Icelandic - Wikilangs Models
Comprehensive Research Report & Full Ablation Study
This repository contains NLP models trained and evaluated by Wikilangs, specifically on Icelandic Wikipedia data. We analyze tokenizers, n-gram models, Markov chains, vocabulary statistics, and word embeddings.
π 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
Analysis and Evaluation
- 1. Tokenizer Evaluation
- 2. N-gram Model Evaluation
- 3. Markov Chain Evaluation
- 4. Vocabulary Analysis
- 5. Word Embeddings Evaluation
- 6. Morphological Analysis (Experimental)
- 7. Summary & Recommendations
- Metrics Glossary
- Visualizations Index
1. Tokenizer Evaluation
Results
| Vocab Size | Compression | Avg Token Len | UNK Rate | Total Tokens |
|---|---|---|---|---|
| 8k | 3.538x | 3.54 | 0.0547% | 1,307,527 |
| 16k | 3.917x | 3.92 | 0.0605% | 1,181,053 |
| 32k | 4.268x | 4.27 | 0.0660% | 1,083,827 |
| 64k | 4.556x π | 4.56 | 0.0704% | 1,015,400 |
Tokenization Examples
Below are sample sentences tokenized with each vocabulary size:
Sample 1: EnsΓmi getur Γ‘tt viΓ°: EnsΓm Γslensku hljΓ³msveitina EnsΓmi
| Vocab | Tokens | Count |
|---|---|---|
| 8k | βen sΓ mi βgetur βΓ‘tt βviΓ° : βen sΓ m ... (+5 more) |
15 |
| 16k | βensΓ mi βgetur βΓ‘tt βviΓ° : βensΓ m βΓslensku βhljΓ³msveitina ... (+2 more) |
12 |
| 32k | βensΓ mi βgetur βΓ‘tt βviΓ° : βensΓm βΓslensku βhljΓ³msveitina βensΓ ... (+1 more) |
11 |
| 64k | βensΓmi βgetur βΓ‘tt βviΓ° : βensΓm βΓslensku βhljΓ³msveitina βensΓmi |
9 |
Sample 2: ArΓs er Γslenskt kvenmannsnafn. Dreifing Γ‘ Γslandi Heimildir kvenmannsnΓΆfn
| Vocab | Tokens | Count |
|---|---|---|
| 8k | βar Γs βer βΓslenskt βkvenmannsnafn . βdreifing βΓ‘ βΓslandi βheimildir ... (+1 more) |
11 |
| 16k | βar Γs βer βΓslenskt βkvenmannsnafn . βdreifing βΓ‘ βΓslandi βheimildir ... (+1 more) |
11 |
| 32k | βar Γs βer βΓslenskt βkvenmannsnafn . βdreifing βΓ‘ βΓslandi βheimildir ... (+1 more) |
11 |
| 64k | βar Γs βer βΓslenskt βkvenmannsnafn . βdreifing βΓ‘ βΓslandi βheimildir ... (+1 more) |
11 |
Sample 3: Start-Up (KΓ³reska: μ€ννΈμ
; Seutateueop) er suΓ°ur-kΓ³reskur sjΓ³nvarpsΓΎΓ‘ttur. sjΓ³nvar...
| Vocab | Tokens | Count |
|---|---|---|
| 8k | βst art - up β( kΓ³ re ska : β ... (+18 more) |
28 |
| 16k | βst art - up β( kΓ³re ska : β μ€ννΈμ
... (+15 more) |
25 |
| 32k | βstart - up β( kΓ³reska : β μ€ννΈμ
; βse ... (+13 more) |
23 |
| 64k | βstart - up β( kΓ³reska : β μ€ννΈμ
; βse ... (+12 more) |
22 |
Key Findings
- Best Compression: 64k achieves 4.556x compression
- Lowest UNK Rate: 8k with 0.0547% 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
Results
| N-gram | Variant | Perplexity | Entropy | Unique N-grams | Top-100 Coverage | Top-1000 Coverage |
|---|---|---|---|---|---|---|
| 2-gram | Word | 76,323 | 16.22 | 290,201 | 7.5% | 20.3% |
| 2-gram | Subword | 360 π | 8.49 | 7,570 | 60.9% | 98.9% |
| 3-gram | Word | 187,198 | 17.51 | 409,948 | 3.6% | 11.1% |
| 3-gram | Subword | 3,285 | 11.68 | 62,993 | 21.8% | 63.7% |
| 4-gram | Word | 412,107 | 18.65 | 661,434 | 2.3% | 6.9% |
| 4-gram | Subword | 19,995 | 14.29 | 386,811 | 10.1% | 32.9% |
| 5-gram | Word | 284,069 | 18.12 | 418,913 | 3.1% | 8.0% |
| 5-gram | Subword | 84,371 | 16.36 | 1,264,141 | 5.6% | 18.9% |
Top 5 N-grams by Size
2-grams (Word):
| Rank | N-gram | Count |
|---|---|---|
| 1 | til aΓ° |
27,637 |
| 2 | ΓΎar sem |
24,592 |
| 3 | Γ‘ Γslandi |
18,253 |
| 4 | ΓΎvΓ aΓ° |
15,183 |
| 5 | ΓΎess aΓ° |
13,286 |
3-grams (Word):
| Rank | N-gram | Count |
|---|---|---|
| 1 | til ΓΎess aΓ° |
8,156 |
| 2 | meΓ° ΓΎvΓ aΓ° |
4,654 |
| 3 | ΓΎar sem hann |
3,445 |
| 4 | dreifing Γ‘ Γslandi |
2,999 |
| 5 | Γ‘ Γslandi heimildir |
2,839 |
4-grams (Word):
| Rank | N-gram | Count |
|---|---|---|
| 1 | dreifing Γ‘ Γslandi heimildir |
2,780 |
| 2 | kvenmannsnafn dreifing Γ‘ Γslandi |
1,520 |
| 3 | Γslenskt kvenmannsnafn dreifing Γ‘ |
1,519 |
| 4 | er Γslenskt kvenmannsnafn dreifing |
1,518 |
| 5 | Γ‘ Γslandi heimildir kvenmannsnΓΆfn |
1,509 |
5-grams (Word):
| Rank | N-gram | Count |
|---|---|---|
| 1 | Γslenskt kvenmannsnafn dreifing Γ‘ Γslandi |
1,519 |
| 2 | er Γslenskt kvenmannsnafn dreifing Γ‘ |
1,518 |
| 3 | dreifing Γ‘ Γslandi heimildir kvenmannsnΓΆfn |
1,509 |
| 4 | kvenmannsnafn dreifing Γ‘ Γslandi heimildir |
1,471 |
| 5 | Γslenskt karlmannsnafn dreifing Γ‘ Γslandi |
1,309 |
2-grams (Subword):
| Rank | N-gram | Count |
|---|---|---|
| 1 | r _ |
1,832,522 |
| 2 | a r |
1,368,870 |
| 3 | _ s |
1,362,774 |
| 4 | i n |
1,140,724 |
| 5 | a _ |
1,027,671 |
3-grams (Subword):
| Rank | N-gram | Count |
|---|---|---|
| 1 | a r _ |
583,858 |
| 2 | o g _ |
458,351 |
| 3 | _ o g |
457,248 |
| 4 | u r _ |
447,514 |
| 5 | _ Γ _ |
435,363 |
4-grams (Subword):
| Rank | N-gram | Count |
|---|---|---|
| 1 | _ o g _ |
456,555 |
| 2 | _ a Γ° _ |
255,398 |
| 3 | s e m _ |
214,724 |
| 4 | _ s e m |
214,407 |
| 5 | _ e r _ |
203,790 |
5-grams (Subword):
| Rank | N-gram | Count |
|---|---|---|
| 1 | _ s e m _ |
212,727 |
| 2 | _ v a r _ |
160,455 |
| 3 | _ t i l _ |
132,778 |
| 4 | _ h a n n |
91,569 |
| 5 | _ v i Γ° _ |
89,262 |
Key Findings
- Best Perplexity: 2-gram (subword) with 360
- Entropy Trend: Decreases with larger n-grams (more predictable)
- Coverage: Top-1000 patterns cover ~19% of corpus
- Recommendation: 4-gram or 5-gram for best predictive performance
3. Markov Chain Evaluation
Results
| Context | Variant | Avg Entropy | Perplexity | Branching Factor | Unique Contexts | Predictability |
|---|---|---|---|---|---|---|
| 1 | Word | 0.8991 | 1.865 | 7.58 | 645,450 | 10.1% |
| 1 | Subword | 0.8434 | 1.794 | 5.91 | 4,305 | 15.7% |
| 2 | Word | 0.3025 | 1.233 | 1.88 | 4,874,320 | 69.8% |
| 2 | Subword | 0.7898 | 1.729 | 5.23 | 25,387 | 21.0% |
| 3 | Word | 0.1108 | 1.080 | 1.21 | 9,119,459 | 88.9% |
| 3 | Subword | 0.8104 | 1.754 | 4.71 | 132,737 | 19.0% |
| 4 | Word | 0.0408 π | 1.029 | 1.06 | 11,025,075 | 95.9% |
| 4 | Subword | 0.7484 | 1.680 | 3.57 | 624,878 | 25.2% |
Generated Text Samples (Word-based)
Below are text samples generated from each word-based Markov chain model:
Context Size 1:
og hentar vel stæðir og bornir fram sΓΆnnunargΓΆgn sem auΓ°mjΓΊkum manni sΓnum fyrir convention on trainΓ helgafellssveit akureyjar ΓΎar sem ΓΎau voru Γ skiftirΓ¦kt hann var formaΓ°ur utanrΓkismΓ‘lanefndar um ...Γ‘ suΓ°ur ΓtalΓu Γ‘kvaΓ° hΓ³purinn aΓ° rÑða Γ ΓΎessu nafni sambandsins og er Γ‘rlega sumarsΓ½ningu norrΓ¦na
Context Size 2:
til aΓ° hjΓ‘lpa til uppΓ‘halds frasinn hans er einkum ΓΎekktur fyrir hlutverk sitt Γ davΓΓ° aΓ° hannΓΎar sem hann naut mikillar virΓ°ingar samtΓΓ°armanna sinna hΓΊn var komin Γ millihΓ½sil ΓΎΓ‘ umbreytast eg...ΓΎvΓ aΓ° ΓΎeir ΓΎorvaldur og andrea Ε‘uΕ‘njara lipeja tena 13 33 12 12 12 18 0 31
Context Size 3:
til ΓΎess aΓ° verΓ°a bandamaΓ°ur michaels Γ fjΓ³rΓ°u serΓu er fariΓ° yfir launasjΓ³Γ°skenninguna og umfjΓΆllun...meΓ° ΓΎvΓ aΓ° stebbi finnur sig fastan Γ‘ milli steins tΓ³ta og sleggju brΓΊnΓ³ sΓΆguΓΎrÑður kvikmyndir is le...ΓΎar sem hann gerΓ°i voru Γ³merktar eins og venjan var Ñður nΓΊverandi rΓkisstjΓ³rn er rÑðuneyti kristrΓΊn...
Context Size 4:
dreifing Γ‘ Γslandi heimildir karlmannsnΓΆfn millinΓΆfnkvenmannsnafn dreifing Γ‘ Γslandi heimildir karlmannsnΓΆfn kvenmannsnΓΆfn mannanΓΆfn sem notuΓ° eru sem s...Γslenskt kvenmannsnafn dreifing Γ‘ Γslandi heimildir karlmannsnΓΆfn karlmannsnΓΆfn karlmannsnΓΆfn karlma...
Generated Text Samples (Subword-based)
Below are text samples generated from each subword-based Markov chain model:
Context Size 1:
_alanleft._sist_a_aΓ°_mariΓ°a_hastr_ng_g_18)._hafr
Context Size 2:
r_og_ver_er_þanduariðlarÑðandurver_skógismeigilsfæd
Context Size 3:
ar_bikarabbΓ_orianog_heitimennda,_mi_og_lankamerΓkur_a
Context Size 4:
_og_mannsson,_ΓΊtgΓ‘f_aΓ°_innarskΓ³garΓΎrΓΊΓ°sem_juttum_mΓ‘gi_sig
Key Findings
- Best Predictability: Context-4 (word) with 95.9% predictability
- Branching Factor: Decreases with context size (more deterministic)
- Memory Trade-off: Larger contexts require more storage (624,878 contexts)
- Recommendation: Context-3 or Context-4 for text generation
4. Vocabulary Analysis
Statistics
| Metric | Value |
|---|---|
| Vocabulary Size | 287,581 |
| Total Tokens | 12,356,689 |
| Mean Frequency | 42.97 |
| Median Frequency | 4 |
| Frequency Std Dev | 1648.11 |
Most Common Words
| Rank | Word | Frequency |
|---|---|---|
| 1 | og | 457,899 |
| 2 | Γ | 437,515 |
| 3 | Γ‘ | 265,620 |
| 4 | aΓ° | 256,592 |
| 5 | sem | 214,678 |
| 6 | er | 205,384 |
| 7 | var | 161,974 |
| 8 | til | 134,849 |
| 9 | viΓ° | 91,854 |
| 10 | af | 91,619 |
Least Common Words (from vocabulary)
| Rank | Word | Frequency |
|---|---|---|
| 1 | ζ΄ | 2 |
| 2 | 리 | 2 |
| 3 | myeongjang | 2 |
| 4 | hitaΓΎolnir | 2 |
| 5 | slΓΈttum | 2 |
| 6 | noregslandi | 2 |
| 7 | triΓ°ja | 2 |
| 8 | beregszΓ‘sziovΓ‘ | 2 |
| 9 | lΓΊΓ³a | 2 |
| 10 | kenΓumanna | 2 |
Zipf's Law Analysis
| Metric | Value |
|---|---|
| Zipf Coefficient | 0.9806 |
| RΒ² (Goodness of Fit) | 0.998336 |
| Adherence Quality | excellent |
Coverage Analysis
| Top N Words | Coverage |
|---|---|
| Top 100 | 36.0% |
| Top 1,000 | 56.0% |
| Top 5,000 | 71.7% |
| Top 10,000 | 78.4% |
Key Findings
- Zipf Compliance: RΒ²=0.9983 indicates excellent adherence to Zipf's law
- High Frequency Dominance: Top 100 words cover 36.0% of corpus
- Long Tail: 277,581 words needed for remaining 21.6% coverage
5. Word Embeddings Evaluation
5.1 Cross-Lingual Alignment
5.2 Model Comparison
| Model | Dimension | Isotropy | Semantic Density | Alignment R@1 | Alignment R@10 |
|---|---|---|---|---|---|
| mono_32d | 32 | 0.8275 | 0.3448 | N/A | N/A |
| mono_64d | 64 | 0.7798 | 0.2809 | N/A | N/A |
| mono_128d | 128 | 0.7263 | 0.2042 | N/A | N/A |
| aligned_32d | 32 | 0.8275 π | 0.3509 | 0.1760 | 0.5520 |
| aligned_64d | 64 | 0.7798 | 0.2744 | 0.3040 | 0.6540 |
| aligned_128d | 128 | 0.7263 | 0.2020 | 0.3960 | 0.6900 |
Key Findings
- Best Isotropy: aligned_32d with 0.8275 (more uniform distribution)
- Semantic Density: Average pairwise similarity of 0.2762. Lower values indicate better semantic separation.
- Alignment Quality: Aligned models achieve up to 39.6% 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 | -0.580 | 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 |
|---|---|
-s |
skrΓΊΓ°sigling, safamΓ½ri, sΓuna |
-a |
alinu, alfariΓ°, alvarlegar |
-b |
byrlaΓ°i, brahes, boΓ°sundssveitar |
-h |
hænis, hryggsúlunnar, heimilisins |
-m |
markΓΊsdΓ³ttur, mΓ³tmΓ¦lendunum, mΓ‘lvΓsindamannsins |
-k |
kesiya, kΓ³ngsstaΓ°adalur, kΓ³rΓ³naveirufaraldurinn |
-ma |
markΓΊsdΓ³ttur, maximine, masterpiece |
-t |
tyrrell, tannþrÑð, teypaða |
Productive Suffixes
| Suffix | Examples |
|---|---|
-r |
markΓΊsdΓ³ttur, lΓ‘gmarkar, boΓ°sundssveitar |
-a |
rΓΆksemdafΓ¦rsla, ΓΊtrΓ½ma, sΓuna |
-i |
byrlaði, safamýri, pósthússtræti |
-n |
indverjinn, notodden, rodman |
-um |
mótmælendunum, gjaldmiðlakerfum, stândum |
-ar |
lΓ‘gmarkar, boΓ°sundssveitar, hryggsΓΊlunnar |
-ur |
markΓΊsdΓ³ttur, ljΓ³stvistur, kΓ³ngsstaΓ°adalur |
-s |
brahes, hænis, ekkekrates |
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 |
|---|---|---|---|
sson |
2.16x | 82 contexts | arsson, jesson, wesson |
nnar |
1.68x | 96 contexts | Γ‘nnar, innar, unnar |
stjΓ³ |
1.86x | 50 contexts | stjΓ³ra, stjΓ³rn, stjΓ³ri |
maΓ°u |
2.17x | 28 contexts | maΓ°ur, ismaΓ°ur, Γ‘rmaΓ°ur |
ngur |
1.63x | 85 contexts | ΓΊngur, ungur, ingur |
ista |
1.38x | 162 contexts | gista, istar, vista |
ngar |
1.56x | 71 contexts | angar, ungar, ingar |
ndar |
1.33x | 133 contexts | undar, andar, endar |
jΓ³rn |
2.04x | 23 contexts | sjΓ³rn, stjΓ³rn, bjΓ³rnum |
egar |
2.03x | 21 contexts | segar, vegar, ΓΎegar |
ndur |
1.33x | 99 contexts | undur, endur, rindur |
ndir |
1.41x | 70 contexts | endir, undir, randir |
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 |
-r |
200 words | sjΓ³Γ°rΓkur, sΓ©rkennilegar |
-s |
-i |
158 words | stuttskΓfunni, seyΓ°i |
-s |
-a |
142 words | saxicola, shimada |
-h |
-r |
131 words | hugprΓ½Γ°innar, hverfisveppur |
-s |
-n |
128 words | schliemann, sΓ©rΓΊtbΓΊin |
-s |
-m |
92 words | sΓΆderstrΓΆm, sigruΓ°um |
-s |
-um |
89 words | sigruΓ°um, strΓ‘knum |
-h |
-a |
88 words | hÑlfbræðranna, helga |
-k |
-r |
87 words | kΓ½lapestar, knapar |
-b |
-r |
83 words | bΓldudalur, beaver |
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 |
|---|---|---|---|
| læknisins | læknis-i-ns |
7.5 | i |
| ΓΎrumuveΓ°ri | ΓΎrumuveΓ°-r-i |
7.5 | r |
| ofbeldisfullra | ofbeldisfull-r-a |
7.5 | r |
| ketilbjΓΆrn | ketilbjΓΆ-r-n |
7.5 | r |
| meΓ°limina | meΓ°lim-i-na |
7.5 | i |
| kambΓ³dΓustjΓ³rn | kambΓ³dΓustjΓ³-r-n |
7.5 | r |
| Γ³breyttri | Γ³breytt-r-i |
7.5 | r |
| norΓ°urodda | norΓ°urod-d-a |
7.5 | d |
| jΓΆhannsson | jΓΆhanns-s-on |
7.5 | s |
| handelman | handelm-a-n |
7.5 | a |
| steypujΓ‘rni | steypujΓ‘-r-ni |
7.5 | r |
| konuvΓsur | konuvΓ-s-ur |
7.5 | s |
| heittempraΓ° | heittempr-a-Γ° |
7.5 | a |
| sororculana | sororcu-la-na |
7.5 | la |
| hryggdΓ½rum | hryggdΓ½-r-um |
7.5 | r |
6.6 Linguistic Interpretation
Automated Insight: The language Icelandic 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
Production Recommendations
| Component | Recommended | Rationale |
|---|---|---|
| Tokenizer | 64k BPE | Best compression (4.56x) |
| N-gram | 2-gram | Lowest perplexity (360) |
| Markov | Context-4 | Highest predictability (95.9%) |
| 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) Γ 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.
RΒ² (Coefficient of Determination)
Definition: Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.
Intuition: RΒ² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.
What to seek: RΒ² > 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
- Compare within model families: Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
- Consider trade-offs: Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
- Context matters: Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
- Corpus influence: All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
- 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 - a monthly snapshot of Wikipedia articles across 300+ languages.
Project
A project by Wikilangs - Open-source NLP models for every Wikipedia language.
Maintainer
Citation
If you use these models in your research, please cite:
@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
- π Website: wikilangs.org
- π€ Models: huggingface.co/wikilangs
- π Data: wikipedia-monthly
- π€ Author: Omar Kamali
- π€ Sponsor: Featherless AI
Generated by Wikilangs Models Pipeline
Report Date: 2026-01-10 06:06:11



















