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”.