LEARNING NEW PHYSICS FROM A MACHINE Raffaele Tito DAgnolo - SLAC - PowerPoint PPT Presentation

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LEARNING NEW PHYSICS FROM A MACHINE Raffaele Tito DAgnolo - SLAC GGI 2018 RTD and Andrea Wulzer arXiv:1806.02350 THE PROBLEM REFERENCE MODEL -

LEARNING NEW PHYSICS FROM A MACHINE Raffaele Tito D’Agnolo - SLAC GGI 2018 RTD and Andrea Wulzer arXiv:1806.02350
THE PROBLEM �� REFERENCE MODEL �� - � �� χ 2 = 47 N bins = 50 p − value < 1 σ
THE PROBLEM �� 4 . 7 σ � �� - � �� " # e − N (NP) n ( x | NP) Y t id ( D ) = 2 log e − N (R) n ( x | R) x ∈ D
WHAT IS A NEURAL NETWORK?
WHAT IS A NEURAL NETWORK? SET OF FUNCTIONS + FITTING ALGORITHM
WHAT IS A NEURAL NETWORK? SET OF FUNCTIONS + ⇣ ⇣ ⌘⌘ f (1) f (2) f (3) w 3 ( ... ) w 1 w 2 FITTING ALGORITHM
https://towardsdatascience.com/
https://towardsdatascience.com/
BUILDING BLOCKS NEURON ~ � ( ~ x + b ) w · ~ x z = ~ w · ~ x + b 1. LINEAR TRANSFORMATION FREE PARAMETERS σ ( z ) 2. NON-LINEAR TRANSFORMATION FIXED
BUILDING BLOCKS NEURON ~ � ( ~ x + b ) w · ~ x 2. NON-LINEAR TRANSFORMATION  tanh( z )   ReLU  σ ( z ) = 1 1+ e − z    ...
THE NETWORK FEEDFORWARD, FULLY CONNECTED ... ~ j i k ... x ... 3 3 d ! ! ! X X X w jk σ k w ki σ i w il x l + b i + b k + b j σ i =1 k =1 l =1
UNIVERSAL APPROXIMANTS INCREASING w σ ( wx + b ) w w w 1 σ 1 + w 2 σ 2 + b 0 w 1 = − w 2 HEIGHT WIDTH b w 1 , w 2

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