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CMS Calorimetry & Neural Network

AbstractWe review an application of neural network feed

forward algorithm in CMS calorimetry ( NIM A482(2002)p776 ). We describe the neural network

feed forward algorithm and its implementation appearing in the reference.

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CMS calorimeter

ECAL

HB1

HB2

HO

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Detector spec

• ECAL : lead tungstate crystal (PbWO4), 26 radiation length

• HB1 + HB2 : copper alloy and stainless steel, 89 cm thick, 5.82 nuclear interaction length

Lateral profile :Energy in a (,) cone with R = 0.85 considered. To reduce large number of tiles, concentric sums are used as shown in left.

30 input variables to NN: Erec, wiEi/Erec (i=1,…,4), 13 inputs from ECAL, 3 x 4 inputs from HB1,HB2,HO

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Key issues of energy resolution• Without fluctuations,

Ei : energy in a detector granule, gi : correction for acceptance and efficiency

• With fluctuations,

Eim : measured energy in a detector granule,

i : relative fluctuation of Eim, event-by-event

<How do we minimize E?>

iiEgE

i

mii

m

miii

mi

miii

imii

EgEEE

EEEEE

EgE

)(/)(

),1(

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What did CMS(local people?) do?

• Two Neural Net– 1st step Neural Net :

• Particle identification– ( e, ), hadron, jet, using 4 inputs EECAL, EHB1, EHB2, EHO

– 2nd step Neural Net :• For the identified particles, estimated event-by-

event fluctuation using all 30 inputs, and optimzed the resolution Robustness and details in investigation by Y. Kwon. Further detail in a week or two.

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Key achievements in paper (I)

SM : E = wiEi, H1 :

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Key achievements in paper (II)

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Neural Network (I)

How do we imitate human recognition?

• Human recognition is complicated network of simple neurons.

• Typical recognition process is as follows. – 1. Multiple dendrites take

input, – 2. Cell body performs linear

sum and discrimination, – 3. output through axon

becomes another dendrite ( i.e. input to new neuron ).

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What does the diagram mean?

x1

x2

x3

w11

w12

w13

w21

)(1

1bXe jijxwX

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Multilayer Feed Forward Network

Layer 1 Layer 2 Layer 3

INPUT OUTPUT

The number of layers and the number of hidden neurons are user parameters.

No activation function

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Summary

• We reviewed a specific application of neural net by a CMS group.

• The example shows – Neural net does good pattern recognition.– Neural net successfully handles event-by-

event energy fluctuations in detector granule, major source of energy resolution.

– Neural net corrects for non-linearity and reconstructs Gaussian energy distribution around ideal energy.