Vertex Reconstructing Neural Networks at the ZEUS Central Tracking Detector FermiLab, October 2000...

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.

Vertex Reconstruction FermiLab, October 2000

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

Ee=27.5 GeV, Ep=820GeV

Vertex Reconstruction 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

• 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)

0016.0005.0)(

TT

T PP

P

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 (XY).

• An active 2ed layer=line segment centered at XY with angle

otherwise

rrif

rrif

JVJgV PT

PT

xyXYxy

xyxyXYXY

0

215.01

25.01

,)( ,2,

Vertex Reconstruction FermiLab, October 2000

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 r-

• Transform the representation of local line segments into arc segments.

• A neuron is labled by 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 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 cross-checks

• 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 k-values (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”.