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Multi-Layer Perceptrons

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MLPfit: a tool to design and use Multi-Layer Perceptrons J. Schwindling, B. Mansoulié CEA / Saclay FRANCE Neural Networks, Multi-Layer Perceptrons: What are they ? Applications Approximation theory Unconstrained Minimization About training ... MLPfit Numerical Linear Algebra Statistics
(Artificial) Neural Networks ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Neural Networks in HEP ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The most wi(l)dely used: the Multi-Layer Perceptron ,[object Object],[object Object],[object Object],[object Object],Input layer Hidden layer(s) Output layer « sigmoid »  w ij neuron i neuron j x 1 x n w jk y k = w 0k +  w jk u j u j = A(w 0j +  w ij x i ) neuron k
2 theorems ,[object Object],[object Object],[object Object],[object Object],[object Object]
About learning ... ,[object Object],[object Object],[object Object],(usually  p = 1)
Remark: derivative of sigmoid function ,[object Object],[object Object],[object Object],[object Object],(exemple on a toy problem) y = 1 / (1+e -x )
Learning methods Stochastic minimization Linear model fixed steps [variable steps] Remarks: - derivatives known - other methods exist Global minimization Non-Linear weights All weights Linear model steepest descent with fixed steps or line search Quadratic model (Newton like) Conjugate gradients or BFGS with line search Solve LLS
The traditional learning method: stochastic minimization ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Stochastic minimization (continued) ,[object Object],[object Object],[object Object],[object Object]
Other methods ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The Hybrid method ,[object Object],[object Object],[object Object],[object Object]
Comparison on a toy problem fit the function x 2 sin(5xy) by a 2-10-1 MLP learning curves: (all curves = 2 minutes CPU)
Comparison on a real problem ,[object Object],[object Object],[object Object],but small
The MLPfit package ,[object Object],[object Object],Based on the mathematical background:
Software process ,[object Object],[object Object],[object Object],[object Object],[object Object],Use the POP (1) methodology to write a code: (1) POP = Performance Oriented Programming
Performances ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Using MLPfit as a standalone package ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],MLP_gen.c MLP_main.c PAWLIB MLP_lapack.c
What is MLP_lapack.c ? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],MLP_lapack.c (~ 9000 lines)
Calling MLPfit from your own code ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],MLP_gen.c MLP_inter.c YourCode MLP_lapack.c
Calling MLPfit from LabVIEW LabVIEW MLPfit vi ’s for interface + ,[object Object],[object Object],[object Object],- automatic process control - image analysis (tested on PC / Windows 95 + LabVIEW 4.1)
Using MLPfit in PAW ,[object Object],[object Object],[object Object],[object Object],PAW ASCII files Ntuples MLPfit (an interface to ROOT is also under study) (tested on HP-UX)
MLPfit in PAW: modified vec/fit command ,[object Object],[object Object],[object Object],Number of hidden neurons Number of epochs
MLPfit in PAW: interface to Ntuples ,[object Object],[object Object],[object Object],[object Object]
Documentation ... ,[object Object],[object Object]
Conclusions ,[object Object],[object Object],[object Object],[object Object]
We are willing to ... ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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Multi-Layer Perceptrons

  • 1. MLPfit: a tool to design and use Multi-Layer Perceptrons J. Schwindling, B. Mansoulié CEA / Saclay FRANCE Neural Networks, Multi-Layer Perceptrons: What are they ? Applications Approximation theory Unconstrained Minimization About training ... MLPfit Numerical Linear Algebra Statistics
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  • 8. Learning methods Stochastic minimization Linear model fixed steps [variable steps] Remarks: - derivatives known - other methods exist Global minimization Non-Linear weights All weights Linear model steepest descent with fixed steps or line search Quadratic model (Newton like) Conjugate gradients or BFGS with line search Solve LLS
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  • 13. Comparison on a toy problem fit the function x 2 sin(5xy) by a 2-10-1 MLP learning curves: (all curves = 2 minutes CPU)
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