RESEARCH_REPORT.md

English — Full Ablation Study & Research Report

Detailed evaluation of all model variants trained on English Wikipedia data by Wikilangs.

👈 Back to README

📋 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)
• Language Vocabulary
• Language Statistics

Analysis and Evaluation

• 1. Tokenizer Evaluation
• 2. N-gram Model Evaluation
• 3. Markov Chain Evaluation
• 4. Vocabulary Analysis
• 5. Word Embeddings Evaluation
• 6. Morphological Analysis (Experimental)
• 7. Summary & Recommendations
• Metrics Glossary
• Visualizations Index

---

1. Tokenizer Evaluation

Results

Vocab Size	Compression	Avg Token Len	UNK Rate	Total Tokens
8k	3.837x	3.84	0.1338%	6,415,993
16k	4.221x	4.22	0.1472%	5,832,191
32k	4.511x	4.51	0.1573%	5,458,111
64k	4.699x 🏆	4.70	0.1638%	5,239,573

Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

Sample 1: Albrecht Achilles may refer to: Albrecht III Achilles, Elector of Brandenburg Al...

Vocab	Tokens	Count
8k	▁alb recht ▁ach illes ▁may ▁refer ▁to : ▁alb recht ... (+27 more)	37
16k	▁alb recht ▁ach illes ▁may ▁refer ▁to : ▁alb recht ... (+26 more)	36
32k	▁albrecht ▁achilles ▁may ▁refer ▁to : ▁albrecht ▁iii ▁achilles , ... (+17 more)	27
64k	▁albrecht ▁achilles ▁may ▁refer ▁to : ▁albrecht ▁iii ▁achilles , ... (+16 more)	26

Sample 2: Alexander V may refer to: Alexander V of Macedon (died 294 BCE) Antipope Alexand...

Vocab	Tokens	Count
8k	▁alexander ▁v ▁may ▁refer ▁to : ▁alexander ▁v ▁of ▁maced ... (+20 more)	30
16k	▁alexander ▁v ▁may ▁refer ▁to : ▁alexander ▁v ▁of ▁macedon ... (+18 more)	28
32k	▁alexander ▁v ▁may ▁refer ▁to : ▁alexander ▁v ▁of ▁macedon ... (+15 more)	25
64k	▁alexander ▁v ▁may ▁refer ▁to : ▁alexander ▁v ▁of ▁macedon ... (+15 more)	25

Sample 3: Two antipopes used the regnal name Victor IV: Antipope Victor IV Antipope Victor...

Vocab	Tokens	Count
8k	▁two ▁antip op es ▁used ▁the ▁reg nal ▁name ▁victor ... (+8 more)	18
16k	▁two ▁antip opes ▁used ▁the ▁reg nal ▁name ▁victor ▁iv ... (+7 more)	17
32k	▁two ▁antip opes ▁used ▁the ▁regnal ▁name ▁victor ▁iv : ... (+6 more)	16
64k	▁two ▁antipopes ▁used ▁the ▁regnal ▁name ▁victor ▁iv : ▁antipope ... (+5 more)	15

Key Findings

• Best Compression: 64k achieves 4.699x compression
• Lowest UNK Rate: 8k with 0.1338% 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

Results

N-gram	Variant	Perplexity	Entropy	Unique N-grams	Top-100 Coverage	Top-1000 Coverage
2-gram	Word	386,225	18.56	9,782,066	8.6%	17.8%
2-gram	Subword	257 🏆	8.01	64,688	68.7%	99.4%
3-gram	Word	4,093,782	21.97	29,170,233	2.0%	6.5%
3-gram	Subword	2,180	11.09	375,974	27.2%	71.8%
4-gram	Word	14,465,722	23.79	54,673,289	1.7%	4.4%
4-gram	Subword	12,758	13.64	2,193,365	14.2%	38.3%
5-gram	Word	12,820,936	23.61	37,691,280	2.5%	5.0%
5-gram	Subword	55,700	15.77	8,078,460	8.7%	23.9%

Top 5 N-grams by Size

2-grams (Word):

Rank	N-gram	Count
1	of the	7,591,708
2	in the	5,221,237
3	to the	2,361,743
4	and the	1,799,614
5	on the	1,518,298

3-grams (Word):

Rank	N-gram	Count
1	the united states	408,936
2	one of the	329,510
3	as well as	264,322
4	part of the	247,900
5	references external links	203,098

4-grams (Word):

Rank	N-gram	Count
1	in the united states	156,847
2	under the age of	101,794
3	the age of 18	97,188
4	the end of the	88,360
5	of age or older	86,112

5-grams (Word):

Rank	N-gram	Count
1	under the age of 18	95,573
2	years of age or older	85,203
3	65 years of age or	84,639
4	of age or older the	81,589
5	the median income for a	59,537

2-grams (Subword):

Rank	N-gram	Count
1	e _	117,498,416
2	_ t	97,071,904
3	t h	84,506,441
4	_ a	84,102,037
5	s _	80,981,888

3-grams (Subword):

Rank	N-gram	Count
1	_ t h	65,028,534
2	t h e	60,632,216
3	h e _	53,951,238
4	e d _	29,954,463
5	_ i n	29,022,901

4-grams (Subword):

Rank	N-gram	Count
1	_ t h e	55,274,199
2	t h e _	50,142,942
3	_ o f _	26,136,576
4	a n d _	22,544,155
5	_ a n d	20,891,023

5-grams (Subword):

Rank	N-gram	Count
1	_ t h e _	49,351,863
2	_ a n d _	20,550,921
3	_ o f _ t	8,921,160
4	n _ t h e	8,394,629
5	o f _ t h	8,311,158

Key Findings

• Best Perplexity: 2-gram (subword) with 257
• Entropy Trend: Decreases with larger n-grams (more predictable)
• Coverage: Top-1000 patterns cover ~24% of corpus
• Recommendation: 4-gram or 5-gram for best predictive performance

---

3. Markov Chain Evaluation

Results

Context	Variant	Avg Entropy	Perplexity	Branching Factor	Unique Contexts	Predictability
1	Word	0.9382	1.916	19.86	4,365,871	6.2%
1	Subword	1.2026	2.302	11.62	32,517	0.0%
2	Word	0.5167	1.431	3.51	86,666,437	48.3%
2	Subword	0.5363	1.450	3.31	377,790	46.4%
3	Word	0.2409	1.182	1.68	303,940,373	75.9%
3	Subword	0.5420	1.456	3.45	1,251,354	45.8%
4	Word	0.1077 🏆	1.078	1.22	509,562,649	89.2%
4	Subword	0.6319	1.550	3.50	4,322,061	36.8%

Generated Text Samples (Word-based)

Below are text samples generated from each word-based Markov chain model:

Context Size 1:

1. the move in july 2 respectively the murders in e bachs art deco building society was
2. of the death in the buachaille etive ship to the signaling involves neuronal signals as the
3. and left by his hysterical night and chieftain of measure in allowed for a number 3

Context Size 2:

1. of the big story is off limits to permanent employment in most notably in the shoot dying
2. in the city of lübeck later sold to supermarkets hotels cinemas and four mpvs on the other
3. to the limestone florida department of veteran hard rock version in featuring another lengthy playof...

Context Size 3:

1. the united states was raised significantly due to the interplay of light color etc hearing protectio...
2. one of the few performed to significant recognition notable achievements include first indian batsma...
3. as well as finishing sixth in the ferrari 312b and stirling mosss lotus in which he took to

Context Size 4:

1. in the united states helped revive the french economy with the marshall plan until the nys w shut do...
2. under the age of 18 living with them 57 1 were married couples living together 9 4 had a
3. the age of 18 living with them 44 6 were married couples living together 13 9 had a female

Generated Text Samples (Subword-based)

Below are text samples generated from each subword-based Markov chain model:

Context Size 1:

1. _an_ainalltyarmo
2. ere_isorandaltii
3. agean._he_trhed,

Context Size 2:

1. e_co-con_ithe_sto
2. _the_gh_todent's_
3. th_arantime'_toft

Context Size 3:

1. _the_abird_native_
2. the_10_olynoldavit
3. he_der_–_to_the_fi

Context Size 4:

1. _the_treased:_"indo
2. the_unit_by_made_fi
3. _of_indies_in_the_s

Key Findings

• Best Predictability: Context-4 (word) with 89.2% predictability
• Branching Factor: Decreases with context size (more deterministic)
• Memory Trade-off: Larger contexts require more storage (4,322,061 contexts)
• Recommendation: Context-3 or Context-4 for text generation

---

4. Vocabulary Analysis

Statistics

Metric	Value
Vocabulary Size	1,867,537
Total Tokens	739,735,080
Mean Frequency	396.10
Median Frequency	4
Frequency Std Dev	51092.36

Most Common Words

Rank	Word	Frequency
1	the	50,118,217
2	of	26,210,950
3	and	20,755,074
4	in	19,609,387
5	a	14,271,839
6	to	14,219,669
7	was	7,449,828
8	for	5,821,739
9	as	5,815,121
10	is	5,683,775

Least Common Words (from vocabulary)

Rank	Word	Frequency
1	brevetting	2
2	karuppukatti	2
3	cirrhatum	2
4	paða	2
5	вим	2
6	correya	2
7	bulamaq	2
8	boorik	2
9	spanishe	2
10	gitarrenmusik	2

Zipf's Law Analysis

Metric	Value
Zipf Coefficient	1.0573
R² (Goodness of Fit)	0.986242
Adherence Quality	excellent

Coverage Analysis

Top N Words	Coverage
Top 100	38.8%
Top 1,000	61.6%
Top 5,000	80.1%
Top 10,000	86.4%

Key Findings

• Zipf Compliance: R²=0.9862 indicates excellent adherence to Zipf's law
• High Frequency Dominance: Top 100 words cover 38.8% of corpus
• Long Tail: 1,857,537 words needed for remaining 13.6% coverage

---

5. Word Embeddings Evaluation

5.1 Cross-Lingual Alignment

Note: Multilingual alignment visualization not available for this language.

5.2 Model Comparison

Model	Dimension	Isotropy	Semantic Density	Alignment R@1	Alignment R@10
mono_32d	32	0.7693 🏆	0.4027	N/A	N/A
mono_64d	64	0.7388	0.3350	N/A	N/A
mono_128d	128	0.6687	0.2629	N/A	N/A

Key Findings

• Best Isotropy: mono_32d with 0.7693 (more uniform distribution)
• Semantic Density: Average pairwise similarity of 0.3335. Lower values indicate better semantic separation.
• Alignment Quality: No aligned models evaluated in this run.
• 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	-0.793	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	skulltrail, scroggins, salatin
-a	alpana, ayopaya, aekyung
-k	kairos, kunigundes, kumwartok
-m	mapae, muktafi, meirás
-c	cutpurses, ceste, centurynear
-p	pustynsky, phet, propertys
-w	wnbd, wrestlerdecember, walska
-t	technor, tvmaze, twistor

Productive Suffixes

Suffix	Examples
-s	scroggins, donoughues, kairos
-e	forebode, mapae, tvmaze
-n	salatin, gedruckten, fursten
-a	alpana, ayopaya, flavicauda
-r	wrestlerdecember, haalandmanchester, shoulder
-i	rosai, badaczewski, muktafi
-es	donoughues, kunigundes, cutpurses
-t	stillmaticchart, phet, quenstedt

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
tter	1.46x	1019 contexts	atter, otter, itter
ubli	1.63x	215 contexts	tubli, ublic, dubli
ttle	1.45x	375 contexts	attle, ittle, ottle
ount	1.52x	208 contexts	count, yount, fount
ontr	1.54x	183 contexts	ontra, kontr, contr
icia	1.44x	202 contexts	licia, ticia, nicia
itie	1.57x	129 contexts	mitie, nitie, itier
esid	1.55x	123 contexts	yesid, cesid, resid
itio	1.46x	142 contexts	aitio, ition, vitio
rsit	1.96x	37 contexts	ḥarsit, parsit, fersit
ucti	1.73x	60 contexts	aucti, fructi, ductis
oduc	1.85x	44 contexts	produc, koduck, roduco

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	-s	117 words	superhumps, squiggs
-c	-s	102 words	cheirogaleus, cuddys
-b	-s	88 words	betlemitas, bracelins
-p	-s	88 words	paros, paars
-a	-s	85 words	abdülhamids, aguasbonenses
-s	-e	82 words	sulene, solene
-m	-s	80 words	mascas, mollis
-t	-s	78 words	tracklines, tirthankaras
-m	-e	70 words	magnetoreceptive, matratze
-c	-e	68 words	coudreville, clanvowe

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
parintintin	parintin-t-in	7.5	t
haakonssen	haakons-s-en	7.5	s
writernet	writern-e-t	7.5	e
kyŏngsang	kyŏngs-a-ng	7.5	a
neoformalism	neoformali-s-m	7.5	s
counterfeit	counterfe-i-t	7.5	i
glossarist	glossari-s-t	7.5	s
guitarless	guitar-le-ss	7.5	le
kyoryusho	kyoryus-h-o	7.5	h
harrisonharrison	harrisonharri-s-on	7.5	s
frankowsk	frankow-s-k	7.5	s
pxseattle	pxseat-t-le	7.5	t
maribulan	maribu-l-an	7.5	l
slighhouses	slighhou-s-es	7.5	s
limaysaurus	limaysau-r-us	7.5	r

6.6 Linguistic Interpretation

Automated Insight: The language English 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

Production Recommendations

Component	Recommended	Rationale
Tokenizer	64k BPE	Best compression (4.70x)
N-gram	2-gram	Lowest perplexity (257)
Markov	Context-4	Highest predictability (89.2%)
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

1. Compare within model families: Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
2. Consider trade-offs: Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
3. Context matters: Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
4. Corpus influence: All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
5. 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

---

👈 Back to README

Generated by Wikilangs Pipeline · 2026-03-04 03:44:40