---
language: ha
language_name: Hausa
language_family: chadic
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-chadic
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: 4.398
  - name: best_isotropy
    type: isotropy
    value: 0.8106
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Hausa** 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** | 3.763x | 3.76 | 0.2087% | 416,305 |
| **16k** | 4.047x | 4.05 | 0.2245% | 387,089 |
| **32k** | 4.258x | 4.26 | 0.2362% | 367,890 |
| **64k** | 4.398x 🏆 | 4.40 | 0.2440% | 356,119 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Luke Ashworth (an haife shi a shekara ta shi ne dan wasan ƙwallon ƙafa ta ƙasar ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁l uke ▁ash worth ▁( an ▁haife ▁shi ▁a ▁shekara ... (+18 more)` | 28 |
| 16k | `▁l uke ▁ash worth ▁( an ▁haife ▁shi ▁a ▁shekara ... (+18 more)` | 28 |
| 32k | `▁luke ▁ash worth ▁( an ▁haife ▁shi ▁a ▁shekara ▁ta ... (+17 more)` | 27 |
| 64k | `▁luke ▁ashworth ▁( an ▁haife ▁shi ▁a ▁shekara ▁ta ▁shi ... (+16 more)` | 26 |

**Sample 2:** `Joshua Ogunlola (an haife shi 19 Afrilu ɗan wasan cricket ne na Najeriya . Ya bu...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁jo shua ▁ogun lo la ▁( an ▁haife ▁shi ▁ ... (+23 more)` | 33 |
| 16k | `▁joshua ▁ogun lola ▁( an ▁haife ▁shi ▁ 1 9 ... (+21 more)` | 31 |
| 32k | `▁joshua ▁ogun lola ▁( an ▁haife ▁shi ▁ 1 9 ... (+21 more)` | 31 |
| 64k | `▁joshua ▁ogun lola ▁( an ▁haife ▁shi ▁ 1 9 ... (+21 more)` | 31 |

**Sample 3:** `Roland Omoruyi (an haife shi 5 ga watan Yuni ɗan damben Najeriya ne. Yayi gasa a...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁r oland ▁om or u yi ▁( an ▁haife ▁shi ... (+22 more)` | 32 |
| 16k | `▁roland ▁om or u yi ▁( an ▁haife ▁shi ▁ ... (+21 more)` | 31 |
| 32k | `▁roland ▁om oru yi ▁( an ▁haife ▁shi ▁ 5 ... (+20 more)` | 30 |
| 64k | `▁roland ▁om oru yi ▁( an ▁haife ▁shi ▁ 5 ... (+20 more)` | 30 |


### Key Findings

- **Best Compression:** 64k achieves 4.398x compression
- **Lowest UNK Rate:** 8k with 0.2087% 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 | 49,621 | 15.60 | 604,355 | 12.3% | 29.9% |
| **2-gram** | Subword | 196 🏆 | 7.61 | 13,430 | 74.9% | 99.3% |
| **3-gram** | Word | 290,081 | 18.15 | 1,505,795 | 4.6% | 13.9% |
| **3-gram** | Subword | 1,547 | 10.60 | 97,163 | 36.1% | 78.3% |
| **4-gram** | Word | 898,959 | 19.78 | 2,859,421 | 2.8% | 8.4% |
| **4-gram** | Subword | 8,574 | 13.07 | 534,835 | 17.2% | 50.0% |
| **5-gram** | Word | 876,152 | 19.74 | 2,080,226 | 2.6% | 7.9% |
| **5-gram** | Subword | 33,589 | 15.04 | 1,728,117 | 9.7% | 31.4% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a cikin` | 313,998 |
| 2 | `tare da` | 141,234 |
| 3 | `a matsayin` | 130,861 |
| 4 | `da aka` | 106,305 |
| 5 | `da kuma` | 89,834 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a shekara ta` | 43,773 |
| 2 | `ci gaba da` | 25,571 |
| 3 | `da ba a` | 20,387 |
| 4 | `an haife shi` | 20,273 |
| 5 | `afirka ta kudu` | 17,311 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `archived from the original` | 15,473 |
| 2 | `from the original on` | 15,162 |
| 3 | `an haife shi a` | 14,183 |
| 4 | `fassarorin da ba a` | 13,066 |
| 5 | `masu fassarorin da ba` | 13,066 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `archived from the original on` | 14,682 |
| 2 | `fassarorin da ba a duba` | 13,066 |
| 3 | `masu fassarorin da ba a` | 13,066 |
| 4 | `da ba a duba ba` | 13,065 |
| 5 | `an haife shi a ranar` | 5,602 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 13,901,672 |
| 2 | `n _` | 6,669,315 |
| 3 | `a n` | 6,077,508 |
| 4 | `a r` | 5,295,640 |
| 5 | `d a` | 4,369,505 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d a` | 3,204,702 |
| 2 | `d a _` | 3,036,418 |
| 3 | `i n _` | 2,924,187 |
| 4 | `a n _` | 2,144,471 |
| 5 | `a r _` | 2,066,174 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d a _` | 2,454,989 |
| 2 | `_ n a _` | 991,541 |
| 3 | `a _ d a` | 987,768 |
| 4 | `_ t a _` | 853,598 |
| 5 | `a _ t a` | 717,349 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _ d a _` | 720,468 |
| 2 | `i k i n _` | 496,368 |
| 3 | `_ c i k i` | 458,937 |
| 4 | `a _ t a _` | 441,174 |
| 5 | `c i k i n` | 435,066 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 196
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~31% 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 | 0.8863 | 1.848 | 10.46 | 661,201 | 11.4% |
| **1** | Subword | 1.0685 | 2.097 | 6.96 | 7,221 | 0.0% |
| **2** | Word | 0.3948 | 1.315 | 2.52 | 6,908,013 | 60.5% |
| **2** | Subword | 0.7292 | 1.658 | 4.69 | 50,274 | 27.1% |
| **3** | Word | 0.2061 | 1.154 | 1.53 | 17,415,052 | 79.4% |
| **3** | Subword | 0.7187 | 1.646 | 4.06 | 235,540 | 28.1% |
| **4** | Word | 0.1035 🏆 | 1.074 | 1.21 | 26,662,755 | 89.6% |
| **4** | Subword | 0.6831 | 1.606 | 3.40 | 956,556 | 31.7% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `da sojojin kasar ke iyakance ma aunin cinikayya da alaƙa da duniya cambridge ta kuma wani`
2. `a kwalejin fort douteuse manazarta nijar da jama a shekara ta bi na wanda aka gudanar`
3. `na shekara ta everett dutton jump gable ray choto an tsare ta wannan baya kudancin tasman`

**Context Size 2:**

1. `a cikin alal misali ƙwararrun hindu sun nuna cewa suna adawa da shi 23 da kwallaye 26`
2. `tare da ƙungiyar ƙwallon ƙafa a ƙayyadaddun su ba bisa ka ida ba ta koma tare da`
3. `a matsayin mai ba da masauki a kowane yanayi taimako ga peter da saint pons de thomières`

**Context Size 3:**

1. `a shekara ta larabci غالية شاكر mawaƙi ne ɗan ƙasar ghana wanda ke taka leda a matsayin ɗan`
2. `ci gaba da amfani duk da wannan karuwar kwanan nan a cikin ya ya shida na yusufu da`
3. `da ba a duba ba wasan kwaikwawo ta kudu`

**Context Size 4:**

1. `archived from the original on 4 march retrieved 23 january ita ce shekara ta goma sha tara a saman`
2. `from the original on retrieved october 1 dajin yana wurin zama ga nau in ruwa da na kogi da`
3. `an haife shi a shekara ta ɗan siyasan najeriya ne daga jihar yobe a yankin arewa maso gabas cen`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `ar_ar_yandu_t_am`
2. `_chea_ƴa_ctar_ki`
3. `n_aya_ar_su,_don`

**Context Size 2:**

1. `a_sc_ake_gwa_gayu`
2. `n_re_que_ta_redea`
3. `an_in_huga_cikar_`

**Context Size 3:**

1. `_daidaraktanin_tsa`
2. `da_ya_kuma_na_doka`
3. `in_mallace_takewac`

**Context Size 4:**

1. `_da_za_manazartar_a`
2. `_na_mai_don_a_kansa`
3. `a_da_no._632._an_fo`


### Key Findings

- **Best Predictability:** Context-4 (word) with 89.6% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (956,556 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 | 289,201 |
| Total Tokens | 38,460,059 |
| Mean Frequency | 132.99 |
| Median Frequency | 4 |
| Frequency Std Dev | 6762.57 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | da | 2,472,553 |
| 2 | a | 1,750,033 |
| 3 | na | 1,000,437 |
| 4 | ta | 870,013 |
| 5 | ya | 735,582 |
| 6 | kuma | 428,826 |
| 7 | cikin | 427,094 |
| 8 | ba | 345,573 |
| 9 | an | 263,110 |
| 10 | daga | 256,194 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | lakisha | 2 |
| 2 | tanish | 2 |
| 3 | katakanaタニシャ | 2 |
| 4 | tanishia | 2 |
| 5 | tinisha | 2 |
| 6 | tír | 2 |
| 7 | sunami | 2 |
| 8 | mamis | 2 |
| 9 | mywo | 2 |
| 10 | iyaz | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.2631 |
| R² (Goodness of Fit) | 0.985164 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 43.1% |
| Top 1,000 | 71.6% |
| Top 5,000 | 87.4% |
| Top 10,000 | 91.4% |

### Key Findings

- **Zipf Compliance:** R²=0.9852 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 43.1% of corpus
- **Long Tail:** 279,201 words needed for remaining 8.6% 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 | 0.8106 | 0.4067 | N/A | N/A |
| **mono_64d** | 64 | 0.7783 | 0.3527 | N/A | N/A |
| **mono_128d** | 128 | 0.6921 | 0.2853 | N/A | N/A |
| **aligned_32d** | 32 | 0.8106 🏆 | 0.3959 | 0.3320 | 0.7500 |
| **aligned_64d** | 64 | 0.7783 | 0.3627 | 0.5680 | 0.8980 |
| **aligned_128d** | 128 | 0.6921 | 0.3062 | 0.6520 | 0.9100 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8106 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3516. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 65.2% R@1 in cross-lingual retrieval.
- **Recommendation:** 128d aligned for best cross-lingual performance

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

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

### 6.1 Productivity & Complexity

| Metric | Value | Interpretation | Recommendation |
|--------|-------|----------------|----------------|
| Productivity Index | **5.000** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **-0.749** | 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 |
|--------|----------|
| `-a` | adéọlá, andros, a9 |
| `-ma` | mahbubani, mackandal, madejski |
| `-s` | spahis, songulashvili, srw |
| `-m` | mohie, mufassir, mahbubani |
| `-n` | nnung, naturist, nogomania |
| `-b` | bachtarzi, bosley, barbashi |
| `-k` | kwararawar, kantako, kalaman |
| `-ba` | bachtarzi, barbashi, balar |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | tsarkakarta, gunilla, ejeagha |
| `-s` | conscripts, chucks, spahis |
| `-e` | coatesville, paleotemperature, renfrewshire |
| `-n` | lallausan, incan, hakannan |
| `-i` | empangeni, bachtarzi, barbashi |
| `-r` | kwararawar, balar, mufassir |
| `-o` | derzhkino, vio, kantako |
| `-an` | lallausan, incan, hakannan |

### 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 |
|------|----------|------------------|----------|
| `ekar` | 2.65x | 71 contexts | ekara, lekar, sekara |
| `ungi` | 2.31x | 129 contexts | bungi, fungi, lungi |
| `ngiy` | 2.51x | 74 contexts | ungiya, tangiya, ungiyar |
| `afir` | 2.80x | 41 contexts | kafir, afire, afira |
| `heka` | 2.48x | 64 contexts | sheka, bheka, cheka |
| `atio` | 2.30x | 89 contexts | ratio, patio, natio |
| `eriy` | 2.31x | 44 contexts | eriyo, eriya, teriy |
| `anay` | 2.31x | 41 contexts | anayi, anaya, anaye |
| `nyar` | 2.01x | 54 contexts | nyara, nyari, cinyar |
| `amfa` | 2.30x | 32 contexts | amfan, camfa, amfar |
| `arsh` | 1.75x | 95 contexts | warsh, karsh, arsht |
| `bban` | 2.12x | 42 contexts | abban, dabban, kibban |

### 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 |
|--------|--------|-----------|----------|
| `-s` | `-a` | 89 words | sonaiya, skikda |
| `-k` | `-a` | 84 words | kwatankwacinsa, kadiyawa |
| `-a` | `-a` | 79 words | adaora, aña |
| `-a` | `-e` | 66 words | alane, aggiunte |
| `-b` | `-a` | 63 words | brunhilda, barasa |
| `-s` | `-e` | 59 words | sinninghe, serere |
| `-ma` | `-a` | 58 words | mashogwawara, maikusa |
| `-t` | `-a` | 53 words | taila, tcha |
| `-a` | `-s` | 52 words | aidas, agnews |
| `-m` | `-a` | 52 words | mujica, musina |

### 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 |
|------|-----------------|------------|------|
| omanawanui | **`omanawan-u-i`** | 7.5 | `u` |
| chickpeas | **`chickpe-a-s`** | 7.5 | `a` |
| chieveley | **`chievel-e-y`** | 7.5 | `e` |
| bunamwaya | **`bunamw-a-ya`** | 7.5 | `a` |
| manawashi | **`ma-na-washi`** | 7.5 | `washi` |
| zamaninsa | **`zamanin-s-a`** | 7.5 | `s` |
| tanacikin | **`ta-na-cikin`** | 7.5 | `cikin` |
| fortalezas | **`fortalez-a-s`** | 7.5 | `a` |
| bangarensa | **`bangaren-s-a`** | 7.5 | `s` |
| equalizing | **`equaliz-i-ng`** | 7.5 | `i` |
| abdulwahid | **`abdulwah-i-d`** | 7.5 | `i` |
| rangitata | **`rangi-ta-ta`** | 7.5 | `ta` |
| parkinsons | **`parkins-on-s`** | 6.0 | `parkins` |
| almajiran | **`al-ma-jiran`** | 6.0 | `jiran` |
| finalises | **`final-is-es`** | 6.0 | `final` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Hausa 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 (4.40x) |
| N-gram | **2-gram** | Lowest perplexity (196) |
| Markov | **Context-4** | Highest predictability (89.6%) |
| 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 03:18:39*