Simplicial Embeddings in Self-Supervised Learning and Downstream ClassificationDownload PDF

Published: 01 Feb 2023, Last Modified: 02 Mar 2023ICLR 2023 notable top 25%Readers: Everyone
Keywords: Self-Supervised learning, Representation learning, Pre-training
TL;DR: We use softmax to embed representations in a collection of simplices in SSL models, which offers improved generalization properties for downstream classification.
Abstract: Simplicial Embeddings (SEM) are representations learned through self-supervised learning (SSL), wherein a representation is projected into $L$ simplices of $V$ dimensions each using a \texttt{softmax} operation. This procedure conditions the representation onto a constrained space during pretraining and imparts an inductive bias for group sparsity. For downstream classification, we formally prove that the SEM representation leads to better generalization than an unnormalized representation. Furthermore, we empirically demonstrate that SSL methods trained with SEMs have improved generalization on natural image datasets such as CIFAR-100 and ImageNet. Finally, when used in a downstream classification task, we show that SEM features exhibit emergent semantic coherence where small groups of learned features are distinctly predictive of semantically-relevant classes.
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