Attempts of Attempts of neural tracking in neural tracking in

ALICEALICE

Alberto Pulvirenti – I.N.F.N. CataniaALICE Week

Monday, March 18 2002

OutlineOutline

MotivationsImplementation

pattern recognition methodcuts and working conditionsreconstruction

ResultsCollateral developments: “combined” trackingSummary and outlook

MotivationsMotivations

High pt trackingTracking without TPC, for high rate events and high transverse momentum particles [ pt > 1 GeV / c ]

This is an useful benchmark for the method.There is a work already in ALICE/ITS 99-34 (1999) to compare with (although the code is not in CVS and worked with an older version of ALICE/ITS geometry and rec-point simulation).

Low pt tracking (main goal)Increase of tracking efficiency for low transverse momentum particles [ pt < 0.2 GeV / c ] or decaying particles which don’t leave enough recpoints in the TPCComparison with ALICE 95-50 (1995)

BasicsBasics

Neural network constituents:an array of “neurons” with a real “activation” value (like a data-member, ai)

a symmetric matrix of “synaptic weights” which represent the correlation between neurons (wij)

Neural network work-flow:random initialization asynchronous updating cycle (one neuron at a time)stabilization final result binary map

Implementation Implementation (1 – (1 – definitions)definitions)

i j k

l

Neurons: oriented track segments 2 indexes: [sij]

link two consecutive points in the particle’s path important to define a directionWeights: correlations between 2 segments 4 indexes [wijkl]

Geometrical constraint: weight is not zero only when the two neurons share a point; two possible configurations, depending on their orientations:

sequence (sij with sjk- a segment starts from the end of another) a possible guess for a tracklet (excitation positive weight)

stronger correlation for well aligned segments (selects high pt particles)

GOOD SEQUENCE

BAD SEQUENCE

crossing (sij with sik (skj) – two segments starting from or ending to the same point) a choice is needed (inhibition negative weight)

CROSSING

0,11sin1 BABQAw ikjljkn

ijlijlijkl

Implementation Implementation (2 (2 – cuts)– cuts)

Needed to limit the number of point pairs used to create neurons

1. Check only couples on adjacent layers2. Cut on the difference in polar angle ()3. Cut on the curvature of the projected circle

passing through the two points and the calculated vertex (by means of the AliITSVertex class)

4. “Helix matching cut” max

j

Vj

i

Viij a

zz

a

zz

jlijijlQ

max2where a is the

projected corresponding

circle arc

Implementation Implementation (3 – work (3 – work flow)flow)

“Step by step” procedure(removing the points used at the end of each one)

Many curvature cut steps, with increasing cut valueSectioning of the ITS barrel into N azymuthal sectors

RISK: edge effectsthe tracks crossing a sector boundary will not be recognizable by the ANN tracker

Implementation Implementation (4 – (4 – classes)classes)

2 AliRoot neural-tracking classes created (already in CVS)

Neuron class (for internal use): AliITSneuronProvided only with a constructor and a method to calculate the segment angle w.r.t. another similar (related) object

Tracker class: AliITSneuralTrackersetters for working params [S , A/B, T, n, min, max ]elaboration global method

…and a service class: AliITSglobalRecPointjust to have the possibility to store into a TObjArray the reconstructed points in global coordinates

Test trial ingredientsTest trial ingredients

All detectors “on” and all physical effects “on”.Full slow simulation and reconstruction in ITS.Default detailed ITS geometry (AliITSvPPRasymm)Parameterized HIJING generator:

84210 particles in | h | < 8.021000 particles in | h | < 0.9

Results (I)Results (I)Number of found tracks, efficiency and CPU time as a function of the # of sectors.Only one event analyzed.

Test choice: 18 sectors

CPU time: ~230 secs

PC used: PIII 1 GHz

Results (II)Results (II)Good track Findable track

“SOFT” criterion

at least 5 right points

Has at least 5 points in ITS

“HARD” criterion

all 6 point must be correct

Has a point for each layer

KalmanNeural

goodfake

goodfake

Note: the “findable” tracks are counted among all ITS findable tracks (not only the ones which are also findable in TPC)

Reconstruction Reconstruction (1 – (1 – method)method)

Two stepsXY plane: fit of the bending circle with the Riemann sphere mapping algorithm (thanks to R. Turrisi for pointing us to the existing bibliography) C, Dt , 0

Whole space: linearized helix equation by calculation of s for each point, using the fit values coming from the previous step (gives tan, Dz)

t

t

z

t

tt

CD

DC

Cs

sDz

CD

DCDC

412arcsin

2

1 where

tan

41

212arcsin

22

0

C = curvature

Dt = transverse impact parameter

Dz = longitudinal impact parameter

= dip angle

0 = momentum azimuthal angle (aka

Reconstruction Reconstruction (2 – (2 – results)results)

Neural Kalman (without vertex. constr.)

pt (%) 12.5 +/- 0.3

1.57 +/- 0.02

0

(mrad)

2.45 +/- 0.06

1.40 +/- 0.08

(mrad)

3.04 +/- 0.11

1.60 +/- 0.08

Impact parameter Impact parameter resolutionresolution

Neural Kalman (for pt

=1 GeV / c)

transv.

139 +/- 2 m

50 m

long. 398 +/- 7 m

150 m

““Combined” trackingCombined” tracking

An attempt to increase the tracking efficiency by trying to use the neural algorithm to recognize some findable tracks with the remaining ITS points after the Kalman TPC + ITS tracking.

Different definition for excitory weight and/or cut criteria No ITS azymuthal sectioning More CPU time required

Kalman only

Kalman + Neural

The “findable” tracks are counted among all

ITS findable tracks (irrespective of the fact

that they are also findable in the TPC)

Summary & outlookSummary & outlook

Neural network tracking for high transverse momentum tracks in ITS stand-alone looks promising.Tracking efficiency for pt > 1 GeV/c tracks is comparable with the TPC+ITS Kalman filter one.Track reconstruction includedALICE Note already submittedIn progress:

Improving the neural algorithm performances for LOW transverse momentum tracks [ pt < 0.2 GeV/c ].Alternative possible techniques for the same purpose (elastic tracking, elastic arms algorithm…)

Other possible developmentsCombined tracking using also the “remaining” TPC points after Kalman tracking

Results (III)Results (III)

Results from work of Kindiziuk et al. [ALICE/ITS 99-34 (1999)]

goodfake

BasicsBasics

Neural network constituents:an array of “neurons” with a real “activation” value (data-member, ai)

a symmetric matrix of “synaptic weights” which represent the correlation between neurons (wij)

Neural network work-flow:random initialization asynchronous updating cycle (one neuron at a time):

sum the activations of all neurons, multiplied by the weight of the connection they have with the one we are updatingput this value as the argument of an activation function, and set the new activation to its value

stabilizationfrom cycle to cycle, the average of the activations variations (taken on the whole network) will fall down. The network is considered “stable” when this average is lesser than a defined threshold S.

final resultcreate a binary map by turning “on” or “off” the neurons, respectively, if their activation is greater or smaller than a threshold value amin

Implementation (I)Implementation (I)

i j k

l

GOOD SEQUENCE

BAD SEQUENCE CROSSIN

G

0,11sin1 BABAw ikjljkn

ijlijkl

1

1

k

kjk

ikk

kikijk

jkijk aaawawB

A

T

B

ij ea

‘gain’ contribution‘cost’

contributionFree parameters: it is enough to define only 2 of them (T and A/B)

Implementation (II)Implementation (II)Neurons: oriented track segments 2 indexes: [sij]

link two consecutive points in the particle’s path important to define a direction

Weights: correlations between 2 segments 4 indexes [wijkl]Geometrical constraint: weight is not zero only when the two neurons share a point; two possible configurations, depending on their orientations:

sequence (sij with sjk- a segment starts from the end of another) a possible guess for a tracklet (excitation positive weight)

stronger correlation for well aligned segments (selects high pt particles)

crossing (sij with sik (skj) – two segments starting from or ending to the same point) a choice is needed (inhibition negative weight)

Activation function: limited within [0,1] low activation units don’t influence the othersincreasing function, so that a weight > 0 increases the activations while a weight < 0 does the opposite

T

x

e

xf

1

1argument

slope parameter

0

1

activation threshold= 0.5

Implementation (I)Implementation (I)Hopfield neural network with real-valued neurons [NIM A279 (1989) 537]

Initialization of activations ai with random values within [0,1]

End updating cycle

Is the mean activation variation

lower than S?

no

Get unit’stotal input Qi = wik ak

Start updating cycle

Loop until all units have

been updated

Calculate the activation by the “logistic” function

1

1

T

x

exf

END yes

Switch “on” all neurons whose activation is >

0.5

Implementation (IV)Implementation (IV)

No cut in (it causes different cut strengths for each couple of layers, due to the different layer distance)

The length of the circle arc (in the outer layer) where the good mates can be found depends on its distance from the inner layer

Test trial ingredientsTest trial ingredients

AliRoot v3-06-Rev-02 and HEAD.All detectors “on” and all phys. eff. “on”.Full slow simulation and reconstruction in ITS.Default detailed ITS geometry (AliITSvPPRasymm)Parameterized HIJING generator:

84210 particles in | h | < 8.021000 particles in | h | < 0.9

cut

T Stab. thresh.

n A/B min

max

Curv steps number

1 deg 2 0.00001 6 4 0.1 0.2 10