1. neural tracking in ALICE Alberto Pulvirenti – I.N.F.N. Catania
Attempts of
neural tracking in ALICE
Alberto Pulvirenti – I.N.F.N. Catania
ALICE Week
Monday, March

2. Outline Motivations Implementation Results
pattern recognition method
cuts and working conditions
reconstruction
Results
Collateral developments: “combined” tracking
Summary and outlook

3. Motivations High pt tracking Low pt tracking (main goal)
Tracking 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 (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 TPC
Comparison with ALICE (1995)

4. Basics Neural network constituents: Neural network work-flow:
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

5. Implementation (1 – definitions)
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)
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 i j k l

6. Implementation (2 – cuts)
Needed to limit the number of point pairs used to create neurons
Check only couples on adjacent layers
Cut on the difference in polar angle (q)
Cut on the curvature of the projected circle passing through the two points and the calculated vertex (by means of the AliITSVertex class)
“Helix matching cut”
where a is the projected corresponding circle arc

7. Implementation (3 – work flow)
“Step by step” procedure
(removing the points used at the end of each one)
Many curvature cut steps, with increasing cut value
Sectioning of the ITS barrel into N azymuthal sectors
RISK: edge effects
the tracks crossing a sector boundary will not be recognizable by the ANN tracker

8. Implementation (4 – classes)
2 AliRoot neural-tracking classes created (already in CVS)
Neuron class (for internal use): AliITSneuron
Provided only with a constructor and a method to calculate the segment angle w.r.t. another similar (related) object
Tracker class: AliITSneuralTracker
setters for working params [S , A/B, T, n, min, max ]
elaboration global method
…and a service class: AliITSglobalRecPoint
just to have the possibility to store into a TObjArray the reconstructed points in global coordinates

9. Test 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 | < 8.0
21000 particles in | h | < 0.9

10. Results (I) Test choice: 18 sectors CPU time: ~230 secs
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

11. Results (II) “SOFT” criterion “HARD” criterion 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
good
fake
good
fake
KalmanNeural
Note: the “findable” tracks are counted among all ITS findable tracks (not only the ones which are also findable in TPC)

12. Reconstruction (1 – method)
C = curvature
Dt = transverse impact parameter
Dz = longitudinal impact parameter
l = dip angle
g0 = momentum azimuthal angle (aka j)
Two steps
XY 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 , g0
Whole space: linearized helix equation by calculation of s for each point, using the fit values coming from the previous step (gives tanl, Dz)

13. Reconstruction (2 – results)
Neural
Kalman (without vertex. constr.)
pt (%)
12.5 +/- 0.3
1.57 +/- 0.02
g0 (mrad)
2.45 +/- 0.06
1.40 +/- 0.08
l (mrad)
3.04 +/- 0.11
1.60 +/- 0.08

14. Impact parameter resolution
Neural
Kalman (for pt =1 GeV / c)
transv.
139 +/- 2 mm
50 mm
long.
398 +/- 7 mm
150 mm

15. “Combined” 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
The “findable” tracks are counted among all ITS findable tracks (irrespective of the fact that they are also findable in the TPC)
Kalman only
Kalman + Neural

16. Summary & 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 included
ALICE Note already submitted
In 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 developments
Combined tracking using also the “remaining” TPC points after Kalman tracking

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

19. Basics Neural network constituents: Neural network work-flow:
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 updating
put this value as the argument of an activation function, and set the new activation to its value
stabilization
from 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 result
create a binary map by turning “on” or “off” the neurons, respectively, if their activation is greater or smaller than a threshold value amin

20. Implementation (I) i j k l ‘cost’ contribution
CROSSING
GOOD SEQUENCE
BAD SEQUENCE
‘cost’ contribution
Free parameters: it is enough to define only 2 of them (T and A/B)
‘gain’ contribution

21. 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 others
increasing function, so that a weight > 0 increases the activations while a weight < 0 does the opposite 1
activation threshold= 0.5
argument
slope parameter

22. Implementation (I)
Hopfield neural network with real-valued neurons [NIM A279 (1989) 537]
END
yes
Switch “on” all neurons whose activation is > 0.5
Initialization of activations ai with random values within [0,1]
End updating cycle
Is the mean activation variation lower than S?
Get unit’stotal input Qi = S wik ak
Start updating cycle
Loop until all units have been updated
Calculate the activation by the “logistic” function no

23. Implementation (IV)
No cut in Dj (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

24. Test 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 | < 8.0
21000 particles in | h | < 0.9
Dq cut T
Stab. thresh. n
A/B
min
max
Curv steps number
1 deg 2 6 4
0.1
0.2 10