Comprehensive Research Report & Full Ablation Study
This repository contains NLP models trained and evaluated by Wikilangs, specifically on Romansh 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
17,916
14.13
74,933
14.7%
35.1%
2-gram
Subword
230 🏆
7.85
3,376
70.8%
99.4%
3-gram
Word
53,185
15.70
119,039
6.2%
19.2%
3-gram
Subword
1,797
10.81
27,903
30.0%
75.9%
4-gram
Word
94,120
16.52
161,618
4.4%
13.1%
4-gram
Subword
9,576
13.23
144,146
14.9%
43.5%
5-gram
Word
54,308
15.73
84,789
5.6%
15.5%
5-gram
Subword
34,278
15.07
382,834
8.4%
26.7%
Top 5 N-grams by Size
2-grams (Word):
Rank
N-gram
Count
1
da la
32,817
2
da l
19,781
3
en il
16,052
4
en la
9,522
5
da las
8,260
3-grams (Word):
Rank
N-gram
Count
1
en il chantun
2,817
2
ultra da quai
1,397
3
svizra en il
1,207
4
è ina vischnanca
1,203
5
en l europa
1,148
4-grams (Word):
Rank
N-gram
Count
1
svizra en il chantun
1,050
2
en il chantun vad
779
3
è ina vischnanca svizra
586
4
vischnanca svizra en il
585
5
è ina vischnanca politica
584
5-grams (Word):
Rank
N-gram
Count
1
ina vischnanca svizra en il
583
2
è ina vischnanca svizra en
582
3
vischnanca svizra en il chantun
565
4
è ina vischnanca politica svizra
508
5
vischnanca politica svizra en il
484
2-grams (Subword):
Rank
N-gram
Count
1
a _
758,306
2
s _
412,089
3
_ d
368,200
4
n _
345,394
5
d a
340,317
3-grams (Subword):
Rank
N-gram
Count
1
_ d a
247,757
2
d a _
210,483
3
_ l a
159,443
4
l a _
151,625
5
a s _
133,920
4-grams (Subword):
Rank
N-gram
Count
1
_ d a _
165,902
2
_ l a _
117,111
3
_ i l _
76,863
4
d a _ l
68,179
5
_ e n _
64,184
5-grams (Subword):
Rank
N-gram
Count
1
_ d a _ l
65,677
2
a _ l a _
48,613
3
d a _ l a
43,880
4
a _ d a _
41,853
5
_ d a l _
40,324
Key Findings
Best Perplexity: 2-gram (subword) with 230
Entropy Trend: Decreases with larger n-grams (more predictable)
Coverage: Top-1000 patterns cover ~27% 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
1.0978
2.140
8.07
124,534
0.0%
1
Subword
1.2098
2.313
10.41
715
0.0%
2
Word
0.3787
1.300
2.03
1,003,829
62.1%
2
Subword
1.0702
2.100
6.71
7,436
0.0%
3
Word
0.1550
1.113
1.30
2,037,689
84.5%
3
Subword
0.9144
1.885
4.63
49,875
8.6%
4
Word
0.0598 🏆
1.042
1.09
2,637,985
94.0%
4
Subword
0.7105
1.636
3.08
231,080
29.0%
Generated Text Samples (Word-based)
Below are text samples generated from each word-based Markov chain model:
Context Size 1:
da chasa nova relaziun tranter ils liuns ma a moda optimala dal 18avel tschientaner èn vastas
la frantscha da meters pudaiva l osce è pront per l emprova da stgaudament global wealth
il palatinat sco terz nivel da la fom vegnivan pretendidas da l enviern utschels aves urden
Context Size 2:
da la pagina center small panorama da hamburg èn ins puspè reavert ina lingia da la musica
da l akademie der wissenschaften minca p 270 christine lienemann perrin wolfgang lienemann ed politi...
en il vest latin da la federaziun da medis ed ospitals privats il tractament dal retg pippin
Context Size 3:
en il chantun vallais dal chantun vallais en il chantun tessin vischnancas svizras maggia
ultra da quai il concept da la strategia u da la tora la quala furma l emprim epos
svizra en il chantun friburg en il district jura nord vaudois en il chantun vad en il district
Context Size 4:
svizra en il chantun vad en il district nyon en il chantun vad dal chantun vad
en il chantun vad dal chantun vad
è ina vischnanca svizra en il chantun tessin che appartegna al circul verzasca dal district locarno ...
Generated Text Samples (Subword-based)
Below are text samples generated from each subword-based Markov chain model:
Context Size 1:
_c_castaun:_s_ch
a_iolasil_ialèn_
ig_ilema_sgn_rim
Context Size 2:
a_che_betg_un_las
s_p._ofarling_prü
_da_l’il_co_er,_d
Context Size 3:
_da_nadella_gronis
da_la_dal_probalk:
_la_da_diffenser_l
Context Size 4:
_da_s._p._38s._part
_la_mauren_ha_il_cu
_il_territoric_è_la
Key Findings
Best Predictability: Context-4 (word) with 94.0% predictability
Branching Factor: Decreases with context size (more deterministic)
Memory Trade-off: Larger contexts require more storage (231,080 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
63,266
Total Tokens
3,028,553
Mean Frequency
47.87
Median Frequency
4
Frequency Std Dev
1094.76
Most Common Words
Rank
Word
Frequency
1
da
166,290
2
la
118,196
3
il
79,956
4
l
69,320
5
en
67,320
6
e
53,149
7
dal
40,449
8
a
39,768
9
è
33,261
10
ils
31,735
Least Common Words (from vocabulary)
Rank
Word
Frequency
1
planisadra
2
2
hzr
2
3
khizr
2
4
pereslawl
2
5
zalesskij
2
6
tawjihi
2
7
gate
2
8
palestinians
2
9
tregua
2
10
cumpusiziun
2
Zipf's Law Analysis
Metric
Value
Zipf Coefficient
1.0749
R² (Goodness of Fit)
0.994918
Adherence Quality
excellent
Coverage Analysis
Top N Words
Coverage
Top 100
45.9%
Top 1,000
68.3%
Top 5,000
84.5%
Top 10,000
90.3%
Key Findings
Zipf Compliance: R²=0.9949 indicates excellent adherence to Zipf's law
High Frequency Dominance: Top 100 words cover 45.9% of corpus
Long Tail: 53,266 words needed for remaining 9.7% 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
0.8474
0.3419
N/A
N/A
mono_64d
64
0.8324
0.2577
N/A
N/A
mono_128d
128
0.8002
0.1915
N/A
N/A
aligned_32d
32
0.8474 🏆
0.3398
0.1380
0.4520
aligned_64d
64
0.8324
0.2625
0.2280
0.5880
aligned_128d
128
0.8002
0.1883
0.2940
0.6020
Key Findings
Best Isotropy: aligned_32d with 0.8474 (more uniform distribution)
Semantic Density: Average pairwise similarity of 0.2636. Lower values indicate better semantic separation.
Alignment Quality: Aligned models achieve up to 29.4% 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
-0.421
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
sylvain, socialdemocratica, strobl
-a
ams, aristocrazia, average
-p
promoturs, passione, pandemias
-b
breton, bloccadas, brünisried
-c
communal, champester, consecrar
-m
magistrat, moëns, metallurgia
-d
demokratisches, dero, deditgà
-g
gruscha, gründliche, grammaticalas
Productive Suffixes
Suffix
Examples
-s
ams, moëns, helveticarchives
-a
socialdemocratica, aristocrazia, metallurgia
-n
sylvain, breton, tessin
-as
explitgadas, aviartas, organellas
-r
champester, consecrar, terrur
-e
älteste, average, homme
-t
magistrat, rendaquint, industriegesellschaft
-er
champester, schindler, hausberger
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
itad
2.01x
54 contexts
mitad, citad, citads
ment
1.73x
88 contexts
mument, dement, mentis
usch
1.62x
86 contexts
kusch, uschè, cusch
tica
1.71x
62 contexts
etica, antica, betica
aziu
1.71x
53 contexts
naziun, raziun, grazius
urma
1.84x
37 contexts
furma, burma, surmar
ntan
1.71x
42 contexts
entant, sentan, muntan
egni
1.68x
42 contexts
regni, vegni, tegnia
iuns
2.11x
18 contexts
liuns, aviuns, uniuns
ents
1.74x
33 contexts
dents, vents, cents
furm
1.57x
47 contexts
furma, furmo, furmà
nter
1.40x
65 contexts
unter, enter, inter
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
-c
-s
216 words
civitates, carstgauns
-s
-s
202 words
sillogissems, soluziuns
-p
-s
163 words
polineices, playmates
-s
-a
161 words
spendra, spezialisada
-c
-a
148 words
cortina, charenta
-p
-a
138 words
primministra, preferescha
-a
-s
131 words
atletas, abstractas
-s
-n
111 words
seen, selen
-m
-s
107 words
mémoires, misteris
-d
-s
97 words
diabetes, digerids
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
modernism
moderni-s-m
7.5
s
promontori
promonto-r-i
7.5
r
democratisà
democrati-s-à
7.5
s
chamutsch
chamut-s-ch
7.5
s
mediatisà
mediati-s-à
7.5
s
hollandse
holland-s-e
7.5
s
novreligiusas
novreligiu-s-as
7.5
s
cinquesensi
cinquesen-s-i
7.5
s
victoriusas
victoriu-s-as
7.5
s
pretensiusas
pretensiu-s-as
7.5
s
extravagant
extravag-a-nt
7.5
a
naziunelas
naziun-el-as
6.0
naziun
mesiradas
mesira-da-s
6.0
mesira
daventond
davent-on-d
6.0
davent
traversavan
traversa-va-n
6.0
traversa
6.6 Linguistic Interpretation
Automated Insight:
The language Romansh 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 (4.36x)
N-gram
2-gram
Lowest perplexity (230)
Markov
Context-4
Highest predictability (94.0%)
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.
