RESEARCH_REPORT.md

French — Full Ablation Study & Research Report

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

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📋 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

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1. Tokenizer Evaluation

Results

Vocab Size	Compression	Avg Token Len	UNK Rate	Total Tokens
8k	3.723x	3.72	0.0810%	7,061,086
16k	4.078x	4.08	0.0887%	6,446,468
32k	4.368x	4.37	0.0950%	6,018,653
64k	4.573x 🏆	4.57	0.0994%	5,748,614

Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

Sample 1: Lapon peut désigner : les Samis ; les langues sames ; Lapon, une ville du Soudan...

Vocab	Tokens	Count
8k	▁lap on ▁peut ▁désigner ▁: ▁les ▁sam is ▁; ▁les ... (+27 more)	37
16k	▁lap on ▁peut ▁désigner ▁: ▁les ▁sam is ▁; ▁les ... (+27 more)	37
32k	▁lap on ▁peut ▁désigner ▁: ▁les ▁sam is ▁; ▁les ... (+26 more)	36
64k	▁lap on ▁peut ▁désigner ▁: ▁les ▁sam is ▁; ▁les ... (+25 more)	35

Sample 2: Le pentadécane est un alcane linéaire de formule brute . Il possède 4 347 isomèr...

Vocab	Tokens	Count
8k	▁le ▁pent ad éc ane ▁est ▁un ▁al c ane ... (+27 more)	37
16k	▁le ▁pent ad éc ane ▁est ▁un ▁alc ane ▁linéaire ... (+22 more)	32
32k	▁le ▁pent ad éc ane ▁est ▁un ▁alc ane ▁linéaire ... (+20 more)	30
64k	▁le ▁pent ad éc ane ▁est ▁un ▁alcane ▁linéaire ▁de ... (+18 more)	28

Sample 3: L'eicosane est un alcane linéaire de formule brute . Il possède isomères structu...

Vocab	Tokens	Count
8k	▁l ' e ic os ane ▁est ▁un ▁al c ... (+22 more)	32
16k	▁l ' e icos ane ▁est ▁un ▁alc ane ▁linéaire ... (+16 more)	26
32k	▁l ' e icos ane ▁est ▁un ▁alc ane ▁linéaire ... (+14 more)	24
64k	▁l ' e icos ane ▁est ▁un ▁alcane ▁linéaire ▁de ... (+12 more)	22

Key Findings

• Best Compression: 64k achieves 4.573x compression
• Lowest UNK Rate: 8k with 0.0810% unknown tokens
• Trade-off: Larger vocabularies improve compression but increase model size
• Recommendation: 32k vocabulary provides optimal balance for production use

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2. N-gram Model Evaluation

Results

N-gram	Variant	Perplexity	Entropy	Unique N-grams	Top-100 Coverage	Top-1000 Coverage
2-gram	Word	197,170	17.59	5,674,755	9.3%	21.3%
2-gram	Subword	251 🏆	7.97	40,333	68.1%	99.4%
3-gram	Word	1,815,223	20.79	18,029,220	2.4%	9.5%
3-gram	Subword	1,988	10.96	269,239	30.3%	73.7%
4-gram	Word	5,518,864	22.40	36,868,834	1.8%	8.6%
4-gram	Subword	11,120	13.44	1,563,238	15.8%	42.2%
5-gram	Word	4,103,331	21.97	28,227,926	2.4%	11.6%
5-gram	Subword	46,850	15.52	5,742,636	8.7%	25.7%

Top 5 N-grams by Size

2-grams (Word):

Rank	N-gram	Count
1	de la	5,296,650
2	de l	3,236,403
3	à la	1,514,334
4	à l	1,261,623
5	dans le	992,683

3-grams (Word):

Rank	N-gram	Count
1	de la commune	330,769
2	notes et références	310,459
3	occupation des sols	189,915
4	et de la	154,877
5	le nom de	144,766

4-grams (Word):

Rank	N-gram	Count
1	l occupation des sols	124,755
2	occupation des sols de	93,658
3	des sols de la	93,553
4	sols de la commune	93,442
5	notes et références voir	79,475

5-grams (Word):

Rank	N-gram	Count
1	occupation des sols de la	93,478
2	des sols de la commune	93,402
3	l occupation des sols de	93,364
4	notes et références voir aussi	79,373
5	notes et références liens externes	68,549

2-grams (Subword):

Rank	N-gram	Count
1	e _	125,785,698
2	s _	74,291,364
3	_ d	73,439,085
4	_ l	55,706,551
5	e s	54,301,349

3-grams (Subword):

Rank	N-gram	Count
1	_ d e	41,554,921
2	e s _	37,119,081
3	d e _	32,944,492
4	e _ d	22,149,546
5	l e _	20,731,208

4-grams (Subword):

Rank	N-gram	Count
1	_ d e _	30,047,475
2	_ l a _	16,205,522
3	e _ d e	12,867,124
4	_ l e _	11,621,670
5	_ e t _	11,489,728

5-grams (Subword):

Rank	N-gram	Count
1	_ d e _ l	9,678,287
2	e _ d e _	9,546,481
3	_ d e s _	7,709,198
4	_ l e s _	7,167,363
5	e _ l a _	6,536,044

Key Findings

• Best Perplexity: 2-gram (subword) with 251
• Entropy Trend: Decreases with larger n-grams (more predictable)
• Coverage: Top-1000 patterns cover ~26% of corpus
• Recommendation: 4-gram or 5-gram for best predictive performance

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3. Markov Chain Evaluation

Results

Context	Variant	Avg Entropy	Perplexity	Branching Factor	Unique Contexts	Predictability
1	Word	0.9052	1.873	14.72	3,729,596	9.5%
1	Subword	1.2049	2.305	9.45	20,472	0.0%
2	Word	0.4648	1.380	3.15	54,852,526	53.5%
2	Subword	0.6045	1.520	3.87	193,340	39.6%
3	Word	0.2551	1.193	1.71	172,431,097	74.5%
3	Subword	0.6357	1.554	3.88	747,541	36.4%
4	Word	0.1275 🏆	1.092	1.26	294,675,620	87.3%
4	Subword	0.6602	1.580	3.61	2,901,861	34.0%

Generated Text Samples (Word-based)

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

Context Size 1:

1. de titan éditions plon 424 p haffner inventaire de paris occupation des modèles différents les début...
2. la haine féroce le bon pasteur afro américaine par la saison régulière se basent sur le
3. le sprinteur britannique de l insigne homologué au rat dû à l ambitieux antipater d apel

Context Size 2:

1. de la légion d honneur fleurs chapelle de la mer alt gauche vignette cimetière protestant de maulbro...
2. de l œuvre est un dessinateur et peintre ses tableaux de derain h 10 min 50 s
3. à la fin du la classe 1 avec un chevalet en butée dans ces moments là le

Context Size 3:

1. de la commune est de 325 soit un indicateur de concentration d emploi de 85 2 la répartition
2. notes et références liens externes sud coréen sorti en d aventure américain d aventure américain met...
3. occupation des sols center carte des infrastructures et de l électromagnétisme universel de vitalité...

Context Size 4:

1. l occupation des sols carte des infrastructures et de l occupation des sols de la commune telle qu e...
2. occupation des sols de la commune telle qu elle ressort de la base de données européenne d occupatio...
3. des sols de la commune en clc risques majeurs le territoire de la commune durant quinze ans christop...

Generated Text Samples (Subword-based)

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

Context Size 1:

1. _partene_doy_e_s
2. e_larit_dus_iome
3. avide_cèsouéoù_c

Context Size 2:

1. e_jam_à_les_du_de
2. s_thé_ilite_la_wa
3. _de_sa_comist_est

Context Size 3:

1. _de_prementrest_un
2. es_non_de_balling_
3. de_canadieurs_la_p

Context Size 4:

1. _de_saxe,_le_cumulu
2. _la_capitalie._8_si
3. e_de_de_fumer_l'éco

Key Findings

• Best Predictability: Context-4 (word) with 87.3% predictability
• Branching Factor: Decreases with context size (more deterministic)
• Memory Trade-off: Larger contexts require more storage (2,901,861 contexts)
• Recommendation: Context-3 or Context-4 for text generation

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4. Vocabulary Analysis

Statistics

Metric	Value
Vocabulary Size	1,519,124
Total Tokens	496,742,137
Mean Frequency	326.99
Median Frequency	4
Frequency Std Dev	37954.61

Most Common Words

Rank	Word	Frequency
1	de	30,301,637
2	la	16,417,649
3	le	11,875,190
4	et	11,702,997
5	l	10,150,468
6	en	9,437,564
7	à	9,348,887
8	des	7,741,717
9	d	7,508,960
10	les	7,283,372

Least Common Words (from vocabulary)

Rank	Word	Frequency
1	caracallæ	2
2	santapaulina	2
3	publinf	2
4	vijñānabhairava	2
5	benbor	2
6	kunpan	2
7	moderndrawings	2
8	jexiste	2
9	ⴰⵣⵎⵎⵓⵔ	2
10	pseudocarcinus	2

Zipf's Law Analysis

Metric	Value
Zipf Coefficient	1.0347
R² (Goodness of Fit)	0.992664
Adherence Quality	excellent

Coverage Analysis

Top N Words	Coverage
Top 100	44.8%
Top 1,000	63.9%
Top 5,000	79.7%
Top 10,000	85.5%

Key Findings

• Zipf Compliance: R²=0.9927 indicates excellent adherence to Zipf's law
• High Frequency Dominance: Top 100 words cover 44.8% of corpus
• Long Tail: 1,509,124 words needed for remaining 14.5% coverage

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5. Word Embeddings Evaluation

5.1 Cross-Lingual Alignment

5.2 Model Comparison

Model	Dimension	Isotropy	Semantic Density	Alignment R@1	Alignment R@10
mono_32d	32	0.7808 🏆	0.3764	N/A	N/A
mono_64d	64	0.7574	0.3033	N/A	N/A
mono_128d	128	0.6995	0.2569	N/A	N/A
aligned_32d	32	0.7808	0.3878	0.4820	0.8240
aligned_64d	64	0.7574	0.3079	0.7080	0.9420
aligned_128d	128	0.6995	0.2657	0.8120	0.9680

Key Findings

• Best Isotropy: mono_32d with 0.7808 (more uniform distribution)
• Semantic Density: Average pairwise similarity of 0.3163. Lower values indicate better semantic separation.
• Alignment Quality: Aligned models achieve up to 81.2% R@1 in cross-lingual retrieval.
• Recommendation: 128d aligned for best cross-lingual performance

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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	-0.550	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	altschloss, aën, alfège
-s	similairesselon, shochugeiko, sodapop
-c	cugn, crocefisso, colomer
-m	maracanaú, mandriole, morzine
-ma	maracanaú, mandriole, mastaï
-d	drăculeștibasarab, déchirent, durégnatons
-p	pame, pichery, pleased
-b	bingoto, blennies, brusuglio

Productive Suffixes

Suffix	Examples
-e	pame, mandriole, morzine
-s	altschloss, blennies, durégnatons
-es	blennies, moyensles, fraternelles
-n	cugn, similairesselon, fransson
-a	occasionna, exea, paçoca
-t	déchirent, lovefist, crabbet
-r	colomer, elvir, eckersbacher
-i	wubi, idiomorphini, oroi

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
ient	2.44x	382 contexts	nient, fient, rient
aphi	2.02x	140 contexts	aphis, aphia, aphid
ienn	1.59x	391 contexts	ienne, vienn, fienne
ogra	1.62x	276 contexts	logra, bogra, fogra
éren	1.81x	150 contexts	héren, kéren, érenn
ontr	1.59x	266 contexts	montr, ontra, kontr
tiqu	1.49x	318 contexts	tiqui, tique, tiqué
aiso	1.66x	172 contexts	baiso, gaiso, daiso
utre	1.56x	215 contexts	butre, outre, autre
niqu	1.42x	248 contexts	nique, niqué, niqua
rtic	1.44x	179 contexts	artic, hrtica, artici
onal	1.50x	136 contexts	conal, monal, sonal

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	143 words	couleuses, cammaerts
-m	-s	137 words	morians, merckens
-c	-e	121 words	clémentine, classessite
-p	-s	115 words	pétards, psylles
-a	-s	114 words	alvaros, aldrinus
-s	-s	107 words	sportpaleis, shaggys
-p	-e	105 words	pédagogique, poursuiveuse
-m	-e	102 words	maastrichtle, martinofiministre
-a	-e	95 words	alboize, autoparodie
-s	-e	92 words	salicyline, studiesthe

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
sarrabeyrouse	sarrabeyrou-s-e	7.5	s
grippement	grippem-e-nt	7.5	e
égalementsite	égalements-i-te	7.5	i
rediviser	redivi-s-er	7.5	s
ambrosini	ambrosi-n-i	7.5	n
rencontrerai	rencontrer-a-i	7.5	a
détroitsaison	détroitsai-s-on	7.5	s
monpalais	monpal-a-is	7.5	a
vieumaison	vieumai-s-on	7.5	s
caractéristise	caractéristi-s-e	7.5	s
circonvient	circonvi-e-nt	7.5	e
tilehurst	tilehur-s-t	7.5	s
chongsheng	chongsh-e-ng	7.5	e
bloemfontein	bloemfont-e-in	7.5	e
voorspoel	voorspo-e-l	7.5	e

6.6 Linguistic Interpretation

Automated Insight: The language French shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.

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7. Summary & Recommendations

Production Recommendations

Component	Recommended	Rationale
Tokenizer	64k BPE	Best compression (4.57x)
N-gram	2-gram	Lowest perplexity (251)
Markov	Context-4	Highest predictability (87.3%)
Embeddings	100d	Balanced semantic capture and isotropy

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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

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Generated by Wikilangs Pipeline · 2026-03-03 09:31:27