arxmliv-embeddings-082018.md

layout: page
title: arXMLiv 08.2018 - Word Embeddings; Token Model

Part of the arXMLiv project at the KWARC research group

Author

• Deyan Ginev

Release

• This page documents: 08.2018
• Latest: 08.2019

Accessibility and License

The content of this Dataset is licensed to SIGMathLing members for research and tool development purposes.

Access is restricted to SIGMathLing members under the SIGMathLing Non-Disclosure-Agreement as for most arXiv articles, the right of distribution was only given (or assumed) to arXiv itself.

Contents

• An 11.5 billion token model for the arXMLiv 08.2018 dataset, including subformula lexemes
  • token_model.zip
• 300 dimensional GloVe word embeddings for the arXMLiv 08.2018 dataset
  • glove.arxmliv.11B.300d.zip and vocab.arxmliv.zip
• 300d GloVe word embeddings for individual subsets
  • glove.subsets.zip
• Embeddings and vocabulary with math lexemes omitted
  • glove.arxmliv.nomath.11B.300d.zip and vocab.arxmliv.nomath.zip
  • added on July 20, 2019
  • used as a control when evaluating the contribution of formula lexemes
• the main arXMLiv dataset is available separately here

Token Model Statistics

subset	documents	paragraphs	sentences
no_problem	137,864	4,646,203	21,533,963
warning	705,095	45,797,794	183,246,777
error	389,225	26,759,524	99,641,978
complete	1,232,184	77,203,521	304,422,718

subset	words	formulas	inline cite	numeric literals
no_problem	430,217,995	20,910,732	3,709,520	11,177,753
warning	3,175,663,430	281,832,412	25,337,574	83,606,897
error	1,731,971,035	153,186,264	13,145,561	43,399,720
complete	5,337,852,460	455,929,408	42,192,655	138,184,370

GloVe Model Statistics

subset	tokens	unique words	unique words (freq 5+ )
no_problem	622,968,267	715,433	219,304
warning	7,203,536,205	3,478,235	666,317
error	3,691,805,321	2,444,532	574,467
complete	11,518,309,793	5,285,379	1,000,295

Citing this Resource

Please cite the main dataset when using the word embeddings, as they are generated and distributed jointly. Instructions here

Download

Download link (SIGMathLing members only)

Generated via

• llamapun 0.2.0,
• GloVe 1.2, 2018

Generation Parameters

• token model distributed as 3 subsets - no_problem, warning and error. complete model is derived via:

    cat token_model_no_problem.txt \
        token_model_warning.txt \
        token_model_error.txt > token_model_complete.txt

• llamapun v0.2, corpus_token_model example used for token model extraction

  • processed logical paragraphs only (excluded non-textual modalities, e.g. tables, figures and their captions, bibliographies, as well as abstracts)
  • excluded paragraphs containing latexml errors (marked via a ltx_ERROR HTML class)
  • used llamapun math-aware sentence and word tokenization, with subformula math lexemes
  • marked up inline citations replaced with citationelement token
  • numeric literals replaced with NUM token (both in text and formulas)
  • ignored sentences with unnaturally long words (>25 characters) - almost always due to latexml conversion errors

• GloVe repository at sha 07d59d

  • build/vocab_count -min-count 5
  • build/cooccur -memory 32.0 -window-size 15
  • build/shuffle -memory 32.0
  • build/glove -threads 16 -x-max 100 -iter 25 -vector-size 300 -binary 2

Examples and baselines

GloVe in-built evaluation (non-expert tasks e.g. language, relationships, geography)

1. no_problem

• Total accuracy: 27.47% (4028/14663)
• Highest score: "gram3-comparative.txt", 75.30% (1003/1332)

2. warning

• Total accuracy: 31.97% (5351/16736)
• Highest score: "gram3-comparative.txt", 77.40% (1031/1332)

3. error

• Total accuracy: 29.67% (4910/16549)
• Highest score: "gram3-comparative.txt", 72.75% (969/1332)

4. complete

• Total accuracy: 35.48% (6298/17750)
• Highest score: "gram3-comparative.txt", 76.65% (1021/1332)

5. demo baseline: text8 demo (first 100M characters of Wikipedia)

• Total accuracy: 23.62% (4211/17827)
• Highest score: "gram6-nationality-adjective.txt", 58.65% (892/1521)

Evaluation note: These in-built evlauation runs are provided as a sanity check that the generated GloVe models pass a basic baseline against the non-expert tasks in the default GloVe suite. One would need a scienctific discourse tailored set of test cases to evaluate the arXiv-based models competitively.

Measuring word analogy

In a cloned GloVe repository, start via:

python2 eval/python/word_analogy.py --vocab_file vocab.arxmliv.txt --vectors_file glove.arxmliv.11B.300d.txt

1. abelian is to group as disjoint is to ?

• Top hit: union, cosine distance 0.653377

2. convex is to concave as positive is to ?

• Top hit: negative, cosine distance 0.786877

3. finite is to infinte as abelian is to ?

• Top hit: nonabelian, cosine distance 0.676042

4. quantum is to classical as bottom is to ?

• Top hit: top, cosine distance 0.734896

5. eq is to proves as figure is to ?

• Top hit: showing, cosine distance 0.668502

6. italic_x is to italic_y as italic_a is to ?

• Top hit: italic_b, cosine distance 0.902608

Nearest word vectors

In a cloned GloVe repository, start via:

python2 eval/python/distance.py --vocab_file vocab.arxmliv.txt --vectors_file glove.arxmliv.11B.300d.txt

1. lattice

   Word: lattice  Position in vocabulary: 488
   
                                 Word       Cosine distance
   
   ---------------------------------------------------------
   
                             lattices		0.853103
   
                           triangular		0.637767
   
                             honeycomb		0.626426
   
                               crystal		0.624397
   
                               finite		0.614720
   
                               spacing		0.603067

2. entanglement

   Word: entanglement  Position in vocabulary: 1568
   
                                 Word       Cosine distance
   
   ---------------------------------------------------------
   
                             entangled		0.780425
   
                         multipartite		0.730968
   
                           concurrence		0.691708
   
                           negativity		0.649595
   
                           tripartite		0.647623
   
                               quantum		0.640395
   
                             fidelity		0.640285
   
                         teleportation		0.616797
   
                               discord		0.613752
   
                               entropy		0.612341
   
                             bipartite		0.608034
   
                             coherence		0.606859
   
                           nonlocality		0.601337

3. forgetful

   Word: forgetful  Position in vocabulary: 11740
   
                                 Word       Cosine distance
   
   ---------------------------------------------------------
   
                               functor		0.723472
   
                             functors		0.656184
   
                             morphism		0.598965

4. eigenvalue

   Word: eigenvalue  Position in vocabulary: 1448
   
                                 Word       Cosine distance
   
   ---------------------------------------------------------
   
                           eigenvalues		0.893073
   
                           eigenvector		0.768380
   
                         eigenvectors		0.765241
   
                         eigenfunction		0.754222
   
                       eigenfunctions		0.686141
   
                           eigenspace		0.666098
   
                                 eigen		0.641422
   
                               matrix		0.616723
   
                             eigenmode		0.613117
   
                           eigenstate		0.612188
   
                             laplacian		0.611396
   
                               largest		0.606122
   
                             smallest		0.605342
   
                           eigenmodes		0.604839
   

5. riemannian

   Word: riemannian  Position in vocabulary: 2285
   
                                 Word       Cosine distance
   
   ---------------------------------------------------------
   
                             manifolds		0.765827
   
                             manifold		0.760806
   
                               metric		0.719817
   
                               finsler		0.687826
   
                             curvature		0.676100
   
                                 ricci		0.664770
   
                               metrics		0.660804
   
                           riemmanian		0.651666
   
                             euclidean		0.644686
   
                           noncompact		0.643878
   
                           conformally		0.638984
   
                             riemanian		0.633814
   
                               kahler		0.632680
   
                               endowed		0.622035
   
                           submanifold		0.613868
   
                         submanifolds		0.612716
   
                             geodesic		0.604488