1. E. Barbuto, C. Bozza, A. Cioffi, M. Giorgini
OPERA Collaboration Meeting
Nagoya, Japan, 30 Jan – 4 Feb 2004
Updated results from a new Neural Network tool: e-/p- separation energy measurement from e.m. showers
E. Barbuto, C. Bozza, A. Cioffi, M. Giorgini

2. Outline Features of the Neural Network (NN) Software
MC simulation used for the training
Results on :
Particle (e-/p-) separation
Energy reconstruction in e.m. showers
Conclusions

3. Neural Network library structure
(see C. Bozza, Gran Sasso Coll. Meeting, May `03)
Full generality/modularity
Platform and language independence (the library has been tested and debugged both under Windows and Linux)
It can be used by any user program, even in server mode
Users can extend the library even without recompiling
GUI and console interface allowing an interactive monitoring of the training and testing phases
Network Type
Output layer
Multilayer Perceptron : several layers of “neurons”, each one with its transfer function
Hidden layer
Input layer

4. MC simulation for training and test
lead (1mm) p ,e x y z
GEANT simulation of a complete OPERA brick (56 lead targets and 56 emulsion-base-emulsion sheets)
First step : e/p discrimination only through their multiple Coulomb scattering before interacting/showering (see E. Barbuto, Phys. Coord. July `03)
New step : algorithm taking into account the showers
Full analysis : MCS of primary particle + shower analysis

5. Shower analysis (MC data)
1 GeV e-
1 GeV p-
5 GeV e-
5 GeV p-
10 GeV p-
10 GeV e-

6. Description of the shower analysis
Goals :
electron/pion separation
electron energy reconstruction
Requests for a good shower description :
Consider as much as possible tracks belonging to the shower
Do not integrate over background tracks
In order to achieve these requirements :
we opened a 50 mrad cone around the primary
for each track, we required a maximum relative angle of 400 mrad with respect to the primary direction
the tracking thresholds was set at ~10 MeV (due to the tracking efficiency)

7. NN structure Input variables Training NN NN Output
INPUT LAYER : 672 NEURONS
Emulsion films crossed by primary particle before showering (1 var.) Number of film where the cone starts (1 var.) Number of charged particle detected per film inside the cone (112 var.) x-coordinates sigma for charged particles in the cone (112 var.) y-coordinates sigma for charged particles in the cone (112 var.) x-angular sigma for charged particles in the cone (112 var.) y-angular sigma for charged particles in the cone (112 var.) Dqx by Multiple Coulomb Scattering of the primary (55 var.) Dqy by Multiple Coulomb Scattering of the primary (55 var.)
Input variables
NN Output NN
Training
HIDDEN LAYER : 100 sigmoid neurons
OUTPUT LAYER : 1 logistic neuron giving a number between 0 and 1
67300 (672x x1) weights

8. A special feature : missing data
Real emulsion data come with inefficiencies (missing tracks in one or more sheets) Each missing track corresponds to some missing network inputs In order to have a tool able to analyze real data, the situation of missing data must be correctly handled
The decreasing of the primary particle energy leads to a higher number of missing input data
Example: percentage of events with a minimum number of films crossed by particles of the shower
E (GeV)
nfilm28
nfilm72
nfilm108 1
67% 2% 0% 3
90%
88% 3% 5
95%
94%
18% 7
96%
29% 9
97%
35%

9. Electron ID: training the network
Training events: 2000 e - with a continuous energy spectrum [0-10] GeV
Weight updating every 10 events
90 epochs

10. Electron ID: test with variable energies
First test : MC data having a continuous spectrum [0-10] GeV
Electrons (5000 ev.)
Pions (2500 ev.)
Testing events: e -
Separation value x]0;1[: if network output < x  electron if network output > x  pion
x = 0.9
A suitable value could be x = 0.9

11. Electron ID: test on fixed energies
We tested the NN also with e-/- particles with fixed energies
3 GeV e-
3 GeV -
NN output
NN output
5 GeV e-
5 GeV -
NN output
NN output

12. e-/p- separation efficiency
ID(e-): fractions of electrons correctly identified ID(-): fractions of pions correctly identified f = ID(e-)ID(-)
E (GeV) f
ID(e-)
ID(-) 1
77.9%
81.3%
95.8% 3
98.3%
99.9% 5
99.3%
100% 7
99%
99.2%
99.8% 9
98%
99.7%
0-10
82%
83.3%
98.5%

13. Energy reconstruction: variable e- energies
GeV electrons Total entries : 5000
Mean Value : RMS : 1.667
Fit Mean: Sigma : 0.885
Ereal-Erec (GeV)
0-2 GeV electrons Total entries : 1000
Mean Value : RMS : 2.084
Fit Mean: Sigma : 0.625
Ereal-Erec (GeV)
GeV electrons
Total entries : 1000
Mean Value: RMS: 1.366
Fit Mean : Sigma: 0.664
Ereal-Erec (GeV)

14. Energy reconstruction: fixed e- energies
1 GeV electrons
Total entries : 5000
Mean Value : RMS : 1.957
Mean Fit : Sigma : 0.795
5 GeV electrons
Total entries : 5000
Mean Value : RMS : 1.502
Mean Fit : Sigma : 1.164
Erec(GeV)
Erec(GeV)
7 GeV electrons
Total entries : 5000
Mean Value : RMS : 1.562
Mean Fit : Sigma : 0.980
9 GeV electrons
Total entries : 5000
Mean Value : RMS : 1.523
Mean Fit : Sigma : 0.512
Erec(GeV)
Erec(GeV)

15. Energy reconstruction resolution
As already said, this NN can work with missing input data, so it was trained and tested with ALL THE
EVENTS, independently from the number of crossed layers or particle produced.
The reconstruction precision could be improved selecting data with a minimum number of emulsion
films crossed by charged particles in the selected cone (this is the usual procedure used in standard NN)
3 GeV electrons (all events)
Total entries : 5000
Mean Value : RMS : 1.444
Mean Fit : Sigma : 0.914
DE/E ≈ 31%
3 GeV electrons, ≥ 28 films Total entries : 4532 Mean Value : RMS : Mean Fit: Sigma : 0.631
Erec(GeV)
DE/E ≈ 23%
Erec(GeV)

16. Conclusions A general neural network software has been developed
Special feature: deals with missing input data
It can be used in various modes and environments (Windows/Linux, Interactive/Server)
Results:
(1) e-/p- separation with f > 98% for 3<E<10 GeV
(2) Electron momentum reconstruction can be done without selecting the data (like in the real case!)

17. Electron ID : 7,9 GeV
7GeV p-
7GeV e-
9GeV e-
9GeV -

18. Energy reconstruction: 3 GeV, 72films
3 GeV electrons, ≥ 72 films Total entries: 4386 Mean Value: RMS: 0.652
Mean Fit : Sigma : 0.620
DE/E ≈ 22%
Erec(GeV)

19. Class hierarchy NeuronDescriptor Constructor TransferFunction
DerivativeOfTransferFunction
BiasNeuronDescriptor
ExpNeuronDescriptor
GaussianNeuronDescriptor
HardLimNeuronDescriptor
LinearNeuronDescriptor
LogisticNeuronDescriptor
SigmoidNeuronDescriptor
TrainingHistoryEntry
TrainingSet
MLPerceptron
Constructor
Evaluate
Train
Weights
MLPerceptronWithBackPropagation
MLPerceptronWithLangevinTraining
MLPerceptronWithManhattanTraining
MLPerceptronWithStabilizedBPTraining

20. Standard back propagation
learning parameter
teaching value
neuron output
 is a global parameter:
if is small the training can be too slow in flat regions and it can be trapped il local minimum
if is too big the training could never converge because it always exceed a minimum