From 2e285f9b6d2675a6491988084367454b52448385 Mon Sep 17 00:00:00 2001 From: Mars Ultor Date: Tue, 29 Apr 2025 20:55:20 -0500 Subject: [PATCH] 1412 words god save me --- EEMLA.aux | 21 +- EEMLA.bbl | 102 ++++++- EEMLA.bcf | 25 +- EEMLA.blg | 34 +-- EEMLA.log | 729 ++++++++++++++++++++++++++--------------------- EEMLA.pdf | Bin 110014 -> 116835 bytes EEMLA.synctex.gz | Bin 25020 -> 0 bytes EEMLA.tex | 40 +++ compile.sh | 2 + references.bib | 9 + 10 files changed, 607 insertions(+), 355 deletions(-) delete mode 100644 EEMLA.synctex.gz create mode 100644 compile.sh diff --git a/EEMLA.aux b/EEMLA.aux index 80f113e..a48c08f 100644 --- a/EEMLA.aux +++ b/EEMLA.aux @@ -1,5 +1,5 @@ \relax -\abx@aux@refcontext{nty/global//global/global} +\abx@aux@refcontext{nty/global//global/global/global} \abx@aux@cite{0}{app14020744} \abx@aux@segm{0}{0}{app14020744} \abx@aux@cite{0}{Wang2024} @@ -16,10 +16,15 @@ \abx@aux@segm{0}{0}{hoffmann2022trainingcomputeoptimallargelanguage} \abx@aux@cite{0}{hoffmann2022trainingcomputeoptimallargelanguage} \abx@aux@segm{0}{0}{hoffmann2022trainingcomputeoptimallargelanguage} -\abx@aux@read@bbl@mdfivesum{117EB34AA21A650891B593351C04032D} -\abx@aux@defaultrefcontext{0}{hoffmann2022trainingcomputeoptimallargelanguage}{nty/global//global/global} -\abx@aux@defaultrefcontext{0}{ivanov2024}{nty/global//global/global} -\abx@aux@defaultrefcontext{0}{app14020744}{nty/global//global/global} -\abx@aux@defaultrefcontext{0}{vaswani2023attentionneed}{nty/global//global/global} -\abx@aux@defaultrefcontext{0}{Wang2024}{nty/global//global/global} -\gdef \@abspage@last{5} +\abx@aux@cite{0}{hendrycks2021measuringmathematicalproblemsolving} +\abx@aux@segm{0}{0}{hendrycks2021measuringmathematicalproblemsolving} +\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Comparison of LLM Sizes and Their Computational Requirements}}{5}{}\protected@file@percent } +\newlabel{tab:model-sizes}{{1}{5}{}{table.1}{}} +\abx@aux@read@bbl@mdfivesum{C2B7A906B5BBD5BA46851A4078C3BC58} +\abx@aux@defaultrefcontext{0}{hendrycks2021measuringmathematicalproblemsolving}{nty/global//global/global/global} +\abx@aux@defaultrefcontext{0}{hoffmann2022trainingcomputeoptimallargelanguage}{nty/global//global/global/global} +\abx@aux@defaultrefcontext{0}{ivanov2024}{nty/global//global/global/global} +\abx@aux@defaultrefcontext{0}{app14020744}{nty/global//global/global/global} +\abx@aux@defaultrefcontext{0}{vaswani2023attentionneed}{nty/global//global/global/global} +\abx@aux@defaultrefcontext{0}{Wang2024}{nty/global//global/global/global} +\gdef \@abspage@last{7} diff --git a/EEMLA.bbl b/EEMLA.bbl index 6112ca9..5ebcdd0 100644 --- a/EEMLA.bbl +++ b/EEMLA.bbl @@ -1,5 +1,5 @@ % $ biblatex auxiliary file $ -% $ biblatex bbl format version 3.2 $ +% $ biblatex bbl format version 3.3 $ % Do not modify the above lines! % % This is an auxiliary file used by the 'biblatex' package. @@ -18,8 +18,86 @@ \refsection{0} - \datalist[entry]{nty/global//global/global} - \entry{hoffmann2022trainingcomputeoptimallargelanguage}{misc}{} + \datalist[entry]{nty/global//global/global/global} + \entry{hendrycks2021measuringmathematicalproblemsolving}{misc}{}{} + \name{author}{8}{}{% + {{un=0,uniquepart=base,hash=86d0b4ecd6b6066d49e7aecde6e5e630}{% + family={Hendrycks}, + familyi={H\bibinitperiod}, + given={Dan}, + giveni={D\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=624605ebd8b6b403b251522e3d1029ff}{% + family={Burns}, + familyi={B\bibinitperiod}, + given={Collin}, + giveni={C\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=ae50339c3e9c1418ade64e74fa002ef5}{% + family={Kadavath}, + familyi={K\bibinitperiod}, + given={Saurav}, + giveni={S\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=a3e8b92acb1bf8b2b186f6b10d4ae704}{% + family={Arora}, + familyi={A\bibinitperiod}, + given={Akul}, + giveni={A\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=35f72302a7aebfd095414ce218b8fb5d}{% + family={Basart}, + familyi={B\bibinitperiod}, + given={Steven}, + giveni={S\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=ffd1907ef0a8bbed89fa04d783f236b6}{% + family={Tang}, + familyi={T\bibinitperiod}, + given={Eric}, + giveni={E\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=d458d5f9b64652055bd81d57e4777b22}{% + family={Song}, + familyi={S\bibinitperiod}, + given={Dawn}, + giveni={D\bibinitperiod}, + givenun=0}}% + {{un=0,uniquepart=base,hash=fe7a7e80c1857d185d3ab01f15fe584d}{% + family={Steinhardt}, + familyi={S\bibinitperiod}, + given={Jacob}, + giveni={J\bibinitperiod}, + givenun=0}}% + } + \strng{namehash}{f461c117afa272374439d2db3ee67282} + \strng{fullhash}{821f0c67ea3dbc37f0422b8c2bda174e} + \strng{fullhashraw}{821f0c67ea3dbc37f0422b8c2bda174e} + \strng{bibnamehash}{f461c117afa272374439d2db3ee67282} + \strng{authorbibnamehash}{f461c117afa272374439d2db3ee67282} + \strng{authornamehash}{f461c117afa272374439d2db3ee67282} + \strng{authorfullhash}{821f0c67ea3dbc37f0422b8c2bda174e} + \strng{authorfullhashraw}{821f0c67ea3dbc37f0422b8c2bda174e} + \field{sortinit}{H} + \field{sortinithash}{23a3aa7c24e56cfa16945d55545109b5} + \true{singletitle} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{eprintclass}{cs.LG} + \field{eprinttype}{arXiv} + \field{title}{Measuring Mathematical Problem Solving With the MATH Dataset} + \field{year}{2021} + \verb{eprint} + \verb 2103.03874 + \endverb + \verb{urlraw} + \verb arxiv.org/abs/2103.03874 + \endverb + \verb{url} + \verb arxiv.org/abs/2103.03874 + \endverb + \endentry + \entry{hoffmann2022trainingcomputeoptimallargelanguage}{misc}{}{} \name{author}{22}{}{% {{un=0,uniquepart=base,hash=92d226c4ea870c0e9df2ceb8bf03d8ff}{% family={Hoffmann}, @@ -160,10 +238,12 @@ } \strng{namehash}{8be79936575bb0d5b77c96da6d2a6d52} \strng{fullhash}{fb6d92421541c28738787855a47da527} + \strng{fullhashraw}{fb6d92421541c28738787855a47da527} \strng{bibnamehash}{8be79936575bb0d5b77c96da6d2a6d52} \strng{authorbibnamehash}{8be79936575bb0d5b77c96da6d2a6d52} \strng{authornamehash}{8be79936575bb0d5b77c96da6d2a6d52} \strng{authorfullhash}{fb6d92421541c28738787855a47da527} + \strng{authorfullhashraw}{fb6d92421541c28738787855a47da527} \field{sortinit}{H} \field{sortinithash}{23a3aa7c24e56cfa16945d55545109b5} \true{singletitle} @@ -183,7 +263,7 @@ \verb arxiv.org/abs/2203.15556 \endverb \endentry - \entry{ivanov2024}{misc}{} + \entry{ivanov2024}{misc}{}{} \name{author}{2}{}{% {{un=0,uniquepart=base,hash=1935b6f0043d4bac823842ff5d478faf}{% family={Ivanov}, @@ -200,10 +280,12 @@ } \strng{namehash}{259e51507bbcab245b7267c088c1998f} \strng{fullhash}{259e51507bbcab245b7267c088c1998f} + \strng{fullhashraw}{259e51507bbcab245b7267c088c1998f} \strng{bibnamehash}{259e51507bbcab245b7267c088c1998f} \strng{authorbibnamehash}{259e51507bbcab245b7267c088c1998f} \strng{authornamehash}{259e51507bbcab245b7267c088c1998f} \strng{authorfullhash}{259e51507bbcab245b7267c088c1998f} + \strng{authorfullhashraw}{259e51507bbcab245b7267c088c1998f} \field{sortinit}{I} \field{sortinithash}{8d291c51ee89b6cd86bf5379f0b151d8} \true{singletitle} @@ -223,7 +305,7 @@ \verb arxiv.org/abs/2412.01020 \endverb \endentry - \entry{app14020744}{article}{} + \entry{app14020744}{article}{}{} \name{author}{1}{}{% {{un=0,uniquepart=base,hash=d8c43e5429158fe51408ffa847a4a856}{% family={Testolin}, @@ -234,10 +316,12 @@ } \strng{namehash}{d8c43e5429158fe51408ffa847a4a856} \strng{fullhash}{d8c43e5429158fe51408ffa847a4a856} + \strng{fullhashraw}{d8c43e5429158fe51408ffa847a4a856} \strng{bibnamehash}{d8c43e5429158fe51408ffa847a4a856} \strng{authorbibnamehash}{d8c43e5429158fe51408ffa847a4a856} \strng{authornamehash}{d8c43e5429158fe51408ffa847a4a856} \strng{authorfullhash}{d8c43e5429158fe51408ffa847a4a856} + \strng{authorfullhashraw}{d8c43e5429158fe51408ffa847a4a856} \field{sortinit}{T} \field{sortinithash}{9af77f0292593c26bde9a56e688eaee9} \true{singletitle} @@ -254,7 +338,7 @@ \verb 10.3390/app14020744 \endverb \endentry - \entry{vaswani2023attentionneed}{misc}{} + \entry{vaswani2023attentionneed}{misc}{}{} \name{author}{8}{}{% {{un=0,uniquepart=base,hash=7f28e84700536646dd6620a0db07ad09}{% family={Vaswani}, @@ -307,10 +391,12 @@ } \strng{namehash}{ee273ab30cfb889666f8c4d806eb9ce7} \strng{fullhash}{f82970bbd2bdd7a002d2af62b743d5cc} + \strng{fullhashraw}{f82970bbd2bdd7a002d2af62b743d5cc} \strng{bibnamehash}{ee273ab30cfb889666f8c4d806eb9ce7} \strng{authorbibnamehash}{ee273ab30cfb889666f8c4d806eb9ce7} \strng{authornamehash}{ee273ab30cfb889666f8c4d806eb9ce7} \strng{authorfullhash}{f82970bbd2bdd7a002d2af62b743d5cc} + \strng{authorfullhashraw}{f82970bbd2bdd7a002d2af62b743d5cc} \field{sortinit}{V} \field{sortinithash}{afb52128e5b4dc4b843768c0113d673b} \true{singletitle} @@ -330,7 +416,7 @@ \verb arxiv.org/abs/1706.03762 \endverb \endentry - \entry{Wang2024}{article}{} + \entry{Wang2024}{article}{}{} \name{author}{6}{}{% {{un=0,uniquepart=base,hash=7cca10cee48e9c197439e4af610acfe5}{% family={Wang}, @@ -371,10 +457,12 @@ } \strng{namehash}{1c3e58e991d8f7a6ae5aee1e95c5cd8a} \strng{fullhash}{391aec39c1c26e8d5e7517c1ab227456} + \strng{fullhashraw}{391aec39c1c26e8d5e7517c1ab227456} \strng{bibnamehash}{1c3e58e991d8f7a6ae5aee1e95c5cd8a} \strng{authorbibnamehash}{1c3e58e991d8f7a6ae5aee1e95c5cd8a} \strng{authornamehash}{1c3e58e991d8f7a6ae5aee1e95c5cd8a} \strng{authorfullhash}{391aec39c1c26e8d5e7517c1ab227456} + \strng{authorfullhashraw}{391aec39c1c26e8d5e7517c1ab227456} \field{sortinit}{W} \field{sortinithash}{4315d78024d0cea9b57a0c6f0e35ed0d} \true{singletitle} diff --git a/EEMLA.bcf b/EEMLA.bcf index cba5d30..ff8c5b3 100644 --- a/EEMLA.bcf +++ b/EEMLA.bcf @@ -1,5 +1,5 @@ - + @@ -717,6 +717,7 @@ inheritance translit uniquenametemplate + namehashtemplate sortingnamekeytemplate sortingtemplate extradatespec @@ -977,9 +978,10 @@ noinherit - nametemplates + nametemplates labelalphanametemplatename uniquenametemplatename + namehashtemplatename sortingnamekeytemplatename presort indexing @@ -1065,9 +1067,10 @@ minalphanames - nametemplates + nametemplates labelalphanametemplatename uniquenametemplatename + namehashtemplatename sortingnamekeytemplatename uniquelist uniquename @@ -1081,9 +1084,10 @@ useprefix - nametemplates + nametemplates labelalphanametemplatename uniquenametemplatename + namehashtemplatename sortingnamekeytemplatename uniquename familyinits @@ -1419,6 +1423,13 @@ family given + + + family + given + prefix + suffix + @@ -2772,6 +2783,7 @@ ivanov2024 hoffmann2022trainingcomputeoptimallargelanguage hoffmann2022trainingcomputeoptimallargelanguage + hendrycks2021measuringmathematicalproblemsolving @@ -2804,12 +2816,13 @@ + labelalphanametemplatename="global" + namehashtemplatename="global"> diff --git a/EEMLA.blg b/EEMLA.blg index bacd07f..a482253 100644 --- a/EEMLA.blg +++ b/EEMLA.blg @@ -1,17 +1,17 @@ -[0] Config.pm:307> INFO - This is Biber 2.19 -[0] Config.pm:310> INFO - Logfile is 'EEMLA.blg' -[38] biber:340> INFO - === Fri Feb 28, 2025, 03:09:32 -[47] Biber.pm:419> INFO - Reading 'EEMLA.bcf' -[81] Biber.pm:979> INFO - Found 5 citekeys in bib section 0 -[89] Biber.pm:4419> INFO - Processing section 0 -[95] Biber.pm:4610> INFO - Looking for bibtex file 'references.bib' for section 0 -[96] bibtex.pm:1713> INFO - LaTeX decoding ... -[98] bibtex.pm:1519> INFO - Found BibTeX data source 'references.bib' -[147] UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'variable = shifted' with 'variable = non-ignorable' -[147] UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'normalization = NFD' with 'normalization = prenormalized' -[147] Biber.pm:4239> INFO - Sorting list 'nty/global//global/global' of type 'entry' with template 'nty' and locale 'en-US' -[147] Biber.pm:4245> INFO - No sort tailoring available for locale 'en-US' -[151] bbl.pm:660> INFO - Writing 'EEMLA.bbl' with encoding 'UTF-8' -[153] bbl.pm:763> INFO - Output to EEMLA.bbl -[158] Biber.pm:131> WARN - legacy month field 'Oct' in entry 'Wang2024' is not an integer - this will probably not sort properly. -[158] Biber.pm:133> INFO - WARNINGS: 1 +[0] Config.pm:308> INFO - This is Biber 2.20 +[0] Config.pm:311> INFO - Logfile is 'EEMLA.blg' +[41] biber:340> INFO - === Tue Apr 29, 2025, 20:53:51 +[49] Biber.pm:420> INFO - Reading 'EEMLA.bcf' +[85] Biber.pm:994> INFO - Found 6 citekeys in bib section 0 +[93] Biber.pm:4463> INFO - Processing section 0 +[98] Biber.pm:4654> INFO - Looking for bibtex file 'references.bib' for section 0 +[98] bibtex.pm:1713> INFO - LaTeX decoding ... +[102] bibtex.pm:1519> INFO - Found BibTeX data source 'references.bib' +[160] UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'variable = shifted' with 'variable = non-ignorable' +[160] UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'normalization = NFD' with 'normalization = prenormalized' +[160] Biber.pm:4283> INFO - Sorting list 'nty/global//global/global/global' of type 'entry' with template 'nty' and locale 'en-US' +[160] Biber.pm:4289> INFO - No sort tailoring available for locale 'en-US' +[165] bbl.pm:676> INFO - Writing 'EEMLA.bbl' with encoding 'UTF-8' +[168] bbl.pm:779> INFO - Output to EEMLA.bbl +[169] Biber.pm:131> WARN - legacy month field 'Oct' in entry 'Wang2024' is not an integer - this will probably not sort properly. +[169] Biber.pm:133> INFO - WARNINGS: 1 diff --git a/EEMLA.log b/EEMLA.log index f7e9598..ae6c857 100644 --- a/EEMLA.log +++ b/EEMLA.log @@ -1,281 +1,307 @@ -This is pdfTeX, Version 3.141592653-2.6-1.40.26 (TeX Live 2024/Arch Linux) (preloaded format=pdflatex 2025.2.20) 28 FEB 2025 03:13 +This is pdfTeX, Version 3.141592653-2.6-1.40.27 (TeX Live 2026/dev/Arch Linux) (preloaded format=pdflatex 2025.3.24) 29 APR 2025 20:53 entering extended mode restricted \write18 enabled. - file:line:error style messages enabled. %&-line parsing enabled. **EEMLA.tex (./EEMLA.tex -LaTeX2e <2023-11-01> patch level 1 -L3 programming layer <2024-02-20> +LaTeX2e <2024-11-01> patch level 2 +L3 programming layer <2025-01-18> (/usr/share/texmf-dist/tex/latex/base/article.cls -Document Class: article 2023/05/17 v1.4n Standard LaTeX document class +Document Class: article 2024/06/29 v1.4n Standard LaTeX document class (/usr/share/texmf-dist/tex/latex/base/size12.clo -File: size12.clo 2023/05/17 v1.4n Standard LaTeX file (size option) +File: size12.clo 2024/06/29 v1.4n Standard LaTeX file (size option) ) -\c@part=\count188 -\c@section=\count189 -\c@subsection=\count190 -\c@subsubsection=\count191 -\c@paragraph=\count192 -\c@subparagraph=\count193 -\c@figure=\count194 -\c@table=\count195 -\abovecaptionskip=\skip48 -\belowcaptionskip=\skip49 -\bibindent=\dimen140 -) (/usr/share/texmf-dist/tex/latex/geometry/geometry.sty +\c@part=\count196 +\c@section=\count197 +\c@subsection=\count198 +\c@subsubsection=\count199 +\c@paragraph=\count266 +\c@subparagraph=\count267 +\c@figure=\count268 +\c@table=\count269 +\abovecaptionskip=\skip49 +\belowcaptionskip=\skip50 +\bibindent=\dimen141 +) +(/usr/share/texmf-dist/tex/latex/geometry/geometry.sty Package: geometry 2020/01/02 v5.9 Page Geometry - 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File: english-mla.lbx 2022/02/22 v2.1a biblatex style localization Package biblatex Info: Trying to load language 'english'... Package biblatex Info: ... file 'english.lbx' found. - (/usr/share/texmf-dist/tex/latex/biblatex/lbx/english.lbx -File: english.lbx 2023/03/05 v3.19 biblatex localization (PK/MW) + +(/usr/share/texmf-dist/tex/latex/biblatex/lbx/english.lbx +File: english.lbx 2024/03/21 v3.20 biblatex localization (PK/MW) ) Package biblatex Info: Trying to load language 'english'... Package biblatex Info: ... file 'english.lbx' found. - (/usr/share/texmf-dist/tex/latex/biblatex/lbx/english.lbx -File: english.lbx 2023/03/05 v3.19 biblatex localization (PK/MW) + +(/usr/share/texmf-dist/tex/latex/biblatex/lbx/english.lbx +File: english.lbx 2024/03/21 v3.20 biblatex localization (PK/MW) )) Package biblatex Info: Input encoding 'utf8' detected. Package biblatex Info: Automatic encoding selection. @@ -430,97 +490,132 @@ Package biblatex Info: Automatic encoding selection. Package biblatex Info: Trying to load bibliographic data... Package biblatex Info: ... file 'EEMLA.bbl' found. 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[2] + Package fancyhdr Warning: \headheight is too small (12.0pt): (fancyhdr) Make it at least 14.49998pt, for example: (fancyhdr) \setlength{\headheight}{14.49998pt}. -(fancyhdr) You might also make \topmargin smaller to compensate: +(fancyhdr) You might also make \topmargin smaller: (fancyhdr) \addtolength{\topmargin}{-2.49998pt}. [3] + Package fancyhdr Warning: \headheight is too small (12.0pt): (fancyhdr) Make it at least 14.49998pt, for example: (fancyhdr) \setlength{\headheight}{14.49998pt}. -(fancyhdr) You might also make \topmargin smaller to compensate: +(fancyhdr) You might also make \topmargin smaller: (fancyhdr) \addtolength{\topmargin}{-2.49998pt}. [4] + Package fancyhdr Warning: \headheight is too small (12.0pt): (fancyhdr) Make it at least 14.49998pt, for example: (fancyhdr) \setlength{\headheight}{14.49998pt}. -(fancyhdr) You might also make \topmargin smaller to compensate: +(fancyhdr) You might also make \topmargin smaller: (fancyhdr) \addtolength{\topmargin}{-2.49998pt}. -[5] (./EEMLA.aux) +[5] + + +Package fancyhdr Warning: \headheight is too small (12.0pt): +(fancyhdr) Make it at least 14.49998pt, for example: +(fancyhdr) \setlength{\headheight}{14.49998pt}. +(fancyhdr) You might also make \topmargin smaller: +(fancyhdr) \addtolength{\topmargin}{-2.49998pt}. + +[6] + + +Package fancyhdr Warning: \headheight is too small (12.0pt): +(fancyhdr) Make it at least 14.49998pt, for example: +(fancyhdr) \setlength{\headheight}{14.49998pt}. +(fancyhdr) You might also make \topmargin smaller: +(fancyhdr) \addtolength{\topmargin}{-2.49998pt}. + +[7] (./EEMLA.aux) *********** -LaTeX2e <2023-11-01> patch level 1 -L3 programming layer <2024-02-20> +LaTeX2e <2024-11-01> patch level 2 +L3 programming layer <2025-01-18> *********** Package logreq Info: Writing requests to 'EEMLA.run.xml'. \openout1 = `EEMLA.run.xml'. ) Here is how much of TeX's memory you used: - 10817 strings out of 476076 - 206378 string characters out of 5793775 - 1933187 words of memory out of 5000000 - 32829 multiletter control sequences out of 15000+600000 - 566628 words of font info for 54 fonts, out of 8000000 for 9000 + 11293 strings out of 475171 + 216231 string characters out of 5767095 + 1100995 words of memory out of 5000000 + 34187 multiletter control sequences out of 15000+600000 + 568981 words of font info for 56 fonts, out of 8000000 for 9000 14 hyphenation exceptions out of 8191 - 72i,11n,81p,1313b,2647s stack positions out of 10000i,1000n,20000p,200000b,200000s - -Output written on EEMLA.pdf (5 pages, 110014 bytes). + 72i,11n,81p,1320b,2647s stack positions out of 10000i,1000n,20000p,200000b,200000s + +Output written on EEMLA.pdf (7 pages, 116835 bytes). 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@@ \usepackage{times} \geometry{top=1.0in, bottom=1.0in, left=1.0in, right=1.0in} \usepackage[style=mla,backend=biber]{biblatex} +\usepackage{comment} % %Doublespacing @@ -24,6 +25,7 @@ %Fancy-header package to modify header/page numbering (insert last name) % \usepackage{fancyhdr} +\usepackage{float} \pagestyle{fancy} \lhead{} \chead{} @@ -102,6 +104,44 @@ Benchmarks for evaluating Large Language Models (LLMs) assess their performance Adding to the complexity of creating increasingly more performant are the computational and capital costs of building AI-capable supercomputers, clusters, and data centers for corpora, or CLM text databases. Improvements in model architecture are sought before attempts to increase the scale of models and their parameter counts because of the prohibitive scaling laws of neural networks. Experimentally, it has been found that increased parameter size has an exponential relationship with FLOPs of computational cost \parencite[2]{hoffmann2022trainingcomputeoptimallargelanguage}. This is seen in relation to the exponentially slowing gain in CLM accuracy with increased compute \parencite[5]{hoffmann2022trainingcomputeoptimallargelanguage}. This is taken to mean that there is a point at which scaling a model to gain accuracy is unsustainable. The Chinchilla scaling law is an experimentally conjectured hypothesis which states that an increase in model scale for a given architecture will tend to reducing model performance as the number of parameters tends to infinity. Although some teams claim to have statistically significant results to disprove it, these results have not been reaffirmed by third parties. +{\raggedright \normalsize \textbf{Problem Statement}} +\begin{table}[H] +\centering +\caption{Comparison of LLM Sizes and Their Computational Requirements} +\label{tab:model-sizes} +\begin{tabular}{|l|r|r|r|r|} +\hline +\textbf{Model Name} & \textbf{Parameters} & \textbf{Training Compute} & \textbf{Inference Time} & \textbf{Memory Usage} \\ + & \textbf{(billions)} & \textbf{(PF-days)} & \textbf{(ms/token)} & \textbf{(GB)} \\ +\hline +GPT-2 & 1.5 & 5.6 & 12 & 3 \\ +\hline +GPT-3 & 175 & 3,640 & 75 & 350 \\ +\hline +Llama-2-7B & 7 & 184 & 18 & 14 \\ +\hline +Llama-2-13B & 13 & 368 & 32 & 26 \\ +\hline +Llama-2-70B & 70 & 1,720 & 145 & 140 \\ +\hline +Claude 2 & $\sim$100 & N/A & 82 & $\sim$200 \\ +\hline +GPT-4 & $\sim$1,500 & $\sim$25,000 & 210 & $\sim$3,000 \\ +\hline +\end{tabular} +\begin{flushleft} +\small{Note: Training compute is measured in petaflop-days. Inference time is measured for a single A100 GPU. Memory usage refers to the VRAM required during inference. Some values for proprietary models are estimated based on public information.} +\end{flushleft} +\end{table} + + +Despite the aforementioned significant advancements in LLMs and their increasingly large reasoning capabilities over time as seen in Figure \ref{tab:model-sizes}, the mathematical capabilities of models have increased in a sub-linear fashion. This also correlates with the decreasing performance as model sizes, even within the same generation, scale up. For example, Figure \ref{tab:model-sizes} displays the Llama-2 generation over 3 different sizes. Current LLMs approach mathematical operations through pattern recognition learned from their training data rather than through formal algorithmic processing, resulting in inconsistent performance when handling numerical calculations beyond simple arithmetic \parencite[3]{hendrycks2021measuringmathematicalproblemsolving}. + +This research aims to investigate the potential integration of rule-based tensor mutations within an existing LLM architecture as a mechanism to enable low-cost, rule-driven (as opposed to pattern driven) mathematical computation. The intended outcome of the experiment detailed below include an increase in mathematical accuracy and a decrease in the Inference Time for prompts with necessary mathematical computation associated. + +\begin{quote} + \textbf{RQ:} How can deterministic rule-based tensor mutations be embedded within LLM architectures to enable more accurate and efficient mathematical operations? +\end{quote} %%%%Works cited \newpage diff --git a/compile.sh b/compile.sh new file mode 100644 index 0000000..94171a2 --- /dev/null +++ b/compile.sh @@ -0,0 +1,2 @@ +biber EEMLA +pdflatex EEMLA.tex diff --git a/references.bib b/references.bib index c0d02b1..c58cd5a 100644 --- a/references.bib +++ b/references.bib @@ -41,3 +41,12 @@ DOI = {10.3390/app14020744} primaryClass={cs.CL}, url={https://arxiv.org/abs/2203.15556}, } +@misc{hendrycks2021measuringmathematicalproblemsolving, + title={Measuring Mathematical Problem Solving With the MATH Dataset}, + author={Dan Hendrycks and Collin Burns and Saurav Kadavath and Akul Arora and Steven Basart and Eric Tang and Dawn Song and Jacob Steinhardt}, + year={2021}, + eprint={2103.03874}, + archivePrefix={arXiv}, + primaryClass={cs.LG}, + url={https://arxiv.org/abs/2103.03874}, +}