RESEARCH_REPORT.md

# Tachelhit — Full Ablation Study & Research Report

Detailed evaluation of all model variants trained on **Tachelhit** Wikipedia data by [Wikilangs](https://wikilangs.org).

👈 [Back to README](README.md)

## 📋 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** | 3.017x | 3.02 | 1.3938% | 408,453 |
| **16k** | 3.301x | 3.30 | 1.5252% | 373,263 |
| **32k** | 3.557x | 3.56 | 1.6432% | 346,460 |
| **64k** | 3.819x 🏆 | 3.82 | 1.7643% | 322,672 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Sstekk iga yan ugḍiḍ imẓẓin. Assaɣ Tuzduɣt Tasnalɣa (morphologie) Tisaɣulin Msmu...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁s ste kk ▁iga ▁yan ▁ugḍiḍ ▁imẓẓin . ▁assaɣ ▁tuzduɣt ... (+19 more)` | 29 |
| 16k | `▁s ste kk ▁iga ▁yan ▁ugḍiḍ ▁imẓẓin . ▁assaɣ ▁tuzduɣt ... (+19 more)` | 29 |
| 32k | `▁s stekk ▁iga ▁yan ▁ugḍiḍ ▁imẓẓin . ▁assaɣ ▁tuzduɣt ▁tasnalɣa ... (+18 more)` | 28 |
| 64k | `▁sstekk ▁iga ▁yan ▁ugḍiḍ ▁imẓẓin . ▁assaɣ ▁tuzduɣt ▁tasnalɣa ▁( ... (+17 more)` | 27 |

**Sample 2:** `Asimwas iga ass wiss Smmus g ussan n imalass. Tisaɣulin`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁as im was ▁iga ▁ass ▁wiss ▁smmus ▁g ▁ussan ▁n ... (+3 more)` | 13 |
| 16k | `▁as imwas ▁iga ▁ass ▁wiss ▁smmus ▁g ▁ussan ▁n ▁imalass ... (+2 more)` | 12 |
| 32k | `▁asimwas ▁iga ▁ass ▁wiss ▁smmus ▁g ▁ussan ▁n ▁imalass . ... (+1 more)` | 11 |
| 64k | `▁asimwas ▁iga ▁ass ▁wiss ▁smmus ▁g ▁ussan ▁n ▁imalass . ... (+1 more)` | 11 |

**Sample 3:** `Turdut (S turdut: اردو ) tga tutlayt nna s sawaln ayt Bakistan d Lhnd. Isuɣal`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁tur dut ▁( s ▁tur dut : ▁ا ر دو ... (+14 more)` | 24 |
| 16k | `▁tur dut ▁( s ▁tur dut : ▁ار دو ▁) ... (+13 more)` | 23 |
| 32k | `▁turdut ▁( s ▁turdut : ▁اردو ▁) ▁tga ▁tutlayt ▁nna ... (+9 more)` | 19 |
| 64k | `▁turdut ▁( s ▁turdut : ▁اردو ▁) ▁tga ▁tutlayt ▁nna ... (+8 more)` | 18 |


### Key Findings

- **Best Compression:** 64k achieves 3.819x compression
- **Lowest UNK Rate:** 8k with 1.3938% 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 | 23,244 | 45.7% | 81.7% |
| **2-gram** | Subword | 255 🏆 | 7.99 | 3,782 | 68.8% | 99.0% |
| **3-gram** | Word | 1,698 | 10.73 | 46,062 | 39.0% | 76.4% |
| **3-gram** | Subword | 1,284 | 10.33 | 29,101 | 35.1% | 84.7% |
| **4-gram** | Word | 3,109 | 11.60 | 90,318 | 35.2% | 68.9% |
| **4-gram** | Subword | 3,345 | 11.71 | 117,821 | 23.5% | 73.6% |
| **5-gram** | Word | 3,900 | 11.93 | 100,607 | 35.2% | 65.7% |
| **5-gram** | Subword | 5,689 | 12.47 | 238,898 | 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 | `n imzdaɣn tasmirit tamattayt n` | 8,910 |
| 3 | `amatay n imzdaɣn tasmirit tamattayt` | 8,910 |
| 4 | `imzdaɣn tasmirit tamattayt n usɣiws` | 8,910 |
| 5 | `ilkm umḍan n imzdaɣn nns` | 8,904 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n _` | 653,950 |
| 2 | `_ n` | 401,960 |
| 3 | `_ t` | 358,450 |
| 4 | `_ i` | 253,361 |
| 5 | `t a` | 205,185 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ n _` | 294,525 |
| 2 | `_ t a` | 132,562 |
| 3 | `n _ t` | 104,642 |
| 4 | `a n _` | 103,515 |
| 5 | `_ ɣ _` | 101,882 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ n _ u` | 84,436 |
| 2 | `t _ n _` | 67,385 |
| 3 | `_ n _ i` | 61,498 |
| 4 | `_ n _ t` | 56,134 |
| 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 | 76,272 | 36.7% |
| **1** | Subword | 1.2927 | 2.450 | 10.38 | 804 | 0.0% |
| **2** | Word | 0.2598 | 1.197 | 1.65 | 308,953 | 74.0% |
| **2** | Subword | 1.0716 | 2.102 | 6.52 | 8,341 | 0.0% |
| **3** | Word | 0.0840 | 1.060 | 1.19 | 508,729 | 91.6% |
| **3** | Subword | 0.8300 | 1.778 | 3.82 | 54,358 | 17.0% |
| **4** | Word | 0.0475 🏆 | 1.033 | 1.13 | 601,513 | 95.2% |
| **4** | Subword | 0.5642 | 1.479 | 2.43 | 207,789 | 43.6% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `n twtmin ɣ tsga n lfṛaṛḥa nna mi ilkm umḍan n ayt ɛli n tarskkilt 43`
2. `ɣ tmnaḍt n urtzaɣ taḍwwaṛḍt n tarwuri 2 aslmd g tlkm tgmiḍi n ism n isrɣinn`
3. `d ublulls dar gr d lli tmmal tflwit yaḍn ngr adrar n bni matar m sidi`

**Context Size 2:**

1. `tgmiḍi n tarskkilt 70 82 gr mddn nna dar gr 6 d 11 n usggʷas niɣ uggar`
2. `n usggʷas 28 48 dar tsdnan 3 5 aslmd g tlkm tgmiḍi n 35 1 ig unammas`
3. `umḍan n imzdaɣn n lmɣrib ɣ tsga n trudant n fas amknas ɣ lmɣrib iḍfaṛ uḍwwaṛ ad`

**Context Size 3:**

1. `tlkm tgmiḍi n uslmd 91 97 gr irban d trbatin nna dar gr 6 d 11 n usggʷas`
2. `tamattayt n usɣiws aṛcif 14 ɣuct tisnaddadin tisnaddadin timatayin iggʷiz umḍan n imzdaɣn n tamyawas...`
3. `tasmirit tamattayt n usɣiws tisaɣulin isɣwan yaḍnin tasmirit tamattayt n usɣiws ɣ iga umḍan n imawaḍ...`

**Context Size 4:**

1. `tasmirit tamattayt n usɣiws aṛcif 14 ɣuct tisnaddadin tisnaddadin timatayin iɣli umḍan n imzdaɣn n a...`
2. `g tlkm tgmiḍi n uslmd 98 7 gr irban d trbatin nna dar gr 6 d 11 n usggʷas`
3. `ad i trfiqt n ifrdaw tiɣanimin nna ɣ llan 20 n iḍuṛan ilkm umḍan n imzdaɣn nns 997 n`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_sgmawimda_tabir`
2. `an_4422._uwafarg`
3. `n),_nartan_49_an`

**Context Size 2:**

1. `n_des_ig_twuṭṭa_u`
2. `_n_10.09_n_uḍwwaṛ`
3. `_tɛṛanbattamaslmd`

**Context Size 3:**

1. `_n_umḍan_d_imir_an`
2. `_tamatay_n_i_tugt_`
3. `n_tznit_taru_260_n`

**Context Size 4:**

1. `_n_umzdaɣn_tasga_n_`
2. `t_n_ayt_baha_ɣ_lli_`
3. `_n_iɣ_isggʷasn_d_tr`


### 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 (207,789 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 | 31,623 |
| Total Tokens | 2,378,986 |
| Mean Frequency | 75.23 |
| Median Frequency | 4 |
| Frequency Std Dev | 1969.53 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | n | 294,723 |
| 2 | ɣ | 102,005 |
| 3 | d | 64,397 |
| 4 | s | 35,003 |
| 5 | nna | 34,361 |
| 6 | imzdaɣn | 31,398 |
| 7 | dar | 30,865 |
| 8 | gr | 30,722 |
| 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 | 1.2850 |
| R² (Goodness of Fit) | 0.988028 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 69.6% |
| Top 1,000 | 90.6% |
| Top 5,000 | 95.5% |
| 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:** 21,623 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 | 0.6948 | 0.3782 | N/A | N/A |
| **mono_64d** | 64 | 0.5226 | 0.3533 | N/A | N/A |
| **mono_128d** | 128 | 0.2352 | 0.3437 | N/A | N/A |
| **aligned_32d** | 32 | 0.6948 🏆 | 0.3868 | 0.0060 | 0.0540 |
| **aligned_64d** | 64 | 0.5226 | 0.3472 | 0.0240 | 0.1280 |
| **aligned_128d** | 128 | 0.2352 | 0.3345 | 0.0360 | 0.1780 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.6948 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3573. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 3.6% 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` | tmurrant, taɣwwaɣt, tuwuri |
| `-i` | ill, itturray, iɛisayn |
| `-ta` | taɣwwaɣt, tagnsant, tabrruct |
| `-a` | anmmassu, asaki, atayn |
| `-u` | umzizwr, uɣnja, umdlu |
| `-l` | lmuddn, lmɣrib, lbadiɛ |
| `-ti` | timqqit, tisutam, tinglizt |
| `-m` | mggrn, mennawt, magẓnt |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | atayn, mggrn, krnun |
| `-t` | tmurrant, priest, taɣwwaɣt |
| `-a` | uɣnja, phoenicia, iɣrruba |
| `-in` | ɛalawiyyin, bdrnin, irwin |
| `-s` | ghosts, yuns, palmas |
| `-i` | asaki, bani, tuwuri |
| `-e` | became, institute, neige |
| `-an` | dan, ubrkan, uljmɛan |

### 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` | 1.68x | 52 contexts | addan, hadda, wadda |
| `ggar` | 1.97x | 22 contexts | uggar, ggarn, iggar |
| `ggʷa` | 1.62x | 43 contexts | ḥggʷa, aggʷa, zggʷar |
| `ugga` | 1.91x | 21 contexts | uggar, uggan, tugga |
| `wuri` | 1.70x | 30 contexts | twuri, tuwuri, twwuri |
| `tion` | 2.05x | 14 contexts | nation, notion, action |
| `matt` | 1.64x | 26 contexts | matta, nmatti, amattu |
| `lati` | 1.61x | 27 contexts | latif, latin, talati |
| `ɣrib` | 1.76x | 20 contexts | aɣrib, mɣrib, lmɣrib |
| `mɣri` | 1.77x | 13 contexts | tmɣri, imɣri, mɣrib |
| `ddad` | 1.62x | 14 contexts | ḥddad, addad, addadn |
| `mata` | 1.54x | 14 contexts | smata, amata, 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` | 636 words | takrrayt, tusnaktant |
| `-i` | `-n` | 489 words | ittajjan, igatn |
| `-t` | `-n` | 323 words | tunisian, tmttawin |
| `-t` | `-in` | 264 words | tmttawin, tmdinin |
| `-l` | `-a` | 101 words | lqliɛa, lɛmaṛa |
| `-t` | `-a` | 71 words | tggʷra, tawayya |
| `-i` | `-an` | 60 words | ittajjan, ixxan |
| `-a` | `-n` | 60 words | aẓuran, ayncṭayn |
| `-l` | `-t` | 39 words | lmɛiṭat, luṭilat |
| `-a` | `-an` | 39 words | aẓuran, alilan |

### 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 |
|------|-----------------|------------|------|
| magrebini | **`magreb-in-i`** | 7.5 | `in` |
| mzaraynin | **`mzaray-n-in`** | 7.5 | `n` |
| imaynutnin | **`imaynut-n-in`** | 7.5 | `n` |
| tiɣrmanin | **`tiɣrm-an-in`** | 7.5 | `an` |
| ikkattinn | **`ikkatt-in-n`** | 7.5 | `in` |
| tisntutin | **`tisntu-t-in`** | 7.5 | `t` |
| tasnmḍant | **`tasnmḍ-an-t`** | 7.5 | `an` |
| tuɣnijinin | **`tuɣnij-in-in`** | 7.5 | `in` |
| ittyawnna | **`ittyaw-n-na`** | 7.5 | `n` |
| tinidlisn | **`t-in-idlisn`** | 7.5 | `idlisn` |
| fransisku | **`fransis-k-u`** | 7.5 | `k` |
| gibraltar | **`gibral-t-ar`** | 7.5 | `t` |
| iblḥsanin | **`iblḥsa-n-in`** | 7.5 | `n` |
| ittyurnan | **`ittyur-n-an`** | 7.5 | `n` |
| africaines | **`africa-in-es`** | 7.5 | `in` |

### 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 |

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*Generated by Wikilangs Pipeline · 2026-03-02 12:00:43*