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Horoi, S.* ; Huang, J.* ; Rieck, B. ; Lajoie, G.* ; Wolf, G.* ; Krishnaswamy, S.*

Exploring the geometry and topology of neural network loss landscapes.

In: (20th International Symposium on Intelligent Data Analysis, IDA 2022, 20-22 April 2022, Rennes). Berlin [u.a.]: Springer, 2022. 171-184 (Lect. Notes Comput. Sc. ; 13205 LNCS)
DOI
Open Access Green: Postprint online verfügbar 08/2023
Recent work has established clear links between the generalization performance of trained neural networks and the geometry of their loss landscape near the local minima to which they converge. This suggests that qualitative and quantitative examination of the loss landscape geometry could yield insights about neural network generalization performance during training. To this end, researchers have proposed visualizing the loss landscape through the use of simple dimensionality reduction techniques. However, such visualization methods have been limited by their linear nature and only capture features in one or two dimensions, thus restricting sampling of the loss landscape to lines or planes. Here, we expand and improve upon these in three ways. First, we present a novel “jump and retrain” procedure for sampling relevant portions of the loss landscape. We show that the resulting sampled data holds more meaningful information about the network’s ability to generalize. Next, we show that non-linear dimensionality reduction of the jump and retrain trajectories via PHATE, a trajectory and manifold-preserving method, allows us to visualize differences between networks that are generalizing well vs poorly. Finally, we combine PHATE trajectories with a computational homology characterization to quantify trajectory differences.
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Publikationstyp Artikel: Konferenzbeitrag
Schlagwörter Artificial Neural Network Loss Landscape ; Non-linear Dimensionality Reduction ; Topological Data Analysis
ISSN (print) / ISBN 0302-9743
e-ISSN 1611-3349
Konferenztitel 20th International Symposium on Intelligent Data Analysis, IDA 2022
Konferzenzdatum 20-22 April 2022
Konferenzort Rennes
Quellenangaben Band: 13205 LNCS, Heft: , Seiten: 171-184 Artikelnummer: , Supplement: ,
Verlag Springer
Verlagsort Berlin [u.a.]