Comprehensive Research Report & Full Ablation Study
This repository contains NLP models trained and evaluated by Wikilangs, specifically on Piedmontese 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)
Below are sample sentences tokenized with each vocabulary size:
Sample 1:Legnaro a l’é na comun-a ëd la provinsa ëd Pàdoa. Region aministrativa Véneto. S...
Vocab
Tokens
Count
8k
▁le gn aro ▁a ▁l ’ é ▁na ▁comun - ... (+17 more)
27
16k
▁le gn aro ▁a ▁l ’ é ▁na ▁comun - ... (+17 more)
27
32k
▁legn aro ▁a ▁l ’ é ▁na ▁comun - a ... (+16 more)
26
64k
▁legn aro ▁a ▁l ’ é ▁na ▁comun - a ... (+16 more)
26
Sample 2:Nozay a l'é 'l nòm: d'un comun fransèis ant ël dipartiment d'Aube d'un comun fra...
Vocab
Tokens
Count
8k
▁no za y ▁a ▁l ' é ▁' l ▁nòm ... (+23 more)
33
16k
▁no zay ▁a ▁l ' é ▁' l ▁nòm : ... (+22 more)
32
32k
▁no zay ▁a ▁l ' é ▁' l ▁nòm : ... (+22 more)
32
64k
▁nozay ▁a ▁l ' é ▁' l ▁nòm : ▁d ... (+21 more)
31
Sample 3:Bellefosse a l'é na comun-a fransèisa ant la region aministrativa dl'Alsassia, a...
Vocab
Tokens
Count
8k
▁belle f osse ▁a ▁l ' é ▁na ▁comun - ... (+22 more)
32
16k
▁belle f osse ▁a ▁l ' é ▁na ▁comun - ... (+22 more)
32
32k
▁belle fosse ▁a ▁l ' é ▁na ▁comun - a ... (+21 more)
31
64k
▁belle fosse ▁a ▁l ' é ▁na ▁comun - a ... (+21 more)
31
Key Findings
Best Compression: 64k achieves 4.075x compression
Lowest UNK Rate: 8k with 0.0838% 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 Unique
N-gram Coverage
Results
N-gram
Variant
Perplexity
Entropy
Unique N-grams
Top-100 Coverage
Top-1000 Coverage
2-gram
Word
3,141
11.62
77,121
41.9%
64.4%
2-gram
Subword
256 🏆
8.00
3,836
69.3%
99.4%
3-gram
Word
5,004
12.29
132,134
37.8%
59.5%
3-gram
Subword
1,638
10.68
31,027
34.2%
77.5%
4-gram
Word
8,275
13.01
214,916
32.4%
54.5%
4-gram
Subword
6,362
12.64
163,804
22.7%
55.2%
5-gram
Word
8,601
13.07
179,908
29.2%
52.3%
5-gram
Subword
16,383
14.00
457,622
17.6%
45.3%
Top 5 N-grams by Size
2-grams (Word):
Rank
N-gram
Count
1
a l
154,306
2
l é
116,837
3
ant ël
45,088
4
dipartiment ëd
43,742
5
é na
41,435
3-grams (Word):
Rank
N-gram
Count
1
a l é
116,563
2
l é na
41,283
3
na comun a
36,182
4
é na comun
36,110
5
ant ël dipartiment
33,155
4-grams (Word):
Rank
N-gram
Count
1
a l é na
41,263
2
é na comun a
36,110
3
l é na comun
36,108
4
con na densità ëd
32,499
5
na comun a fransèisa
30,354
5-grams (Word):
Rank
N-gram
Count
1
l é na comun a
36,108
2
a l é na comun
36,104
3
é na comun a fransèisa
30,343
4
abitant scond ël censiment dël
29,591
5
na comun a fransèisa ant
29,152
2-grams (Subword):
Rank
N-gram
Count
1
a _
1,165,352
2
_ a
759,939
3
a n
521,874
4
_ d
517,379
5
_ l
463,625
3-grams (Subword):
Rank
N-gram
Count
1
_ a _
302,714
2
n t _
258,541
3
_ ë d
251,242
4
ë d _
246,081
5
ë l _
238,083
4-grams (Subword):
Rank
N-gram
Count
1
_ ë d _
245,889
2
_ a _ l
160,115
3
a _ l '
147,963
4
e n t _
137,969
5
m e n t
134,438
5-grams (Subword):
Rank
N-gram
Count
1
_ a _ l '
139,497
2
m e n t _
128,287
3
_ d ë l _
126,779
4
i m e n t
119,300
5
a _ l ' é
108,685
Key Findings
Best Perplexity: 2-gram (subword) with 256
Entropy Trend: Decreases with larger n-grams (more predictable)
Coverage: Top-1000 patterns cover ~45% 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
0.8327
1.781
5.52
169,530
16.7%
1
Subword
0.8751
1.834
6.71
1,490
12.5%
2
Word
0.3305
1.257
1.89
927,581
67.0%
2
Subword
0.8947
1.859
6.10
9,975
10.5%
3
Word
0.1336
1.097
1.29
1,740,248
86.6%
3
Subword
0.7906
1.730
4.36
60,753
20.9%
4
Word
0.0669 🏆
1.047
1.14
2,223,801
93.3%
4
Subword
0.6809
1.603
3.09
264,501
31.9%
Generated Text Samples (Word-based)
Below are text samples generated from each word-based Markov chain model:
Context Size 1:
a së stend për na comun a l é parlà minca casela a l anglèis national
ëd le ròche o gbiri niragu o kaqchikel akatenango sud con na densità a fransèisa ant
l é vincenzo civitali vincenzo andrea guglielminetti lese ij cas assolù la region sardëgna d américa
Context Size 2:
a l é na comun a fransèisa ant la literatura a l é un comun dla lombardìa
l é gemelà con anliure esterne sit istitussional dla provincia ëd turin a l é parlà la
ant ël dipartiment ëd vaucluse as dëstend an sna surfassa ëd 85 ab km dël dipartiment dla
Context Size 3:
a l é na comun a fransèisa ant la region aministrativa dl àuta normandìa ant ël dipartiment ëd
l é na comun a fransèisa ant la region aministrativa dla picardìa ant ël dipartiment ëd creuse a
na comun a fransèisa ant la region aministrativa dla bassa normandìa ant ël dipartiment ëd la nièvre...
Context Size 4:
a l é na comun a fransèisa ant la region aministrativa dla picardìa ant ël dipartiment ëd cantal a
é na comun a fransèisa ant la region aministrativa ëd champagne ardënne ant ël dipartiment d allier ...
l é na comun a fransèisa ant la region aministrativa ëd champagne ardënne ant ël dipartiment d hérau...
Generated Text Samples (Subword-based)
Below are text samples generated from each subword-based Markov chain model:
Context Size 1:
_pondan-ntré_d_t
a_sst_latrsio_so
n_chentet_pel'al
Context Size 2:
a_ëd_a_la_cottera
_agna_la_rep_decì
an_gruzeyrus_a_tu
Context Size 3:
_a_concorphan._com
nt_ëd_va_a_l'é_d'u
_ëd_km²,_cons_(tal
Context Size 4:
_ëd_tarda_ant_ij_27
_a_l'arnota_l'é_par
a_l'é_na_dense_regi
Key Findings
Best Predictability: Context-4 (word) with 93.3% predictability
Branching Factor: Decreases with context size (more deterministic)
Memory Trade-off: Larger contexts require more storage (264,501 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
80,217
Total Tokens
5,297,235
Mean Frequency
66.04
Median Frequency
5
Frequency Std Dev
2213.41
Most Common Words
Rank
Word
Frequency
1
a
388,771
2
ëd
246,106
3
l
200,451
4
dël
126,964
5
é
118,244
6
na
116,817
7
ël
109,927
8
la
108,231
9
ant
97,115
10
e
91,172
Least Common Words (from vocabulary)
Rank
Word
Frequency
1
andividuassion
2
2
sètim
2
3
guacamole
2
4
anviromentaj
2
5
tonelé
2
6
spurgh
2
7
solidëssa
2
8
ruscha
2
9
houten
2
10
maudagna
2
Zipf's Law Analysis
Metric
Value
Zipf Coefficient
1.1911
R² (Goodness of Fit)
0.999309
Adherence Quality
excellent
Coverage Analysis
Top N Words
Coverage
Top 100
61.6%
Top 1,000
80.4%
Top 5,000
89.7%
Top 10,000
92.9%
Key Findings
Zipf Compliance: R²=0.9993 indicates excellent adherence to Zipf's law
High Frequency Dominance: Top 100 words cover 61.6% of corpus
Long Tail: 70,217 words needed for remaining 7.1% 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
0.7640 🏆
0.3601
N/A
N/A
mono_64d
64
0.7270
0.2907
N/A
N/A
mono_128d
128
0.6128
0.2654
N/A
N/A
aligned_32d
32
0.7640
0.3674
0.0740
0.3760
aligned_64d
64
0.7270
0.2772
0.1400
0.5080
aligned_128d
128
0.6128
0.2519
0.1600
0.5340
Key Findings
Best Isotropy: mono_32d with 0.7640 (more uniform distribution)
Semantic Density: Average pairwise similarity of 0.3021. Lower values indicate better semantic separation.
Alignment Quality: Aligned models achieve up to 16.0% 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
0.156
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
-a
anvità, anetù, awun
-s
sie, sorcière, surrender
-c
conession, cyrano, celtica
-b
bassin, be, braunfels
-ma
magnolia, martinsicuro, marchisio
-m
mecatrònich, magnolia, miria
-p
pratica, prèivi, passo
-t
teatino, thomasset, tip
Productive Suffixes
Suffix
Examples
-a
ghilarza, hepatica, magnolia
-e
sie, urbe, sorcière
-n
bassin, conession, ecitassion
-s
facilitates, braunfels, heidekreis
-o
teatino, cyrano, martinsicuro
-i
flavi, canzoni, gritti
-on
conession, ecitassion, incursion
-t
nuriment, riconossiment, thomasset
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
assa
1.63x
143 contexts
lassa, nassa, fassa
ssio
1.80x
86 contexts
possio, fassio, lassio
ensi
1.52x
80 contexts
sensi, kensiu, mensis
imen
1.81x
39 contexts
imeni, ciment, crimen
cond
1.63x
59 contexts
condé, conde, scond
sten
1.54x
51 contexts
stend, osten, stent
leng
1.83x
26 contexts
eleng, lengo, lenga
nist
1.72x
31 contexts
sniste, snistr, snista
inis
1.55x
43 contexts
finiss, cinism, inisse
istr
1.43x
53 contexts
istro, bistr, istria
itan
1.36x
59 contexts
titan, ritan, gitan
engh
1.77x
20 contexts
fengh, vengh, lenghe
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
-a
149 words
cussìtica, castagnòla
-p
-a
136 words
predecessora, praetoria
-a
-a
126 words
agta, arcostruìa
-s
-a
105 words
sewa, sarvaja
-c
-o
94 words
capitignano, caivano
-c
-e
84 words
cane, castroreale
-c
-s
72 words
candicans, cruzières
-a
-e
68 words
avvenire, abele
-b
-a
63 words
bauma, brunetta
-s
-e
62 words
suceduje, strutture
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
williamson
william-s-on
7.5
s
lombardore
lombard-o-re
7.5
o
spantiasse
spantia-s-se
7.5
s
yutanduchi
yutandu-ch-i
7.5
ch
castiadas
castiad-a-s
7.5
a
costituent
costitu-e-nt
7.5
e
rochester
ro-ch-ester
7.5
ester
condorcet
condorc-e-t
7.5
e
camposano
campo-sa-no
7.5
sa
lalacelle
la-la-celle
7.5
celle
franchetii
franchet-i-i
7.5
i
napolioni
napoli-on-i
6.0
napoli
alcantara
al-cantar-a
6.0
cantar
paternità
pa-terni-tà
6.0
terni
franchista
franch-is-ta
6.0
franch
6.6 Linguistic Interpretation
Automated Insight:
The language Piedmontese 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 (4.08x)
N-gram
2-gram
Lowest perplexity (256)
Markov
Context-4
Highest predictability (93.3%)
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.
