5 problems

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Progressive Feedforward Collapse conjecture for ResNet training
Progressive Feedforward Collapse conjecture. At the terminal phase of ResNet training, neural collapse emerges in the last-layer features. Before the effective depth, there exists…
Conjectureopendeep-learning-theory neural-collapse resnetarXiv posted 2 days ago
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Weight-feature equality conjecture at full-rank stationary points
Weight-feature equality conjecture. Then
Conjectureopenneural-collapse optimization representation-learningarXiv posted 2 days ago
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Self-duality conjecture for neural-collapse solutions
Self-duality conjecture. The class feature aggregate is proportional to its corresponding classifier weight: for each $k=1,\ldots,K$ , $\boldsymbol{h}_k^*=\alpha\boldsymbol{w}_k^*$ …
Conjectureopenclassification neural-collapse representation-learningarXiv posted 2 days ago
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Within-class collapsing conjecture for neural features
Within-class collapsing. All features within each class are identical: for each $k=1,\ldots,K$ , $\boldsymbol{h}_{k,i}^*\equiv\boldsymbol{h}_k^*$ for every $i$ .
Conjectureopenclassification neural-collapse representation-learningarXiv posted 2 days ago
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Neural-collapse characterization for the graph unconstrained feature model
Consider the graph unconstrained feature model (gUFM) in the objective defined by equation ( … (s{c1,1},ldots,s{cC,1})=cdots=(s{c1,n},ldots,s{cC,n}),qquad forall cin[C]. … ), if an…
Conjectureopengraph-neural-networks neural-collapse optimizationarXiv posted 2 days ago

5 problems

Progressive Feedforward Collapse conjecture for ResNet training

Weight-feature equality conjecture at full-rank stationary points

Self-duality conjecture for neural-collapse solutions

Within-class collapsing conjecture for neural features

Neural-collapse characterization for the graph unconstrained feature model