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Related Experiment Video

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A New Straightforward Method for Lipophilicity logP Measurement using 19F NMR Spectroscopy

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Published on: January 30, 2019

Log-Sum-Exp Neural Networks and Posynomial Models for Convex and Log-Log-Convex Data.

Giuseppe C Calafiore, Stephane Gaubert, Corrado Possieri

IEEE Transactions on Neural Networks and Learning Systems

|May 17, 2019

Summary

This study introduces log-sum-exp (LSE_T) neural networks as universal approximators for convex functions. These networks enable efficient convex optimization and design, with applications in physical processes.

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Deep Neural Networks for Image-Based Dietary Assessment

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Area of Science:

Machine Learning
Optimization
Convex Analysis

Background:

Neural networks are powerful function approximators.
Convex functions and their optimization are crucial in many scientific and engineering fields.
Existing methods may lack efficiency or applicability to specific function classes.

Purpose of the Study:

To introduce a novel neural network architecture for approximating convex functions.
To establish the universal approximation capabilities of log-sum-exp (LSE_T) networks.
To demonstrate the applicability of LSE_T and generalized posynomial (GPOS_T) models in optimization-based design.

Main Methods:

Utilizing feedforward neural networks with specific activation functions (exponential and logarithmic).
Establishing theoretical links between LSE_T functions and generalized posynomials (GPOS_T) via exponential transformations.
Applying convex optimization and geometric programming (GP) for model design and optimization.

Main Results:

Demonstrated that LSE_T networks are universal approximators of convex functions.
Showed that GPOS_T functions are universal approximators of log-log-convex functions.
Developed a methodology for efficient model construction and optimization from data using convex optimization and GP.

Conclusions:

LSE_T networks provide a convex model amenable to efficient convex optimization.
GPOS_T models derived from LSE_T networks are efficiently optimizable using geometric programming.
The proposed methodology is effective for optimization-based design in physical systems.