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poster-spring2023.tm
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poster-spring2023.tm
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<TeXmacs|2.1.1>
<style|<tuple|poster|a1-poster|reduced-margins|rough-paper|topless-poster-title|compact-list>>
<\body>
<\hide-preamble>
\;
<assign|par-width|auto>
<assign|poster-title|<\macro|body|ldeco|rdeco>
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<\with|par-columns|1|deco-hook|<macro|body|<with|ornament-border|0em|ornament-hpadding|<value|title-hpadding>|ornament-vpadding|<value|title-vpadding>|<arg|body>>>>
<\surround||<vspace|<value|title-vsep>>>
<\title-block>
<\surround|<resize|<arg|ldeco>|||1l|><htab|5mm>|<htab|5mm><resize|<arg|rdeco>|1r|||>>
<arg|body>
</surround>
</title-block>
</surround>
</with>
</no-margins>
</macro>>
<assign|title-ver-padding|4spc>
<assign|infix-iff|<macro|<math-imply|<text|
<localize|<space|1em>iff<space|1em>> >>>>
\;
<assign|garnet|<macro|body|<with|color|#990002|<arg|body>>>>
<assign|myblue|<macro|body|<with|color|#0749ac|<arg|body>>>>
<assign|key|<macro|body|<myblue|<strong|<arg|body>>>>>
<assign|Model|<with|font|cal|M>>
<assign|Net|<with|font|cal|N>>
<assign|Set|<with|font-family|ss|Set>>
<assign|Primes|<with|font-family|ss|P>>
<assign|semantics|<macro|body|<around*|\<llbracket\>|<arg|body>|\<rrbracket\>>>>
<assign|Lang|<with|font|cal|L>>
<assign|Logic|<with|font-series|bold|<text|L>>>
<assign|vocab|<with|font|cal|V>>
<assign|wocab|<with|font|cal|W>>
<assign|proves|\<vdash\>>
<assign|orr|\<vee\>>
<assign|land|\<wedge\>>
<assign|NP|<with|font-shape|small-caps|NP>>
<assign|axiom|<macro|body|<with|font-shape|small-caps|<arg|body>>>>
<assign|bigchi|<larger|\<chi\>>>
<assign|powerset|<with|font|cal|P>>
\;
<assign|hash|<with|font-family|ss|hash>>
<assign|unique|<with|font-family|ss|unique>>
<assign|Know|<with|font-series|bold|<text|K>>>
<assign|Knownby|<with|font-series|bold|<text|K><rsup|\<downarrow\>>>>
<assign|diaKnow|\<langle\><value|Know>\<rangle\>>
<assign|diaKnownby|\<langle\><value|Knownby>\<rangle\>>
<assign|Typ|<with|font-series|bold|<text|T>>>
<assign|diaTyp|\<langle\><value|Typ>\<rangle\>>
<assign|Reach|<with|font-family|ss|Reach>>
<assign|Reachedby|<with|font-family|ss|Reach><rsup|\<downarrow\>>>
<assign|Prop|<with|font-family|ss|Prop>>
<assign|Hebb|<with|font-family|ss|Update>>
<assign|Activ|<with|font-family|ss|Act>>
<assign|Inc|<with|font-family|ss|Inc>>
<assign|AllNets|<with|font-family|ss|Net>>
<assign|AllModels|<with|font-family|ss|Model>>
<assign|axiom|<macro|x|<text|<name|(<arg|x>)>>>>
<assign|precede|<with|font-family|ss|prec>>
<assign|enunciation-name|<macro|x|<with|font-series|bold|<arg|x>>>>
<assign|render-theorem|<\macro|which|body>
<render-enunciation|<theorem-name|<arg|which><theorem-sep>>|<arg|body>>
</macro>>
</hide-preamble>
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Network Semantics>>|<cell|>>|<row|<cell|>|<cell|<with|font-series|medium|Caleb
Schultz Kisby>, <with|font-series|medium|Saúl Blanco>, and
<with|font-series|medium|Lawrence Moss>>|<cell|>>|<row|<cell|>|<cell|Luddy
School of Informatics, Computing, and Engineering>|<cell|>>>>>>
<\center>
<tabular|<tformat|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|-1|1|-1|cell-width|0.3par>|<cwith|1|-1|1|-1|cell-hmode|exact>|<cwith|1|-1|1|-1|cell-hyphen|t>|<twith|table-height|0.4par>|<twith|table-vmode|exact>|<twith|table-hyphen|n>|<cwith|1|-1|1|-1|cell-block|auto>|<cwith|1|-1|1|-1|cell-valign|t>|<cwith|1|-1|1|-1|cell-halign|c>|<cwith|1|1|2|2|cell-row-span|2>|<cwith|1|1|2|2|cell-col-span|1>|<cwith|1|-1|1|-1|cell-bsep|0.5em>|<cwith|1|-1|1|-1|cell-tsep|0.5em>|<cwith|1|1|1|1|cell-row-span|2>|<cwith|1|1|1|1|cell-col-span|1>|<cwith|1|1|3|3|cell-row-span|2>|<cwith|1|1|3|3|cell-col-span|1>|<twith|table-lsep|0em>|<twith|table-rsep|0em>|<twith|table-bsep|0em>|<twith|table-tsep|0em>|<table|<row|<\cell>
<\framed-titled-block|The Logic>
<\equation*>
<tabular|<tformat|<cwith|2|-1|1|1|cell-halign|c>|<cwith|1|1|1|-1|cell-halign|c>|<cwith|1|1|1|-1|cell-tborder|0ln>|<cwith|1|1|1|-1|cell-bborder|1ln>|<cwith|2|2|1|-1|cell-tborder|1ln>|<cwith|1|1|1|1|cell-lborder|0ln>|<cwith|1|1|2|2|cell-rborder|0ln>|<cwith|2|2|1|-1|cell-tsep|0.25em>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|1|2|2|cell-halign|l>|<cwith|1|-1|2|2|cell-lsep|0.5em>|<cwith|4|4|2|2|cell-hyphen|t>|<cwith|5|5|2|2|cell-hyphen|t>|<cwith|6|6|2|2|cell-hyphen|t>|<table|<row|<cell|<text|<with|font-series|bold|Syntax>>>|<cell|<with|font-series|bold|<text|Neural
Net Semantics>>>>|<row|<cell|p>|<cell|<text|a (fuzzy) set of
neurons>>>|<row|<cell|A\<wedge\>B>|<cell|A\<cup\>B>>|<row|<cell|<value|Know>A>|<\cell>
the set of <text|neurons graph-reachable from >A
</cell>>|<row|<cell|<value|Typ>A>|<\cell>
<text|the set of neurons activated by >A
</cell>>|<row|<cell|<around*|[|A|]>B>|<\cell>
<text|after repeated Hebbian update, >B
</cell>>>>>
</equation*>
For formulas <math|\<varphi\>,\<psi\>>, we have material implication
<\equation*>
\<varphi\>\<rightarrow\>\<psi\>
</equation*>
<\small>
<\note*>
We can \Pflip\Q the semantics replacing <math|\<wedge\>> with
<math|\<cap\>>, <math|<value|Know>>,<value|Typ> with their duals
<math|<value|diaKnow>>,<math|<value|diaTyp>>, and exactly the
same axioms hold.
</note*>
</small>
</framed-titled-block>
\;
<\framed-titled-block|Static Net Axioms>
<\equation*>
<tabular|<tformat|<cwith|1|1|1|1|cell-row-span|1>|<cwith|1|1|1|1|cell-col-span|2>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|1|1|-1|cell-tborder|0ln>|<cwith|1|1|1|-1|cell-bborder|1ln>|<cwith|2|2|1|1|cell-tborder|1ln>|<cwith|1|1|1|-1|cell-rborder|0ln>|<cwith|1|1|1|-1|cell-lborder|0ln>|<cwith|6|6|1|1|cell-row-span|1>|<cwith|6|6|1|1|cell-col-span|2>|<cwith|6|6|1|-1|cell-tborder|0ln>|<cwith|5|5|1|1|cell-bborder|0ln>|<cwith|6|6|1|-1|cell-bborder|1ln>|<cwith|7|7|1|1|cell-tborder|1ln>|<cwith|6|6|1|-1|cell-rborder|0ln>|<cwith|6|6|1|-1|cell-lborder|0ln>|<cwith|2|2|1|-1|cell-tsep|0.5em>|<cwith|7|7|1|-1|cell-tsep|0.5em>|<cwith|6|6|1|1|cell-tsep|0.75em>|<cwith|10|10|2|2|cell-hyphen|t>|<cwith|10|10|1|1|cell-valign|t>|<table|<row|<cell|<text|<with|font-series|bold|Properties
of ><value|Know>>>|<cell|<text|<with|font-series|bold|Basic Modal
Axioms>>>>|<row|<cell|<text|Refl>>|<cell|<value|Know>A\<rightarrow\>A>>|<row|<cell|<text|Trans>>|<cell|<value|Know>A\<rightarrow\><value|Know><value|Know>A>>|<row|<cell|<text|Acyclic>>|<cell|<value|Know><around*|(|<value|Know><around*|(|A\<rightarrow\><value|Know>A|)>\<rightarrow\>A|)>\<rightarrow\>A>>|<row|<cell|<text|Monotone>>|<cell|If
<value|Know><around*|(|A\<rightarrow\>B|)> then
<around*|(|<value|Know>A\<rightarrow\><value|Know>B|)>>>|<row|<cell|<text|<with|font-series|bold|Properties
of ><value|Typ>>>|<cell|>>|<row|<cell|<text|Refl>>|<cell|<value|Typ>A\<rightarrow\>A>>|<row|<cell|<text|Trans>>|<cell|<value|Typ>A\<rightarrow\><value|Typ><value|Typ>A>>|<row|<cell|<text|Interact>>|<cell|<value|Know>A\<rightarrow\><value|Typ>A>>|<row|<cell|<text|Loop>>|<\cell>
<tabular|<tformat|<table|<row|<cell|<around*|(|<value|Typ>A<rsub|1>\<rightarrow\>A<rsub|2>|)>\<ldots\><around*|(|<value|Typ>A<rsub|n>\<rightarrow\>A<rsub|1>|)>>>|<row|<cell|<space|1em>\<rightarrow\><around*|(|<value|Typ>A<rsub|i>\<leftrightarrow\>A<rsub|j>|)>>>>>>
</cell>>>>>
</equation*>
\;
</framed-titled-block>
</cell>|<\cell>
<\framed-titled-block|Neural Net Model Building>
<\padded-center>
<tabular|<tformat|<twith|table-valign|c>|<cwith|3|3|1|1|cell-bsep|0.5em>|<cwith|5|5|1|1|cell-bsep|0.5em>|<twith|table-tsep|0em>|<cwith|1|1|1|1|cell-bsep|0em>|<cwith|1|1|1|1|cell-tsep|0em>|<cwith|3|3|1|1|cell-tsep|0em>|<cwith|5|5|1|1|cell-tsep|0em>|<cwith|1|-1|1|1|cell-halign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|2|2|1|1|cell-bsep|0.5em>|<cwith|2|2|1|1|cell-tsep|0.5em>|<cwith|4|4|1|1|cell-bsep|0.5em>|<cwith|4|4|1|1|cell-tsep|0.5em>|<table|<row|<cell|<tabular|<tformat|<cwith|1|1|1|1|cell-hyphen|t>|<twith|table-lborder|0.05em>|<twith|table-rborder|0.05em>|<twith|table-bborder|0.05em>|<twith|table-tborder|0.05em>|<twith|table-lsep|0.2em>|<twith|table-rsep|0.2em>|<twith|table-bsep|0.2em>|<twith|table-tsep|0.2em>|<cwith|1|-1|1|1|cell-bsep|0.1em>|<cwith|1|-1|1|1|cell-tsep|0.1em>|<cwith|1|-1|1|1|cell-lsep|0.4em>|<cwith|1|-1|1|1|cell-rsep|0.4em>|<cwith|1|1|1|1|cell-tsep|0.4em>|<cwith|3|3|1|1|cell-bsep|0.4em>|<table|<row|<\cell>
penguin <math|\<rightarrow\>> bird
</cell>>|<row|<cell|<math|<value|Typ>>bird <math|\<rightarrow\>>
flies>>|<row|<cell|<with|font-series|bold|not>
<math|<value|Typ>>penguin <math|\<rightarrow\>>
flies>>>>>>>|<row|<cell|<with|color|#800000|<with|font-size|3|<with|font|Mononoki|<math|\<downarrow\>>>>>>>|<row|<cell|<tabular|<tformat|<cwith|1|1|1|1|cell-hyphen|t>|<twith|table-lborder|0.05em>|<twith|table-rborder|0.05em>|<twith|table-bborder|0.05em>|<twith|table-tborder|0.05em>|<twith|table-halign|c>|<cwith|1|1|1|1|cell-row-span|1>|<cwith|1|1|1|1|cell-col-span|2>|<cwith|4|4|1|1|cell-row-span|1>|<cwith|4|4|1|1|cell-col-span|2>|<cwith|1|1|1|1|cell-halign|c>|<cwith|3|3|1|1|cell-row-span|1>|<cwith|3|3|1|1|cell-col-span|2>|<cwith|1|1|1|1|cell-lsep|0.2em>|<cwith|1|1|1|1|cell-rsep|0.2em>|<cwith|1|1|1|1|cell-bsep|0.2em>|<cwith|1|1|1|1|cell-tsep|0.2em>|<cwith|4|4|1|1|cell-halign|c>|<cwith|3|3|1|1|cell-halign|c>|<table|<row|<\cell>
<math|W=<around*|{|a,b,c,d,e,f,g,h|}>>
</cell>|<cell|>>|<row|<cell|<math|<semantics|bird>=<around*|{|b,g|}>>>|<cell|<math|<semantics|flies>=<around*|{|e,g,h|}>>>>|<row|<cell|<math|<semantics|penguin>=<around*|{|a,b,c,e,g|}>>>|<cell|>>|<row|<cell|<center|<image|<tuple|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</padded-center>
</framed-titled-block>
</cell>|<\cell>
<\framed-titled-block|Hebbian Learning Axioms>
We can reduce (repeated) Hebbian Learning to the static base
language:
<\equation*>
<tabular|<tformat|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|4|4|3|3|cell-hyphen|t>|<cwith|4|4|1|1|cell-valign|t>|<cwith|4|4|2|2|cell-valign|t>|<table|<row|<cell|<around*|[|A|]>p>|<cell|\<leftrightarrow\>>|<cell|p>>|<row|<cell|<around*|[|A|]><around*|(|B\<wedge\>C|)>>|<cell|\<leftrightarrow\>>|<cell|<around*|[|A|]>B\<wedge\><around*|[|A|]>C>>|<row|<cell|<around*|[|A|]><value|Know>B>|<cell|\<leftrightarrow\>>|<cell|<value|Know><around*|[|A|]>B>>|<row|<cell|<around*|[|A|]><value|Typ>B>|<cell|\<leftrightarrow\>>|<\cell>
<choice|<tformat|<table|<row|<cell|<tabular|<tformat|<table|<row|<cell|<value|Typ><around*|[|A|]>B>>|<row|<cell|<space|1em><text|if
><value|Typ>A\<cap\><value|Typ>B<text| is
>\<emptyset\>>>>>>>>|<row|<cell|<tabular|<tformat|<table|<row|<cell|<value|Typ><around*|[|A|]>B\<wedge\><around*|(|<value|Typ>A\<vee\><value|Know>B|)>>>|<row|<cell|<space|1em><text|otherwise>>>>>>>>>>>
</cell>>>>>
</equation*>
</framed-titled-block>
\;
<\framed-titled-block|Current & Future Work>
<\conjecture*>
Our net-building construction is correct, i.e. given
<math|\<Gamma\>>, the net <math|<value|Net>\<models\>\<Gamma\>>.
</conjecture*>
<\conjecture*>
The Minimal Cause axiom
<\equation*>
<value|diaKnownby>\<psi\>\<rightarrow\><around*|(|<value|Typ>\<varphi\>\<leftrightarrow\><value|Typ><around*|(|<value|diaKnownby>\<psi\>\<rightarrow\><value|Typ>\<varphi\>|)>|)>
</equation*>
is sound, and adding <math|<value|Knownby>> completes the logic.
</conjecture*>
<\note*>
I'm currently verifying all this using the Lean proof assistant.
</note*>
<\conjecture*>
All of this still holds for <with|font-shape|italic|fuzzy> sets &
<with|font-shape|italic|fuzzy> activation functions
</conjecture*>
\;
<\small>
<\acknowledgments*>
This work was funded by the US Department of Defense (Contract
W52P1J2093009).<nbsp> Thank you for your support!
</acknowledgments*>
</small>
</framed-titled-block>
</cell>>|<row|<\cell>
\;
</cell>|<\cell>
\;
</cell>|<\cell>
<tabular|<tformat|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|-1|1|1|cell-halign|c>|<cwith|1|-1|1|1|cell-valign|t>|<cwith|1|-1|1|1|cell-hyphen|t>|<cwith|1|1|1|1|cell-row-span|2>|<cwith|1|1|1|1|cell-col-span|1>|<table|<row|<\cell>
<framed-titled-block|Title 6|blah blah blah more text more text
here's some more text blah blah blah more text more text here's some
more text blah blah blah more text more text here's some more text >
</cell>>|<row|<\cell>
<\framed-titled-block|Acknowledgements>
blah blah blah more text more text here's some more text blah blah
blah more text more text here's some more text\
</framed-titled-block>
</cell>>>>>
</cell>>>>>
</center>
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