On the capacity and superposition of minima in neural network loss function landscapes


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Abstract

jats:titleAbstract</jats:title> jats:pMinima of the loss function landscape (LFL) of a neural network are locally optimal sets of weights that extract and process information from the input data to make outcome predictions. In underparameterised networks, the capacity of the weights may be insufficient to fit all the relevant information. We demonstrate that different local minima specialise in certain aspects of the learning problem, and process the input information differently. This effect can be exploited using a meta-network in which the predictive power from multiple minima of the LFL is combined to produce a better classifier. With this approach, we can increase the area under the receiver operating characteristic curve by around jats:inline-formula jats:tex-math</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> mml:mn20</mml:mn> <mml:mi mathvariant="normal">%</mml:mi> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="mlstac64e6ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> for a complex learning problem. We propose a theoretical basis for combining minima and show how a meta-network can be trained to select the representative that is used for classification of a specific data item. Finally, we present an analysis of symmetry-equivalent solutions to machine learning problems, which provides a systematic means to improve the efficiency of this approach.</jats:p>

Publication Date
2022
Online Publication Date
2022-04-20
Acceptance Date
2022-04-06
Keywords
ensemble learning, interpretability, loss function landscape, theoretical chemistry
Journal Title
Machine Learning: Science and Technology
Journal ISSN
2632-2153
2632-2153
Volume Title
3
Publisher
IOP Publishing
Sponsorship
Agence Nationale de la Recherche (ANR-19-P3IA-0002)