---
language: shi
language_name: Tachelhit
language_family: berber
tags:
  - wikilangs
  - nlp
  - tokenizer
  - embeddings
  - n-gram
  - markov
  - wikipedia
  - feature-extraction
  - sentence-similarity
  - tokenization
  - n-grams
  - markov-chain
  - text-mining
  - fasttext
  - babelvec
  - vocabulous
  - vocabulary
  - monolingual
  - family-berber
license: mit
library_name: wikilangs
pipeline_tag: text-generation
datasets:
  - omarkamali/wikipedia-monthly
dataset_info:
  name: wikipedia-monthly
  description: Monthly snapshots of Wikipedia articles across 300+ languages
metrics:
  - name: best_compression_ratio
    type: compression
    value: 3.819
  - name: best_isotropy
    type: isotropy
    value: 0.7173
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

# Tachelhit - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Tachelhit** Wikipedia data.
We analyze tokenizers, n-gram models, Markov chains, vocabulary statistics, and word embeddings.

## 📋 Repository Contents

### Models & Assets

- Tokenizers (8k, 16k, 32k, 64k)
- N-gram models (2, 3, 4, 5-gram)
- Markov chains (context of 1, 2, 3, 4 and 5)
- Subword N-gram and Markov chains
- Embeddings in various sizes and dimensions (aligned and unaligned)
- Language Vocabulary
- Language Statistics

![Performance Dashboard](visualizations/performance_dashboard.png)

### Analysis and Evaluation

- [1. Tokenizer Evaluation](#1-tokenizer-evaluation)
- [2. N-gram Model Evaluation](#2-n-gram-model-evaluation)
- [3. Markov Chain Evaluation](#3-markov-chain-evaluation)
- [4. Vocabulary Analysis](#4-vocabulary-analysis)
- [5. Word Embeddings Evaluation](#5-word-embeddings-evaluation)
- [6. Morphological Analysis (Experimental)](#6--morphological-analysis-experimental)
- [7. Summary & Recommendations](#7-summary--recommendations)
- [Metrics Glossary](#appendix-metrics-glossary--interpretation-guide)
- [Visualizations Index](#visualizations-index)

---
## 1. Tokenizer Evaluation

![Tokenizer Compression](visualizations/tokenizer_compression.png)

![Tokenizer Fertility](visualizations/tokenizer_fertility.png)

![Tokenizer OOV](visualizations/tokenizer_oov.png)

![Total Tokens](visualizations/tokenizer_total_tokens.png)

### Results

| Vocab Size | Compression | Avg Token Len | UNK Rate | Total Tokens |
|------------|-------------|---------------|----------|--------------|
| **8k** | 3.016x | 3.02 | 1.3945% | 407,897 |
| **16k** | 3.301x | 3.30 | 1.5260% | 372,731 |
| **32k** | 3.556x | 3.56 | 1.6440% | 345,980 |
| **64k** | 3.819x 🏆 | 3.82 | 1.7653% | 322,212 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Talggut neɣ Algu tga yat tasklut ur iskaren awd yat ugummu, tesker ifrawen zund ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁tal gg ut ▁neɣ ▁al gu ▁tga ▁yat ▁tas klut ... (+29 more)` | 39 |
| 16k | `▁tal ggut ▁neɣ ▁algu ▁tga ▁yat ▁tasklut ▁ur ▁iskar en ... (+22 more)` | 32 |
| 32k | `▁talggut ▁neɣ ▁algu ▁tga ▁yat ▁tasklut ▁ur ▁iskaren ▁awd ▁yat ... (+20 more)` | 30 |
| 64k | `▁talggut ▁neɣ ▁algu ▁tga ▁yat ▁tasklut ▁ur ▁iskaren ▁awd ▁yat ... (+19 more)` | 29 |

**Sample 2:** `1 000 iga yan umḍan imqquṛn, ism ns s tmaziɣt igat ifḍ (s tfinaɣ : ⵉⴼⴹ). Msmun a...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ 1 ▁ 0 0 0 ▁iga ▁yan ▁umḍan ▁imqquṛn ... (+30 more)` | 40 |
| 16k | `▁ 1 ▁ 0 0 0 ▁iga ▁yan ▁umḍan ▁imqquṛn ... (+29 more)` | 39 |
| 32k | `▁ 1 ▁ 0 0 0 ▁iga ▁yan ▁umḍan ▁imqquṛn ... (+29 more)` | 39 |
| 64k | `▁ 1 ▁ 0 0 0 ▁iga ▁yan ▁umḍan ▁imqquṛn ... (+29 more)` | 39 |

**Sample 3:** `Iga Q yan sg iskkiln n ugmmay alatin n tmaziɣt. Tisaɣulin amaziɣ tamaziɣt`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁iga ▁q ▁yan ▁sg ▁iskkiln ▁n ▁ugmmay ▁alatin ▁n ▁tmaziɣt ... (+4 more)` | 14 |
| 16k | `▁iga ▁q ▁yan ▁sg ▁iskkiln ▁n ▁ugmmay ▁alatin ▁n ▁tmaziɣt ... (+4 more)` | 14 |
| 32k | `▁iga ▁q ▁yan ▁sg ▁iskkiln ▁n ▁ugmmay ▁alatin ▁n ▁tmaziɣt ... (+4 more)` | 14 |
| 64k | `▁iga ▁q ▁yan ▁sg ▁iskkiln ▁n ▁ugmmay ▁alatin ▁n ▁tmaziɣt ... (+4 more)` | 14 |


### Key Findings

- **Best Compression:** 64k achieves 3.819x compression
- **Lowest UNK Rate:** 8k with 1.3945% unknown tokens
- **Trade-off:** Larger vocabularies improve compression but increase model size
- **Recommendation:** 32k vocabulary provides optimal balance for production use

---
## 2. N-gram Model Evaluation

![N-gram Perplexity](visualizations/ngram_perplexity.png)

![N-gram Unique](visualizations/ngram_unique.png)

![N-gram Coverage](visualizations/ngram_coverage.png)

### Results

| N-gram | Variant | Perplexity | Entropy | Unique N-grams | Top-100 Coverage | Top-1000 Coverage |
|--------|---------|------------|---------|----------------|------------------|-------------------|
| **2-gram** | Word | 1,027 | 10.00 | 23,236 | 45.7% | 81.7% |
| **2-gram** | Subword | 255 🏆 | 7.99 | 3,781 | 68.8% | 99.0% |
| **3-gram** | Word | 1,698 | 10.73 | 46,052 | 39.0% | 76.4% |
| **3-gram** | Subword | 1,284 | 10.33 | 29,091 | 35.1% | 84.7% |
| **4-gram** | Word | 3,109 | 11.60 | 90,307 | 35.2% | 68.9% |
| **4-gram** | Subword | 3,344 | 11.71 | 117,787 | 23.5% | 73.6% |
| **5-gram** | Word | 3,900 | 11.93 | 100,603 | 35.2% | 65.7% |
| **5-gram** | Subword | 5,685 | 12.47 | 238,802 | 18.6% | 68.5% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `tgmiḍi n` | 30,047 |
| 2 | `n usggʷas` | 27,406 |
| 3 | `umḍan n` | 26,921 |
| 4 | `n imzdaɣn` | 25,250 |
| 5 | `tlkm tgmiḍi` | 24,096 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `tlkm tgmiḍi n` | 24,096 |
| 2 | `tamattayt n usɣiws` | 16,122 |
| 3 | `tasmirit tamattayt n` | 15,740 |
| 4 | `umḍan n imzdaɣn` | 14,946 |
| 5 | `g tlkm tgmiḍi` | 12,050 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `tasmirit tamattayt n usɣiws` | 15,739 |
| 2 | `g tlkm tgmiḍi n` | 12,050 |
| 3 | `ad i trfiqt n` | 8,924 |
| 4 | `uḍwwaṛ ad i trfiqt` | 8,917 |
| 5 | `umḍan n imzdaɣn nns` | 8,916 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `uḍwwaṛ ad i trfiqt n` | 8,916 |
| 2 | `amatay n imzdaɣn tasmirit tamattayt` | 8,910 |
| 3 | `imzdaɣn tasmirit tamattayt n usɣiws` | 8,910 |
| 4 | `n imzdaɣn tasmirit tamattayt n` | 8,910 |
| 5 | `ilkm umḍan n imzdaɣn nns` | 8,904 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n _` | 653,867 |
| 2 | `_ n` | 401,914 |
| 3 | `_ t` | 358,373 |
| 4 | `_ i` | 253,323 |
| 5 | `t a` | 205,156 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ n _` | 294,487 |
| 2 | `_ t a` | 132,536 |
| 3 | `n _ t` | 104,627 |
| 4 | `a n _` | 103,501 |
| 5 | `_ ɣ _` | 101,865 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ n _ u` | 84,430 |
| 2 | `t _ n _` | 67,376 |
| 3 | `_ n _ i` | 61,495 |
| 4 | `_ n _ t` | 56,122 |
| 5 | `n _ u s` | 52,239 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ n _ u s` | 51,413 |
| 2 | `m z d a ɣ` | 46,710 |
| 3 | `g g ʷ a s` | 34,963 |
| 4 | `s g g ʷ a` | 34,938 |
| 5 | `_ n n a _` | 34,315 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 255
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~68% of corpus
- **Recommendation:** 4-gram or 5-gram for best predictive performance

---
## 3. Markov Chain Evaluation

![Markov Entropy](visualizations/markov_entropy.png)

![Markov Contexts](visualizations/markov_contexts.png)

![Markov Branching](visualizations/markov_branching.png)

### Results

| Context | Variant | Avg Entropy | Perplexity | Branching Factor | Unique Contexts | Predictability |
|---------|---------|-------------|------------|------------------|-----------------|----------------|
| **1** | Word | 0.6330 | 1.551 | 4.06 | 76,235 | 36.7% |
| **1** | Subword | 1.2937 | 2.452 | 10.38 | 803 | 0.0% |
| **2** | Word | 0.2598 | 1.197 | 1.65 | 308,778 | 74.0% |
| **2** | Subword | 1.0718 | 2.102 | 6.52 | 8,338 | 0.0% |
| **3** | Word | 0.0839 | 1.060 | 1.19 | 508,428 | 91.6% |
| **3** | Subword | 0.8300 | 1.778 | 3.82 | 54,347 | 17.0% |
| **4** | Word | 0.0475 🏆 | 1.033 | 1.13 | 601,160 | 95.2% |
| **4** | Subword | 0.5641 | 1.478 | 2.43 | 207,735 | 43.6% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `n ayt twayya nna dar irgazn d amatay n usggʷas niɣ uggar ɣ ɛin ijri s`
2. `ɣ uḍwwaṛ innazwan yili ɣ lmɣrib iḍfaṛ uḍwwaṛ ad i twuri tannayin tisaɣulin ɣ llan 4`
3. `d 11 n tarwuri 2 ig unammas n tznit tamnaḍt n iḍuṛan ilkm wawtay nnsn iẓḍiṛn`

**Context Size 2:**

1. `tgmiḍi n uslmd 92 86 gr irban d trbatin nna dar 15 n usggʷas démographiques et socio`
2. `n usggʷas démographiques et socio économiques de la population rurale hors nomades par douar selon l...`
3. `umḍan n imzdaɣn n usun ad 20 n iḍuṛan ilkm umḍan n twjiwin s 32 7 gr`

**Context Size 3:**

1. `tlkm tgmiḍi n uslmd 100 gr irban d trbatin nna dar gr 6 d 11 n usggʷas ɣ`
2. `tamattayt n usɣiws tannayin tisaɣulin ɣ lmɣrib ɣ tsga n lḥuz n lḥuz n lḥuz n lḥuz n`
3. `tasmirit tamattayt n usɣiws ɣ iga umḍan n imawaḍn 224 n umzdaɣ gisn 581 n iwtman d 329`

**Context Size 4:**

1. `tasmirit tamattayt n usɣiws ɣ iga umḍan n imawaḍn 236 n umzdaɣ gisn 110 n iwtman d 101 n`
2. `g tlkm tgmiḍi n uslmd 89 66 gr irban d trbatin nna dar gr 6 d 11 n usggʷas`
3. `ad i trfiqt n ayt iɛzman nna ɣ llan 4 n iḍuṛan ilkm umḍan n imzdaɣn nns 251 n`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_5_wtaṛsɣ_t_tana`
2. `aḍas_tm_aɣnaphon`
3. `nn_nn_puriquriɣ_`

**Context Size 2:**

1. `n_muḍwwawtmas_soc`
2. `_n_et_tamklattamk`
3. `_tawtmadin_tlkm_u`

**Context Size 3:**

1. `_n_imzdaɣn_nit_soc`
2. `_tarwurin_i_trfiqt`
3. `n_tawuri._tluḥarch`

**Context Size 4:**

1. `_n_usɣiws._aṛcif,_1`
2. `t_n_iwtman_d_23.95_`
3. `_n_imzdaɣn_n_iwtman`


### Key Findings

- **Best Predictability:** Context-4 (word) with 95.2% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (207,735 contexts)
- **Recommendation:** Context-3 or Context-4 for text generation

---
## 4. Vocabulary Analysis

![Zipf's Law](visualizations/zipf_law.png)

![Top Words](visualizations/top20_words.png)

![Coverage Curve](visualizations/vocab_coverage.png)

### Statistics

| Metric | Value |
|--------|-------|
| Vocabulary Size | 31,610 |
| Total Tokens | 2,378,642 |
| Mean Frequency | 75.25 |
| Median Frequency | 4 |
| Frequency Std Dev | 1969.69 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | n | 294,685 |
| 2 | ɣ | 101,988 |
| 3 | d | 64,374 |
| 4 | s | 34,997 |
| 5 | nna | 34,361 |
| 6 | imzdaɣn | 31,398 |
| 7 | dar | 30,865 |
| 8 | gr | 30,721 |
| 9 | tgmiḍi | 30,050 |
| 10 | usggʷas | 28,210 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | tdarwinit | 2 |
| 2 | talmuqqdimt | 2 |
| 3 | ttawnn | 2 |
| 4 | taggrgist | 2 |
| 5 | umdgar | 2 |
| 6 | uqṛiḍ | 2 |
| 7 | dearborn | 2 |
| 8 | ghosts | 2 |
| 9 | tremblay | 2 |
| 10 | tmmndl | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.2849 |
| R² (Goodness of Fit) | 0.988016 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 69.6% |
| Top 1,000 | 90.6% |
| Top 5,000 | 95.6% |
| Top 10,000 | 97.3% |

### Key Findings

- **Zipf Compliance:** R²=0.9880 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 69.6% of corpus
- **Long Tail:** 21,610 words needed for remaining 2.7% coverage

---
## 5. Word Embeddings Evaluation

![Embedding Isotropy](visualizations/embedding_isotropy.png)

![Similarity Matrix](visualizations/embedding_similarity.png)

![t-SNE Words](visualizations/tsne_words.png)

![t-SNE Sentences](visualizations/tsne_sentences.png)


### 5.1 Cross-Lingual Alignment

![Alignment Quality](visualizations/embedding_alignment_quality.png)

![Multilingual t-SNE](visualizations/embedding_tsne_multilingual.png)


### 5.2 Model Comparison

| Model | Dimension | Isotropy | Semantic Density | Alignment R@1 | Alignment R@10 |
|-------|-----------|----------|------------------|---------------|----------------|
| **mono_32d** | 32 | 0.7173 | 0.3723 | N/A | N/A |
| **mono_64d** | 64 | 0.5707 | 0.3238 | N/A | N/A |
| **mono_128d** | 128 | 0.2225 | 0.3121 | N/A | N/A |
| **aligned_32d** | 32 | 0.7173 🏆 | 0.3624 | 0.0140 | 0.0980 |
| **aligned_64d** | 64 | 0.5707 | 0.3343 | 0.0280 | 0.1200 |
| **aligned_128d** | 128 | 0.2225 | 0.3186 | 0.0400 | 0.1960 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.7173 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3372. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 4.0% R@1 in cross-lingual retrieval.
- **Recommendation:** 128d aligned for best cross-lingual performance

---
## 6.  Morphological Analysis (Experimental)

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

### 6.1 Productivity & Complexity

| Metric | Value | Interpretation | Recommendation |
|--------|-------|----------------|----------------|
| Productivity Index | **5.000** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **-0.041** | Low formulaic content | - |

### 6.2 Affix Inventory (Productive Units)

These are the most productive prefixes and suffixes identified by sampling the vocabulary for global substitutability patterns. A unit is considered an affix if stripping it leaves a valid stem that appears in other contexts.

#### Productive Prefixes
| Prefix | Examples |
|--------|----------|
| `-t` | tugt, tattuyt, tyyuga |
| `-i` | issiks, imẓyann, izdg |
| `-ta` | tattuyt, taryal, tamaẓuẓt |
| `-a` | azdawan, amazɣ, afnsu |
| `-u` | utin, uswaɣ, uzzugz |
| `-l` | lmṣalḥa, lbkr, lmujawharat |
| `-ti` | tizrigin, tidzi, timdst |
| `-m` | maskurt, mḥda, mmaggarn |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | utin, azdawan, tɣmriwin |
| `-t` | tugt, tattuyt, trifiyt |
| `-a` | tyyuga, mḥda, tssa |
| `-in` | utin, tɣmriwin, ɣwin |
| `-s` | issiks, chaouis, nations |
| `-i` | inlbi, uɣri, igiddi |
| `-e` | conduite, historique, déchirée |
| `-an` | azdawan, zyyan, franslyan |

### 6.3 Bound Stems (Lexical Roots)

Bound stems are high-frequency subword units that are semantically cohesive but rarely appear as standalone words. These often correspond to the 'core' of a word that requires inflection or derivation to be valid.

| Stem | Cohesion | Substitutability | Examples |
|------|----------|------------------|----------|
| `adda` | 1.65x | 52 contexts | addad, wadda, jadda |
| `ggʷa` | 1.63x | 43 contexts | aggʷa, ḥggʷa, zggʷar |
| `ggar` | 1.94x | 22 contexts | iggar, uggar, ggarn |
| `ugga` | 1.94x | 21 contexts | uggar, uggan, yugga |
| `wuri` | 1.68x | 30 contexts | twuri, iswuri, swurin |
| `tion` | 2.09x | 14 contexts | notion, action, nation |
| `ɣrib` | 1.80x | 20 contexts | aɣrib, mɣrib, lɣribi |
| `lati` | 1.61x | 27 contexts | latin, latif, mulati |
| `matt` | 1.60x | 26 contexts | matta, tmatti, umatta |
| `mɣri` | 1.79x | 13 contexts | tmɣri, mɣrib, imɣri |
| `atio` | 1.86x | 8 contexts | nation, nations, national |
| `mata` | 1.45x | 14 contexts | amata, smata, umata |

### 6.4 Affix Compatibility (Co-occurrence)

This table shows which prefixes and suffixes most frequently co-occur on the same stems, revealing the 'stacking' rules of the language's morphology.

| Prefix | Suffix | Frequency | Examples |
|--------|--------|-----------|----------|
| `-t` | `-t` | 610 words | tifrirt, tdrfit |
| `-i` | `-n` | 465 words | ittmttatn, ibṛbbachn |
| `-t` | `-n` | 321 words | ttyussanin, tigtfulin |
| `-t` | `-in` | 263 words | ttyussanin, tigtfulin |
| `-l` | `-a` | 84 words | lbṛaṭla, lɛnabsa |
| `-t` | `-a` | 65 words | tiṛṛuyṣa, tzuna |
| `-i` | `-an` | 45 words | inultan, ilawan |
| `-a` | `-i` | 39 words | adarazi, abriṭani |
| `-a` | `-n` | 38 words | agwensan, agaman |
| `-l` | `-t` | 32 words | lfwarat, lfuqqiyyat |

### 6.5 Recursive Morpheme Segmentation

Using **Recursive Hierarchical Substitutability**, we decompose complex words into their constituent morphemes. This approach handles nested affixes (e.g., `prefix-prefix-root-suffix`).

| Word | Suggested Split | Confidence | Stem |
|------|-----------------|------------|------|
| tasnmḍant | **`tasnmḍ-an-t`** | 7.5 | `an` |
| africaine | **`africa-in-e`** | 7.5 | `in` |
| ttyawssannin | **`ttyawssan-n-in`** | 7.5 | `n` |
| ittyurnan | **`ittyur-n-an`** | 7.5 | `n` |
| ittusɣẓnn | **`ittusɣẓ-n-n`** | 7.5 | `n` |
| zzuzzarnit | **`zzuzzar-n-it`** | 7.5 | `n` |
| tutlayyin | **`tutlay-y-in`** | 7.5 | `y` |
| ttaggʷanin | **`ttaggʷa-n-in`** | 7.5 | `n` |
| marocaines | **`maroca-in-es`** | 7.5 | `in` |
| government | **`governme-n-t`** | 7.5 | `n` |
| ttussiḍannt | **`ttussiḍ-an-nt`** | 7.5 | `an` |
| ittyawstay | **`ittyaws-t-ay`** | 7.5 | `t` |
| patrimoine | **`patrimo-in-e`** | 7.5 | `in` |
| ittuzdaɣn | **`it-tu-zdaɣn`** | 6.0 | `zdaɣn` |
| tinsmunin | **`ti-nsmun-in`** | 6.0 | `nsmun` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Tachelhit shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.

---
## 7. Summary & Recommendations

![Performance Dashboard](visualizations/performance_dashboard.png)

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **64k BPE** | Best compression (3.82x) |
| N-gram | **2-gram** | Lowest perplexity (255) |
| Markov | **Context-4** | Highest predictability (95.2%) |
| Embeddings | **100d** | Balanced semantic capture and isotropy |


---
## Appendix: Metrics Glossary & Interpretation Guide

This section provides definitions, intuitions, and guidance for interpreting the metrics used throughout this report.

### Tokenizer Metrics

**Compression Ratio**
> *Definition:* The ratio of characters to tokens (chars/token). Measures how efficiently the tokenizer represents text.
>
> *Intuition:* Higher compression means fewer tokens needed to represent the same text, reducing sequence lengths for downstream models. A 3x compression means ~3 characters per token on average.
>
> *What to seek:* Higher is generally better for efficiency, but extremely high compression may indicate overly aggressive merging that loses morphological information.

**Average Token Length (Fertility)**
> *Definition:* Mean number of characters per token produced by the tokenizer.
>
> *Intuition:* Reflects the granularity of tokenization. Longer tokens capture more context but may struggle with rare words; shorter tokens are more flexible but increase sequence length.
>
> *What to seek:* Balance between 2-5 characters for most languages. Arabic/morphologically-rich languages may benefit from slightly longer tokens.

**Unknown Token Rate (OOV Rate)**
> *Definition:* Percentage of tokens that map to the unknown/UNK token, indicating words the tokenizer cannot represent.
>
> *Intuition:* Lower OOV means better vocabulary coverage. High OOV indicates the tokenizer encounters many unseen character sequences.
>
> *What to seek:* Below 1% is excellent; below 5% is acceptable. BPE tokenizers typically achieve very low OOV due to subword fallback.

### N-gram Model Metrics

**Perplexity**
> *Definition:* Measures how "surprised" the model is by test data. Mathematically: 2^(cross-entropy). Lower values indicate better prediction.
>
> *Intuition:* If perplexity is 100, the model is as uncertain as if choosing uniformly among 100 options at each step. A perplexity of 10 means effectively choosing among 10 equally likely options.
>
> *What to seek:* Lower is better. Perplexity decreases with larger n-grams (more context). Values vary widely by language and corpus size.

**Entropy**
> *Definition:* Average information content (in bits) needed to encode the next token given the context. Related to perplexity: perplexity = 2^entropy.
>
> *Intuition:* High entropy means high uncertainty/randomness; low entropy means predictable patterns. Natural language typically has entropy between 1-4 bits per character.
>
> *What to seek:* Lower entropy indicates more predictable text patterns. Entropy should decrease as n-gram size increases.

**Coverage (Top-K)**
> *Definition:* Percentage of corpus occurrences explained by the top K most frequent n-grams.
>
> *Intuition:* High coverage with few patterns indicates repetitive/formulaic text; low coverage suggests diverse vocabulary usage.
>
> *What to seek:* Depends on use case. For language modeling, moderate coverage (40-60% with top-1000) is typical for natural text.

### Markov Chain Metrics

**Average Entropy**
> *Definition:* Mean entropy across all contexts, measuring average uncertainty in next-word prediction.
>
> *Intuition:* Lower entropy means the model is more confident about what comes next. Context-1 has high entropy (many possible next words); Context-4 has low entropy (few likely continuations).
>
> *What to seek:* Decreasing entropy with larger context sizes. Very low entropy (<0.1) indicates highly deterministic transitions.

**Branching Factor**
> *Definition:* Average number of unique next tokens observed for each context.
>
> *Intuition:* High branching = many possible continuations (flexible but uncertain); low branching = few options (predictable but potentially repetitive).
>
> *What to seek:* Branching factor should decrease with context size. Values near 1.0 indicate nearly deterministic chains.

**Predictability**
> *Definition:* Derived metric: (1 - normalized_entropy) × 100%. Indicates how deterministic the model's predictions are.
>
> *Intuition:* 100% predictability means the next word is always certain; 0% means completely random. Real text falls between these extremes.
>
> *What to seek:* Higher predictability for text generation quality, but too high (>98%) may produce repetitive output.

### Vocabulary & Zipf's Law Metrics

**Zipf's Coefficient**
> *Definition:* The slope of the log-log plot of word frequency vs. rank. Zipf's law predicts this should be approximately -1.
>
> *Intuition:* A coefficient near -1 indicates the corpus follows natural language patterns where a few words are very common and most words are rare.
>
> *What to seek:* Values between -0.8 and -1.2 indicate healthy natural language distribution. Deviations may suggest domain-specific or artificial text.

**R² (Coefficient of Determination)**
> *Definition:* Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.
>
> *Intuition:* R² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.
>
> *What to seek:* R² > 0.95 is excellent; > 0.99 indicates near-perfect Zipf adherence typical of large natural corpora.

**Vocabulary Coverage**
> *Definition:* Cumulative percentage of corpus tokens accounted for by the top N words.
>
> *Intuition:* Shows how concentrated word usage is. If top-100 words cover 50% of text, the corpus relies heavily on common words.
>
> *What to seek:* Top-100 covering 30-50% is typical. Higher coverage indicates more repetitive text; lower suggests richer vocabulary.

### Word Embedding Metrics

**Isotropy**
> *Definition:* Measures how uniformly distributed vectors are in the embedding space. Computed as the ratio of minimum to maximum singular values.
>
> *Intuition:* High isotropy (near 1.0) means vectors spread evenly in all directions; low isotropy means vectors cluster in certain directions, reducing expressiveness.
>
> *What to seek:* Higher isotropy generally indicates better-quality embeddings. Values > 0.1 are reasonable; > 0.3 is good. Lower-dimensional embeddings tend to have higher isotropy.

**Average Norm**
> *Definition:* Mean magnitude (L2 norm) of word vectors in the embedding space.
>
> *Intuition:* Indicates the typical "length" of vectors. Consistent norms suggest stable training; high variance may indicate some words are undertrained.
>
> *What to seek:* Relatively consistent norms across models. The absolute value matters less than consistency (low std deviation).

**Cosine Similarity**
> *Definition:* Measures angular similarity between vectors, ranging from -1 (opposite) to 1 (identical direction).
>
> *Intuition:* Words with similar meanings should have high cosine similarity. This is the standard metric for semantic relatedness in embeddings.
>
> *What to seek:* Semantically related words should score > 0.5; unrelated words should be near 0. Synonyms often score > 0.7.

**t-SNE Visualization**
> *Definition:* t-Distributed Stochastic Neighbor Embedding - a dimensionality reduction technique that preserves local structure for visualization.
>
> *Intuition:* Clusters in t-SNE plots indicate groups of semantically related words. Spread indicates vocabulary diversity; tight clusters suggest semantic coherence.
>
> *What to seek:* Meaningful clusters (e.g., numbers together, verbs together). Avoid over-interpreting distances - t-SNE preserves local, not global, structure.

### General Interpretation Guidelines

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


### Visualizations Index

| Visualization | Description |
|---------------|-------------|
| Tokenizer Compression | Compression ratios by vocabulary size |
| Tokenizer Fertility | Average token length by vocabulary |
| Tokenizer OOV | Unknown token rates |
| Tokenizer Total Tokens | Total tokens by vocabulary |
| N-gram Perplexity | Perplexity by n-gram size |
| N-gram Entropy | Entropy by n-gram size |
| N-gram Coverage | Top pattern coverage |
| N-gram Unique | Unique n-gram counts |
| Markov Entropy | Entropy by context size |
| Markov Branching | Branching factor by context |
| Markov Contexts | Unique context counts |
| Zipf's Law | Frequency-rank distribution with fit |
| Vocab Frequency | Word frequency distribution |
| Top 20 Words | Most frequent words |
| Vocab Coverage | Cumulative coverage curve |
| Embedding Isotropy | Vector space uniformity |
| Embedding Norms | Vector magnitude distribution |
| Embedding Similarity | Word similarity heatmap |
| Nearest Neighbors | Similar words for key terms |
| t-SNE Words | 2D word embedding visualization |
| t-SNE Sentences | 2D sentence embedding visualization |
| Position Encoding | Encoding method comparison |
| Model Sizes | Storage requirements |
| Performance Dashboard | Comprehensive performance overview |

---
## About This Project

### Data Source

Models trained on [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly) - a monthly snapshot of Wikipedia articles across 300+ languages.

### Project

A project by **[Wikilangs](https://wikilangs.org)** - Open-source NLP models for every Wikipedia language.

### Maintainer

[Omar Kamali](https://omarkamali.com) - [Omneity Labs](https://omneitylabs.com)

### Citation

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

```bibtex
@misc{wikilangs2025,
  author = {Kamali, Omar},
  title = {Wikilangs: Open NLP Models for Wikipedia Languages},
  year = {2025},
  doi = {10.5281/zenodo.18073153},
  publisher = {Zenodo},
  url = {https://huggingface.co/wikilangs}
  institution = {Omneity Labs}
}
```

### License

MIT License - Free for academic and commercial use.

### Links

- 🌐 Website: [wikilangs.org](https://wikilangs.org)
- 🤗 Models: [huggingface.co/wikilangs](https://huggingface.co/wikilangs)
- 📊 Data: [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly)
- 👤 Author: [Omar Kamali](https://huggingface.co/omarkamali)
- 🤝 Sponsor: [Featherless AI](https://featherless.ai)
---
*Generated by Wikilangs Models Pipeline*

*Report Date: 2026-01-10 20:02:34*