Upload all models and assets for be (20251201)
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- .gitattributes +6 -0
- README.md +560 -0
- models/embeddings/monolingual/be_128d.bin +3 -0
- models/embeddings/monolingual/be_128d.meta.json +1 -0
- models/embeddings/monolingual/be_128d_metadata.json +13 -0
- models/embeddings/monolingual/be_32d.bin +3 -0
- models/embeddings/monolingual/be_32d.meta.json +1 -0
- models/embeddings/monolingual/be_32d_metadata.json +13 -0
- models/embeddings/monolingual/be_64d.bin +3 -0
- models/embeddings/monolingual/be_64d.meta.json +1 -0
- models/embeddings/monolingual/be_64d_metadata.json +13 -0
- models/subword_markov/be_markov_ctx1_subword.parquet +3 -0
- models/subword_markov/be_markov_ctx1_subword_metadata.json +7 -0
- models/subword_markov/be_markov_ctx2_subword.parquet +3 -0
- models/subword_markov/be_markov_ctx2_subword_metadata.json +7 -0
- models/subword_markov/be_markov_ctx3_subword.parquet +3 -0
- models/subword_markov/be_markov_ctx3_subword_metadata.json +7 -0
- models/subword_markov/be_markov_ctx4_subword.parquet +3 -0
- models/subword_markov/be_markov_ctx4_subword_metadata.json +7 -0
- models/subword_ngram/be_2gram_subword.parquet +3 -0
- models/subword_ngram/be_2gram_subword_metadata.json +7 -0
- models/subword_ngram/be_3gram_subword.parquet +3 -0
- models/subword_ngram/be_3gram_subword_metadata.json +7 -0
- models/subword_ngram/be_4gram_subword.parquet +3 -0
- models/subword_ngram/be_4gram_subword_metadata.json +7 -0
- models/tokenizer/be_tokenizer_16k.model +3 -0
- models/tokenizer/be_tokenizer_16k.vocab +0 -0
- models/tokenizer/be_tokenizer_32k.model +3 -0
- models/tokenizer/be_tokenizer_32k.vocab +0 -0
- models/tokenizer/be_tokenizer_64k.model +3 -0
- models/tokenizer/be_tokenizer_64k.vocab +0 -0
- models/tokenizer/be_tokenizer_8k.model +3 -0
- models/tokenizer/be_tokenizer_8k.vocab +0 -0
- models/vocabulary/be_vocabulary.parquet +3 -0
- models/vocabulary/be_vocabulary_metadata.json +16 -0
- models/word_markov/be_markov_ctx1_word.parquet +3 -0
- models/word_markov/be_markov_ctx1_word_metadata.json +7 -0
- models/word_markov/be_markov_ctx2_word.parquet +3 -0
- models/word_markov/be_markov_ctx2_word_metadata.json +7 -0
- models/word_markov/be_markov_ctx3_word.parquet +3 -0
- models/word_markov/be_markov_ctx3_word_metadata.json +7 -0
- models/word_markov/be_markov_ctx4_word.parquet +3 -0
- models/word_markov/be_markov_ctx4_word_metadata.json +7 -0
- models/word_ngram/be_2gram_word.parquet +3 -0
- models/word_ngram/be_2gram_word_metadata.json +7 -0
- models/word_ngram/be_3gram_word.parquet +3 -0
- models/word_ngram/be_3gram_word_metadata.json +7 -0
- models/word_ngram/be_4gram_word.parquet +3 -0
- models/word_ngram/be_4gram_word_metadata.json +7 -0
- visualizations/embedding_isotropy.png +0 -0
.gitattributes
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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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*.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/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
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README.md
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| 1 |
+
---
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| 2 |
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language: be
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| 3 |
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language_name: BE
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| 4 |
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language_family: slavic_east
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tags:
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- wikilangs
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| 7 |
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- nlp
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- tokenizer
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| 9 |
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- embeddings
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| 10 |
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- n-gram
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| 11 |
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- markov
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- wikipedia
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- monolingual
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- family-slavic_east
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license: mit
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| 16 |
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library_name: wikilangs
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| 17 |
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pipeline_tag: feature-extraction
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| 18 |
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datasets:
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- omarkamali/wikipedia-monthly
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dataset_info:
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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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| 25 |
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type: compression
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value: 3.609
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- name: best_isotropy
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type: isotropy
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value: 0.6652
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- name: vocabulary_size
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| 31 |
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type: vocab
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| 32 |
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value: 834514
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| 33 |
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generated: 2025-12-28
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---
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# BE - Wikilangs Models
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| 37 |
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## Comprehensive Research Report & Full Ablation Study
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| 38 |
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| 39 |
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This repository contains NLP models trained and evaluated by Wikilangs, specifically on **BE** Wikipedia data.
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| 40 |
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We analyze tokenizers, n-gram models, Markov chains, vocabulary statistics, and word embeddings.
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## 📋 Repository Contents
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| 43 |
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| 44 |
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### Models & Assets
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| 45 |
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- Tokenizers (8k, 16k, 32k, 64k)
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- N-gram models (2, 3, 4-gram)
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| 48 |
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- Markov chains (context of 1, 2, 3 and 4)
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| 49 |
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- Subword N-gram and Markov chains
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| 50 |
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- Embeddings in various sizes and dimensions
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| 51 |
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- Language Vocabulary
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| 52 |
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- Language Statistics
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| 53 |
+

|
| 54 |
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| 55 |
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### Analysis and Evaluation
|
| 56 |
+
|
| 57 |
+
- [1. Tokenizer Evaluation](#1-tokenizer-evaluation)
|
| 58 |
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- [2. N-gram Model Evaluation](#2-n-gram-model-evaluation)
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| 59 |
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- [3. Markov Chain Evaluation](#3-markov-chain-evaluation)
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| 60 |
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- [4. Vocabulary Analysis](#4-vocabulary-analysis)
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| 61 |
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- [5. Word Embeddings Evaluation](#5-word-embeddings-evaluation)
|
| 62 |
+
- [6. Summary & Recommendations](#6-summary--recommendations)
|
| 63 |
+
- [Metrics Glossary](#appendix-metrics-glossary--interpretation-guide)
|
| 64 |
+
- [Visualizations Index](#visualizations-index)
|
| 65 |
+
|
| 66 |
+
---
|
| 67 |
+
## 1. Tokenizer Evaluation
|
| 68 |
+
|
| 69 |
+

|
| 70 |
+
|
| 71 |
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### Results
|
| 72 |
+
|
| 73 |
+
| Vocab Size | Compression | Avg Token Len | UNK Rate | Total Tokens |
|
| 74 |
+
|------------|-------------|---------------|----------|--------------|
|
| 75 |
+
| **8k** | 2.945x | 2.88 | 0.0099% | 395,619 |
|
| 76 |
+
| **16k** | 3.198x | 3.13 | 0.0107% | 364,322 |
|
| 77 |
+
| **32k** | 3.434x | 3.36 | 0.0115% | 339,332 |
|
| 78 |
+
| **64k** | 3.609x 🏆 | 3.53 | 0.0121% | 322,873 |
|
| 79 |
+
|
| 80 |
+
### Tokenization Examples
|
| 81 |
+
|
| 82 |
+
Below are sample sentences tokenized with each vocabulary size:
|
| 83 |
+
|
| 84 |
+
**Sample 1:** `Адаі () — вёска ў Акнянскім раёне Адэскай вобласці Украіны.
|
| 85 |
+
|
| 86 |
+
Крыніцы
|
| 87 |
+
|
| 88 |
+
Катэгоры...`
|
| 89 |
+
|
| 90 |
+
| Vocab | Tokens | Count |
|
| 91 |
+
|-------|--------|-------|
|
| 92 |
+
| 8k | `▁ада і ▁() ▁— ▁вёска ▁ў ▁ак ня нскім ▁раёне ... (+14 more)` | 24 |
|
| 93 |
+
| 16k | `▁ада і ▁() ▁— ▁вёска ▁ў ▁ак ня нскім ▁раёне ... (+13 more)` | 23 |
|
| 94 |
+
| 32k | `▁ада і ▁() ▁— ▁вёска ▁ў ▁ак ня нскім ▁раёне ... (+12 more)` | 22 |
|
| 95 |
+
| 64k | `▁ада і ▁() ▁— ▁вёска ▁ў ▁ак нянскім ▁раёне ▁адэскай ... (+11 more)` | 21 |
|
| 96 |
+
|
| 97 |
+
**Sample 2:** `Назву Асманіе маюць: горад і правінцыя ў Турцыі.`
|
| 98 |
+
|
| 99 |
+
| Vocab | Tokens | Count |
|
| 100 |
+
|-------|--------|-------|
|
| 101 |
+
| 8k | `▁назву ▁ас мані е ▁маюць : ▁горад ▁і ▁правінцыя ▁ў ... (+2 more)` | 12 |
|
| 102 |
+
| 16k | `▁назву ▁ас мані е ▁маюць : ▁горад ▁і ▁правінцыя ▁ў ... (+2 more)` | 12 |
|
| 103 |
+
| 32k | `▁назву ▁ас мані е ▁маюць : ▁горад ▁і ▁правінцыя ▁ў ... (+2 more)` | 12 |
|
| 104 |
+
| 64k | `▁назву ▁ас мані е ▁маюць : ▁горад ▁і ▁правінцыя ▁ў ... (+2 more)` | 12 |
|
| 105 |
+
|
| 106 |
+
**Sample 3:** `M21 (каталог Месье) — рассеянае скопішча ў сузор'і Стральца.
|
| 107 |
+
|
| 108 |
+
Катэгорыя:Астранам...`
|
| 109 |
+
|
| 110 |
+
| Vocab | Tokens | Count |
|
| 111 |
+
|-------|--------|-------|
|
| 112 |
+
| 8k | `▁m 2 1 ▁( ката лог ▁месье ) ▁— ▁рас ... (+39 more)` | 49 |
|
| 113 |
+
| 16k | `▁m 2 1 ▁( ката лог ▁месье ) ▁— ▁рассея ... (+36 more)` | 46 |
|
| 114 |
+
| 32k | `▁m 2 1 ▁( ката лог ▁месье ) ▁— ▁рассеянае ... (+35 more)` | 45 |
|
| 115 |
+
| 64k | `▁m 2 1 ▁( каталог ▁месье ) ▁— ▁рассеянае ▁скопішча ... (+34 more)` | 44 |
|
| 116 |
+
|
| 117 |
+
|
| 118 |
+
### Key Findings
|
| 119 |
+
|
| 120 |
+
- **Best Compression:** 64k achieves 3.609x compression
|
| 121 |
+
- **Lowest UNK Rate:** 8k with 0.0099% unknown tokens
|
| 122 |
+
- **Trade-off:** Larger vocabularies improve compression but increase model size
|
| 123 |
+
- **Recommendation:** 32k vocabulary provides optimal balance for production use
|
| 124 |
+
|
| 125 |
+
---
|
| 126 |
+
## 2. N-gram Model Evaluation
|
| 127 |
+
|
| 128 |
+

|
| 129 |
+
|
| 130 |
+

|
| 131 |
+
|
| 132 |
+
### Results
|
| 133 |
+
|
| 134 |
+
| N-gram | Perplexity | Entropy | Unique N-grams | Top-100 Coverage | Top-1000 Coverage |
|
| 135 |
+
|--------|------------|---------|----------------|------------------|-------------------|
|
| 136 |
+
| **2-gram** | 79,086 🏆 | 16.27 | 1,374,832 | 15.1% | 29.5% |
|
| 137 |
+
| **2-gram** | 534 🏆 | 9.06 | 19,108 | 52.5% | 95.6% |
|
| 138 |
+
| **3-gram** | 294,087 | 18.17 | 2,802,568 | 8.0% | 20.4% |
|
| 139 |
+
| **3-gram** | 5,046 | 12.30 | 199,361 | 17.9% | 56.0% |
|
| 140 |
+
| **4-gram** | 713,543 | 19.44 | 5,150,781 | 6.7% | 16.8% |
|
| 141 |
+
| **4-gram** | 30,738 | 14.91 | 1,228,443 | 8.4% | 28.2% |
|
| 142 |
+
|
| 143 |
+
### Top 5 N-grams by Size
|
| 144 |
+
|
| 145 |
+
**2-grams:**
|
| 146 |
+
|
| 147 |
+
| Rank | N-gram | Count |
|
| 148 |
+
|------|--------|-------|
|
| 149 |
+
| 1 | `0 ,` | 1,884,848 |
|
| 150 |
+
| 2 | `катэгорыя :` | 589,578 |
|
| 151 |
+
| 3 | `. у` | 390,424 |
|
| 152 |
+
| 4 | `) .` | 239,852 |
|
| 153 |
+
| 5 | `) —` | 224,324 |
|
| 154 |
+
|
| 155 |
+
**3-grams:**
|
| 156 |
+
|
| 157 |
+
| Rank | N-gram | Count |
|
| 158 |
+
|------|--------|-------|
|
| 159 |
+
| 1 | `0 , 10` | 188,226 |
|
| 160 |
+
| 2 | `0 , 09` | 178,159 |
|
| 161 |
+
| 3 | `0 , 11` | 136,658 |
|
| 162 |
+
| 4 | `0 , 08` | 133,746 |
|
| 163 |
+
| 5 | `0 , 07` | 96,108 |
|
| 164 |
+
|
| 165 |
+
**4-grams:**
|
| 166 |
+
|
| 167 |
+
| Rank | N-gram | Count |
|
| 168 |
+
|------|--------|-------|
|
| 169 |
+
| 1 | `катэгорыя : населеныя пункты` | 53,581 |
|
| 170 |
+
| 2 | `) — вёска ў` | 38,538 |
|
| 171 |
+
| 3 | `. уваходзіць у склад` | 36,002 |
|
| 172 |
+
| 4 | `. — с .` | 29,359 |
|
| 173 |
+
| 5 | `, 44 0 ,` | 29,322 |
|
| 174 |
+
|
| 175 |
+
|
| 176 |
+
### Key Findings
|
| 177 |
+
|
| 178 |
+
- **Best Perplexity:** 2-gram with 534
|
| 179 |
+
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
|
| 180 |
+
- **Coverage:** Top-1000 patterns cover ~28% of corpus
|
| 181 |
+
- **Recommendation:** 4-gram or 5-gram for best predictive performance
|
| 182 |
+
|
| 183 |
+
---
|
| 184 |
+
## 3. Markov Chain Evaluation
|
| 185 |
+
|
| 186 |
+

|
| 187 |
+
|
| 188 |
+

|
| 189 |
+
|
| 190 |
+
### Results
|
| 191 |
+
|
| 192 |
+
| Context | Avg Entropy | Perplexity | Branching Factor | Unique Contexts | Predictability |
|
| 193 |
+
|---------|-------------|------------|------------------|-----------------|----------------|
|
| 194 |
+
| **1** | 0.5334 | 1.447 | 6.21 | 2,760,646 | 46.7% |
|
| 195 |
+
| **1** | 0.5275 | 1.441 | 4.42 | 17,006 | 47.2% |
|
| 196 |
+
| **2** | 0.3318 | 1.259 | 2.22 | 17,120,073 | 66.8% |
|
| 197 |
+
| **2** | 0.7155 | 1.642 | 5.63 | 75,115 | 28.5% |
|
| 198 |
+
| **3** | 0.1509 | 1.110 | 1.38 | 37,905,234 | 84.9% |
|
| 199 |
+
| **3** | 0.8770 | 1.837 | 5.02 | 422,960 | 12.3% |
|
| 200 |
+
| **4** | 0.0724 🏆 | 1.051 | 1.16 | 52,452,226 | 92.8% |
|
| 201 |
+
| **4** | 0.7380 🏆 | 1.668 | 3.59 | 2,124,122 | 26.2% |
|
| 202 |
+
|
| 203 |
+
### Generated Text Samples
|
| 204 |
+
|
| 205 |
+
Below are text samples generated from each Markov chain model:
|
| 206 |
+
|
| 207 |
+
**Context Size 1:**
|
| 208 |
+
|
| 209 |
+
1. `, аэрапорт знаходзіцца ў свеце вядома з сакрысціямі і іншыя матэрыялы , створаных самім фактам ,`
|
| 210 |
+
2. `. 3 адкрыты чэмпіянат па 21 кастрычніка 1957 — супраціўнае звычайна была прысвоена званне « за`
|
| 211 |
+
3. `0 , лячэбны факультэт кіравання версіямі , евангелле паводле ніпурскага , а ў сялянскай сям ’`
|
| 212 |
+
|
| 213 |
+
**Context Size 2:**
|
| 214 |
+
|
| 215 |
+
1. `0 , 41 0 , 11 1912897 0 , 47 0 , 44 0 , 81 0`
|
| 216 |
+
2. `катэгорыя : лігатуры кірыліцы катэгорыя : паняцці індуізму катэгорыя : будынкі і збудаванні бабруйск...`
|
| 217 |
+
3. `. у 1932 — 1982 ) , святы рпцз . 12 . 3 . игнатенко , в`
|
| 218 |
+
|
| 219 |
+
**Context Size 3:**
|
| 220 |
+
|
| 221 |
+
1. `0 , 10 47053 sd 1 , 20 0 , 09 21985 e - so 0 , 93`
|
| 222 |
+
2. `0 , 09 637479 0 , 39 0 , 11 88688 0 , 60 0 , 08 310690`
|
| 223 |
+
3. `0 , 11 348939 0 , 60 0 , 08 2587753 0 , 73 0 , 07 838578`
|
| 224 |
+
|
| 225 |
+
**Context Size 4:**
|
| 226 |
+
|
| 227 |
+
1. `катэгорыя : населеныя пункты гарадэнкіўскага раёна катэгорыя : населеныя пункты на дняпры катэгорыя ...`
|
| 228 |
+
2. `) — вёска ў сосныцкім раёне чарнігаўскай вобласці украіны . крыніцы катэгорыя : населеныя пункты аст...`
|
| 229 |
+
3. `. уваходзіць у склад сямлёўскага сельскага паселішча . гісторыя 25 сакавіка 1918 года згодна з трэця...`
|
| 230 |
+
|
| 231 |
+
|
| 232 |
+
### Key Findings
|
| 233 |
+
|
| 234 |
+
- **Best Predictability:** Context-4 with 92.8% predictability
|
| 235 |
+
- **Branching Factor:** Decreases with context size (more deterministic)
|
| 236 |
+
- **Memory Trade-off:** Larger contexts require more storage (2,124,122 contexts)
|
| 237 |
+
- **Recommendation:** Context-3 or Context-4 for text generation
|
| 238 |
+
|
| 239 |
+
---
|
| 240 |
+
## 4. Vocabulary Analysis
|
| 241 |
+
|
| 242 |
+

|
| 243 |
+
|
| 244 |
+

|
| 245 |
+
|
| 246 |
+

|
| 247 |
+
|
| 248 |
+
### Statistics
|
| 249 |
+
|
| 250 |
+
| Metric | Value |
|
| 251 |
+
|--------|-------|
|
| 252 |
+
| Vocabulary Size | 834,514 |
|
| 253 |
+
| Total Tokens | 59,867,674 |
|
| 254 |
+
| Mean Frequency | 71.74 |
|
| 255 |
+
| Median Frequency | 4 |
|
| 256 |
+
| Frequency Std Dev | 3746.92 |
|
| 257 |
+
|
| 258 |
+
### Most Common Words
|
| 259 |
+
|
| 260 |
+
| Rank | Word | Frequency |
|
| 261 |
+
|------|------|-----------|
|
| 262 |
+
| 1 | 0 | 1,972,029 |
|
| 263 |
+
| 2 | і | 1,334,509 |
|
| 264 |
+
| 3 | у | 1,241,263 |
|
| 265 |
+
| 4 | ў | 1,163,394 |
|
| 266 |
+
| 5 | з | 869,929 |
|
| 267 |
+
| 6 | на | 710,982 |
|
| 268 |
+
| 7 | катэгорыя | 590,266 |
|
| 269 |
+
| 8 | года | 368,272 |
|
| 270 |
+
| 9 | да | 291,578 |
|
| 271 |
+
| 10 | годзе | 258,701 |
|
| 272 |
+
|
| 273 |
+
### Least Common Words (from vocabulary)
|
| 274 |
+
|
| 275 |
+
| Rank | Word | Frequency |
|
| 276 |
+
|------|------|-----------|
|
| 277 |
+
| 1 | мурашава | 2 |
|
| 278 |
+
| 2 | девятке | 2 |
|
| 279 |
+
| 3 | дэкунаў | 2 |
|
| 280 |
+
| 4 | iovine | 2 |
|
| 281 |
+
| 5 | аёвіну | 2 |
|
| 282 |
+
| 6 | джэніка | 2 |
|
| 283 |
+
| 7 | мэрылінам | 2 |
|
| 284 |
+
| 8 | сардэшная | 2 |
|
| 285 |
+
| 9 | івасю | 2 |
|
| 286 |
+
| 10 | стеценко | 2 |
|
| 287 |
+
|
| 288 |
+
### Zipf's Law Analysis
|
| 289 |
+
|
| 290 |
+
| Metric | Value |
|
| 291 |
+
|--------|-------|
|
| 292 |
+
| Zipf Coefficient | 0.9824 |
|
| 293 |
+
| R² (Goodness of Fit) | 0.995868 |
|
| 294 |
+
| Adherence Quality | **excellent** |
|
| 295 |
+
|
| 296 |
+
### Coverage Analysis
|
| 297 |
+
|
| 298 |
+
| Top N Words | Coverage |
|
| 299 |
+
|-------------|----------|
|
| 300 |
+
| Top 100 | 28.3% |
|
| 301 |
+
| Top 1,000 | 50.1% |
|
| 302 |
+
| Top 5,000 | 67.4% |
|
| 303 |
+
| Top 10,000 | 74.4% |
|
| 304 |
+
|
| 305 |
+
### Key Findings
|
| 306 |
+
|
| 307 |
+
- **Zipf Compliance:** R²=0.9959 indicates excellent adherence to Zipf's law
|
| 308 |
+
- **High Frequency Dominance:** Top 100 words cover 28.3% of corpus
|
| 309 |
+
- **Long Tail:** 824,514 words needed for remaining 25.6% coverage
|
| 310 |
+
|
| 311 |
+
---
|
| 312 |
+
## 5. Word Embeddings Evaluation
|
| 313 |
+
|
| 314 |
+

|
| 315 |
+
|
| 316 |
+

|
| 317 |
+
|
| 318 |
+

|
| 319 |
+
|
| 320 |
+

|
| 321 |
+
|
| 322 |
+
### Model Comparison
|
| 323 |
+
|
| 324 |
+
| Model | Vocab Size | Dimension | Avg Norm | Std Norm | Isotropy |
|
| 325 |
+
|-------|------------|-----------|----------|----------|----------|
|
| 326 |
+
| **mono_32d** | 563,209 | 32 | 4.064 | 1.812 | 0.6194 |
|
| 327 |
+
| **mono_64d** | 563,209 | 64 | 4.475 | 1.623 | 0.6528 |
|
| 328 |
+
| **mono_128d** | 563,209 | 128 | 4.940 | 1.374 | 0.6652 🏆 |
|
| 329 |
+
| **embeddings_enhanced** | 0 | 0 | 0.000 | 0.000 | 0.0000 |
|
| 330 |
+
|
| 331 |
+
### Key Findings
|
| 332 |
+
|
| 333 |
+
- **Best Isotropy:** mono_128d with 0.6652 (more uniform distribution)
|
| 334 |
+
- **Dimension Trade-off:** Higher dimensions capture more semantics but reduce isotropy
|
| 335 |
+
- **Vocabulary Coverage:** All models cover 563,209 words
|
| 336 |
+
- **Recommendation:** 100d for balanced semantic capture and efficiency
|
| 337 |
+
|
| 338 |
+
---
|
| 339 |
+
## 6. Summary & Recommendations
|
| 340 |
+
|
| 341 |
+

|
| 342 |
+
|
| 343 |
+
### Production Recommendations
|
| 344 |
+
|
| 345 |
+
| Component | Recommended | Rationale |
|
| 346 |
+
|-----------|-------------|-----------|
|
| 347 |
+
| Tokenizer | **32k BPE** | Best compression (3.61x) with low UNK rate |
|
| 348 |
+
| N-gram | **5-gram** | Lowest perplexity (534) |
|
| 349 |
+
| Markov | **Context-4** | Highest predictability (92.8%) |
|
| 350 |
+
| Embeddings | **100d** | Balanced semantic capture and isotropy |
|
| 351 |
+
|
| 352 |
+
---
|
| 353 |
+
## Appendix: Metrics Glossary & Interpretation Guide
|
| 354 |
+
|
| 355 |
+
This section provides definitions, intuitions, and guidance for interpreting the metrics used throughout this report.
|
| 356 |
+
|
| 357 |
+
### Tokenizer Metrics
|
| 358 |
+
|
| 359 |
+
**Compression Ratio**
|
| 360 |
+
> *Definition:* The ratio of characters to tokens (chars/token). Measures how efficiently the tokenizer represents text.
|
| 361 |
+
>
|
| 362 |
+
> *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.
|
| 363 |
+
>
|
| 364 |
+
> *What to seek:* Higher is generally better for efficiency, but extremely high compression may indicate overly aggressive merging that loses morphological information.
|
| 365 |
+
|
| 366 |
+
**Average Token Length (Fertility)**
|
| 367 |
+
> *Definition:* Mean number of characters per token produced by the tokenizer.
|
| 368 |
+
>
|
| 369 |
+
> *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.
|
| 370 |
+
>
|
| 371 |
+
> *What to seek:* Balance between 2-5 characters for most languages. Arabic/morphologically-rich languages may benefit from slightly longer tokens.
|
| 372 |
+
|
| 373 |
+
**Unknown Token Rate (OOV Rate)**
|
| 374 |
+
> *Definition:* Percentage of tokens that map to the unknown/UNK token, indicating words the tokenizer cannot represent.
|
| 375 |
+
>
|
| 376 |
+
> *Intuition:* Lower OOV means better vocabulary coverage. High OOV indicates the tokenizer encounters many unseen character sequences.
|
| 377 |
+
>
|
| 378 |
+
> *What to seek:* Below 1% is excellent; below 5% is acceptable. BPE tokenizers typically achieve very low OOV due to subword fallback.
|
| 379 |
+
|
| 380 |
+
### N-gram Model Metrics
|
| 381 |
+
|
| 382 |
+
**Perplexity**
|
| 383 |
+
> *Definition:* Measures how "surprised" the model is by test data. Mathematically: 2^(cross-entropy). Lower values indicate better prediction.
|
| 384 |
+
>
|
| 385 |
+
> *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.
|
| 386 |
+
>
|
| 387 |
+
> *What to seek:* Lower is better. Perplexity decreases with larger n-grams (more context). Values vary widely by language and corpus size.
|
| 388 |
+
|
| 389 |
+
**Entropy**
|
| 390 |
+
> *Definition:* Average information content (in bits) needed to encode the next token given the context. Related to perplexity: perplexity = 2^entropy.
|
| 391 |
+
>
|
| 392 |
+
> *Intuition:* High entropy means high uncertainty/randomness; low entropy means predictable patterns. Natural language typically has entropy between 1-4 bits per character.
|
| 393 |
+
>
|
| 394 |
+
> *What to seek:* Lower entropy indicates more predictable text patterns. Entropy should decrease as n-gram size increases.
|
| 395 |
+
|
| 396 |
+
**Coverage (Top-K)**
|
| 397 |
+
> *Definition:* Percentage of corpus occurrences explained by the top K most frequent n-grams.
|
| 398 |
+
>
|
| 399 |
+
> *Intuition:* High coverage with few patterns indicates repetitive/formulaic text; low coverage suggests diverse vocabulary usage.
|
| 400 |
+
>
|
| 401 |
+
> *What to seek:* Depends on use case. For language modeling, moderate coverage (40-60% with top-1000) is typical for natural text.
|
| 402 |
+
|
| 403 |
+
### Markov Chain Metrics
|
| 404 |
+
|
| 405 |
+
**Average Entropy**
|
| 406 |
+
> *Definition:* Mean entropy across all contexts, measuring average uncertainty in next-word prediction.
|
| 407 |
+
>
|
| 408 |
+
> *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).
|
| 409 |
+
>
|
| 410 |
+
> *What to seek:* Decreasing entropy with larger context sizes. Very low entropy (<0.1) indicates highly deterministic transitions.
|
| 411 |
+
|
| 412 |
+
**Branching Factor**
|
| 413 |
+
> *Definition:* Average number of unique next tokens observed for each context.
|
| 414 |
+
>
|
| 415 |
+
> *Intuition:* High branching = many possible continuations (flexible but uncertain); low branching = few options (predictable but potentially repetitive).
|
| 416 |
+
>
|
| 417 |
+
> *What to seek:* Branching factor should decrease with context size. Values near 1.0 indicate nearly deterministic chains.
|
| 418 |
+
|
| 419 |
+
**Predictability**
|
| 420 |
+
> *Definition:* Derived metric: (1 - normalized_entropy) × 100%. Indicates how deterministic the model's predictions are.
|
| 421 |
+
>
|
| 422 |
+
> *Intuition:* 100% predictability means the next word is always certain; 0% means completely random. Real text falls between these extremes.
|
| 423 |
+
>
|
| 424 |
+
> *What to seek:* Higher predictability for text generation quality, but too high (>98%) may produce repetitive output.
|
| 425 |
+
|
| 426 |
+
### Vocabulary & Zipf's Law Metrics
|
| 427 |
+
|
| 428 |
+
**Zipf's Coefficient**
|
| 429 |
+
> *Definition:* The slope of the log-log plot of word frequency vs. rank. Zipf's law predicts this should be approximately -1.
|
| 430 |
+
>
|
| 431 |
+
> *Intuition:* A coefficient near -1 indicates the corpus follows natural language patterns where a few words are very common and most words are rare.
|
| 432 |
+
>
|
| 433 |
+
> *What to seek:* Values between -0.8 and -1.2 indicate healthy natural language distribution. Deviations may suggest domain-specific or artificial text.
|
| 434 |
+
|
| 435 |
+
**R² (Coefficient of Determination)**
|
| 436 |
+
> *Definition:* Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.
|
| 437 |
+
>
|
| 438 |
+
> *Intuition:* R² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.
|
| 439 |
+
>
|
| 440 |
+
> *What to seek:* R² > 0.95 is excellent; > 0.99 indicates near-perfect Zipf adherence typical of large natural corpora.
|
| 441 |
+
|
| 442 |
+
**Vocabulary Coverage**
|
| 443 |
+
> *Definition:* Cumulative percentage of corpus tokens accounted for by the top N words.
|
| 444 |
+
>
|
| 445 |
+
> *Intuition:* Shows how concentrated word usage is. If top-100 words cover 50% of text, the corpus relies heavily on common words.
|
| 446 |
+
>
|
| 447 |
+
> *What to seek:* Top-100 covering 30-50% is typical. Higher coverage indicates more repetitive text; lower suggests richer vocabulary.
|
| 448 |
+
|
| 449 |
+
### Word Embedding Metrics
|
| 450 |
+
|
| 451 |
+
**Isotropy**
|
| 452 |
+
> *Definition:* Measures how uniformly distributed vectors are in the embedding space. Computed as the ratio of minimum to maximum singular values.
|
| 453 |
+
>
|
| 454 |
+
> *Intuition:* High isotropy (near 1.0) means vectors spread evenly in all directions; low isotropy means vectors cluster in certain directions, reducing expressiveness.
|
| 455 |
+
>
|
| 456 |
+
> *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.
|
| 457 |
+
|
| 458 |
+
**Average Norm**
|
| 459 |
+
> *Definition:* Mean magnitude (L2 norm) of word vectors in the embedding space.
|
| 460 |
+
>
|
| 461 |
+
> *Intuition:* Indicates the typical "length" of vectors. Consistent norms suggest stable training; high variance may indicate some words are undertrained.
|
| 462 |
+
>
|
| 463 |
+
> *What to seek:* Relatively consistent norms across models. The absolute value matters less than consistency (low std deviation).
|
| 464 |
+
|
| 465 |
+
**Cosine Similarity**
|
| 466 |
+
> *Definition:* Measures angular similarity between vectors, ranging from -1 (opposite) to 1 (identical direction).
|
| 467 |
+
>
|
| 468 |
+
> *Intuition:* Words with similar meanings should have high cosine similarity. This is the standard metric for semantic relatedness in embeddings.
|
| 469 |
+
>
|
| 470 |
+
> *What to seek:* Semantically related words should score > 0.5; unrelated words should be near 0. Synonyms often score > 0.7.
|
| 471 |
+
|
| 472 |
+
**t-SNE Visualization**
|
| 473 |
+
> *Definition:* t-Distributed Stochastic Neighbor Embedding - a dimensionality reduction technique that preserves local structure for visualization.
|
| 474 |
+
>
|
| 475 |
+
> *Intuition:* Clusters in t-SNE plots indicate groups of semantically related words. Spread indicates vocabulary diversity; tight clusters suggest semantic coherence.
|
| 476 |
+
>
|
| 477 |
+
> *What to seek:* Meaningful clusters (e.g., numbers together, verbs together). Avoid over-interpreting distances - t-SNE preserves local, not global, structure.
|
| 478 |
+
|
| 479 |
+
### General Interpretation Guidelines
|
| 480 |
+
|
| 481 |
+
1. **Compare within model families:** Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
|
| 482 |
+
2. **Consider trade-offs:** Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
|
| 483 |
+
3. **Context matters:** Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
|
| 484 |
+
4. **Corpus influence:** All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
|
| 485 |
+
5. **Language-specific patterns:** Morphologically rich languages (like Arabic) may show different optimal ranges than analytic languages.
|
| 486 |
+
|
| 487 |
+
|
| 488 |
+
### Visualizations Index
|
| 489 |
+
|
| 490 |
+
| Visualization | Description |
|
| 491 |
+
|---------------|-------------|
|
| 492 |
+
| Tokenizer Compression | Compression ratios by vocabulary size |
|
| 493 |
+
| Tokenizer Fertility | Average token length by vocabulary |
|
| 494 |
+
| Tokenizer OOV | Unknown token rates |
|
| 495 |
+
| Tokenizer Total Tokens | Total tokens by vocabulary |
|
| 496 |
+
| N-gram Perplexity | Perplexity by n-gram size |
|
| 497 |
+
| N-gram Entropy | Entropy by n-gram size |
|
| 498 |
+
| N-gram Coverage | Top pattern coverage |
|
| 499 |
+
| N-gram Unique | Unique n-gram counts |
|
| 500 |
+
| Markov Entropy | Entropy by context size |
|
| 501 |
+
| Markov Branching | Branching factor by context |
|
| 502 |
+
| Markov Contexts | Unique context counts |
|
| 503 |
+
| Zipf's Law | Frequency-rank distribution with fit |
|
| 504 |
+
| Vocab Frequency | Word frequency distribution |
|
| 505 |
+
| Top 20 Words | Most frequent words |
|
| 506 |
+
| Vocab Coverage | Cumulative coverage curve |
|
| 507 |
+
| Embedding Isotropy | Vector space uniformity |
|
| 508 |
+
| Embedding Norms | Vector magnitude distribution |
|
| 509 |
+
| Embedding Similarity | Word similarity heatmap |
|
| 510 |
+
| Nearest Neighbors | Similar words for key terms |
|
| 511 |
+
| t-SNE Words | 2D word embedding visualization |
|
| 512 |
+
| t-SNE Sentences | 2D sentence embedding visualization |
|
| 513 |
+
| Position Encoding | Encoding method comparison |
|
| 514 |
+
| Model Sizes | Storage requirements |
|
| 515 |
+
| Performance Dashboard | Comprehensive performance overview |
|
| 516 |
+
|
| 517 |
+
---
|
| 518 |
+
## About This Project
|
| 519 |
+
|
| 520 |
+
### Data Source
|
| 521 |
+
|
| 522 |
+
Models trained on [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly) - a monthly snapshot of Wikipedia articles across 300+ languages.
|
| 523 |
+
|
| 524 |
+
### Project
|
| 525 |
+
|
| 526 |
+
A project by **[Wikilangs](https://wikilangs.org)** - Open-source NLP models for every Wikipedia language.
|
| 527 |
+
|
| 528 |
+
### Maintainer
|
| 529 |
+
|
| 530 |
+
[Omar Kamali](https://omarkamali.com) - [Omneity Labs](https://omneitylabs.com)
|
| 531 |
+
|
| 532 |
+
### Citation
|
| 533 |
+
|
| 534 |
+
If you use these models in your research, please cite:
|
| 535 |
+
|
| 536 |
+
```bibtex
|
| 537 |
+
@misc{wikilangs2025,
|
| 538 |
+
author = {Kamali, Omar},
|
| 539 |
+
title = {Wikilangs: Open NLP Models for Wikipedia Languages},
|
| 540 |
+
year = {2025},
|
| 541 |
+
publisher = {HuggingFace},
|
| 542 |
+
url = {https://huggingface.co/wikilangs}
|
| 543 |
+
institution = {Omneity Labs}
|
| 544 |
+
}
|
| 545 |
+
```
|
| 546 |
+
|
| 547 |
+
### License
|
| 548 |
+
|
| 549 |
+
MIT License - Free for academic and commercial use.
|
| 550 |
+
|
| 551 |
+
### Links
|
| 552 |
+
|
| 553 |
+
- 🌐 Website: [wikilangs.org](https://wikilangs.org)
|
| 554 |
+
- 🤗 Models: [huggingface.co/wikilangs](https://huggingface.co/wikilangs)
|
| 555 |
+
- 📊 Data: [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly)
|
| 556 |
+
- 👤 Author: [Omar Kamali](https://huggingface.co/omarkamali)
|
| 557 |
+
---
|
| 558 |
+
*Generated by Wikilangs Models Pipeline*
|
| 559 |
+
|
| 560 |
+
*Report Date: 2025-12-28 02:15:50*
|
models/embeddings/monolingual/be_128d.bin
ADDED
|
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|
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|
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|
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|
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|
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|
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ADDED
|
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|
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{"lang": "be", "dim": 32, "max_seq_len": 512, "is_aligned": false}
|
models/embeddings/monolingual/be_32d_metadata.json
ADDED
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|
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|
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"language": "be",
|
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|
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|
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},
|
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|
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|
models/embeddings/monolingual/be_64d.bin
ADDED
|
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models/embeddings/monolingual/be_64d.meta.json
ADDED
|
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|
|
|
|
|
|
| 1 |
+
{"lang": "be", "dim": 64, "max_seq_len": 512, "is_aligned": false}
|
models/embeddings/monolingual/be_64d_metadata.json
ADDED
|
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|
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|
| 1 |
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{
|
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"language": "be",
|
| 3 |
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"dimension": 64,
|
| 4 |
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"version": "monolingual",
|
| 5 |
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"training_params": {
|
| 6 |
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"dim": 64,
|
| 7 |
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"min_count": 5,
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"window": 5,
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"negative": 5,
|
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"epochs": 5
|
| 11 |
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},
|
| 12 |
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|
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|
models/subword_markov/be_markov_ctx1_subword.parquet
ADDED
|
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version https://git-lfs.github.com/spec/v1
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models/subword_markov/be_markov_ctx1_subword_metadata.json
ADDED
|
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|
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|
| 1 |
+
{
|
| 2 |
+
"context_size": 1,
|
| 3 |
+
"variant": "subword",
|
| 4 |
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"language": "be",
|
| 5 |
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"unique_contexts": 17006,
|
| 6 |
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|
| 7 |
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|
models/subword_markov/be_markov_ctx2_subword.parquet
ADDED
|
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version https://git-lfs.github.com/spec/v1
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size 3387673
|
models/subword_markov/be_markov_ctx2_subword_metadata.json
ADDED
|
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|
| 1 |
+
{
|
| 2 |
+
"context_size": 2,
|
| 3 |
+
"variant": "subword",
|
| 4 |
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"language": "be",
|
| 5 |
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"unique_contexts": 75115,
|
| 6 |
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|
| 7 |
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|
models/subword_markov/be_markov_ctx3_subword.parquet
ADDED
|
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| 1 |
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version https://git-lfs.github.com/spec/v1
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|
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size 16387590
|
models/subword_markov/be_markov_ctx3_subword_metadata.json
ADDED
|
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|
| 1 |
+
{
|
| 2 |
+
"context_size": 3,
|
| 3 |
+
"variant": "subword",
|
| 4 |
+
"language": "be",
|
| 5 |
+
"unique_contexts": 422960,
|
| 6 |
+
"total_transitions": 433347109
|
| 7 |
+
}
|
models/subword_markov/be_markov_ctx4_subword.parquet
ADDED
|
@@ -0,0 +1,3 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
version https://git-lfs.github.com/spec/v1
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| 2 |
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|
| 3 |
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size 64453185
|
models/subword_markov/be_markov_ctx4_subword_metadata.json
ADDED
|
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|
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|
| 1 |
+
{
|
| 2 |
+
"context_size": 4,
|
| 3 |
+
"variant": "subword",
|
| 4 |
+
"language": "be",
|
| 5 |
+
"unique_contexts": 2124122,
|
| 6 |
+
"total_transitions": 433089588
|
| 7 |
+
}
|
models/subword_ngram/be_2gram_subword.parquet
ADDED
|
@@ -0,0 +1,3 @@
|
|
|
|
|
|
|
|
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|
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|
|
| 1 |
+
version https://git-lfs.github.com/spec/v1
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| 2 |
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oid sha256:c0e30a48df55f96d4bf2b8dc208c62d144ebf34b1a70cfcf18baab44a7ed51fd
|
| 3 |
+
size 267023
|
models/subword_ngram/be_2gram_subword_metadata.json
ADDED
|
@@ -0,0 +1,7 @@
|
|
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|
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|
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|
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|
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|
| 1 |
+
{
|
| 2 |
+
"n": 2,
|
| 3 |
+
"variant": "subword",
|
| 4 |
+
"language": "be",
|
| 5 |
+
"unique_ngrams": 19108,
|
| 6 |
+
"total_ngrams": 433862151
|
| 7 |
+
}
|
models/subword_ngram/be_3gram_subword.parquet
ADDED
|
@@ -0,0 +1,3 @@
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|
|
| 1 |
+
version https://git-lfs.github.com/spec/v1
|
| 2 |
+
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| 3 |
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size 2504735
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models/subword_ngram/be_3gram_subword_metadata.json
ADDED
|
@@ -0,0 +1,7 @@
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|
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|
|
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|
|
|
|
|
|
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|
| 1 |
+
{
|
| 2 |
+
"n": 3,
|
| 3 |
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"variant": "subword",
|
| 4 |
+
"language": "be",
|
| 5 |
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|
| 6 |
+
"total_ngrams": 433604630
|
| 7 |
+
}
|
models/subword_ngram/be_4gram_subword.parquet
ADDED
|
@@ -0,0 +1,3 @@
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| 1 |
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version https://git-lfs.github.com/spec/v1
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| 3 |
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|
models/subword_ngram/be_4gram_subword_metadata.json
ADDED
|
@@ -0,0 +1,7 @@
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| 1 |
+
{
|
| 2 |
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"n": 4,
|
| 3 |
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"variant": "subword",
|
| 4 |
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"language": "be",
|
| 5 |
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|
| 6 |
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|
| 7 |
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}
|
models/tokenizer/be_tokenizer_16k.model
ADDED
|
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| 1 |
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version https://git-lfs.github.com/spec/v1
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models/tokenizer/be_tokenizer_16k.vocab
ADDED
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|
models/tokenizer/be_tokenizer_32k.model
ADDED
|
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version https://git-lfs.github.com/spec/v1
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models/tokenizer/be_tokenizer_32k.vocab
ADDED
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|
models/tokenizer/be_tokenizer_64k.model
ADDED
|
@@ -0,0 +1,3 @@
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| 1 |
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version https://git-lfs.github.com/spec/v1
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models/tokenizer/be_tokenizer_64k.vocab
ADDED
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models/tokenizer/be_tokenizer_8k.model
ADDED
|
@@ -0,0 +1,3 @@
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| 1 |
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version https://git-lfs.github.com/spec/v1
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models/tokenizer/be_tokenizer_8k.vocab
ADDED
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|
|
models/vocabulary/be_vocabulary.parquet
ADDED
|
@@ -0,0 +1,3 @@
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|
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| 1 |
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version https://git-lfs.github.com/spec/v1
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models/vocabulary/be_vocabulary_metadata.json
ADDED
|
@@ -0,0 +1,16 @@
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| 1 |
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{
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| 2 |
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"language": "be",
|
| 3 |
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| 4 |
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| 5 |
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| 6 |
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| 7 |
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| 11 |
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| 13 |
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|
| 15 |
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}
|
| 16 |
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models/word_markov/be_markov_ctx1_word.parquet
ADDED
|
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version https://git-lfs.github.com/spec/v1
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| 3 |
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models/word_markov/be_markov_ctx1_word_metadata.json
ADDED
|
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|
| 1 |
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{
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| 2 |
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| 3 |
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| 4 |
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| 5 |
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|
| 6 |
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|
| 7 |
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models/word_markov/be_markov_ctx2_word.parquet
ADDED
|
@@ -0,0 +1,3 @@
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| 1 |
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version https://git-lfs.github.com/spec/v1
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models/word_markov/be_markov_ctx2_word_metadata.json
ADDED
|
@@ -0,0 +1,7 @@
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|
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|
| 1 |
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{
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| 2 |
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|
| 3 |
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| 4 |
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| 5 |
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|
| 6 |
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|
| 7 |
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models/word_markov/be_markov_ctx3_word.parquet
ADDED
|
@@ -0,0 +1,3 @@
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| 1 |
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version https://git-lfs.github.com/spec/v1
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| 3 |
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size 1226716369
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models/word_markov/be_markov_ctx3_word_metadata.json
ADDED
|
@@ -0,0 +1,7 @@
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|
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|
| 1 |
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{
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| 2 |
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|
| 3 |
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| 4 |
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"language": "be",
|
| 5 |
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|
| 6 |
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|
| 7 |
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models/word_markov/be_markov_ctx4_word.parquet
ADDED
|
@@ -0,0 +1,3 @@
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| 1 |
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version https://git-lfs.github.com/spec/v1
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| 3 |
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size 1617896422
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models/word_markov/be_markov_ctx4_word_metadata.json
ADDED
|
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|
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|
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|
| 1 |
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{
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| 2 |
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|
| 3 |
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| 4 |
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|
| 5 |
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|
| 6 |
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|
| 7 |
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}
|
models/word_ngram/be_2gram_word.parquet
ADDED
|
@@ -0,0 +1,3 @@
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|
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|
| 1 |
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version https://git-lfs.github.com/spec/v1
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| 3 |
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size 33153735
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models/word_ngram/be_2gram_word_metadata.json
ADDED
|
@@ -0,0 +1,7 @@
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|
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|
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|
|
|
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|
| 1 |
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{
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| 2 |
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| 3 |
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| 4 |
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|
| 5 |
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|
| 6 |
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|
| 7 |
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|
models/word_ngram/be_3gram_word.parquet
ADDED
|
@@ -0,0 +1,3 @@
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|
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|
|
|
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|
| 1 |
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version https://git-lfs.github.com/spec/v1
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| 3 |
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models/word_ngram/be_3gram_word_metadata.json
ADDED
|
@@ -0,0 +1,7 @@
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|
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|
|
|
|
|
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|
| 1 |
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{
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| 2 |
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| 3 |
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| 4 |
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| 5 |
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|
| 6 |
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|
| 7 |
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|
models/word_ngram/be_4gram_word.parquet
ADDED
|
@@ -0,0 +1,3 @@
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|
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| 1 |
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version https://git-lfs.github.com/spec/v1
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size 147804215
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models/word_ngram/be_4gram_word_metadata.json
ADDED
|
@@ -0,0 +1,7 @@
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|
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|
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|
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|
|
|
|
|
|
|
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|
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|
| 1 |
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{
|
| 2 |
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|
| 3 |
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| 4 |
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|
| 5 |
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|
| 6 |
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|
| 7 |
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|
visualizations/embedding_isotropy.png
ADDED
|