Comprehensive Research Report & Full Ablation Study
This repository contains NLP models trained and evaluated by Wikilangs, specifically on Luxembourgish 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)
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 Unique
N-gram Coverage
Results
N-gram
Variant
Perplexity
Entropy
Unique N-grams
Top-100 Coverage
Top-1000 Coverage
2-gram
Word
62,562
15.93
314,805
10.7%
24.2%
2-gram
Subword
318 🏆
8.31
7,549
63.0%
98.9%
3-gram
Word
192,148
17.55
547,285
5.0%
13.5%
3-gram
Subword
2,850
11.48
64,806
23.1%
66.6%
4-gram
Word
356,085
18.44
876,356
4.3%
11.3%
4-gram
Subword
16,948
14.05
383,042
12.4%
36.3%
5-gram
Word
281,035
18.10
647,259
4.7%
12.1%
5-gram
Subword
67,612
16.04
1,248,329
8.3%
23.2%
Top 5 N-grams by Size
2-grams (Word):
Rank
N-gram
Count
1
vun der
83,364
2
an der
70,319
3
um spaweck
36,982
4
vun de
26,136
5
ass eng
25,638
3-grams (Word):
Rank
N-gram
Count
1
an der regioun
10,968
2
ass eng franséisch
8,527
3
franséisch administrativ andeelung
5,357
4
administrativ andeelung am
5,155
5
gemeng am departement
5,056
4-grams (Word):
Rank
N-gram
Count
1
franséisch administrativ andeelung am
5,149
2
administrativ andeelung am arrondissement
4,760
3
ass eng franséisch gemeng
4,208
4
ëm wat geet et
4,198
5
wat geet et am
4,109
5-grams (Word):
Rank
N-gram
Count
1
franséisch administrativ andeelung am arrondissement
4,759
2
ëm wat geet et am
4,109
3
wat geet et am film
4,060
4
ass eng franséisch gemeng am
3,394
5
eng franséisch gemeng am departement
3,212
2-grams (Subword):
Rank
N-gram
Count
1
e r
2,283,425
2
e n
1,750,568
3
n _
1,684,884
4
_ d
1,610,037
5
e _
1,476,507
3-grams (Subword):
Rank
N-gram
Count
1
e r _
951,492
2
_ d e
876,571
3
e n _
679,558
4
s c h
638,025
5
n _ d
455,328
4-grams (Subword):
Rank
N-gram
Count
1
n _ d e
312,530
2
d e r _
303,229
3
_ a n _
280,443
4
_ d e _
275,944
5
_ d e r
254,059
5-grams (Subword):
Rank
N-gram
Count
1
_ d e r _
250,063
2
_ v u n _
204,878
3
n _ d e r
163,335
4
_ v u m _
162,050
5
_ a n _ d
155,413
Key Findings
Best Perplexity: 2-gram (subword) with 318
Entropy Trend: Decreases with larger n-grams (more predictable)
Coverage: Top-1000 patterns cover ~23% of corpus
Recommendation: 4-gram or 5-gram for best predictive performance
3. Markov Chain Evaluation
Markov Entropy
Markov Contexts
Markov Branching
Results
Context
Variant
Avg Entropy
Perplexity
Branching Factor
Unique Contexts
Predictability
1
Word
0.9491
1.931
7.90
521,387
5.1%
1
Subword
0.9460
1.927
6.76
3,270
5.4%
2
Word
0.3309
1.258
1.98
4,108,190
66.9%
2
Subword
0.8550
1.809
5.87
22,062
14.5%
3
Word
0.1377
1.100
1.27
8,097,151
86.2%
3
Subword
0.8305
1.778
4.76
129,396
17.0%
4
Word
0.0569 🏆
1.040
1.09
10,254,064
94.3%
4
Subword
0.7479
1.679
3.58
615,656
25.2%
Generated Text Samples (Word-based)
Below are text samples generated from each word-based Markov chain model:
Context Size 1:
de la résistance boîte vun der haiteger perspektiv am juni huet zur trounfollgerin akzeptabel d shir...
an technik gebuer den oflaf vum walter hill haaptacteuren nathalie reuter lëtzebuergesch grammaire d...
der iau offiziell nom brittesche science 2 etapp 50 m den traité vu montpellier am arrondissement
Context Size 2:
vun der gemeng miersch e läit um zesammenfluss vun der zäit wou en zanterhier all kéier fréizäiteg
an der atmosphär ionosphär magnetosphär plasmasphär no physiko cheemesche prozesser ozonosphär respe...
um spaweck chris s 33 35 artikel aus der circonscriptioun vun de ponts et chaussées zu lëtzebuerg
Context Size 3:
an der regioun bretagne bei der kantonalreform vun gouf de kanton gegrënnt gemengen am kanton bellev...
ass eng franséisch harfspillerin mat néng joer hat an eng ofsécherungze vill e groussen deel vun de ...
franséisch administrativ andeelung am arrondissement thonon les bains ouest war bis mäerz eng fransé...
Context Size 4:
franséisch administrativ andeelung am arrondissement bayonne am arrondissement bayonne op der via po...
administrativ andeelung am arrondissement toulon am departement var an der regioun provence alpes cô...
ass eng franséisch gemeng an de vogesen an der regioun grand est d gemeng val de meuse ass duerch
Generated Text Samples (Subword-based)
Below are text samples generated from each subword-based Markov chain model:
Context Size 1:
_den_(kitesinge_
enit_wäerengi_lë
nodun_1_che_hen:
Context Size 2:
errevo,_opgebsäit
en_ster_den._joen
n_ofeng_mist_um_(
Context Size 3:
er_war_bruce_filme
_de_mobizent_gi_ma
en_1_ster_-_repren
Context Size 4:
n_den_eng_belschaft
der_revolumbahnen_d
_an_der_a_pilger_im
Key Findings
Best Predictability: Context-4 (word) with 94.3% predictability
Branching Factor: Decreases with context size (more deterministic)
Memory Trade-off: Larger contexts require more storage (615,656 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
248,214
Total Tokens
13,192,531
Mean Frequency
53.15
Median Frequency
4
Frequency Std Dev
1571.96
Most Common Words
Rank
Word
Frequency
1
de
305,799
2
an
283,342
3
der
250,632
4
d
249,992
5
vun
205,518
6
a
182,029
7
vum
162,657
8
den
146,511
9
am
141,289
10
ass
127,097
Least Common Words (from vocabulary)
Rank
Word
Frequency
1
enquêteprozedur
2
2
notifikatioun
2
3
jauferbësch
2
4
jauf
2
5
sabigotho
2
6
proprietärintern
2
7
lëtzebuergfir
2
8
multicentrisch
2
9
urbanem
2
10
neytiri
2
Zipf's Law Analysis
Metric
Value
Zipf Coefficient
1.0100
R² (Goodness of Fit)
0.999149
Adherence Quality
excellent
Coverage Analysis
Top N Words
Coverage
Top 100
37.9%
Top 1,000
60.1%
Top 5,000
75.1%
Top 10,000
81.5%
Key Findings
Zipf Compliance: R²=0.9991 indicates excellent adherence to Zipf's law
High Frequency Dominance: Top 100 words cover 37.9% of corpus
Long Tail: 238,214 words needed for remaining 18.5% coverage
5. Word Embeddings Evaluation
Embedding Isotropy
Similarity Matrix
t-SNE Words
t-SNE Sentences
5.1 Cross-Lingual Alignment
Alignment Quality
Multilingual t-SNE
5.2 Model Comparison
Model
Dimension
Isotropy
Semantic Density
Alignment R@1
Alignment R@10
mono_32d
32
0.8333 🏆
0.3443
N/A
N/A
mono_64d
64
0.8177
0.2743
N/A
N/A
mono_128d
128
0.7923
0.2124
N/A
N/A
aligned_32d
32
0.8333
0.3472
0.1420
0.4680
aligned_64d
64
0.8177
0.2730
0.2800
0.6120
aligned_128d
128
0.7923
0.2086
0.3360
0.7540
Key Findings
Best Isotropy: mono_32d with 0.8333 (more uniform distribution)
Semantic Density: Average pairwise similarity of 0.2766. Lower values indicate better semantic separation.
Alignment Quality: Aligned models achieve up to 33.6% 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
-0.481
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
saviez, storeria, semoy
-a
autrichienne, antiker, augh
-b
baleareschen, bongaert, braunsberger
-ma
markéieren, maserati, marsas
-m
markéieren, methodologescher, montlauzun
-p
puren, premièren, prange
-d
diestro, dumcke, dinas
-c
chrétienne, cazilhac, carvifolia
Productive Suffixes
Suffix
Examples
-n
markéieren, zommen, guzman
-en
markéieren, zommen, baleareschen
-e
chrétienne, hennie, dumcke
-er
methodologescher, antiker, gruppementer
-r
methodologescher, antiker, gruppementer
-t
bongaert, renfort, individualitéit
-s
fraissines, oenomaus, fourons
-g
verëffentlechung, udeng, combining
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
chte
1.91x
259 contexts
achte, echte, fechte
tiou
2.50x
52 contexts
actioun, natioun, optioun
nner
1.82x
209 contexts
inner, önner, anner
ller
1.73x
232 contexts
eller, aller, iller
atio
2.10x
88 contexts
natio, ratio, patio
teur
2.17x
71 contexts
teuro, moteur, steurs
emen
2.10x
82 contexts
jemen, gemen, semen
erge
1.82x
145 contexts
perge, uerge, verge
cteu
2.83x
22 contexts
acteur, vecteur, facteur
nger
1.74x
150 contexts
inger, anger, unger
ioun
2.23x
44 contexts
aioun, spioun, unioun
regi
2.12x
38 contexts
regis, regia, regie
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
-n
115 words
schouluniformen, siphonen
-s
-e
106 words
semide, schreckliche
-s
-r
103 words
saulzoir, schmidhauser
-a
-e
88 words
arbeitspapiere, aushale
-s
-er
88 words
schmidhauser, stralungsdetekter
-s
-en
82 words
schouluniformen, siphonen
-b
-e
76 words
bewäertbare, breve
-g
-n
73 words
guidesektioun, germaniséieren
-p
-n
71 words
plädéieren, phalempin
-c
-s
71 words
companions, crus
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
moschtgewiicht
moschtgewii-ch-t
7.5
ch
approcher
appro-ch-er
7.5
ch
sommernacht
sommerna-ch-t
7.5
ch
opgebauscht
opgebaus-ch-t
7.5
ch
haaptobjet
haaptobj-e-t
7.5
e
disquisitiones
disquisitio-n-es
7.5
n
iwwerierdesche
iwwerierdes-ch-e
7.5
ch
interprétations
interprétatio-n-s
7.5
n
bekanntlich
bekanntl-i-ch
7.5
i
schläicht
schläi-ch-t
7.5
ch
averstanen
aversta-n-en
7.5
n
gestatten
gestat-t-en
7.5
t
dokumentaresche
dokumentares-ch-e
7.5
ch
criticism
critici-s-m
7.5
s
concoules
concou-le-s
7.5
le
6.6 Linguistic Interpretation
Automated Insight:
The language Luxembourgish 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
Production Recommendations
Component
Recommended
Rationale
Tokenizer
64k BPE
Best compression (4.80x)
N-gram
2-gram
Lowest perplexity (318)
Markov
Context-4
Highest predictability (94.3%)
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.
