Comprehensive Research Report & Full Ablation Study
This repository contains NLP models trained and evaluated by Wikilangs, specifically on Tumbuka 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
5,474
12.42
34,661
26.6%
53.6%
2-gram
Subword
223 🏆
7.80
2,837
70.7%
99.6%
3-gram
Word
7,258
12.83
50,253
25.2%
51.5%
3-gram
Subword
1,577
10.62
22,530
33.2%
78.3%
4-gram
Word
8,704
13.09
75,625
23.5%
52.0%
4-gram
Subword
6,842
12.74
113,445
19.8%
51.7%
5-gram
Word
5,344
12.38
48,307
25.0%
58.2%
5-gram
Subword
18,567
14.18
275,747
13.9%
38.3%
Top 5 N-grams by Size
2-grams (Word):
Rank
N-gram
Count
1
charu cha
18,086
2
mu charu
13,923
3
boma la
13,289
4
chigaŵa cha
11,295
5
mu boma
11,014
3-grams (Word):
Rank
N-gram
Count
1
mu charu cha
13,110
2
mu boma la
8,192
3
chilwa chikulu cha
6,204
4
mu chigaŵa cha
5,908
5
mu chilwa chikulu
5,874
4-grams (Word):
Rank
N-gram
Count
1
mu chilwa chikulu cha
5,874
2
chilwa chikulu cha ulaya
5,097
3
ghakusangika mu boma la
4,333
4
chikulu cha ulaya europe
3,052
5
cha ulaya europe yaku
2,824
5-grams (Word):
Rank
N-gram
Count
1
mu chilwa chikulu cha ulaya
5,062
2
chilwa chikulu cha ulaya europe
3,052
3
chikulu cha ulaya europe yaku
2,824
4
ni msumba mu boma la
2,193
5
malo agho ghakusangika mu boma
2,176
2-grams (Subword):
Rank
N-gram
Count
1
a _
622,907
2
u _
234,729
3
_ m
226,843
4
a n
215,484
5
_ c
199,145
3-grams (Subword):
Rank
N-gram
Count
1
_ c h
141,906
2
a _ m
107,357
3
m u _
99,923
4
_ m u
99,086
5
_ k u
93,801
4-grams (Subword):
Rank
N-gram
Count
1
_ c h a
81,345
2
_ m u _
79,144
3
u _ c h
62,069
4
a _ k u
61,056
5
_ g h a
55,352
5-grams (Subword):
Rank
N-gram
Count
1
_ c h a _
51,011
2
a _ m u _
45,337
3
u _ c h a
42,760
4
m u _ c h
31,681
5
_ m u _ c
29,948
Key Findings
Best Perplexity: 2-gram (subword) with 223
Entropy Trend: Decreases with larger n-grams (more predictable)
Coverage: Top-1000 patterns cover ~38% 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
0.8434
1.794
5.85
97,126
15.7%
1
Subword
1.1331
2.193
9.11
745
0.0%
2
Word
0.2898
1.223
1.75
567,037
71.0%
2
Subword
1.0193
2.027
6.22
6,781
0.0%
3
Word
0.1172
1.085
1.22
988,755
88.3%
3
Subword
0.8781
1.838
4.40
42,130
12.2%
4
Word
0.0476 🏆
1.034
1.07
1,202,229
95.2%
4
Subword
0.6747
1.596
2.89
185,249
32.5%
Generated Text Samples (Word-based)
Below are text samples generated from each word-based Markov chain model:
Context Size 1:
mu boma la karonga chigaŵa cha greece ghakusangika mu austria yulaya austria ghakusangika mu charu c...
cha kummwela mu catechetical lectures wakaŵa nduna yikuru comene iyo yikusambizga ŵanthu ŵanandi mu ...
na zina zina la lilongwe mu bunda college ku namibia na mtima pa mndandanda wa ŵanthu
Context Size 2:
charu cha malaŵi la dowa ghakusangika mu mangochi mu ŵamalonda ŵanandi ŵa ku zimbabwe sumu iyo yinga...
mu charu cha turkey mu chilwa chikulu cha adana mu charu cha malaŵi la chiradzulu cha kummwela
boma la libya ŵakakana ivyo ŵakayowoya kale kufika mu mafuko gha rozvi changamire dombo wakaparanya ...
Context Size 3:
mu charu cha united states of america ndipouli mu vyaka vyasonosono apa ukuchepa wupu wa zimbabwe el...
mu boma la ceyhan mu chigaŵa chikulu cha kwazulu natal ku south africa ilo likususkana na wagner gro...
chilwa chikulu cha ulaya ikulu na idoko yamu germany ghamu germany wa misumba na matauni ghachoko gh...
Context Size 4:
mu chilwa chikulu cha ulaya ikulu na idoko yamu germany ghamu germany wa misumba na matauni ghachoko...
chilwa chikulu cha ulaya europe yaku austria ghakusangika mu austria yulaya austria austria
ghakusangika mu boma la machinga cha kummwela ndi dela limene limapezeka anthu awulemu ndi ozichepet...
Generated Text Samples (Subword-based)
Below are text samples generated from each subword-based Markov chain model:
Context Size 1:
_ptef_muna_kiper
amulo,_tedo_gwu_
ichinapermse_ŵik
Context Size 2:
a_vinee_li_ghakaŵ
u_anthen,_mulies,
_matricassanne_ŵa
Context Size 3:
_chigaŵa_maland_so
a_magazi_milira_ro
mu_boma_zakwa_mwap
Context Size 4:
_charu_cha_gandambo
_mu_chilwa_yikakhum
u_cha_germanyuma_pa
Key Findings
Best Predictability: Context-4 (word) with 95.2% predictability
Branching Factor: Decreases with context size (more deterministic)
Memory Trade-off: Larger contexts require more storage (185,249 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
45,104
Total Tokens
1,805,602
Mean Frequency
40.03
Median Frequency
4
Frequency Std Dev
678.44
Most Common Words
Rank
Word
Frequency
1
mu
81,954
2
cha
51,027
3
na
50,305
4
ku
29,094
5
la
26,744
6
ni
25,502
7
wa
23,621
8
boma
21,934
9
charu
21,617
10
pa
21,122
Least Common Words (from vocabulary)
Rank
Word
Frequency
1
vyakuseŵera
2
2
hypervisor
2
3
kuzima
2
4
muzakaŵe
2
5
maloboti
2
6
lichitira
2
7
chindale
2
8
tum_latntum_latntum_latn
2
9
yikupangikira
2
10
sae
2
Zipf's Law Analysis
Metric
Value
Zipf Coefficient
1.2067
R² (Goodness of Fit)
0.995267
Adherence Quality
excellent
Coverage Analysis
Top N Words
Coverage
Top 100
47.4%
Top 1,000
74.5%
Top 5,000
88.7%
Top 10,000
93.0%
Key Findings
Zipf Compliance: R²=0.9953 indicates excellent adherence to Zipf's law
High Frequency Dominance: Top 100 words cover 47.4% of corpus
Long Tail: 35,104 words needed for remaining 7.0% 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
0.8058
0.3384
N/A
N/A
mono_64d
64
0.7416
0.2724
N/A
N/A
mono_128d
128
0.4731
0.2502
N/A
N/A
aligned_32d
32
0.8058 🏆
0.3446
0.1300
0.4640
aligned_64d
64
0.7416
0.2694
0.1620
0.5160
aligned_128d
128
0.4731
0.2503
0.2340
0.6120
Key Findings
Best Isotropy: aligned_32d with 0.8058 (more uniform distribution)
Semantic Density: Average pairwise similarity of 0.2875. Lower values indicate better semantic separation.
Alignment Quality: Aligned models achieve up to 23.4% 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
0.520
High formulaic/idiomatic 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
-m
mutesi, mikhail, mtimabi
-ma
mandinka, masheke, mafinga
-s
sexagesimal, soviet, sirte
-a
amelika, apr, achikulire
-c
chakukolerana, chitambo, cigaŵa
-k
kununkhira, kukhazikiska, kumanyuma
-b
bantus, barrios, beach
-ku
kununkhira, kukhazikiska, kumanyuma
Productive Suffixes
Suffix
Examples
-a
pakutonda, chakukolerana, wakadangilira
-ka
wakabapatizika, ghakusinthiska, amelika
-e
ŵayowoyanenge, dale, charlottesville
-ra
wakadangilira, ghangaŵawovwira, ukuyendera
-s
bantus, iranians, prestigious
-o
chitambo, chigaŵo, too
-ga
wakawoneseskanga, wakachenjezga, ŵakalenga
-n
traunstein, nastätten, lahnstein
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
tion
2.51x
41 contexts
notion, option, motion
stri
2.63x
23 contexts
strip, strife, strict
chik
2.04x
38 contexts
chiku, chika, chikwi
umba
1.94x
43 contexts
sumba, rumba, tumba
angi
1.73x
51 contexts
bangi, ubangi, tangier
haku
2.13x
22 contexts
chaku, ghaku, chakum
hiku
2.25x
17 contexts
chiku, chikulu, chikung
chil
1.86x
28 contexts
child, chili, chile
ghak
2.03x
20 contexts
ghake, ghaku, ghakhe
anth
1.72x
35 contexts
anthu, kanthu, anthus
chig
2.05x
17 contexts
chigha, chigez, chigwa
higa
2.09x
14 contexts
shiga, vihiga, chigaŵo
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
-ŵa
-a
285 words
ŵakwimikika, ŵakucitira
-k
-a
284 words
kakoma, kulekeka
-c
-a
202 words
cafika, chikazura
-m
-a
153 words
mawema, mataka
-ŵa
-ga
100 words
ŵakafikanga, ŵakawonekanga
-k
-ka
92 words
kulekeka, kupokeka
-c
-s
83 words
circles, credentials
-ŵa
-e
73 words
ŵasande, ŵandaŵathereske
-m
-o
70 words
mulatho, mphalamuko
-k
-ra
70 words
kuzunura, kuchokera
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
accipitridae
accipitrid-a-e
7.5
a
ŵakavwara
ŵakavw-a-ra
7.5
a
ghakuperekeka
ghakuperek-e-ka
7.5
e
wachiŵili
wachiŵi-l-i
7.5
l
pakacitikaso
pakaciti-ka-so
7.5
ka
landkreis
landkre-i-s
7.5
i
yikawonekaso
yikawone-ka-so
7.5
ka
wakunyang
wakuny-a-ng
7.5
a
expressway
express-wa-y
7.5
wa
ghakatora
ghakat-o-ra
7.5
o
kupambanako
kupamban-a-ko
7.5
a
wakuphika
wakuph-i-ka
7.5
i
ghakwambukira
ghakwambuk-i-ra
7.5
i
ŵakasamira
ŵakasam-i-ra
7.5
i
treasuries
treasur-i-es
7.5
i
6.6 Linguistic Interpretation
Automated Insight:
The language Tumbuka shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.
Note on Idiomaticity: The high Idiomaticity Gap suggests a large number of frequent multi-word expressions or formulaic sequences that are statistically distinct from their component parts.
7. Summary & Recommendations
Performance Dashboard
Production Recommendations
Component
Recommended
Rationale
Tokenizer
64k BPE
Best compression (4.76x)
N-gram
2-gram
Lowest perplexity (223)
Markov
Context-4
Highest predictability (95.2%)
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.
