Download Vertex Reconstructing Neural Networks at the ZEUS Central

Vertex Reconstructing Neural Networks
at the ZEUS
Central Tracking Detector
FermiLab, October 2000
Erez Etzion1,
Gideon Dror2, David Horn1, Halina Abramowicz1
1. Tel-Aviv University, Tel Aviv, Israel.
2. The Academic College of Tel-Aviv-Yaffo, Tel Aviv, Israel.
Physics @ HERA
• High energy e – p
scattering probe deep
inside the proton in
order to study its
constituents structure
• Study substructure of
quarks, electrons, N
and C current
procesesss, tests of
QCD and search fo
new particles
Vertex Reconstruction
Ee=27.5 GeV, Ep=820GeV
FermiLab, October 2000
ZEUS
• 3 level trigger
• Collision
every 96 nsec
(10MHz), FLT
~ 1MHz,
SLT<100Khz
Vertex Reconstruction
FermiLab, October 2000
Zeus Central Tracking Detector
 ( PT )
PT
•
•
•
•
 0.005PT  0.0016
205 cm long, 18.2<R<79.4.
Magnetic field 1.43 T.
24192 wires, 4608 signal wires, 9 superlayers (8 wire layer each)
Axial wires Superlayer 1,3,5,7,9, Stereo (+/- 50) 2,4,6,8. 1,3,5 – z
meas. (+/- 4cm)
Vertex Reconstruction
FermiLab, October 2000
Input Data
• The Input SLT data:
• Xy position of
superlayers 1,3,5,7,9
• Z-by-timing in 1,3,5
(red)
Vertex Reconstruction
FermiLab, October 2000
Ghost hits
Vertex Reconstruction
FermiLab, October 2000
Z measurement uncertinties
• Example of z Meas. Uncertainty
• Left – single track in xy; Right – z vs r
Vertex Reconstruction
FermiLab, October 2000
The Network
•
Based on step-wise changes in the data
representation: input points ->local line segments>global arcs.
• Two parallel networks:
1. Construct arcs & correctly find some of the tracks
2. Evaluate z location of the interaction point
Vertex Reconstruction
FermiLab, October 2000
Arc Identification Network
• Follow the primary visual
system
• Input 100000 neurons (the
retina like) cover 5000cm2
• Neuron fire when hitted in
its receptive field. (xy)
• Second layer – line
segment detector (XYa).
• An active 2ed layer=line
segment centered at XY
with angle a
Vertex Reconstruction
VXYa  g ( J XYa , xyVxy  2 ) , J XYa , xy
xy
FermiLab, October 2000
 1

  1
 0

if
if
rT  0.5  rP  2
0.5  rT  1  rP  2
otherwise
Receptive fields of line segment
neuron
• A line segment
centered about the
central black dot with
orientation parallel to
the oblique line is
connected to the input
neurons(squares) with
weight: pink +1
Blue=-1 Yellow=0
Vertex Reconstruction
FermiLab, October 2000
Third layer Network
• A track from the IP
project into circle in rf
• Transform the
representation of local
line segments into arc
segments.
• A neuron is labled by
k, q, I (curvature,
slope and ring).
• Mapping = winner
take all.
Vertex Reconstruction
FermiLab, October 2000
Arc Identification last stage
• Neurons are global arc
detectors.
• Detect tracks projected
in z=0 plane.
• Each active neuron kq
is equivalent in the xy
plane to one arc in the
plot.
Vertex Reconstruction
FermiLab, October 2000
z Location Network
• Similar architecture to the first net
• A first layer input from the receptive field as its
corresponding neuron in the first net.
• Get the mean of the z values of the points within the
receptieve field.
• Second layer compute the mean value of the z of the first
layer.
• The z averaging procedure is similary propagated to the
third layer.
• Last layer evaluate the z value of the origin of each arc
identified by the first network by simple linear
extrapolation.
• The final z estimate of the vertex is calculated by
averaging the output of all active fourth layer neurons.
Vertex Reconstruction
FermiLab, October 2000
z-location resolution
Vertex Reconstruction
FermiLab, October 2000
Number of track found
Vertex Reconstruction
FermiLab, October 2000
Network Performance
• Study performed with
324 Networks
• Sigma vs number of
neurons
• Small correlation -.26
• The classical
histogram method
width ~8.5 cm.
Vertex Reconstruction
FermiLab, October 2000
Network Performance (2)
• The network output
width as a function of
N1 and N2
• N1=# neurons in the
first layer
• N2=#neurons in the
third layer
Vertex Reconstruction
FermiLab, October 2000
New developments and crosschecks
• Form lateral connection between 1st layer, which
enabled us to reduce threshold still with good
signal to noise - > reduce network size.
• Study network size –> x10 reduction.
parameters: size and shape of receptive fields in 1st
layer, resolution in k-theta space, range of kvalues (loosing tracks with r<45 cm)
Vertex Reconstruction
FermiLab, October 2000
Summary
• FF double NN for pattern identification, selecting
a subset of which is simple to derive the answer.
• Fixed architecture – can be implemented in HW.
• 1st NN partial tracking in xy.
• The 2ed NN handles z-values of the trajectories
estimating the z arcs origin.
• Performance is better than the “clasical method”.
Vertex Reconstruction
FermiLab, October 2000