1. 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. 2 CMS calorimeter ECAL HB1 HB2 HO

3. 3 Detector spec ECAL : lead tungstate crystal (PbWO 4 ), 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: E rec, w i E i /E rec (i=1,…,4), 13 inputs from ECAL, 3 x 4 inputs from HB1,HB2,HO

4. 4 Key issues of energy resolution Without fluctuations, E i : energy in a detector granule, g i : correction for acceptance and efficiency With fluctuations, E i m : measured energy in a detector granule,  i : relative fluctuation of E i m, event-by-event

5. 5 What did CMS(local people?) do? Two Neural Net –1 st step Neural Net : Particle identification –( e,  ), hadron, jet,  using 4 inputs E ECAL, E HB1, E HB2, E HO –2 nd 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. 6 Key achievements in paper (I) SM : E =  w i E i, H1 :

7. 7 Key achievements in paper (II)

8. 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. 9 What does the diagram mean? x1x1 x2x2 x3x3 w 11 w 12 w 13 w 21

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

11. 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.