Implemented a first verion of the text #7
@ -13,4 +13,14 @@ jobs:
|
|||||||
steps:
|
steps:
|
||||||
- name: Checkout
|
- name: Checkout
|
||||||
uses: actions/checkout@v3
|
uses: actions/checkout@v3
|
||||||
- run: pdflatex conference_101719.tex
|
- name: Compile
|
||||||
|
run: |
|
||||||
|
pdflatex pal-vorstellung.tex
|
||||||
|
biber pal-vorstellung
|
||||||
|
pdflatex pal-vorstellung.tex
|
||||||
|
pdflatex pal-vorstellung.tex
|
||||||
|
pdflatex pal-vorstellung.tex
|
||||||
|
- uses: actions/upload-artifact@v3
|
||||||
|
with:
|
||||||
|
path: pal-vorstellung.pdf
|
||||||
|
name: pal-vorstellung
|
||||||
|
|||||||
305
.gitignore
vendored
305
.gitignore
vendored
@ -164,13 +164,6 @@ cython_debug/
|
|||||||
# gitignore template for Jupyter Notebooks
|
# gitignore template for Jupyter Notebooks
|
||||||
# website: http://jupyter.org/
|
# website: http://jupyter.org/
|
||||||
|
|
||||||
.ipynb_checkpoints
|
|
||||||
*/.ipynb_checkpoints/*
|
|
||||||
|
|
||||||
# IPython
|
|
||||||
profile_default/
|
|
||||||
ipython_config.py
|
|
||||||
|
|
||||||
# Remove previous ipynb_checkpoints
|
# Remove previous ipynb_checkpoints
|
||||||
# git rm -r .ipynb_checkpoints/
|
# git rm -r .ipynb_checkpoints/
|
||||||
|
|
||||||
@ -178,7 +171,6 @@ ipython_config.py
|
|||||||
## Core latex/pdflatex auxiliary files:
|
## Core latex/pdflatex auxiliary files:
|
||||||
*.aux
|
*.aux
|
||||||
*.lof
|
*.lof
|
||||||
*.log
|
|
||||||
*.lot
|
*.lot
|
||||||
*.fls
|
*.fls
|
||||||
*.out
|
*.out
|
||||||
@ -480,7 +472,6 @@ TSWLatexianTemp*
|
|||||||
### Text template
|
### Text template
|
||||||
*.doc
|
*.doc
|
||||||
*.docx
|
*.docx
|
||||||
*.log
|
|
||||||
*.msg
|
*.msg
|
||||||
*.pages
|
*.pages
|
||||||
*.rtf
|
*.rtf
|
||||||
@ -490,301 +481,6 @@ TSWLatexianTemp*
|
|||||||
|
|
||||||
### LaTeX template
|
### LaTeX template
|
||||||
## Core latex/pdflatex auxiliary files:
|
## Core latex/pdflatex auxiliary files:
|
||||||
*.aux
|
|
||||||
*.lof
|
|
||||||
*.log
|
|
||||||
*.lot
|
|
||||||
*.fls
|
|
||||||
*.out
|
|
||||||
*.toc
|
|
||||||
*.fmt
|
|
||||||
*.fot
|
|
||||||
*.cb
|
|
||||||
*.cb2
|
|
||||||
.*.lb
|
|
||||||
|
|
||||||
## Intermediate documents:
|
|
||||||
*.dvi
|
|
||||||
*.xdv
|
|
||||||
*-converted-to.*
|
|
||||||
# these rules might exclude image files for figures etc.
|
|
||||||
# *.ps
|
|
||||||
# *.eps
|
|
||||||
# *.pdf
|
|
||||||
|
|
||||||
## Generated if empty string is given at "Please type another file name for output:"
|
|
||||||
.pdf
|
|
||||||
|
|
||||||
## Bibliography auxiliary files (bibtex/biblatex/biber):
|
|
||||||
*.bbl
|
|
||||||
*.bcf
|
|
||||||
*.blg
|
|
||||||
*-blx.aux
|
|
||||||
*-blx.bib
|
|
||||||
*.run.xml
|
|
||||||
|
|
||||||
## Build tool auxiliary files:
|
|
||||||
*.fdb_latexmk
|
|
||||||
*.synctex
|
|
||||||
*.synctex(busy)
|
|
||||||
*.synctex.gz
|
|
||||||
*.synctex.gz(busy)
|
|
||||||
*.pdfsync
|
|
||||||
|
|
||||||
## Build tool directories for auxiliary files
|
|
||||||
# latexrun
|
|
||||||
latex.out/
|
|
||||||
|
|
||||||
## Auxiliary and intermediate files from other packages:
|
|
||||||
# algorithms
|
|
||||||
*.alg
|
|
||||||
*.loa
|
|
||||||
|
|
||||||
# achemso
|
|
||||||
acs-*.bib
|
|
||||||
|
|
||||||
# amsthm
|
|
||||||
*.thm
|
|
||||||
|
|
||||||
# beamer
|
|
||||||
*.nav
|
|
||||||
*.pre
|
|
||||||
*.snm
|
|
||||||
*.vrb
|
|
||||||
|
|
||||||
# changes
|
|
||||||
*.soc
|
|
||||||
|
|
||||||
# comment
|
|
||||||
*.cut
|
|
||||||
|
|
||||||
# cprotect
|
|
||||||
*.cpt
|
|
||||||
|
|
||||||
# elsarticle (documentclass of Elsevier journals)
|
|
||||||
*.spl
|
|
||||||
|
|
||||||
# endnotes
|
|
||||||
*.ent
|
|
||||||
|
|
||||||
# fixme
|
|
||||||
*.lox
|
|
||||||
|
|
||||||
# feynmf/feynmp
|
|
||||||
*.mf
|
|
||||||
*.mp
|
|
||||||
*.t[1-9]
|
|
||||||
*.t[1-9][0-9]
|
|
||||||
*.tfm
|
|
||||||
|
|
||||||
#(r)(e)ledmac/(r)(e)ledpar
|
|
||||||
*.end
|
|
||||||
*.?end
|
|
||||||
*.[1-9]
|
|
||||||
*.[1-9][0-9]
|
|
||||||
*.[1-9][0-9][0-9]
|
|
||||||
*.[1-9]R
|
|
||||||
*.[1-9][0-9]R
|
|
||||||
*.[1-9][0-9][0-9]R
|
|
||||||
*.eledsec[1-9]
|
|
||||||
*.eledsec[1-9]R
|
|
||||||
*.eledsec[1-9][0-9]
|
|
||||||
*.eledsec[1-9][0-9]R
|
|
||||||
*.eledsec[1-9][0-9][0-9]
|
|
||||||
*.eledsec[1-9][0-9][0-9]R
|
|
||||||
|
|
||||||
# glossaries
|
|
||||||
*.acn
|
|
||||||
*.acr
|
|
||||||
*.glg
|
|
||||||
*.glo
|
|
||||||
*.gls
|
|
||||||
*.glsdefs
|
|
||||||
*.lzo
|
|
||||||
*.lzs
|
|
||||||
*.slg
|
|
||||||
*.slo
|
|
||||||
*.sls
|
|
||||||
|
|
||||||
# uncomment this for glossaries-extra (will ignore makeindex's style files!)
|
|
||||||
# *.ist
|
|
||||||
|
|
||||||
# gnuplot
|
|
||||||
*.gnuplot
|
|
||||||
*.table
|
|
||||||
|
|
||||||
# gnuplottex
|
|
||||||
*-gnuplottex-*
|
|
||||||
|
|
||||||
# gregoriotex
|
|
||||||
*.gaux
|
|
||||||
*.glog
|
|
||||||
*.gtex
|
|
||||||
|
|
||||||
# htlatex
|
|
||||||
*.4ct
|
|
||||||
*.4tc
|
|
||||||
*.idv
|
|
||||||
*.lg
|
|
||||||
*.trc
|
|
||||||
*.xref
|
|
||||||
|
|
||||||
# hyperref
|
|
||||||
*.brf
|
|
||||||
|
|
||||||
# knitr
|
|
||||||
*-concordance.tex
|
|
||||||
# TODO Uncomment the next line if you use knitr and want to ignore its generated tikz files
|
|
||||||
# *.tikz
|
|
||||||
*-tikzDictionary
|
|
||||||
|
|
||||||
# listings
|
|
||||||
*.lol
|
|
||||||
|
|
||||||
# luatexja-ruby
|
|
||||||
*.ltjruby
|
|
||||||
|
|
||||||
# makeidx
|
|
||||||
*.idx
|
|
||||||
*.ilg
|
|
||||||
*.ind
|
|
||||||
|
|
||||||
# minitoc
|
|
||||||
*.maf
|
|
||||||
*.mlf
|
|
||||||
*.mlt
|
|
||||||
*.mtc[0-9]*
|
|
||||||
*.slf[0-9]*
|
|
||||||
*.slt[0-9]*
|
|
||||||
*.stc[0-9]*
|
|
||||||
|
|
||||||
# minted
|
|
||||||
_minted*
|
|
||||||
*.pyg
|
|
||||||
|
|
||||||
# morewrites
|
|
||||||
*.mw
|
|
||||||
|
|
||||||
# newpax
|
|
||||||
*.newpax
|
|
||||||
|
|
||||||
# nomencl
|
|
||||||
*.nlg
|
|
||||||
*.nlo
|
|
||||||
*.nls
|
|
||||||
|
|
||||||
# pax
|
|
||||||
*.pax
|
|
||||||
|
|
||||||
# pdfpcnotes
|
|
||||||
*.pdfpc
|
|
||||||
|
|
||||||
# sagetex
|
|
||||||
*.sagetex.sage
|
|
||||||
*.sagetex.py
|
|
||||||
*.sagetex.scmd
|
|
||||||
|
|
||||||
# scrwfile
|
|
||||||
*.wrt
|
|
||||||
|
|
||||||
# svg
|
|
||||||
svg-inkscape/
|
|
||||||
|
|
||||||
# sympy
|
|
||||||
*.sout
|
|
||||||
*.sympy
|
|
||||||
sympy-plots-for-*.tex/
|
|
||||||
|
|
||||||
# pdfcomment
|
|
||||||
*.upa
|
|
||||||
*.upb
|
|
||||||
|
|
||||||
# pythontex
|
|
||||||
*.pytxcode
|
|
||||||
pythontex-files-*/
|
|
||||||
|
|
||||||
# tcolorbox
|
|
||||||
*.listing
|
|
||||||
|
|
||||||
# thmtools
|
|
||||||
*.loe
|
|
||||||
|
|
||||||
# TikZ & PGF
|
|
||||||
*.dpth
|
|
||||||
*.md5
|
|
||||||
*.auxlock
|
|
||||||
|
|
||||||
# titletoc
|
|
||||||
*.ptc
|
|
||||||
|
|
||||||
# todonotes
|
|
||||||
*.tdo
|
|
||||||
|
|
||||||
# vhistory
|
|
||||||
*.hst
|
|
||||||
*.ver
|
|
||||||
|
|
||||||
# easy-todo
|
|
||||||
*.lod
|
|
||||||
|
|
||||||
# xcolor
|
|
||||||
*.xcp
|
|
||||||
|
|
||||||
# xmpincl
|
|
||||||
*.xmpi
|
|
||||||
|
|
||||||
# xindy
|
|
||||||
*.xdy
|
|
||||||
|
|
||||||
# xypic precompiled matrices and outlines
|
|
||||||
*.xyc
|
|
||||||
*.xyd
|
|
||||||
|
|
||||||
# endfloat
|
|
||||||
*.ttt
|
|
||||||
*.fff
|
|
||||||
|
|
||||||
# Latexian
|
|
||||||
TSWLatexianTemp*
|
|
||||||
|
|
||||||
## Editors:
|
|
||||||
# WinEdt
|
|
||||||
*.bak
|
|
||||||
*.sav
|
|
||||||
|
|
||||||
# Texpad
|
|
||||||
.texpadtmp
|
|
||||||
|
|
||||||
# LyX
|
|
||||||
*.lyx~
|
|
||||||
|
|
||||||
# Kile
|
|
||||||
*.backup
|
|
||||||
|
|
||||||
# gummi
|
|
||||||
.*.swp
|
|
||||||
|
|
||||||
# KBibTeX
|
|
||||||
*~[0-9]*
|
|
||||||
|
|
||||||
# TeXnicCenter
|
|
||||||
*.tps
|
|
||||||
|
|
||||||
# auto folder when using emacs and auctex
|
|
||||||
./auto/*
|
|
||||||
*.el
|
|
||||||
|
|
||||||
# expex forward references with \gathertags
|
|
||||||
*-tags.tex
|
|
||||||
|
|
||||||
# standalone packages
|
|
||||||
*.sta
|
|
||||||
|
|
||||||
# Makeindex log files
|
|
||||||
*.lpz
|
|
||||||
|
|
||||||
# xwatermark package
|
|
||||||
*.xwm
|
|
||||||
|
|
||||||
# REVTeX puts footnotes in the bibliography by default, unless the nofootinbib
|
# REVTeX puts footnotes in the bibliography by default, unless the nofootinbib
|
||||||
# option is specified. Footnotes are the stored in a file with suffix Notes.bib.
|
# option is specified. Footnotes are the stored in a file with suffix Notes.bib.
|
||||||
@ -792,3 +488,4 @@ TSWLatexianTemp*
|
|||||||
#*Notes.bib
|
#*Notes.bib
|
||||||
|
|
||||||
/*.pdf
|
/*.pdf
|
||||||
|
/out/
|
||||||
|
|||||||
3
.idea/.gitignore
generated
vendored
Normal file
3
.idea/.gitignore
generated
vendored
Normal file
@ -0,0 +1,3 @@
|
|||||||
|
# Default ignored files
|
||||||
|
/shelf/
|
||||||
|
/workspace.xml
|
||||||
8
.idea/Konferenzseminar-ML-PAL.iml
generated
Normal file
8
.idea/Konferenzseminar-ML-PAL.iml
generated
Normal file
@ -0,0 +1,8 @@
|
|||||||
|
<?xml version="1.0" encoding="UTF-8"?>
|
||||||
|
<module type="EMPTY_MODULE" version="4">
|
||||||
|
<component name="NewModuleRootManager">
|
||||||
|
<content url="file://$MODULE_DIR$" />
|
||||||
|
<orderEntry type="inheritedJdk" />
|
||||||
|
<orderEntry type="sourceFolder" forTests="false" />
|
||||||
|
</component>
|
||||||
|
</module>
|
||||||
8
.idea/modules.xml
generated
Normal file
8
.idea/modules.xml
generated
Normal file
@ -0,0 +1,8 @@
|
|||||||
|
<?xml version="1.0" encoding="UTF-8"?>
|
||||||
|
<project version="4">
|
||||||
|
<component name="ProjectModuleManager">
|
||||||
|
<modules>
|
||||||
|
<module fileurl="file://$PROJECT_DIR$/.idea/Konferenzseminar-ML-PAL.iml" filepath="$PROJECT_DIR$/.idea/Konferenzseminar-ML-PAL.iml" />
|
||||||
|
</modules>
|
||||||
|
</component>
|
||||||
|
</project>
|
||||||
6
.idea/vcs.xml
generated
Normal file
6
.idea/vcs.xml
generated
Normal file
@ -0,0 +1,6 @@
|
|||||||
|
<?xml version="1.0" encoding="UTF-8"?>
|
||||||
|
<project version="4">
|
||||||
|
<component name="VcsDirectoryMappings">
|
||||||
|
<mapping directory="" vcs="Git" />
|
||||||
|
</component>
|
||||||
|
</project>
|
||||||
@ -47,10 +47,8 @@ repos:
|
|||||||
hooks:
|
hooks:
|
||||||
- id: american-eg-ie
|
- id: american-eg-ie
|
||||||
- id: cleveref-capitalization
|
- id: cleveref-capitalization
|
||||||
- id: consistent-spelling
|
# - id: csquotes
|
||||||
args: [--emph=et al., --emph=a priori, --emph=a posteriori, --regex=naive=\bna(i|\\"i)ve]
|
# - id: ensure-labels-for-sections
|
||||||
- id: csquotes
|
|
||||||
- id: ensure-labels-for-sections
|
|
||||||
- id: no-space-in-cite
|
- id: no-space-in-cite
|
||||||
- id: tilde-cite
|
- id: tilde-cite
|
||||||
- id: unique-labels
|
- id: unique-labels
|
||||||
|
|||||||
64
PAL Example Expanded.drawio
Normal file
64
PAL Example Expanded.drawio
Normal file
@ -0,0 +1,64 @@
|
|||||||
|
<mxfile host="Electron" modified="2023-11-18T18:08:40.966Z" agent="Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) draw.io/21.7.5 Chrome/114.0.5735.289 Electron/25.8.1 Safari/537.36" etag="bgGioe3vAgUXMqkOKeQ4" version="21.7.5" type="device">
|
||||||
|
<diagram name="Seite-1" id="3Sw_KYT27iZ8JMehEK1P">
|
||||||
|
<mxGraphModel dx="1456" dy="734" grid="1" gridSize="10" guides="1" tooltips="1" connect="1" arrows="1" fold="1" page="1" pageScale="1" pageWidth="827" pageHeight="1169" math="0" shadow="0">
|
||||||
|
<root>
|
||||||
|
<mxCell id="0" />
|
||||||
|
<mxCell id="1" parent="0" />
|
||||||
|
<mxCell id="7yxbpYrR7u7Zo4rXAfb2-31" value="<h2><br></h2>" style="rounded=1;whiteSpace=wrap;html=1;labelPosition=center;verticalLabelPosition=top;align=center;verticalAlign=bottom;spacingTop=11;" vertex="1" parent="1">
|
||||||
|
<mxGeometry x="550" y="230" width="270" height="740" as="geometry" />
|
||||||
|
</mxCell>
|
||||||
|
<mxCell id="7yxbpYrR7u7Zo4rXAfb2-32" value="<h2>ChatGPT 4 Example</h2>" style="text;html=1;strokeColor=none;fillColor=none;align=center;verticalAlign=middle;whiteSpace=wrap;rounded=0;" vertex="1" parent="1">
|
||||||
|
<mxGeometry x="580" y="240" width="210" height="30" as="geometry" />
|
||||||
|
</mxCell>
|
||||||
|
<mxCell id="7yxbpYrR7u7Zo4rXAfb2-29" value="<h2><br></h2>" style="rounded=1;whiteSpace=wrap;html=1;labelPosition=center;verticalLabelPosition=top;align=center;verticalAlign=bottom;spacingTop=11;" vertex="1" parent="1">
|
||||||
|
<mxGeometry x="280" y="230" width="270" height="740" as="geometry" />
|
||||||
|
</mxCell>
|
||||||
|
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<mxCell id="7yxbpYrR7u7Zo4rXAfb2-1" value="<b>Q</b>: Roger has 5 tennis balls. He buys 2 more cans of tennis balls. Each can has 3 tennis balls. How many tennis balls does he have now?<br><br><b>A</b>: Roger started with 5 tennis balls. 2 cans of 3 tennis<br>balls each is 6 tennis balls. 5 + 6 = 11. The answer is 11.<br><br><b>Q</b>: The bakers at the Beverly Hills Bakery baked 200 loaves of bread on Monday morning. They sold 93 loaves in the morning and 39 loaves in the afternoon. A grocery<br>store returned 6 unsold loaves. How many loaves of bread did they have left?" style="rounded=1;whiteSpace=wrap;html=1;align=left;spacingTop=0;spacingLeft=10;" vertex="1" parent="1">
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<mxCell id="7yxbpYrR7u7Zo4rXAfb2-8" value="<div><b>Q</b>: Roger has 5 tennis balls. He buys 2 more cans of&nbsp;<span style="background-color: initial;">tennis balls. Each can has 3 tennis balls. How many&nbsp;</span><span style="background-color: initial;">tennis balls does he have now?</span></div><div><br></div><div><b>A</b>:&nbsp;</div><div style="font-size: 10px;"><pre class="python"><i># Roger started with 5 tennis balls.</i><br>tennis_balls <span style="color: #66cc66;">=</span> <span style="color: #ff4500;">5</span><br><span style="color: #808080; font-style: italic;"># 2 cans of 3 tennis balls each is</span><br>bought_balls <span style="color: #66cc66;">=</span> <span style="color: #ff4500;">2</span> * <span style="color: #ff4500;">3</span><br><span style="color: #808080; font-style: italic;"># tennis balls. The answer is</span><br>answer <span style="color: #66cc66;">=</span> tennis_balls + bought_balls</pre></div><div><span style="background-color: initial;"><b>Q</b>: The bakers at the Beverly Hills Bakery baked 200&nbsp;</span><span style="background-color: initial;">loaves of bread on Monday morning. They sold 93 loaves&nbsp;</span><span style="background-color: initial;">in the morning and 39 loaves in the afternoon. A grocery</span></div><div>store returned 6 unsold loaves. How many loaves of bread&nbsp;<span style="background-color: initial;">did they have left?</span></div>" style="rounded=1;whiteSpace=wrap;html=1;align=left;spacingTop=0;spacingLeft=10;" vertex="1" parent="1">
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<mxCell id="7yxbpYrR7u7Zo4rXAfb2-12" value="<b>A</b>: The bakers started with 200 loaves. They sold 93 in<br>the morning and 39 in the afternoon. So they sold 93 +<br>39 = 132 loaves. The grocery store returned 6 loaves. So<br>they had 200 - 132 - 6 = 62 loaves left.<br>The answer is 62." style="rounded=1;whiteSpace=wrap;html=1;align=left;spacingTop=0;spacingLeft=10;fontSize=12;fillColor=#f8cecc;strokeColor=#b85450;" vertex="1" parent="1">
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<mxCell id="7yxbpYrR7u7Zo4rXAfb2-13" value="<div style=""><b>A</b>:&nbsp;<span style="background-color: initial;"><font face="monospace"># The bakers started with 200&nbsp;</font></span></div><div style=""><div style="" class="row mt-2" id="preview"><pre style="" class="python"><font style="font-size: 12px;"># loaves</font></pre><pre style="" class="python"><font style="font-size: 12px;">loaves_baked <span style="color: #66cc66;">=</span> <span style="color: #ff4500;">200</span><br><span style="color: #808080; font-style: italic;"># They sold 93 in the morning <br># and 39 in the afternoon</span><br>loaves_sold_morning <span style="color: #66cc66;">=</span> <span style="color: #ff4500;">93</span><br>loaves_sold_afternoon <span style="color: #66cc66;">=</span> <span style="color: #ff4500;">39</span><br><span style="color: #808080; font-style: italic;"># The grocery store returned <br># 6 loaves.</span><br>loaves_returned <span style="color: #66cc66;">=</span> <span style="color: #ff4500;">6</span><br><span style="color: #808080; font-style: italic;"># The answer is</span><br>answer <span style="color: #66cc66;">=</span> (<br></font> loaves_baked <br> - loaves_sold_morning<br> - loaves_sold_afternoon <br> + loaves_returned<br></pre><pre style="" class="python"><font style="font-size: 12px;"><span style="color: #ff7700;font-weight:bold;">print</span>(answer) <span style="color: #808080; font-style: italic;"># -&gt; 74</span></font></pre></div></div>When the script is executed 74 is printed." style="rounded=1;whiteSpace=wrap;html=1;align=left;spacingTop=0;spacingLeft=10;fontSize=12;fillColor=#d5e8d4;strokeColor=#82b366;" vertex="1" parent="1">
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<mxCell id="7yxbpYrR7u7Zo4rXAfb2-18" value="<div style="font-size: 11px;"><div><font style="font-size: 11px;"><b>A</b>: </font><font style="font-size: 11px;">The Beverly Hills Bakery had 74 loaves of bread left after their sales and the return of unsold loaves. </font><font face="monospace" style="font-size: 11px;"><br></font><span style="background-color: initial;"><b style=""><i>Internal executed Analysis:</i></b></span><font face="monospace" style="font-size: 11px;"><br></font></div></div><div style="font-size: 11px;"><pre class="python"><pre class="python"># Number of loaves baked<br>loaves_baked <span style="color: #66cc66;">=</span> <span style="color: #ff4500;">200</span><br><span style="color: #808080; font-style: italic;"># Number of loaves sold in the </span><br><span style="color: #808080; font-style: italic;"># morning and afternoon</span><br>loaves_sold_morning <span style="color: #66cc66;">=</span> <span style="color: #ff4500;">93</span><br>loaves_sold_afternoon <span style="color: #66cc66;">=</span> <span style="color: #ff4500;">39</span><br><span style="color: #808080; font-style: italic;"># Number of loaves returned </span><br><span style="color: #808080; font-style: italic;"># from the grocery store</span><br>loaves_returned <span style="color: #66cc66;">=</span> <span style="color: #ff4500;">6</span><br><span style="color: #808080; font-style: italic;"># Calculating the remaining loaves</span><br>remaining_loaves <span style="color: #66cc66;">=</span> (<br> loaves_baked<br> - (<br> loaves_sold_morning<br> + loaves_sold_afternoon<br> ) <br> + loaves_returned<br>remaining_loaves</pre></pre></div><div class="flex justify-between empty:hidden gizmo:mt-1 gizmo:justify-start gizmo:gap-3 lg:block gizmo:lg:flex"><div class="text-gray-400 flex self-end lg:self-center justify-center gizmo:lg:justify-start mt-2 gizmo:mt-0 visible gap-1"></div></div>" style="rounded=1;whiteSpace=wrap;html=1;align=left;spacingTop=0;spacingLeft=10;fillColor=#d5e8d4;strokeColor=#82b366;" vertex="1" parent="1">
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\def\BibTeX{{\rm B\kern-.05em{\sc i\kern-.025em b}\kern-.08em
|
|
||||||
T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}}
|
|
||||||
\begin{document}
|
|
||||||
|
|
||||||
\title{Conference Paper Title*\\
|
|
||||||
{\footnotesize \textsuperscript{*}Note: Sub-titles are not captured in Xplore and
|
|
||||||
should not be used}
|
|
||||||
\thanks{Identify applicable funding agency here. If none, delete this.}
|
|
||||||
}
|
|
||||||
|
|
||||||
\author{\IEEEauthorblockN{1\textsuperscript{st} Given Name Surname}
|
|
||||||
\IEEEauthorblockA{\textit{dept. name of organization (of Aff.)} \\
|
|
||||||
\textit{name of organization (of Aff.)}\\
|
|
||||||
City, Country \\
|
|
||||||
email address or ORCID}
|
|
||||||
\and
|
|
||||||
\IEEEauthorblockN{2\textsuperscript{nd} Given Name Surname}
|
|
||||||
\IEEEauthorblockA{\textit{dept. name of organization (of Aff.)} \\
|
|
||||||
\textit{name of organization (of Aff.)}\\
|
|
||||||
City, Country \\
|
|
||||||
email address or ORCID}
|
|
||||||
\and
|
|
||||||
\IEEEauthorblockN{3\textsuperscript{rd} Given Name Surname}
|
|
||||||
\IEEEauthorblockA{\textit{dept. name of organization (of Aff.)} \\
|
|
||||||
\textit{name of organization (of Aff.)}\\
|
|
||||||
City, Country \\
|
|
||||||
email address or ORCID}
|
|
||||||
\and
|
|
||||||
\IEEEauthorblockN{4\textsuperscript{th} Given Name Surname}
|
|
||||||
\IEEEauthorblockA{\textit{dept. name of organization (of Aff.)} \\
|
|
||||||
\textit{name of organization (of Aff.)}\\
|
|
||||||
City, Country \\
|
|
||||||
email address or ORCID}
|
|
||||||
\and
|
|
||||||
\IEEEauthorblockN{5\textsuperscript{th} Given Name Surname}
|
|
||||||
\IEEEauthorblockA{\textit{dept. name of organization (of Aff.)} \\
|
|
||||||
\textit{name of organization (of Aff.)}\\
|
|
||||||
City, Country \\
|
|
||||||
email address or ORCID}
|
|
||||||
\and
|
|
||||||
\IEEEauthorblockN{6\textsuperscript{th} Given Name Surname}
|
|
||||||
\IEEEauthorblockA{\textit{dept. name of organization (of Aff.)} \\
|
|
||||||
\textit{name of organization (of Aff.)}\\
|
|
||||||
City, Country \\
|
|
||||||
email address or ORCID}
|
|
||||||
}
|
|
||||||
|
|
||||||
\maketitle
|
|
||||||
|
|
||||||
\begin{abstract}
|
|
||||||
This document is a model and instructions for \LaTeX.
|
|
||||||
This and the IEEEtran.cls file define the components of your paper [title, text, heads, etc.]. *CRITICAL: Do Not Use Symbols, Special Characters, Footnotes,
|
|
||||||
or Math in Paper Title or Abstract.
|
|
||||||
\end{abstract}
|
|
||||||
|
|
||||||
\begin{IEEEkeywords}
|
|
||||||
component, formatting, style, styling, insert
|
|
||||||
\end{IEEEkeywords}
|
|
||||||
|
|
||||||
\section{Introduction}
|
|
||||||
This document is a model and instructions for \LaTeX.
|
|
||||||
Please observe the conference page limits.
|
|
||||||
|
|
||||||
\section{Ease of Use}
|
|
||||||
|
|
||||||
\subsection{Maintaining the Integrity of the Specifications}
|
|
||||||
|
|
||||||
The IEEEtran class file is used to format your paper and style the text. All margins,
|
|
||||||
column widths, line spaces, and text fonts are prescribed; please do not
|
|
||||||
alter them. You may note peculiarities. For example, the head margin
|
|
||||||
measures proportionately more than is customary. This measurement
|
|
||||||
and others are deliberate, using specifications that anticipate your paper
|
|
||||||
as one part of the entire proceedings, and not as an independent document.
|
|
||||||
Please do not revise any of the current designations.
|
|
||||||
|
|
||||||
\section{Prepare Your Paper Before Styling}
|
|
||||||
Before you begin to format your paper, first write and save the content as a
|
|
||||||
separate text file. Complete all content and organizational editing before
|
|
||||||
formatting. Please note sections \ref{AA}--\ref{SCM} below for more information on
|
|
||||||
proofreading, spelling and grammar.
|
|
||||||
|
|
||||||
Keep your text and graphic files separate until after the text has been
|
|
||||||
formatted and styled. Do not number text heads---{\LaTeX} will do that
|
|
||||||
for you.
|
|
||||||
|
|
||||||
\subsection{Abbreviations and Acronyms}\label{AA}
|
|
||||||
Define abbreviations and acronyms the first time they are used in the text,
|
|
||||||
even after they have been defined in the abstract. Abbreviations such as
|
|
||||||
IEEE, SI, MKS, CGS, ac, dc, and rms do not have to be defined. Do not use
|
|
||||||
abbreviations in the title or heads unless they are unavoidable.
|
|
||||||
|
|
||||||
\subsection{Units}
|
|
||||||
\begin{itemize}
|
|
||||||
\item Use either SI (MKS) or CGS as primary units. (SI units are encouraged.) English units may be used as secondary units (in parentheses). An exception would be the use of English units as identifiers in trade, such as ``3.5-inch disk drive''.
|
|
||||||
\item Avoid combining SI and CGS units, such as current in amperes and magnetic field in oersteds. This often leads to confusion because equations do not balance dimensionally. If you must use mixed units, clearly state the units for each quantity that you use in an equation.
|
|
||||||
\item Do not mix complete spellings and abbreviations of units: ``Wb/m\textsuperscript{2}'' or ``webers per square meter'', not ``webers/m\textsuperscript{2}''. Spell out units when they appear in text: ``. . . a few henries'', not ``. . . a few H''.
|
|
||||||
\item Use a zero before decimal points: ``0.25'', not ``.25''. Use ``cm\textsuperscript{3}'', not ``cc''.)
|
|
||||||
\end{itemize}
|
|
||||||
|
|
||||||
\subsection{Equations}
|
|
||||||
Number equations consecutively. To make your
|
|
||||||
equations more compact, you may use the solidus (~/~), the exp function, or
|
|
||||||
appropriate exponents. Italicize Roman symbols for quantities and variables,
|
|
||||||
but not Greek symbols. Use a long dash rather than a hyphen for a minus
|
|
||||||
sign. Punctuate equations with commas or periods when they are part of a
|
|
||||||
sentence, as in:
|
|
||||||
\begin{equation}
|
|
||||||
a+b=\gamma\label{eq}
|
|
||||||
\end{equation}
|
|
||||||
|
|
||||||
Be sure that the
|
|
||||||
symbols in your equation have been defined before or immediately following
|
|
||||||
the equation. Use ``\eqref{eq}'', not ``Eq.~\eqref{eq}'' or ``equation \eqref{eq}'', except at
|
|
||||||
the beginning of a sentence: ``Equation \eqref{eq} is . . .''
|
|
||||||
|
|
||||||
\subsection{\LaTeX-Specific Advice}
|
|
||||||
|
|
||||||
Please use ``soft'' (e.g., \verb|\eqref{Eq}|) cross references instead
|
|
||||||
of ``hard'' references (e.g., \verb|(1)|). That will make it possible
|
|
||||||
to combine sections, add equations, or change the order of figures or
|
|
||||||
citations without having to go through the file line by line.
|
|
||||||
|
|
||||||
Please don't use the \verb|{eqnarray}| equation environment. Use
|
|
||||||
\verb|{align}| or \verb|{IEEEeqnarray}| instead. The \verb|{eqnarray}|
|
|
||||||
environment leaves unsightly spaces around relation symbols.
|
|
||||||
|
|
||||||
Please note that the \verb|{subequations}| environment in {\LaTeX}
|
|
||||||
will increment the main equation counter even when there are no
|
|
||||||
equation numbers displayed. If you forget that, you might write an
|
|
||||||
article in which the equation numbers skip from (17) to (20), causing
|
|
||||||
the copy editors to wonder if you've discovered a new method of
|
|
||||||
counting.
|
|
||||||
|
|
||||||
{\BibTeX} does not work by magic. It doesn't get the bibliographic
|
|
||||||
data from thin air but from .bib files. If you use {\BibTeX} to produce a
|
|
||||||
bibliography you must send the .bib files.
|
|
||||||
|
|
||||||
{\LaTeX} can't read your mind. If you assign the same label to a
|
|
||||||
subsubsection and a table, you might find that Table I has been cross
|
|
||||||
referenced as Table IV-B3.
|
|
||||||
|
|
||||||
{\LaTeX} does not have precognitive abilities. If you put a
|
|
||||||
\verb|\label| command before the command that updates the counter it's
|
|
||||||
supposed to be using, the label will pick up the last counter to be
|
|
||||||
cross referenced instead. In particular, a \verb|\label| command
|
|
||||||
should not go before the caption of a figure or a table.
|
|
||||||
|
|
||||||
Do not use \verb|\nonumber| inside the \verb|{array}| environment. It
|
|
||||||
will not stop equation numbers inside \verb|{array}| (there won't be
|
|
||||||
any anyway) and it might stop a wanted equation number in the
|
|
||||||
surrounding equation.
|
|
||||||
|
|
||||||
\subsection{Some Common Mistakes}\label{SCM}
|
|
||||||
\begin{itemize}
|
|
||||||
\item The word ``data'' is plural, not singular.
|
|
||||||
\item The subscript for the permeability of vacuum $\mu_{0}$, and other common scientific constants, is zero with subscript formatting, not a lowercase letter ``o''.
|
|
||||||
\item In American English, commas, semicolons, periods, question and exclamation marks are located within quotation marks only when a complete thought or name is cited, such as a title or full quotation. When quotation marks are used, instead of a bold or italic typeface, to highlight a word or phrase, punctuation should appear outside of the quotation marks. A parenthetical phrase or statement at the end of a sentence is punctuated outside of the closing parenthesis (like this). (A parenthetical sentence is punctuated within the parentheses.)
|
|
||||||
\item A graph within a graph is an ``inset'', not an ``insert''. The word alternatively is preferred to the word ``alternately'' (unless you really mean something that alternates).
|
|
||||||
\item Do not use the word ``essentially'' to mean ``approximately'' or ``effectively''.
|
|
||||||
\item In your paper title, if the words ``that uses'' can accurately replace the word ``using'', capitalize the ``u''; if not, keep using lower-cased.
|
|
||||||
\item Be aware of the different meanings of the homophones ``affect'' and ``effect'', ``complement'' and ``compliment'', ``discreet'' and ``discrete'', ``principal'' and ``principle''.
|
|
||||||
\item Do not confuse ``imply'' and ``infer''.
|
|
||||||
\item The prefix ``non'' is not a word; it should be joined to the word it modifies, usually without a hyphen.
|
|
||||||
\item There is no period after the ``et'' in the Latin abbreviation ``et al.''.
|
|
||||||
\item The abbreviation ``i.e.'' means ``that is'', and the abbreviation ``e.g.'' means ``for example''.
|
|
||||||
\end{itemize}
|
|
||||||
An excellent style manual for science writers is \cite{b7}.
|
|
||||||
|
|
||||||
\subsection{Authors and Affiliations}
|
|
||||||
\textbf{The class file is designed for, but not limited to, six authors.} A
|
|
||||||
minimum of one author is required for all conference articles. Author names
|
|
||||||
should be listed starting from left to right and then moving down to the
|
|
||||||
next line. This is the author sequence that will be used in future citations
|
|
||||||
and by indexing services. Names should not be listed in columns nor group by
|
|
||||||
affiliation. Please keep your affiliations as succinct as possible (for
|
|
||||||
example, do not differentiate among departments of the same organization).
|
|
||||||
|
|
||||||
\subsection{Identify the Headings}
|
|
||||||
Headings, or heads, are organizational devices that guide the reader through
|
|
||||||
your paper. There are two types: component heads and text heads.
|
|
||||||
|
|
||||||
Component heads identify the different components of your paper and are not
|
|
||||||
topically subordinate to each other. Examples include Acknowledgments and
|
|
||||||
References and, for these, the correct style to use is ``Heading 5''. Use
|
|
||||||
``figure caption'' for your Figure captions, and ``table head'' for your
|
|
||||||
table title. Run-in heads, such as ``Abstract'', will require you to apply a
|
|
||||||
style (in this case, italic) in addition to the style provided by the drop
|
|
||||||
down menu to differentiate the head from the text.
|
|
||||||
|
|
||||||
Text heads organize the topics on a relational, hierarchical basis. For
|
|
||||||
example, the paper title is the primary text head because all subsequent
|
|
||||||
material relates and elaborates on this one topic. If there are two or more
|
|
||||||
sub-topics, the next level head (uppercase Roman numerals) should be used
|
|
||||||
and, conversely, if there are not at least two sub-topics, then no subheads
|
|
||||||
should be introduced.
|
|
||||||
|
|
||||||
\subsection{Figures and Tables}
|
|
||||||
\paragraph{Positioning Figures and Tables} Place figures and tables at the top and
|
|
||||||
bottom of columns. Avoid placing them in the middle of columns. Large
|
|
||||||
figures and tables may span across both columns. Figure captions should be
|
|
||||||
below the figures; table heads should appear above the tables. Insert
|
|
||||||
figures and tables after they are cited in the text. Use the abbreviation
|
|
||||||
``Fig.~\ref{fig}'', even at the beginning of a sentence.
|
|
||||||
|
|
||||||
\begin{table}[htbp]
|
|
||||||
\caption{Table Type Styles}
|
|
||||||
\begin{center}
|
|
||||||
\begin{tabular}{|c|c|c|c|}
|
|
||||||
\hline
|
|
||||||
\textbf{Table}&\multicolumn{3}{|c|}{\textbf{Table Column Head}} \\
|
|
||||||
\cline{2-4}
|
|
||||||
\textbf{Head} & \textbf{\textit{Table column subhead}}& \textbf{\textit{Subhead}}& \textbf{\textit{Subhead}} \\
|
|
||||||
\hline
|
|
||||||
copy& More table copy$^{\mathrm{a}}$& & \\
|
|
||||||
\hline
|
|
||||||
\multicolumn{4}{l}{$^{\mathrm{a}}$Sample of a Table footnote.}
|
|
||||||
\end{tabular}
|
|
||||||
\label{tab1}
|
|
||||||
\end{center}
|
|
||||||
\end{table}
|
|
||||||
|
|
||||||
\begin{figure}[htbp]
|
|
||||||
\centerline{\includegraphics{fig1.png}}
|
|
||||||
\caption{Example of a figure caption.}
|
|
||||||
\label{fig}
|
|
||||||
\end{figure}
|
|
||||||
|
|
||||||
Figure Labels: Use 8 point Times New Roman for Figure labels. Use words
|
|
||||||
rather than symbols or abbreviations when writing Figure axis labels to
|
|
||||||
avoid confusing the reader. As an example, write the quantity
|
|
||||||
``Magnetization'', or ``Magnetization, M'', not just ``M''. If including
|
|
||||||
units in the label, present them within parentheses. Do not label axes only
|
|
||||||
with units. In the example, write ``Magnetization (A/m)'' or ``Magnetization
|
|
||||||
\{A[m(1)]\}'', not just ``A/m''. Do not label axes with a ratio of
|
|
||||||
quantities and units. For example, write ``Temperature (K)'', not
|
|
||||||
``Temperature/K''.
|
|
||||||
|
|
||||||
\section*{Acknowledgment}
|
|
||||||
|
|
||||||
The preferred spelling of the word ``acknowledgment'' in America is without
|
|
||||||
an ``e'' after the ``g''. Avoid the stilted expression ``one of us (R. B.
|
|
||||||
G.) thanks $\ldots$''. Instead, try ``R. B. G. thanks$\ldots$''. Put sponsor
|
|
||||||
acknowledgments in the unnumbered footnote on the first page.
|
|
||||||
|
|
||||||
\section*{References}
|
|
||||||
|
|
||||||
Please number citations consecutively within brackets \cite{b1}. The
|
|
||||||
sentence punctuation follows the bracket \cite{b2}. Refer simply to the reference
|
|
||||||
number, as in \cite{b3}---do not use ``Ref. \cite{b3}'' or ``reference \cite{b3}'' except at
|
|
||||||
the beginning of a sentence: ``Reference \cite{b3} was the first $\ldots$''
|
|
||||||
|
|
||||||
Number footnotes separately in superscripts. Place the actual footnote at
|
|
||||||
the bottom of the column in which it was cited. Do not put footnotes in the
|
|
||||||
abstract or reference list. Use letters for table footnotes.
|
|
||||||
|
|
||||||
Unless there are six authors or more give all authors' names; do not use
|
|
||||||
``et al.''. Papers that have not been published, even if they have been
|
|
||||||
submitted for publication, should be cited as ``unpublished'' \cite{b4}. Papers
|
|
||||||
that have been accepted for publication should be cited as ``in press'' \cite{b5}.
|
|
||||||
Capitalize only the first word in a paper title, except for proper nouns and
|
|
||||||
element symbols.
|
|
||||||
|
|
||||||
For papers published in translation journals, please give the English
|
|
||||||
citation first, followed by the original foreign-language citation \cite{b6}.
|
|
||||||
|
|
||||||
\begin{thebibliography}{00}
|
|
||||||
\bibitem{b1} G. Eason, B. Noble, and I. N. Sneddon, ``On certain integrals of Lipschitz-Hankel type involving products of Bessel functions,'' Phil. Trans. Roy. Soc. London, vol. A247, pp. 529--551, April 1955.
|
|
||||||
\bibitem{b2} J. Clerk Maxwell, A Treatise on Electricity and Magnetism, 3rd ed., vol. 2. Oxford: Clarendon, 1892, pp.68--73.
|
|
||||||
\bibitem{b3} I. S. Jacobs and C. P. Bean, ``Fine particles, thin films and exchange anisotropy,'' in Magnetism, vol. III, G. T. Rado and H. Suhl, Eds. New York: Academic, 1963, pp. 271--350.
|
|
||||||
\bibitem{b4} K. Elissa, ``Title of paper if known,'' unpublished.
|
|
||||||
\bibitem{b5} R. Nicole, ``Title of paper with only first word capitalized,'' J. Name Stand. Abbrev., in press.
|
|
||||||
\bibitem{b6} Y. Yorozu, M. Hirano, K. Oka, and Y. Tagawa, ``Electron spectroscopy studies on magneto-optical media and plastic substrate interface,'' IEEE Transl. J. Magn. Japan, vol. 2, pp. 740--741, August 1987 [Digests 9th Annual Conf. Magnetics Japan, p. 301, 1982].
|
|
||||||
\bibitem{b7} M. Young, The Technical Writer's Handbook. Mill Valley, CA: University Science, 1989.
|
|
||||||
\end{thebibliography}
|
|
||||||
\vspace{12pt}
|
|
||||||
\color{red}
|
|
||||||
IEEE conference templates contain guidance text for composing and formatting conference papers. Please ensure that all template text is removed from your conference paper prior to submission to the conference. Failure to remove the template text from your paper may result in your paper not being published.
|
|
||||||
|
|
||||||
\end{document}
|
|
||||||
128
literatur.bib
Normal file
128
literatur.bib
Normal file
@ -0,0 +1,128 @@
|
|||||||
|
@misc{gao2023pal,
|
||||||
|
title={PAL: Program-aided Language Models},
|
||||||
|
author={Luyu Gao and Aman Madaan and Shuyan Zhou and Uri Alon and Pengfei Liu and Yiming Yang and Jamie Callan and Graham Neubig},
|
||||||
|
year={2023},
|
||||||
|
eprint={2211.10435},
|
||||||
|
archivePrefix={arXiv},
|
||||||
|
primaryClass={cs.CL}
|
||||||
|
}
|
||||||
|
|
||||||
|
@misc{CoT,
|
||||||
|
title={Chain-of-Thought Prompting Elicits Reasoning in Large Language Models},
|
||||||
|
author={Jason Wei and Xuezhi Wang and Dale Schuurmans and Maarten Bosma and Brian Ichter and Fei Xia and Ed Chi and Quoc Le and Denny Zhou},
|
||||||
|
year={2023},
|
||||||
|
eprint={2201.11903},
|
||||||
|
archivePrefix={arXiv},
|
||||||
|
primaryClass={cs.CL}
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
@misc{few-shot1,
|
||||||
|
title={ReAct: Synergizing Reasoning and Acting in Language Models},
|
||||||
|
author={Shunyu Yao and Jeffrey Zhao and Dian Yu and Nan Du and Izhak Shafran and Karthik Narasimhan and Yuan Cao},
|
||||||
|
year={2023},
|
||||||
|
eprint={2210.03629},
|
||||||
|
archivePrefix={arXiv},
|
||||||
|
primaryClass={cs.CL}
|
||||||
|
}
|
||||||
|
|
||||||
|
@inproceedings{few-shot2,
|
||||||
|
author = {Brown, Tom and Mann, Benjamin and Ryder, Nick and Subbiah, Melanie and Kaplan, Jared D and Dhariwal, Prafulla and Neelakantan, Arvind and Shyam, Pranav and Sastry, Girish and Askell, Amanda and Agarwal, Sandhini and Herbert-Voss, Ariel and Krueger, Gretchen and Henighan, Tom and Child, Rewon and Ramesh, Aditya and Ziegler, Daniel and Wu, Jeffrey and Winter, Clemens and Hesse, Chris and Chen, Mark and Sigler, Eric and Litwin, Mateusz and Gray, Scott and Chess, Benjamin and Clark, Jack and Berner, Christopher and McCandlish, Sam and Radford, Alec and Sutskever, Ilya and Amodei, Dario},
|
||||||
|
booktitle = {Advances in Neural Information Processing Systems},
|
||||||
|
editor = {H. Larochelle and M. Ranzato and R. Hadsell and M.F. Balcan and H. Lin},
|
||||||
|
pages = {1877--1901},
|
||||||
|
publisher = {Curran Associates, Inc.},
|
||||||
|
title = {Language Models are Few-Shot Learners},
|
||||||
|
url = {https://proceedings.neurips.cc/paper_files/paper/2020/file/1457c0d6bfcb4967418bfb8ac142f64a-Paper.pdf},
|
||||||
|
volume = {33},
|
||||||
|
year = {2020}
|
||||||
|
}
|
||||||
|
|
||||||
|
@misc{ChatGPTexample,
|
||||||
|
author = {ChatGPT},
|
||||||
|
title = {{C}hat{G}{P}{T} {P}rogram-aided {L}angauge {M}odel {E}xample},
|
||||||
|
howpublished = {\url{https://chat.openai.com/share/3a78d9db-9caa-4745-a417-0ef229bd7728}},
|
||||||
|
year = {2023},
|
||||||
|
note = {[Accessed 18-11-2023]},
|
||||||
|
}
|
||||||
|
|
||||||
|
@article{Demeter_Downey_2020,
|
||||||
|
title={Just Add Functions: A Neural-Symbolic Language Model},
|
||||||
|
volume={34},
|
||||||
|
url={https://ojs.aaai.org/index.php/AAAI/article/view/6264},
|
||||||
|
DOI={10.1609/aaai.v34i05.6264},
|
||||||
|
abstractNote={<p>Neural network language models (NNLMs) have achieved ever-improving accuracy due to more sophisticated architectures and increasing amounts of training data. However, the inductive bias of these models (formed by the distributional hypothesis of language), while ideally suited to modeling most running text, results in key limitations for today’s models. In particular, the models often struggle to learn certain spatial, temporal, or quantitative relationships, which are commonplace in text and are second-nature for human readers. Yet, in many cases, these relationships can be encoded with simple mathematical or logical expressions. How can we augment today’s neural models with such encodings?</p><p>In this paper, we propose a general methodology to enhance the inductive bias of NNLMs by incorporating simple functions into a neural architecture to form a hierarchical neural-symbolic language model (NSLM). These functions explicitly encode symbolic deterministic relationships to form probability distributions over words. We explore the effectiveness of this approach on numbers and geographic locations, and show that NSLMs significantly reduce perplexity in small-corpus language modeling, and that the performance improvement persists for rare tokens even on much larger corpora. The approach is simple and general, and we discuss how it can be applied to other word classes beyond numbers and geography.</p>},
|
||||||
|
number={05},
|
||||||
|
journal={Proceedings of the AAAI Conference on Artificial Intelligence},
|
||||||
|
author={Demeter, David and Downey, Doug},
|
||||||
|
year={2020}, month={Apr.},
|
||||||
|
pages={7634-7642}
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
@misc{pi2022reasoning,
|
||||||
|
title={Reasoning Like Program Executors},
|
||||||
|
author={Xinyu Pi and Qian Liu and Bei Chen and Morteza Ziyadi and Zeqi Lin and Qiang Fu and Yan Gao and Jian-Guang Lou and Weizhu Chen},
|
||||||
|
year={2022},
|
||||||
|
eprint={2201.11473},
|
||||||
|
archivePrefix={arXiv},
|
||||||
|
primaryClass={cs.CL}
|
||||||
|
}
|
||||||
|
|
||||||
|
@misc{chen2023program,
|
||||||
|
title={Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks},
|
||||||
|
author={Wenhu Chen and Xueguang Ma and Xinyi Wang and William W. Cohen},
|
||||||
|
year={2023},
|
||||||
|
eprint={2211.12588},
|
||||||
|
archivePrefix={arXiv},
|
||||||
|
primaryClass={cs.CL}
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
@misc{Venturi, title={Pandasai}, url={https://docs.pandas-ai.com/},
|
||||||
|
journal={PandasAI}, author={Venturi, Gabriele}}
|
||||||
|
|
||||||
|
@misc{zhao2023automatic,
|
||||||
|
title={Automatic Model Selection with Large Language Models for Reasoning},
|
||||||
|
author={James Xu Zhao and Yuxi Xie and Kenji Kawaguchi and Junxian He and Michael Qizhe Xie},
|
||||||
|
year={2023},
|
||||||
|
eprint={2305.14333},
|
||||||
|
archivePrefix={arXiv},
|
||||||
|
primaryClass={cs.CL}
|
||||||
|
}
|
||||||
|
|
||||||
|
@misc{kabra2023programaided,
|
||||||
|
title={Program-Aided Reasoners (better) Know What They Know},
|
||||||
|
author={Anubha Kabra and Sanketh Rangreji and Yash Mathur and Aman Madaan and Emmy Liu and Graham Neubig},
|
||||||
|
year={2023},
|
||||||
|
eprint={2311.09553},
|
||||||
|
archivePrefix={arXiv},
|
||||||
|
primaryClass={cs.AI}
|
||||||
|
}
|
||||||
|
|
||||||
|
@software{langchain,
|
||||||
|
author = {Chase, Harrison},
|
||||||
|
month = oct,
|
||||||
|
title = {{LangChain}},
|
||||||
|
url = {https://github.com/langchain-ai/langchain},
|
||||||
|
year = {2022}
|
||||||
|
}
|
||||||
|
|
||||||
|
@misc{paranjape2023art,
|
||||||
|
title={ART: Automatic multi-step reasoning and tool-use for large language models},
|
||||||
|
author={Bhargavi Paranjape and Scott Lundberg and Sameer Singh and Hannaneh Hajishirzi and Luke Zettlemoyer and Marco Tulio Ribeiro},
|
||||||
|
year={2023},
|
||||||
|
eprint={2303.09014},
|
||||||
|
archivePrefix={arXiv},
|
||||||
|
primaryClass={cs.CL}
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
@misc{binder,
|
||||||
|
title={Binding Language Models in Symbolic Languages},
|
||||||
|
author={Zhoujun Cheng and Tianbao Xie and Peng Shi and Chengzu Li and Rahul Nadkarni and Yushi Hu and Caiming Xiong and Dragomir Radev and Mari Ostendorf and Luke Zettlemoyer and Noah A. Smith and Tao Yu},
|
||||||
|
year={2023},
|
||||||
|
eprint={2210.02875},
|
||||||
|
archivePrefix={arXiv},
|
||||||
|
primaryClass={cs.CL}
|
||||||
|
}
|
||||||
466
pal-vorstellung.tex
Normal file
466
pal-vorstellung.tex
Normal file
@ -0,0 +1,466 @@
|
|||||||
|
%! suppress = EscapeAmpersand
|
||||||
|
%! suppress = DocumentclassNotInRoot
|
||||||
|
\documentclass[a4paper, twoside]{IEEEtran}
|
||||||
|
|
||||||
|
\usepackage{array}
|
||||||
|
\usepackage[utf8]{inputenc}
|
||||||
|
\usepackage[T1]{fontenc}
|
||||||
|
\usepackage{lmodern}
|
||||||
|
\usepackage[ngerman]{babel}
|
||||||
|
\usepackage[style=ieee, backend=biber, bibencoding=utf8]{biblatex}
|
||||||
|
\addbibresource{literatur.bib}\usepackage{csquotes}
|
||||||
|
\renewcommand*{\bibfont}{\footnotesize}
|
||||||
|
\usepackage{booktabs}
|
||||||
|
\usepackage{microtype}
|
||||||
|
\usepackage{xcolor}
|
||||||
|
\usepackage{graphicx}
|
||||||
|
\usepackage{listings}
|
||||||
|
\lstset{basicstyle=\footnotesize\ttfamily, breaklines=true, keepspaces=true, columns=fixed, numberstyle=\tiny, keywordstyle=\color{blue}}
|
||||||
|
\usepackage{tikz}
|
||||||
|
\usepackage{pgfplots}
|
||||||
|
\usetikzlibrary{positioning,fit,calc,backgrounds,patterns}
|
||||||
|
\usepackage{tabularray}
|
||||||
|
\usepackage{stfloats}
|
||||||
|
\usepackage{float}
|
||||||
|
|
||||||
|
% Definiert die Kompatibilität mit der Version von pgfplots
|
||||||
|
\pgfplotsset{compat=1.17}
|
||||||
|
|
||||||
|
\renewcommand{\lstlistingname}{Codebeispiel}
|
||||||
|
|
||||||
|
\lstdefinestyle{mystyle}{
|
||||||
|
language=Python,
|
||||||
|
basicstyle=\ttfamily\small,
|
||||||
|
commentstyle=\color{green},
|
||||||
|
keywordstyle=\color{blue},
|
||||||
|
numberstyle=\tiny\color{gray},
|
||||||
|
stringstyle=\color{purple},
|
||||||
|
breakatwhitespace=false,
|
||||||
|
breaklines=true,
|
||||||
|
captionpos=b,
|
||||||
|
keepspaces=true,
|
||||||
|
numbers=left,
|
||||||
|
numbersep=5pt,
|
||||||
|
showspaces=false,
|
||||||
|
showstringspaces=false,
|
||||||
|
showtabs=false,
|
||||||
|
tabsize=2,
|
||||||
|
escapeinside={(*@}{@*)} % for escaping to LaTeX
|
||||||
|
}
|
||||||
|
|
||||||
|
\lstset{style=mystyle}
|
||||||
|
|
||||||
|
\newcommand{\DavinciCode}{code\babelhyphen{nobreak}davinci\babelhyphen{nobreak}002}
|
||||||
|
|
||||||
|
\title{Vorstellung von Program-aided Language Model Prompts
|
||||||
|
\thanks{Dieser Beitrag entstand im Rahmen des \emph{Konferenzseminars Machine Learning}, das im Wintersemester 2023/24 vom Fachbereich Informatik und Naturwissenschaften der Fachhochschule Südwestfalen durchgeführt wurde. --- Als Basis für diese \LaTeX-Vorlage dient das IEEE Conference Template der IEEE Computational Intelligence Society.}}
|
||||||
|
|
||||||
|
\author{
|
||||||
|
\IEEEauthorblockN{Philipp Horstenkamp\\}
|
||||||
|
\IEEEauthorblockA{Fachhochschule Südwestfalen}
|
||||||
|
|
||||||
|
\vspace{3mm}
|
||||||
|
Konferenzseminar Machine Learning\\
|
||||||
|
Wintersemester 2023/24
|
||||||
|
}
|
||||||
|
|
||||||
|
\begin{document}
|
||||||
|
|
||||||
|
\maketitle
|
||||||
|
|
||||||
|
\begin{abstract}
|
||||||
|
Eine der Herausforderungen bei der Nutzung von umfangreichen Sprachmodellen (Large Language Models, LLMs) ist die eingeschränkte Fähigkeit,
|
||||||
|
mathematische Operationen präzise auszuführen.
|
||||||
|
Ähnlich wie der menschliche Verstand neigen sie dazu, mathematische Ergebnisse fehlerhaft zu berechnen.
|
||||||
|
Eine Lösung hierfür bietet die Umwandlung von mathematischen Problemstellungen in einfachen Programmcode.
|
||||||
|
Der hier vorgestellte Ansatz der Programm-unterstützten Sprachmodelle (Program-aided Language Models, PAL)
|
||||||
|
verwendet Python ähnlich einem Taschenrechner, um arithmetisch-logische Berechnungen durchzuführen und den Lösungsaufbau zu strukturieren.
|
||||||
|
Dabei wird nicht auf die Generierung des nächsten wahrscheinlichen Tokens durch das Sprachmodell als Lösungsansatz
|
||||||
|
für mathematisch-logische Operationen vertraut.
|
||||||
|
Stattdessen werden die Stärken des LLMs mit denen der direkten Ausführung mathematischer Operationen über einen Interpreter kombiniert,
|
||||||
|
um mathematisch präzisere Ergebnisse zu erzielen.
|
||||||
|
Dieses Prinzip wird im Paper „PAL: Programming Aided Language Model“~\cite{gao2023pal} eingehend vorgestellt und die aktuelle Implementierung werden aufgezeigt.
|
||||||
|
\end{abstract}
|
||||||
|
|
||||||
|
%„PAL: Programming Aided Language Model“
|
||||||
|
|
||||||
|
\begin{IEEEkeywords}
|
||||||
|
LLM, Prompt-Engineering, Mathematical, Informatik, NL
|
||||||
|
\end{IEEEkeywords}
|
||||||
|
|
||||||
|
\section{Einleitung}\label{sec:einleitung}
|
||||||
|
Seit der Veröffentlichung von ChatGPT im Jahr 2023 haben umfangreichen Sprachmodellen (Large Language Models, LLMs) stark an Popularität gewonnen.
|
||||||
|
Allerdings begann ihre Entwicklung bereits früher.
|
||||||
|
Schon seit einigen Jahren ist es möglich, LLMs einzusetzen,
|
||||||
|
um Rechenwege auszuformulieren und so zu symbolischen Lösungen zu gelangen,
|
||||||
|
die anschließend konkret berechnet werden konnten.
|
||||||
|
Jedoch hat diese schrittweise Berechnung das Problem, dass mathematische Operationen innerhalb eines Sprachmodells gelöst werden müssen,
|
||||||
|
das seine Kenntnisse aus einem Textkorpus ableitet, welcher als Grundlage zum Lernen dient.
|
||||||
|
Dies und die Tatsache, dass LLMs darauf ausgelegt sind, die nächsten Zeichen vorherzusagen, erschweren es ihnen,
|
||||||
|
konkret formulierte Probleme präzise zu lösen.
|
||||||
|
Gerade dann wenn sich eine Mathematische Operation sich nicht genau so im Textkorpus wiederfindet
|
||||||
|
da Mathematische Operationen aus Text zu Interpolieren einen sehr hohen grad an abstraktion erfordern.
|
||||||
|
Verlagert man jedoch die Berechnung in eine Software, die vom LLM generiert wird,
|
||||||
|
kann dieses Problem umgangen und so eine deutlich höhere Ergebnisqualität erzielt werden.
|
||||||
|
Zum Zeitpunkt des PAL-Papers wurde das Lösen von solchen Problemen mittels Few-Shot-Learning im Style von Chain of Though (CoT)~\cite{CoT} vorangetrieben.
|
||||||
|
Few-Shot-Learning verwendet eine Reihe von Frage- und Antwortpaaren als Beispiele, um zu zeigen, wie eine Problemlösung aussehen könnte.
|
||||||
|
Dies führt dazu, dass Fragestellungen vom LLM im Schema der Beispiele angegangen werden und das LLM somit eine gewisse Führung erhält.
|
||||||
|
CoT ist ein Promptpattern welches das LLM dazu anhält die eine Antwort schrittweise und Systematisch aufzubauen und nicht das Ergebnis zu raten.
|
||||||
|
PAL nutzt Few-Shot-Prompting, um ein LLM dazu zu bringen, eine Python-Funktion als Antwort zurückzugeben.
|
||||||
|
Dabei ist es wichtig zu Wissen, dass die verwendeten Beispiele in Prompts maßgeblich auf die zu lösenden Probleme zugeschnitten sind.
|
||||||
|
|
||||||
|
Das im Januar 2023 vorgestellte PAL-Verfahren oder eine Variante davon ist nun ein integrierter Teil von beispielsweise ChatGPT oder LangChain~\cite{langchain}.
|
||||||
|
Ob dies eine Parallelentwicklung ist oder auf PAL basiert lässt sich zumindest bei OpenAI nur schwer sagen.
|
||||||
|
|
||||||
|
In Abbildung \ref{fig:cot-pal-chatgpg} findet man ein Vergleich, wie das Lösen von mathematischen Problemen in Chain-of-Thought~\cite{CoT}, PAL~\cite{gao2023pal} und dem aktuellen ChatGPT4~\cite{ChatGPTexample} aussehen kann.
|
||||||
|
|
||||||
|
\begin{figure*}[htbp]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=\textwidth]{PAL Example Expanded.drawio.pdf}
|
||||||
|
\caption{CoT\cite{CoT} vs. PAL\cite{gao2023pal} vs. ChatGPT4\cite{ChatGPTexample} nach\cite{gao2023pal}}
|
||||||
|
\label{fig:cot-pal-chatgpg}
|
||||||
|
\end{figure*}
|
||||||
|
|
||||||
|
\section{Hintergrund}\label{sec:hintergrund}
|
||||||
|
|
||||||
|
\subsection{Few-shot Prompting}
|
||||||
|
Eine der erstaunlichen Fähigkeiten von Large Language Models (LLMs) besteht darin,
|
||||||
|
dass sie anhand weniger Beispiele, die zeigen, wie man eine Problemstellung einer bestimmten Art lösen könnte,
|
||||||
|
diese Lösungsansätze oft auf andere Probleme übertragen können~\cite{few-shot2}~\cite{few-shot1}.
|
||||||
|
|
||||||
|
Dies geschieht of nur mit einer wirklich geringen Anzahl an Beispielen.
|
||||||
|
Typischerweise ist dies eine Anzahl im kleineren Einstelligen bereich.
|
||||||
|
Wichtig dabei ist, dass sich die Lösungen auch stilistisch sehr stark an den gegebenen Beispielen orientieren.
|
||||||
|
Dies ist eine Technik zur Nutzung eines LLMs im Englischen auch genant Prompting und keine Modifikation am LLM selbst.
|
||||||
|
Alternative zu Few-Shot Prompts gibt es Zero-Shot Prompts.
|
||||||
|
Bei diesen wird lediglich eine Beschreibung des Lösungsansatzes oder eine Formatierungsanweisung gegeben.
|
||||||
|
|
||||||
|
\subsection{Chain of Thought (CoT)}
|
||||||
|
|
||||||
|
Eine der weit verbreiteten Techniken, um mehr aus LLMs herauszuholen, ist, diese anzuregen, ihre Antwort schrittweise aufzubauen.
|
||||||
|
Dies geschieht oft über eine Few-shot-Variante namens Chain of Though (CoT)~\cite{CoT} welche LLM durch Beispielhafte Lösungswege
|
||||||
|
mit zwischenschritten dazu anregt,
|
||||||
|
das Lösungswege mit sauber ausgeführten Zwischenschritten inhaltlich ausformuliert werden und die notwendigen mathematischen Operationen strukturieren niedergeschrieben werden.
|
||||||
|
Dies verbessert sowohl den Lösungsansatz und Schreibt die mthematischen Operationen sauber nieder.
|
||||||
|
Was deren lösung dann weniger Abstrakt werden lässt.
|
||||||
|
Dadurch wird das LLM angeregt, sowohl den Gedankengang, der zum Ergebnis führt, durchzuführen,
|
||||||
|
als auch nicht einfach zu einem Ergebnis wie z. B. „42“ zu gelangen, weil „42“ oft als Beispiel genutzt wird.
|
||||||
|
Chain of Thought kann nicht nur für Mathematische Problemstellungen verwendet werden.
|
||||||
|
|
||||||
|
\section{Program-aided Language Models}
|
||||||
|
|
||||||
|
Die natürliche Fortsetzung von Chain of Thought (CoT)~\cite{CoT} besteht darin, das Modell anzuregen,
|
||||||
|
mathematische und logische Probleme in Form von Programmcode zu formatieren,
|
||||||
|
welcher dann ausgeführt wird um die eigentlichen mathematischen Operationen auszuführen.
|
||||||
|
Dieser Ansatz umgeht die Schwachstelle der mathematischen Operation vollständig.
|
||||||
|
Indem der Programmcode so gestaltet wird, dass er den Gedankengang der Problemlösung nachzeichnet,
|
||||||
|
werden die Stärken von Chain of Thought-Prompts genutzt und die Schwächen von LLMs bei mathematischen Operationen effektiv umgangen.
|
||||||
|
|
||||||
|
Beim Aufbau von Program-Aided Language (PAL) Prompt-Beispielen ist zu beachten,
|
||||||
|
dass die Variablen sich an den Grundsatz der Verbalisierung halten und aussagekräftige Namen haben sollten,
|
||||||
|
die möglichst gut den einzelnen Werten aus dem Fließtext der Aufgabenstellung zuzuordnen sind
|
||||||
|
und das Beispiel dadurch besondere Klarheit bekommt.
|
||||||
|
|
||||||
|
Obwohl es möglich ist, die Schritte einzeln auszuführen und dann mit den Ergebnissen weiterzuarbeiten,
|
||||||
|
wurde der Ansatz der einfachen, statt der einmaligen Ausführung gewählt.
|
||||||
|
|
||||||
|
\section{Experimente}
|
||||||
|
|
||||||
|
Die Experimente zur Quantifizierung der Effizienz von Program-Aided Language (PAL) wurden auf Datensätzen durchgeführt,
|
||||||
|
die bereits für Chain of Thought Experimente verwendet wurden~\cite{CoT}.
|
||||||
|
Für PAL wurde sowohl die Fähigkeit zum Lösen mathematischer, abstrakter als auch algorithmischer Probleme quantifiziert.
|
||||||
|
Die CoT-Prompt-Beispiele, welche die Lösungsstile/Wege aufzeigen, wurden direkt übernommen und in den PAL-Prompt Stil übertragen.
|
||||||
|
Um eine gute Vergleichbarkeit zu gewährleisten, wurden äquivalente Beispiele in beiden Stilen verwendet,
|
||||||
|
um die Qualität der Ergebnisse beider Algorithmen unter gleichen Bedingungen zu testen.
|
||||||
|
|
||||||
|
Beispielsweise wurden zufällig die CoT Beispiele 3, 6 und 8 aus der Menge der Beispiele ausgewählt.
|
||||||
|
Probleme wurden sowohl mit CoT als auch mit PAL unter Verwendung derselben zufälligen Kombination gelöst.
|
||||||
|
Auf diese Weise kann der Zufallsfaktor, der die Passgenauigkeit der Beispiele zum Problem beeinflusst,
|
||||||
|
ausgeschlossen werden, was die Ergebnisse vergleichbarer macht.
|
||||||
|
Auf die Beispiele und die Fragestellung folgt stets die Aufforderung, Antworten in Python zu formulieren mit einem Hinweis auf die Formatbeispiele.
|
||||||
|
|
||||||
|
Neben CoT und PAL wurde auch die direkte Frage nach einem Ergebnis getestet, um die qualitativen Unterschiede deutlich aufzeigen zu können.
|
||||||
|
Die direkt Frage nach einem Ergebnis ist genau wie es klingt eine Einfache bitte um Antwort nach schilderung des Sachverhalts.
|
||||||
|
|
||||||
|
\subsection{Mathematische Berechnungen}
|
||||||
|
|
||||||
|
Zur Evaluation des KI-Modells wurden mathematische Aufgaben aus acht Datensätzen auf Grundschulniveau verwendet.
|
||||||
|
Die Experimente zeigten, dass Kommentare und lange Beschreibungen zwischen den Codezeilen die Ergebnisse nicht verbessern.
|
||||||
|
Daher sind die Beispiele recht schlicht gehalten.
|
||||||
|
|
||||||
|
Codebeispiel \ref{list:math-prompt-example} ist ein Beispiel aus dem PAL-Repository, welches zeigt,
|
||||||
|
wie ein solches Lösungsbeispiel für einen mathematischen Prompt aussehen kann.
|
||||||
|
Das Beispiel wurde dabei nicht übersetzt, da unklar ist,
|
||||||
|
inwiefern eine Übersetzung die Qualität von generiertem Code schwächt,
|
||||||
|
besonders da Code im Wesentlichen in Englisch geschrieben wird.
|
||||||
|
|
||||||
|
Um die mathematischen Anteile von den Lösungsansätzen zu unterscheiden,
|
||||||
|
wurde einer der Datensätze (GSM8K) editiert und die Zahlen durch große Zahlen ersetzt,
|
||||||
|
bei denen die Ergebnisse von mathematischen Operationen nicht aus dem Gedächtnis kommen können, sondern definitiv gerechnet werden müssen.
|
||||||
|
Dies ermöglicht einen guten Vergleich, wie gut oder schlecht die Lösungsansätze im Gegensatz zur direkten Mathematik sind.
|
||||||
|
Es wird so ausgeschlossen, dass die korrekten Ergebnisse einfach geraten werden.
|
||||||
|
Dieser so editierte Datensatz wird als GSM-HARD bezeichnet und ist über Huggingface frei verfügbar.
|
||||||
|
|
||||||
|
\begin{lstlisting}[language=Python, caption=Prompt Beispiel für mathematische Probleme, label=list:math-prompt-example]
|
||||||
|
(*@\textbf{Q: Olivia has \$23. She bought five bagels for \$3 each. How much money does she have left?}@*)
|
||||||
|
|
||||||
|
# solution in Python:
|
||||||
|
|
||||||
|
ddef solution():
|
||||||
|
"""Olivia has $23. She bought five bagels for $3 each. How much money does she have left?"""
|
||||||
|
money_initial = 23
|
||||||
|
bagels = 5
|
||||||
|
bagel_cost = 3
|
||||||
|
money_spent = bagels * bagel_cost
|
||||||
|
money_left = money_initial - money_spent
|
||||||
|
result = money_left
|
||||||
|
return result
|
||||||
|
\end{lstlisting}
|
||||||
|
|
||||||
|
\subsection{Abstraktes Denken}
|
||||||
|
|
||||||
|
In diesem Abschnitt wurden verschiedene Probleme gelöst, die sich auf die räumliche Beziehung und Attribute von Objekten beziehen.
|
||||||
|
Ein Beispiel dafür sind Probleme wie: "Ein grauer Esel, ein brauner Hund, eine graue Katze und ein roter Hahn stehen aufeinander.
|
||||||
|
Welche Farbe hat das Tier unter dem Hund?" Des Weiteren wurden Aufgaben zu verschobenen und gefilterten Daten bearbeitet.
|
||||||
|
Im Beispiel gibt es tabellarische Daten über Pinguine, die nach Attributen gefiltert und anschließend gezählt werden müssen.
|
||||||
|
Dies wird anhand eines Beispieldatensatzes über Pinguine demonstriert.
|
||||||
|
Zuletzt wurden Probleme bezüglich des Verständnisses von Datum und Zeitabständen behandelt, wie zum Beispiel: "Peters Reise sollte 5 Stunden dauern.
|
||||||
|
Er hat aber doppelt so lange gebraucht wie geplant. Wenn er um 23 Uhr angekommen ist, wann wollte er ankommen?"
|
||||||
|
|
||||||
|
Für alle drei Problemstellungen gibt es jeweils separate Prompts im Stil von Codebeispiel \ref{list:math-prompt-example}.
|
||||||
|
|
||||||
|
\subsection{Algorithmische Aufgaben}
|
||||||
|
|
||||||
|
Hier wird sich mit dem Lösen von deterministischen Aufgabenstellungen auseinandergesetzt, nicht mit allgemeinen,
|
||||||
|
sondern mit spezifischen Fragestellungen wie dem kategorischen Zählen von Objekten oder dem Erstellen von Sequenzen nach Anweisungen.
|
||||||
|
|
||||||
|
Codebeispiel \ref{list:obj-count} zeigt, wie ein mögliches Beispiel für einen Zähler-Prompt aussehen kann.
|
||||||
|
|
||||||
|
\begin{lstlisting}[language=Python, caption=Prompt Beispiel zum Zählen von Objekten, label=list:obj-count]
|
||||||
|
(*@\textbf{Q: I have a chair, two potatoes, a cauliflower, a lettuce head, two tables, a
|
||||||
|
cabbage, two onions, and three fridges. How many vegetables do I have?}@*)
|
||||||
|
|
||||||
|
# solution in Python:
|
||||||
|
|
||||||
|
def solution():
|
||||||
|
"""Olivia has $23. She bought five bagels for $3 each. How much money does she have left?"""
|
||||||
|
|
||||||
|
def soloution()
|
||||||
|
"""Counting all vagetables. Chair, table and friges arn't counted."""
|
||||||
|
vegetables_to_count = {
|
||||||
|
'potato': 2,
|
||||||
|
'cauliflower': 1,
|
||||||
|
'lettuce head': 1,
|
||||||
|
'cabbage': 1,
|
||||||
|
'onion': 2
|
||||||
|
}
|
||||||
|
return sum(vegetables_to_count.values())
|
||||||
|
\end{lstlisting}
|
||||||
|
|
||||||
|
Als Standard-LLM für die Experimente welche PAL quantifizieren wurde das CODEX LLM model \DavinciCode genutzt.
|
||||||
|
Experimente mit andern Modellen wurden der einfachheit halber aus dieser Vorstellung herausgenommen.
|
||||||
|
|
||||||
|
\section{Ergebnisse}
|
||||||
|
|
||||||
|
Die Ergebnisse in den Tabellen \ref{tab:math-performance} und \ref{tab:algo-performance} zeigen,
|
||||||
|
dass PAL-Prompts wesentlich besser funktionieren als CoT Prompts und die direkte Anfrage an LLMs.
|
||||||
|
|
||||||
|
\subsection{Ergebnisse der mathematischen Aufgaben}
|
||||||
|
|
||||||
|
\begin{table*}[t]
|
||||||
|
\centering
|
||||||
|
\resizebox{\linewidth}{!}{%
|
||||||
|
\begin{tabular}{l|cccccccc||r}
|
||||||
|
Algorithm & GSM8K & GSM-HARD & SVAMP & ASDIV & SINGLEEQ & SINGLEOP & ADDSUB & MULTIARITH & Ø \\
|
||||||
|
\hline
|
||||||
|
\hline
|
||||||
|
DIRECT & 19,7 & 5,0 & 69,9 & 74,0 & 86,8 & 93,1 & 90,9 & 44,0 & 60,42 \\
|
||||||
|
CoT & 65,6 & 23,1 & 74,8 & 76,9 & 89,1 & 91,9 & 86,0 & 95,9 & 75,41 \\
|
||||||
|
PAL & 72,0 & 61,2 & 79,4 & 79,6 & 96,1 & 94,6 & 92,5 & 99,2 & 84,32 \\
|
||||||
|
\hline
|
||||||
|
\end{tabular}
|
||||||
|
}
|
||||||
|
\caption[Mathematik prompt ergebnisse]{
|
||||||
|
Ergebnisqualität von verschiedenen Prompttechniken gegenüber verschiedenen Datensätzen.\\
|
||||||
|
Ausgelassen wurden dabei Ergebnisse von abweichenden LLMs.
|
||||||
|
}
|
||||||
|
\label{tab:math-performance}
|
||||||
|
\end{table*}
|
||||||
|
|
||||||
|
In Tabelle \ref{tab:math-performance} zeigt sich, besonders durch den Unterschied zwischen GSM8K und GSM-HARD,
|
||||||
|
wie groß die Schwierigkeiten von CoT und der direkten Berechnung bei mathematischen Operationen sind.
|
||||||
|
Die wird dadurch unterstrichen das der einzige Unterschied die Größe der Zahlen ist.
|
||||||
|
Die direkte Berechnung fällt von ohnehin schon schlechten $19,7\%$ auf $5,0\%$ ($\Delta_{Direkt}=-74\%$).
|
||||||
|
Ähnlich verhält es sich bei der Berechnung mit CoT-Prompts, die von $65,6\%$ auf $23,1\%$ fallen ($\Delta_{CoT}=-70$).
|
||||||
|
Auch wenn die Qualität der Berechnungen für PAL fällt, geschieht dies nur von $72,0\%$ auf $61,2\%$ ($\Delta_{PAL}=-14,3\%$).
|
||||||
|
Das deutlich robustere Verhalten gegenüber komplexen Rechenoperationen macht sich mit einem Qualitätsunterschied von $1224\%$
|
||||||
|
zwischen der Direktberechnung und PAL bemerkbar.
|
||||||
|
Auch das wesentlich bessere CoT hat immer noch einen Qualitätsunterschied von $264\%$ zu PAL unter GSM-HARD.
|
||||||
|
Aber auch mit allen anderen Datensätzen sind PAL-Prompts CoT-Prompts und direkten Anfragen überlegen.
|
||||||
|
|
||||||
|
Eine manuelle Analyse der Prompts zeigt, dass das Vorgehen bei CoT- und PAL-Prompts in 16 von 25 Fällen die Antworten annähernd gleich aufbaut,
|
||||||
|
was wiederum die „einfache“ mathematische Operation mit komplexeren Zahlen als Fehlerquelle hinweist.
|
||||||
|
|
||||||
|
Die Ergebnisqualität kann weiter gesteigert werden,
|
||||||
|
wenn man die Qualität des Ergebnisses über einen Mehrheitsentscheidung gegenüber Fehlern stabilisiert.
|
||||||
|
Die Ergebnisse von PAL steigen von $72,0\%$ auf $80,4\%$ ($\Delta_{PAL-M}=11\%$),
|
||||||
|
die von CoT von $65,6\%$ auf $78,4\%$ ($\Delta_{CoT-M}=19\%$).
|
||||||
|
Die Qualitätsverbesserung durch Mehrheitsentscheidungen ist zwar für PAL nicht so stark wie für CoT,
|
||||||
|
was allein schon durch das geringere Verbesserungspotenzial und den geringeren Zufallsanteil bei Berechnungen via PAL zu erklären ist.
|
||||||
|
Die Experimente zum Mehrheitsentscheid wurden nur auf GSM8K durchgeführt.
|
||||||
|
|
||||||
|
\subsection{Ergebnisse der Aufgaben zum Abstrakten Denken \& Algorithmen}
|
||||||
|
|
||||||
|
Die Ergebnisse zum abstrakten Denken und zu Algorithmen können in Tabelle \ref{tab:algo-performance} gefunden werden.
|
||||||
|
Auch hier wurden die Ergebnisse, die nicht mit dem Codex-Modell \DavinciCode berechnet wurden, ausgelassen.
|
||||||
|
|
||||||
|
So steigt das Lösen von Positionsaufgaben in Objektfolgen um $8,8\%$ (COLORED OBJECT).
|
||||||
|
Aussagen über tabellierte Daten steigen in ihrer Qualität um $14\%$ am Beispiel der Pinguin-Daten.
|
||||||
|
|
||||||
|
Das Zählen von Objekten, welches bei der direkten Verwendung von LLMs besonders schwierig ist,
|
||||||
|
erreicht mit PAL eine Erfolgsrate von $96,7\%$. CoT erreicht hier immerhin $73\%$.
|
||||||
|
|
||||||
|
Auch hier sind wieder deutliche Qualitätssteigerungen zu erkennen.
|
||||||
|
Dabei ist wichtig zu erwähnen, dass die Ergebnisqualität beim Handeln von mehren Objekten bei PAL-Prompts stabil ist und bei CoT-Prompts annähernd stetig abnimmt.
|
||||||
|
Auch hier wird, wie bei den mathematischen Aufgaben, gezeigt, dass der Umgang mit mehr Datenpunkten für PAL wesentlich einfacher ist als für CoT.
|
||||||
|
Dieses Verhalten findet sich in allen Ergebnissen wieder.
|
||||||
|
Die Stabilität von PAL ist auch hier messbar höher, insbesondere bei gesteigerter Komplexität.
|
||||||
|
|
||||||
|
\begin{table}[H]
|
||||||
|
\centering
|
||||||
|
\resizebox{\linewidth}{!}{%
|
||||||
|
\begin{tabular}{l|ccccc}
|
||||||
|
\hline
|
||||||
|
Algorithm & COLORED OBJECT & PENGUINS & DATE & REPEAT COPY & OBJECT COUNTING \\
|
||||||
|
\hline
|
||||||
|
DIRECT & 75,7 & 71,1 & 49,9 & 81,3 & 37,6 \\
|
||||||
|
COT & 86,3 & 79,2 & 64,8 & 68,8 & 73,0 \\
|
||||||
|
PAL & 95,1 & 93,3 & 76,2 & 90,6 & 96,7 \\
|
||||||
|
\hline
|
||||||
|
\end{tabular}
|
||||||
|
}
|
||||||
|
\caption{
|
||||||
|
Ergebnisqualität von verschiedenen Prompt Techniken gegenüber logischen und algorithmischen Aufgaben.\\
|
||||||
|
Ausgelassen wurden dabei Ergebnisse von abweichenden LLMs.
|
||||||
|
}
|
||||||
|
\label{tab:algo-performance}
|
||||||
|
\end{table}
|
||||||
|
|
||||||
|
\subsection{Analyseergebnisse}
|
||||||
|
|
||||||
|
Neben den oben beschriebenen Experimenten wurden weitere Fragestellungen untersucht. Hier sind die Ergebnisse:
|
||||||
|
|
||||||
|
\begin{itemize}
|
||||||
|
\item PAL funktioniert auch auf schwächeren LLMs. Die Vorteile skalieren etwa mit der Qualität des Modells.
|
||||||
|
\item Experimente, die Modelle vergleichen, welche sowohl Code als auch Text generieren, zeigen,
|
||||||
|
dass diese nur eine Mindestqualität erfüllen müssen. Funktionieren tut es mit beiden.
|
||||||
|
\item Experimente, bei denen Python-Syntax als Strukturierungshilfe für CoT genutzt wurde,
|
||||||
|
zeigten nur eine geringe Verbesserung gegenüber der direkten Berechnung.
|
||||||
|
\item Experimente zur Quantifizierung, ob und inwieweit Kommentare und gute Variablennamen eine Rolle spielen, zeigen, dass:
|
||||||
|
\begin{enumerate}
|
||||||
|
\item Code-Kommentare die Qualität von PAL leicht verbessern.
|
||||||
|
\item Werden Variablennamen und Kommentare weggelassen, erhält man Ergebnisse, welche die Qualität von CoT-Prompts oft nicht erreichen.
|
||||||
|
\end{enumerate}
|
||||||
|
\item Steigende LLM Qualität verringert das durch PAL erschließbare Verbesserungspotential (Abbildung\ref{fig:diff-llm}).
|
||||||
|
Daher sind qualitative verbesserungen bei Besseren LLMs weniger stark sichtbar.
|
||||||
|
Auch bei geringerer Prozentualer verbesserung ist PAL für die Nachvollziehbarkeit durch den Nutzer aber sehr dankbar.
|
||||||
|
\end{itemize}
|
||||||
|
|
||||||
|
\begin{figure}[htbp]
|
||||||
|
\centering
|
||||||
|
\begin{tikzpicture}
|
||||||
|
\begin{axis}[
|
||||||
|
ybar,
|
||||||
|
bar width=20pt,
|
||||||
|
symbolic x coords={text-davinci-001, text-davinci-002, text-davinci-003},
|
||||||
|
xtick=data,
|
||||||
|
nodes near coords,
|
||||||
|
nodes near coords align={vertical},
|
||||||
|
ymin=0,ymax=80,
|
||||||
|
enlarge x limits=0.2,
|
||||||
|
ylabel={Lösungsqualität $[\%]$},
|
||||||
|
legend style={at={(0.5,-0.15)},
|
||||||
|
anchor=north,legend columns=-1},
|
||||||
|
width=\columnwidth,
|
||||||
|
height=6cm,
|
||||||
|
]
|
||||||
|
\addplot
|
||||||
|
[fill=red,postaction={pattern=north east lines}]
|
||||||
|
coordinates {(text-davinci-001,26.5) (text-davinci-002,65.8) (text-davinci-003,65.3)};
|
||||||
|
\addplot
|
||||||
|
[fill=blue]
|
||||||
|
coordinates {(text-davinci-001,8.6) (text-davinci-002,46.9) (text-davinci-003,69.8)};
|
||||||
|
\legend{CoT,PAL}
|
||||||
|
\end{axis}
|
||||||
|
\end{tikzpicture}
|
||||||
|
\caption{Vergleich der Ergebnisqualität von PAL und CoT bei verschiedenen LLM modellen.}
|
||||||
|
\label{fig:diff-llm}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
\section{Ähnliche Werke \& Implementierungen}
|
||||||
|
|
||||||
|
Die Entwicklung des PAL-Papers wurde durch das Few-shot Prompting~\cite{few-shot2}~\cite{few-shot1} und das Konzept des
|
||||||
|
Chain of Thought (CoT) angeregt, erreichte jedoch eine überlegene Qualität in den Ergebnissen.
|
||||||
|
Weitere Ansätze, die zusätzliche Tokens für Daten und mathematische Operationen einsetzen~\cite{Demeter_Downey_2020},
|
||||||
|
sind zwar vorhanden, erweisen sich jedoch als komplexer, weniger zuverlässig und weniger universell einsetzbar.
|
||||||
|
|
||||||
|
Es existieren Large Language Models (LLMs), die speziell auf mathematische Probleme und Codeausgabe ausgerichtet sind
|
||||||
|
und eine höhere Ergebnisqualität als Standardmodelle aufweisen, allerdings nur marginal~\cite{pi2022reasoning}.
|
||||||
|
Diese Modelle sind ebenfalls fähig, Code zu generieren und auszuführen.
|
||||||
|
|
||||||
|
Ein zeitgleich mit PAL veröffentlichter Ansatz, das Program of Thought (PoT)~\cite{chen2023program},
|
||||||
|
konzentriert sich stärker auf mathematische Probleme und wird in PAL zitiert.
|
||||||
|
Es scheint, dass dort weniger Wert auf die Gestaltung von Prompts gelegt wird und auch keine Vergleiche mit dem
|
||||||
|
aussagekräftigen Datensatz GSM-HARD gezogen werden, stattdessen werden andere Datensätze verwendet.
|
||||||
|
Dies macht die Vergleichbarkeit schwierig.
|
||||||
|
|
||||||
|
Neue Techniken wie die "Automatic Model Selection with Large Language Models for Reasoning" kombinieren CoT und PAL und
|
||||||
|
überlassen die Entscheidung über die Korrektheit beider Ergebnisse einem LLM,
|
||||||
|
wodurch die Qualität der Ergebnisse für GSM8K auf $96,5\%$ gesteigert werden konnte, eine Verbesserung um $34\%$~\cite{zhao2023automatic}.
|
||||||
|
|
||||||
|
Die weit verbreitete Python/JavaScript-Bibliothek LangChain hat PAL-Prompts in ihr Repertoire aufgenommen~\cite{langchain}.
|
||||||
|
Aktuelle Studien belegen, dass die Qualität von PAL auch bei neueren LLMs besser ist als die von CoT~\cite{kabra2023programaided},
|
||||||
|
wobei dort noch andere Experimente gemacht werden und weitere Verbesserungen vorgenommen wurden.
|
||||||
|
|
||||||
|
Eine vergleichbare Integration von Programmiersprachen findet in Tools wie Binder~\cite{binder} statt,
|
||||||
|
die sich hauptsächlich auf die Datenanalyse mit Python's Pandas und SQL konzentrieren.
|
||||||
|
Moderne Python-Libraries wie PandasAI~\cite{Venturi} setzen diesen Ansatz ein,
|
||||||
|
um Datenabfragen und -operationen zu bearbeiten, und gehen dabei über Zero-shot-Prompts vor.
|
||||||
|
|
||||||
|
Alternative Ansätze wie "Automatic Multi-Step Reasoning and Tool-Use for Large Language Models"~\cite{paranjape2023art}
|
||||||
|
frieren das LLM während der Codeausführung ein und fügen die Ergebnisse direkt in den Text ein,
|
||||||
|
bevor die Ausführung des LLMs basierend auf diesen Ergebnissen fortgesetzt wird.
|
||||||
|
|
||||||
|
Das in ChatGPT verwendete Analysemodul erzeugt schnell Code, ohne die Berechnungen direkt im Code durchzuführen,
|
||||||
|
was einen weiteren interessanten Anwendungsfall darstellt.
|
||||||
|
|
||||||
|
\section{Ausblick}
|
||||||
|
|
||||||
|
Die vorgestellte PAL-Technik illustriert einen innovativen Schritt,
|
||||||
|
indem sie Python-Code während der Beantwortung von Fragen oder Aufgaben durch LLMs ausführt.
|
||||||
|
Das aufgedeckte Verbesserungspotenzial für mathematisch-logische Operationen innerhalb von LLMs ist beeindruckend und zeugt von schlichter technischer Eleganz.
|
||||||
|
|
||||||
|
Die Quantifizierung von Einflussfaktoren, wie die Reihenfolge und Art der Beispiele, trägt zur Verlässlichkeit der Methode bei.
|
||||||
|
Die Tatsache, dass PAL-Prompts als erweiterte CoT-Prompts fungieren, stärkt das Vertrauen in die Ergebnisse.
|
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|
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Der rasante technische Fortschritt im Bereich der LLMs und deren Integration in Software zeigt,
|
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|
wie effektiv der von PAL verfolgte Ansatz ist.
|
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Trotz der Versuche des PAL-Papers, die Ergebnisse des 175-Milliarden-Parameter-Modells zu kontextualisieren,
|
||||||
|
bleibt unklar, wie aktuelle LLMs abschneiden würden.
|
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Dennoch ist es unwahrscheinlich, dass die Ergebnisse schlechter ausfallen als direkte Anfragen oder CoT-Resultate auf denselben Modellen.
|
||||||
|
|
||||||
|
Eine kritische Information, die im PAL-Paper fehlt, ist die Häufigkeit nicht ausführbaren Codes.
|
||||||
|
LLMs sind oft in der Lage, mit einem Fehler-Traceback den Code zu korrigieren, was eine Verbesserung darstellen könnte,
|
||||||
|
ohne den CPU-Aufwand einer mehrfachen Ausführung für einen Mehrheitsentscheid zu erhöhen.
|
||||||
|
|
||||||
|
Es bleibt zu untersuchen, ob PAL in anderen Sprachen ähnlich effektiv ist,
|
||||||
|
da eine weniger enge Verknüpfung zwischen Aufgabenstellungen und Codevariablen in verschiedenen Sprachen
|
||||||
|
die Qualität potenziell beeinträchtigen könnte. Eine Quantifizierung dieser Effekte stellt sicherlich eine Herausforderung dar.
|
||||||
|
|
||||||
|
Neben den Wirklich beeindruckenden ergebnissen die PAL vorweisen kann ist aber besonders die Technische Implementierung
|
||||||
|
welche unabhängig voneinander in Verschiedenen Tools vorgenomen wurde ein Zeichen davon wie Zielführen die Nutzung von PAL oder der Interpretierung
|
||||||
|
von Python code Ausführungen zur Laufzeit ist.
|
||||||
|
|
||||||
|
Dabei ist aber klar zu sehen das oft weit über das Prompt-Engineering hinausgegangen wurde sondern aktuelle LLMs ohne spezielle Aufforderung interpretierbaren code generieren.
|
||||||
|
\printbibliography
|
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|
\end{document}
|
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Reference in New Issue
Block a user