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CMS Calorimetry & Neural Network

CMS Calorimetry & Neural Network. Abstract We 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. HO. HB2. HB1. ECAL.

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CMS Calorimetry & Neural Network

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  1. CMS Calorimetry & Neural Network Abstract We 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.

  2. HO HB2 HB1 ECAL CMS calorimeter

  3. 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

  4. 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?>

  5. 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.

  6. Key achievements in paper (I) SM : E = wiEi, H1 :

  7. Key achievements in paper (II)

  8. 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 ).

  9. w11 x1 w12 x2 w13 x3 What does the diagram mean? w21

  10. Multilayer Feed Forward Network Layer 2 Layer 3 Layer 1 No activation function OUTPUT INPUT The number of layers and the number of hidden neurons are user parameters.

  11. 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.

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