Adding content for the triple collinear ML study

proceedings/jet_sub.tex

@@ -129,6 +129,26 @@ \subsubsection{Triple Collinear Splitting Functions}
 \end{figure}
 
 
+Events are treated as sets of particles, with each particle $p_i$ specified by its momentum $\vec p_i^\mu$, mass, and particle-type.
+%
+The events are rotated to a consistent orientation by vertically aligning the second moment of the energy flow~\cite{Komiske:2019asc}.
+%
+This is accomplished by diagonalizing the spatial component of $\mathcal I^{\mu\nu} = \sum_{i=1}^M E_i v_i^\mu v_i^\nu$, where $v_i^\mu = p_i^\mu/E_i$ is the particle velocity.
+
+
+As a machine learning architecture to process the entire events in their natural representation as sets of particles, we use Particle Flow Networks (PFNs)~\cite{Komiske:2018cqr} (see also \Ref{DBLP:conf/nips/ZaheerKRPSS17}).
+%
+Intuitively, PFNs learn a collection of additive observables which are processed by a fully-connected network.
+%
+A PFN acts on an event with $M$ particles $p_i$ as $\text{PFN}(\{p_i\}_{i=1}^M) = F\left(\sum_{i=1}^M \Phi(p_i)\right)$, where $F$ and $\Phi$ are parameterized by dense networks.
+%
+The network sizes of $F$ and $\Phi$ are identical to those in \Ref{Komiske:2018cqr}, with a latent space dimension of 256.
+%
+The train, validation, and test set sizes were 175k, 10k, and 15k, respectively.
+%
+The PFN classifiers were trained for 25 epochs with a batch size of 500.
+
+
 \subsubsection{$g\to b \bar b$}
 \label{sec:jets:gbb}
 (Helen, Davide)

proceedings/lh2019.bib

@@ -120,6 +120,36 @@ @article{Komiske:2018cqr
       SLACcitation   = "%%CITATION = ARXIV:1810.05165;%%"
 }
 
+@article{Komiske:2019asc,
+      author         = "Komiske, Patrick T. and Metodiev, Eric M. and Thaler,
+                        Jesse",
+      title          = "{Cutting Multiparticle Correlators Down to Size}",
+      year           = "2019",
+      eprint         = "1911.04491",
+      archivePrefix  = "arXiv",
+      primaryClass   = "hep-ph",
+      reportNumber   = "MIT-CTP 5150",
+      SLACcitation   = "%%CITATION = ARXIV:1911.04491;%%"
+}
+
+@inproceedings{DBLP:conf/nips/ZaheerKRPSS17,
+  author    = {Manzil Zaheer and
+               Satwik Kottur and
+               Siamak Ravanbakhsh and
+               Barnab{\'{a}}s P{\'{o}}czos and
+               Ruslan Salakhutdinov and
+               Alexander J. Smola},
+  title     = {Deep Sets},
+  booktitle = {Advances in Neural Information Processing Systems 30: Annual Conference
+               on Neural Information Processing Systems 2017, 4-9 December 2017,
+               Long Beach, CA, {USA}},
+  pages     = {3391--3401},
+  year      = {2017},
+  url       = {http://papers.nips.cc/paper/6931-deep-sets},
+  timestamp = {Tue, 23 Jul 2019 12:44:35 +0200},
+  biburl    = {https://dblp.org/rec/bib/conf/nips/ZaheerKRPSS17},
+  bibsource = {dblp computer science bibliography, https://dblp.org}
+}
 
 @article{Aaboud:2018ibj,
       author         = "Aaboud, Morad and others",
@@ -361,15 +391,15 @@ @Article{DELPHICollaboration1997
 volume="73",
 number="2",
 pages="229--242",
-abstract="Inclusive charged particle and event shape distributions are measured using 321 hadronic events collected with the DELPHI experiment at LEP at effective centre of mass energies of 130 to 136 GeV. These distributions are presented and compared to data at lower energies, in particular to the precise Z data. Fragmentation models describe the observed changes of the distributions well. The energy dependence of the means of the event shape variables can also be described using second order QCD plus power terms. A method independent of fragmentation model corrections is used to determine $\alpha$s from the energy dependence of the mean thrust and heavy jet mass. It is measured to be: {\$}{\$}{\textleftarrow}pha {\_}s(133 {\{}⤪ GeV{\}})={\{}0.116{\}}pm {\{}0.007{\}}{\_}{\{}exp-0.004theo{\}}^{\{}+0.005{\}}{\$}{\$} from the high energy data.",
+abstract="Inclusive charged particle and event shape distributions are measured using 321 hadronic events collected with the DELPHI experiment at LEP at effective centre of mass energies of 130 to 136 GeV. These distributions are presented and compared to data at lower energies, in particular to the precise Z data. Fragmentation models describe the observed changes of the distributions well. The energy dependence of the means of the event shape variables can also be described using second order QCD plus power terms. A method independent of fragmentation model corrections is used to determine $\alpha$s from the energy dependence of the mean thrust and heavy jet mass. It is measured to be: {\$}{\$}{\textleftarrow}pha {\_}s(133 {\{}⤪ GeV{\}})={\{}0.116{\}}pm {\{}0.007{\}}{\_}{\{}exp-0.004theo{\}}^{\{}+0.005{\}}{\$}{\$} from the high energy data.",
 issn="1431-5858",
 doi="10.1007/s002880050312",
 url="https://doi.org/10.1007/s002880050312"
 }
 
 
 @article{Hoang:2015hka,
-      author         = "Hoang, Andr� H. and Kolodrubetz, Daniel W. and Mateu,
+      author         = "Hoang, André H. and Kolodrubetz, Daniel W. and Mateu,
                         Vicent and Stewart, Iain W.",
       title          = "{Precise determination of $\alpha_s$ from the
                         $C$-parameter distribution}",
@@ -487,7 +517,7 @@ @article{Abdesselam:2010pt
 }
 
 @article{Kardos:2018kth,
-      author         = "Kardos, Adam and Somogyi, G�bor and Trocsanyi,
+      author         = "Kardos, Adam and Somogyi, Gábor and Trocsanyi,
                         Zoltan",
       title          = "{Soft-drop event shapes in electron?positron
                         annihilation at next-to-next-to-leading order accuracy}",
@@ -619,7 +649,7 @@ @article{Larkoski:2014wba
       SLACcitation   = "%%CITATION = ARXIV:1402.2657;%%"
 }
 @article{Hoang:2019ceu,
-      author         = "Hoang, Andr� H. and Mantry, Sonny and Pathak, Aditya and
+      author         = "Hoang, André H. and Mantry, Sonny and Pathak, Aditya and
                         Stewart, Iain W.",
       title          = "{Nonperturbative Corrections to Soft Drop Jet Mass}",
       journal        = "JHEP",
@@ -1076,7 +1106,7 @@ @article{Harland-Lang:2014zoa
 }
 
 @article{Gieseke:2016fpz,
-      author         = "Gieseke, Stefan and Loshaj, Frashër and Kirchgaeßer,
+      author         = "Gieseke, Stefan and Loshaj, Frashër and Kirchgaeßer,
                         Patrick",
       title          = "{Soft and diffractive scattering with the cluster model
                         in Herwig}",
@@ -4664,7 +4694,7 @@ @article{Hoang:2014wka
 	Primaryclass = {hep-ph},
 	Reportnumber = {UWTHPH-2014-07, MIT-CTP-4596, LPN14-123},
 	Slaccitation = {%%CITATION = ARXIV:1411.6633;%%},
-	Title = {{$C$-parameter distribution at N$^3$LL‚{\"A}≤ including power corrections}},
+	Title = {{$C$-parameter distribution at N$^3$LL‚{\"A}≤ including power corrections}},
 	Volume = {D91},
 	Year = {2015},
 	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevD.91.094017}}
@@ -5267,7 +5297,7 @@ @article{Banfi:2014sua
 	Primaryclass = {hep-ph},
 	Reportnumber = {OUTP-14-18P},
 	Slaccitation = {%%CITATION = ARXIV:1412.2126;%%},
-	Title = {{A general method for the resummation of event-shape distributions in $e^{+} e^{‚{\`a}{\'\i}}$ annihilation}},
+	Title = {{A general method for the resummation of event-shape distributions in $e^{+} e^{‚{\`a}{\'\i}}$ annihilation}},
 	Volume = {05},
 	Year = {2015},
 	Bdsk-Url-1 = {http://dx.doi.org/10.1007/JHEP05(2015)102}}