `-ᑦ` | 46 words | ᐃᓅᖃᑎᒌᑦ, ᐃᓯᒐᐃᑦ |
502
+ | `-ᐅ` | `-ᑦ` | 41 words | ᐅᑭᐅᖃᓕᖅᑎᓪᓗᒋᑦ, ᐅᖃᓕᒫᒐᓄᑦ |
503
+ | `-ᐊ` | `-ᖅ` | 37 words | ᐊᑐᖅᑕᐅᓯᒪᔪᖅ, ᐊᖏᓛᖑᔪᖅ |
504
+ | `-ᐃ` | `-ᒃ` | 33 words | ᐃᓄᒃ, ᐃᓕᓐᓂᐊᕈᑎᒥᒃ |
505
+ | `-ᐊ` | `-ᒃ` | 24 words | ᐊᑕᐅᓯᕐᒥᒃ, ᐊᑯᓕᕕᒃ |
506
+ | `-ᐃ` | `-ᓂᒃ` | 19 words | ᐃᓄᖕᓂᒃ, ᐃᕐᕋᕕᖏᓐᓂᒃ |
507
+ | `-ᐅ` | `-ᖅ` | 19 words | ᐅᐱᕐᖓᖅ, ᐅᖃᐅᓯᖅ |
508
+ | `-ᐊ` | `-ᓂ` | 17 words | ᐊᑐᖅᑕᐅᓪᓗᓂ, ᐊᖏᔪᒻᒪᕆᐊᓘᓪᓗᓂ |
509
+
510
+ ### 6.5 Recursive Morpheme Segmentation
511
+
512
+ Using **Recursive Hierarchical Substitutability**, we decompose complex words into their constituent morphemes. This approach handles nested affixes (e.g., `prefix-prefix-root-suffix`).
513
+
514
+ | Word | Suggested Split | Confidence | Stem |
515
+ |------|-----------------|------------|------|
516
+ | ᐋᖅᑭᒃᓯᒪᓂᖓᓄᑦ | **`ᐋᖅᑭᒃᓯᒪᓂᖓ-ᓄᑦ`** | 4.5 | `ᐋᖅᑭᒃᓯᒪᓂᖓ` |
517
+ | presented | **`present-ed`** | 4.5 | `present` |
518
+ | uniformed | **`uniform-ed`** | 4.5 | `uniform` |
519
+ | ᓄᓇᓕᐸᐅᔭᖓᓄᑦ | **`ᓄᓇᓕᐸᐅᔭᖓ-ᓄᑦ`** | 4.5 | `ᓄᓇᓕᐸᐅᔭᖓ` |
520
+ | ᑖᒃᓰᔭᐃᔭᕈᑎᑦ | **`ᑖᒃᓰᔭᐃᔭᕈᑎ-ᑦ`** | 4.5 | `ᑖᒃᓰᔭᐃᔭᕈᑎ` |
521
+ | ᑖᒃᓰᔭᐃᔭᕈᑎᓄᑦ | **`ᑖᒃᓰᔭᐃᔭᕈᑎ-ᓄᑦ`** | 4.5 | `ᑖᒃᓰᔭᐃᔭᕈᑎ` |
522
+ | ᑖᒃᓰᔭᐃᔭᕈᑎᓂᒃ | **`ᑖᒃᓰᔭᐃᔭᕈᑎ-ᓂᒃ`** | 4.5 | `ᑖᒃᓰᔭᐃᔭᕈᑎ` |
523
+ | ᒫᓐᑎᕕᐅᓪᑐᒧᑦ | **`ᒫᓐᑎᕕᐅᓪᑐ-ᒧᑦ`** | 4.5 | `ᒫᓐᑎᕕᐅᓪᑐ` |
524
+ | ᐊᕕᑦᑐᖅᓯᒪᔪᓂᑦ | **`ᐊᕕᑦᑐᖅᓯᒪᔪᓂ-ᑦ`** | 4.5 | `ᐊᕕᑦᑐᖅᓯᒪᔪᓂ` |
525
+ | ᐃᓕᓐᓂᐊᕈᑎᒥᒃ | **`ᐃᓕᓐᓂᐊᕈᑎ-ᒥᒃ`** | 4.5 | `ᐃᓕᓐᓂᐊᕈᑎ` |
526
+ | ᐃᓕᓐᓂᐊᖅᑎᓂᒃ | **`ᐃᓕᓐᓂᐊᖅᑎ-ᓂᒃ`** | 4.5 | `ᐃᓕᓐᓂᐊᖅᑎ` |
527
+ | ᐋᖅᑭᒃᓯᒪᓂᖓᓂᒃ | **`ᐋᖅᑭᒃᓯᒪᓂᖓ-ᓂᒃ`** | 4.5 | `ᐋᖅᑭᒃᓯᒪᓂᖓ` |
528
+ | ᐃᓚᒋᔭᐅᓕᖅᑐᖅ | **`ᐃᓚᒋᔭᐅᓕ-ᖅ-ᑐᖅ`** | 3.0 | `ᐃᓚᒋᔭᐅᓕ` |
529
+ | ᐊᒥᐊᖅᑕᐅᓯᒪᔪᑦ | **`ᐊ-ᒥᐊᖅᑕᐅᓯᒪᔪ-ᑦ`** | 3.0 | `ᒥᐊᖅᑕᐅᓯᒪᔪ` |
530
+ | ᐃᓄᑐᐃᓐᓇᕐᓂᒃ | **`ᐃᓄ-ᑐᐃᓐᓇᕐ-ᓂᒃ`** | 3.0 | `ᑐᐃᓐᓇᕐ` |
531
+
532
+ ### 6.6 Linguistic Interpretation
533
+
534
+ > **Automated Insight:**
535
+ The language Inuktitut shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.
536
+
537
+ > **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.
538
+
539
+ ---
540
+ ## 7. Summary & Recommendations
541
+
542
+ ![Performance Dashboard](visualizations/performance_dashboard.png)
543
+
544
+ ### Production Recommendations
545
+
546
+ | Component | Recommended | Rationale |
547
+ |-----------|-------------|-----------|
548
+ | Tokenizer | **32k BPE** | Best compression (3.91x) |
549
+ | N-gram | **2-gram** | Lowest perplexity (93) |
550
+ | Markov | **Context-4** | Highest predictability (99.5%) |
551
+ | Embeddings | **100d** | Balanced semantic capture and isotropy |
552
+
553
+
554
+ ---
555
+ ## Appendix: Metrics Glossary & Interpretation Guide
556
+
557
+ This section provides definitions, intuitions, and guidance for interpreting the metrics used throughout this report.
558
+
559
+ ### Tokenizer Metrics
560
+
561
+ **Compression Ratio**
562
+ > *Definition:* The ratio of characters to tokens (chars/token). Measures how efficiently the tokenizer represents text.
563
+ >
564
+ > *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.
565
+ >
566
+ > *What to seek:* Higher is generally better for efficiency, but extremely high compression may indicate overly aggressive merging that loses morphological information.
567
+
568
+ **Average Token Length (Fertility)**
569
+ > *Definition:* Mean number of characters per token produced by the tokenizer.
570
+ >
571
+ > *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.
572
+ >
573
+ > *What to seek:* Balance between 2-5 characters for most languages. Arabic/morphologically-rich languages may benefit from slightly longer tokens.
574
+
575
+ **Unknown Token Rate (OOV Rate)**
576
+ > *Definition:* Percentage of tokens that map to the unknown/UNK token, indicating words the tokenizer cannot represent.
577
+ >
578
+ > *Intuition:* Lower OOV means better vocabulary coverage. High OOV indicates the tokenizer encounters many unseen character sequences.
579
+ >
580
+ > *What to seek:* Below 1% is excellent; below 5% is acceptable. BPE tokenizers typically achieve very low OOV due to subword fallback.
581
+
582
+ ### N-gram Model Metrics
583
+
584
+ **Perplexity**
585
+ > *Definition:* Measures how "surprised" the model is by test data. Mathematically: 2^(cross-entropy). Lower values indicate better prediction.
586
+ >
587
+ > *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.
588
+ >
589
+ > *What to seek:* Lower is better. Perplexity decreases with larger n-grams (more context). Values vary widely by language and corpus size.
590
+
591
+ **Entropy**
592
+ > *Definition:* Average information content (in bits) needed to encode the next token given the context. Related to perplexity: perplexity = 2^entropy.
593
+ >
594
+ > *Intuition:* High entropy means high uncertainty/randomness; low entropy means predictable patterns. Natural language typically has entropy between 1-4 bits per character.
595
+ >
596
+ > *What to seek:* Lower entropy indicates more predictable text patterns. Entropy should decrease as n-gram size increases.
597
+
598
+ **Coverage (Top-K)**
599
+ > *Definition:* Percentage of corpus occurrences explained by the top K most frequent n-grams.
600
+ >
601
+ > *Intuition:* High coverage with few patterns indicates repetitive/formulaic text; low coverage suggests diverse vocabulary usage.
602
+ >
603
+ > *What to seek:* Depends on use case. For language modeling, moderate coverage (40-60% with top-1000) is typical for natural text.
604
+
605
+ ### Markov Chain Metrics
606
+
607
+ **Average Entropy**
608
+ > *Definition:* Mean entropy across all contexts, measuring average uncertainty in next-word prediction.
609
+ >
610
+ > *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).
611
+ >
612
+ > *What to seek:* Decreasing entropy with larger context sizes. Very low entropy (<0.1) indicates highly deterministic transitions.
613
+
614
+ **Branching Factor**
615
+ > *Definition:* Average number of unique next tokens observed for each context.
616
+ >
617
+ > *Intuition:* High branching = many possible continuations (flexible but uncertain); low branching = few options (predictable but potentially repetitive).
618
+ >
619
+ > *What to seek:* Branching factor should decrease with context size. Values near 1.0 indicate nearly deterministic chains.
620
+
621
+ **Predictability**
622
+ > *Definition:* Derived metric: (1 - normalized_entropy) × 100%. Indicates how deterministic the model's predictions are.
623
+ >
624
+ > *Intuition:* 100% predictability means the next word is always certain; 0% means completely random. Real text falls between these extremes.
625
+ >
626
+ > *What to seek:* Higher predictability for text generation quality, but too high (>98%) may produce repetitive output.
627
+
628
+ ### Vocabulary & Zipf's Law Metrics
629
+
630
+ **Zipf's Coefficient**
631
+ > *Definition:* The slope of the log-log plot of word frequency vs. rank. Zipf's law predicts this should be approximately -1.
632
+ >
633
+ > *Intuition:* A coefficient near -1 indicates the corpus follows natural language patterns where a few words are very common and most words are rare.
634
+ >
635
+ > *What to seek:* Values between -0.8 and -1.2 indicate healthy natural language distribution. Deviations may suggest domain-specific or artificial text.
636
+
637
+ **R² (Coefficient of Determination)**
638
+ > *Definition:* Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.
639
+ >
640
+ > *Intuition:* R² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.
641
+ >
642
+ > *What to seek:* R² > 0.95 is excellent; > 0.99 indicates near-perfect Zipf adherence typical of large natural corpora.
643
+
644
+ **Vocabulary Coverage**
645
+ > *Definition:* Cumulative percentage of corpus tokens accounted for by the top N words.
646
+ >
647
+ > *Intuition:* Shows how concentrated word usage is. If top-100 words cover 50% of text, the corpus relies heavily on common words.
648
+ >
649
+ > *What to seek:* Top-100 covering 30-50% is typical. Higher coverage indicates more repetitive text; lower suggests richer vocabulary.
650
+
651
+ ### Word Embedding Metrics
652
+
653
+ **Isotropy**
654
+ > *Definition:* Measures how uniformly distributed vectors are in the embedding space. Computed as the ratio of minimum to maximum singular values.
655
+ >
656
+ > *Intuition:* High isotropy (near 1.0) means vectors spread evenly in all directions; low isotropy means vectors cluster in certain directions, reducing expressiveness.
657
+ >
658
+ > *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.
659
+
660
+ **Average Norm**
661
+ > *Definition:* Mean magnitude (L2 norm) of word vectors in the embedding space.
662
+ >
663
+ > *Intuition:* Indicates the typical "length" of vectors. Consistent norms suggest stable training; high variance may indicate some words are undertrained.
664
+ >
665
+ > *What to seek:* Relatively consistent norms across models. The absolute value matters less than consistency (low std deviation).
666
+
667
+ **Cosine Similarity**
668
+ > *Definition:* Measures angular similarity between vectors, ranging from -1 (opposite) to 1 (identical direction).
669
+ >
670
+ > *Intuition:* Words with similar meanings should have high cosine similarity. This is the standard metric for semantic relatedness in embeddings.
671
+ >
672
+ > *What to seek:* Semantically related words should score > 0.5; unrelated words should be near 0. Synonyms often score > 0.7.
673
+
674
+ **t-SNE Visualization**
675
+ > *Definition:* t-Distributed Stochastic Neighbor Embedding - a dimensionality reduction technique that preserves local structure for visualization.
676
+ >
677
+ > *Intuition:* Clusters in t-SNE plots indicate groups of semantically related words. Spread indicates vocabulary diversity; tight clusters suggest semantic coherence.
678
+ >
679
+ > *What to seek:* Meaningful clusters (e.g., numbers together, verbs together). Avoid over-interpreting distances - t-SNE preserves local, not global, structure.
680
+
681
+ ### General Interpretation Guidelines
682
+
683
+ 1. **Compare within model families:** Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
684
+ 2. **Consider trade-offs:** Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
685
+ 3. **Context matters:** Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
686
+ 4. **Corpus influence:** All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
687
+ 5. **Language-specific patterns:** Morphologically rich languages (like Arabic) may show different optimal ranges than analytic languages.
688
+
689
+
690
+ ### Visualizations Index
691
+
692
+ | Visualization | Description |
693
+ |---------------|-------------|
694
+ | Tokenizer Compression | Compression ratios by vocabulary size |
695
+ | Tokenizer Fertility | Average token length by vocabulary |
696
+ | Tokenizer OOV | Unknown token rates |
697
+ | Tokenizer Total Tokens | Total tokens by vocabulary |
698
+ | N-gram Perplexity | Perplexity by n-gram size |
699
+ | N-gram Entropy | Entropy by n-gram size |
700
+ | N-gram Coverage | Top pattern coverage |
701
+ | N-gram Unique | Unique n-gram counts |
702
+ | Markov Entropy | Entropy by context size |
703
+ | Markov Branching | Branching factor by context |
704
+ | Markov Contexts | Unique context counts |
705
+ | Zipf's Law | Frequency-rank distribution with fit |
706
+ | Vocab Frequency | Word frequency distribution |
707
+ | Top 20 Words | Most frequent words |
708
+ | Vocab Coverage | Cumulative coverage curve |
709
+ | Embedding Isotropy | Vector space uniformity |
710
+ | Embedding Norms | Vector magnitude distribution |
711
+ | Embedding Similarity | Word similarity heatmap |
712
+ | Nearest Neighbors | Similar words for key terms |
713
+ | t-SNE Words | 2D word embedding visualization |
714
+ | t-SNE Sentences | 2D sentence embedding visualization |
715
+ | Position Encoding | Encoding method comparison |
716
+ | Model Sizes | Storage requirements |
717
+ | Performance Dashboard | Comprehensive performance overview |
718
+
719
+ ---
720
+ ## About This Project
721
+
722
+ ### Data Source
723
+
724
+ Models trained on [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly) - a monthly snapshot of Wikipedia articles across 300+ languages.
725
+
726
+ ### Project
727
+
728
+ A project by **[Wikilangs](https://wikilangs.org)** - Open-source NLP models for every Wikipedia language.
729
+
730
+ ### Maintainer
731
+
732
+ [Omar Kamali](https://omarkamali.com) - [Omneity Labs](https://omneitylabs.com)
733
+
734
+ ### Citation
735
+
736
+ If you use these models in your research, please cite:
737
+
738
+ ```bibtex
739
+ @misc{wikilangs2025,
740
+ author = {Kamali, Omar},
741
+ title = {Wikilangs: Open NLP Models for Wikipedia Languages},
742
+ year = {2025},
743
+ doi = {10.5281/zenodo.18073153},
744
+ publisher = {Zenodo},
745
+ url = {https://huggingface.co/wikilangs}
746
+ institution = {Omneity Labs}
747
+ }
748
+ ```
749
+
750
+ ### License
751
+
752
+ MIT License - Free for academic and commercial use.
753
+
754
+ ### Links
755
+
756
+ - 🌐 Website: [wikilangs.org](https://wikilangs.org)
757
+ - 🤗 Models: [huggingface.co/wikilangs](https://huggingface.co/wikilangs)
758
+ - 📊 Data: [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly)
759
+ - 👤 Author: [Omar Kamali](https://huggingface.co/omarkamali)
760
+ - 🤝 Sponsor: [Featherless AI](https://featherless.ai)
761
+ ---
762
+ *Generated by Wikilangs Models Pipeline*
763
+
764
+ *Report Date: 2026-01-10 04:55:45*
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