Comprehensive Research Report & Full Ablation Study
This repository contains NLP models trained and evaluated by Wikilangs, specifically on German Wikipedia data.
We analyze tokenizers, n-gram models, Markov chains, vocabulary statistics, and word embeddings.
Sample 3: `Băltăreți ist der Name mehrerer Orte in Rumänien:
Băltăreți (Buzău), Dorf im K...`
Vocab
Tokens
Count
8k
▁b ă lt ă re ț i ▁ist ▁der ▁name ... (+47 more)
57
16k
▁b ă lt ă re ț i ▁ist ▁der ▁name ... (+45 more)
55
32k
▁b ă lt ă re ț i ▁ist ▁der ▁name ... (+45 more)
55
64k
▁b ă lt ă re ț i ▁ist ▁der ▁name ... (+44 more)
54
Key Findings
Best Compression: 64k achieves 4.386x compression
Lowest UNK Rate: 8k with 0.1233% 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
N-gram Coverage
Results
N-gram
Perplexity
Entropy
Unique N-grams
Top-100 Coverage
Top-1000 Coverage
2-gram
397,539 🏆
18.60
14,975,925
8.9%
20.8%
2-gram
330 🏆
8.37
56,875
63.2%
98.5%
3-gram
4,321,490
22.04
46,313,184
3.0%
7.5%
3-gram
3,011
11.56
458,754
25.3%
66.1%
4-gram
16,869,913
24.01
94,033,907
1.7%
4.3%
4-gram
18,869
14.20
3,362,393
12.7%
36.5%
Top 5 N-grams by Size
2-grams:
Rank
N-gram
Count
1
kategorie :
6,792,008
2
) ,
4,653,717
3
in der
3,680,160
4
. die
3,639,368
5
, die
3,186,807
3-grams:
Rank
N-gram
Count
1
, s .
2,005,174
2
) kategorie :
1,889,059
3
. in :
957,571
4
isbn 3 -
658,242
5
einzelnachweise kategorie :
655,352
4-grams:
Rank
N-gram
Count
1
, isbn 3 -
601,963
2
, isbn 978 -
507,252
3
( hrsg . )
456,446
4
978 - 3 -
454,406
5
isbn 978 - 3
452,207
Key Findings
Best Perplexity: 2-gram with 330
Entropy Trend: Decreases with larger n-grams (more predictable)
Coverage: Top-1000 patterns cover ~37% of corpus
Recommendation: 4-gram or 5-gram for best predictive performance
3. Markov Chain Evaluation
Markov Entropy
Markov Branching
Results
Context
Avg Entropy
Perplexity
Branching Factor
Unique Contexts
Predictability
1
0.8229
1.769
11.84
11,563,865
17.7%
1
0.3027
1.233
3.76
97,717
69.7%
2
0.4537
1.370
3.19
136,857,243
54.6%
2
0.4680
1.383
3.48
367,392
53.2%
3
0.2356
1.177
1.69
435,861,393
76.4%
3
0.6899
1.613
4.59
1,279,274
31.0%
4
0.1157 🏆
1.084
1.25
735,113,439
88.4%
4
0.7766 🏆
1.713
4.12
5,873,337
22.3%
Generated Text Samples
Below are text samples generated from each Markov chain model:
Context Size 1:
. - richemont - hot 100 quadratkilometer , welche einflüsse wie beispielsweise in verbreitung ist ,
, s . nach 1945 - us navy siehe auch niklaas c2 und mühevollen aufbau befindlichen
der partei chinas größenwahn und kunstgewerbeschule zürich erschienenen faksimile “ ( landkreis gibt...
Context Size 2:
kategorie : autor kategorie : deutscher kategorie : mediziner ( 20 . rang schweizer cup und den
) , haselmusch ( pongau , salzburg u . a . glienke : die etwa drei weiher
in der die wache sowie geschätzt 7 , 5 – 6 ( 0 , 0554 6 +
Context Size 3:
, s . 296 widmete ihr die vehbi koç foundation contemporary art collection . the magazine of fantasy
) kategorie : wärmekennwert kategorie : messgröße ( abwasserbehandlung ) kategorie : träger der army...
. in : der tagesspiegel , 13 . juli 1267 , tochter von luigi vittorio bertarelli ( 1859
Context Size 4:
, isbn 3 - 930167 - 61 - 1 , s . 179 . untersuchungen und dokumentationen , die
, isbn 978 - 3 - 00 - 000367 - 7 . wilfried seeba ( für das landesmuseum oldenburg
( hrsg . ) : erwin piscator . das politische theater . ein kommentar . verlag schnell & steiner
Key Findings
Best Predictability: Context-4 with 88.4% predictability
Branching Factor: Decreases with context size (more deterministic)
Memory Trade-off: Larger contexts require more storage (5,873,337 contexts)
Recommendation: Context-3 or Context-4 for text generation
4. Vocabulary Analysis
Zipf's Law
Top Words
Coverage Curve
Statistics
Metric
Value
Vocabulary Size
1,000,000
Total Tokens
970,645,273
Mean Frequency
970.65
Median Frequency
50
Frequency Std Dev
60089.51
Most Common Words
Rank
Word
Frequency
1
der
31,690,610
2
und
23,476,283
3
die
22,916,244
4
in
19,437,122
5
von
12,408,327
6
im
9,096,641
7
des
8,632,745
8
den
8,213,258
9
mit
7,476,726
10
das
6,990,663
Least Common Words (from vocabulary)
Rank
Word
Frequency
1
flugzeugfertigung
18
2
erzgebirgsklinikum
18
3
kayoru
18
4
sumino
18
5
flüssigkeitskupplung
18
6
02599
18
7
purvaranga
18
8
piassava
18
9
domenick
18
10
artentstehung
18
Zipf's Law Analysis
Metric
Value
Zipf Coefficient
1.0172
R² (Goodness of Fit)
0.998135
Adherence Quality
excellent
Coverage Analysis
Top N Words
Coverage
Top 100
35.0%
Top 1,000
55.9%
Top 5,000
71.4%
Top 10,000
77.6%
Key Findings
Zipf Compliance: R²=0.9981 indicates excellent adherence to Zipf's law
High Frequency Dominance: Top 100 words cover 35.0% of corpus
Long Tail: 990,000 words needed for remaining 22.4% coverage
5. Word Embeddings Evaluation
Embedding Isotropy
Similarity Matrix
t-SNE Words
t-SNE Sentences
Model Comparison
Model
Vocab Size
Dimension
Avg Norm
Std Norm
Isotropy
mono_32d
4,270,148
32
3.020
0.882
0.7104 🏆
mono_64d
4,270,148
64
3.422
0.855
0.6896
mono_128d
4,270,148
128
3.801
0.852
0.6174
embeddings_enhanced
0
0
0.000
0.000
0.0000
Key Findings
Best Isotropy: mono_32d with 0.7104 (more uniform distribution)
Dimension Trade-off: Higher dimensions capture more semantics but reduce isotropy
Vocabulary Coverage: All models cover 4,270,148 words
Recommendation: 100d for balanced semantic capture and efficiency
6. Summary & Recommendations
Performance Dashboard
Production Recommendations
Component
Recommended
Rationale
Tokenizer
32k BPE
Best compression (4.39x) with low UNK rate
N-gram
5-gram
Lowest perplexity (330)
Markov
Context-4
Highest predictability (88.4%)
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
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.
