Simplicial Embeddings in Self-Supervised Learning and Downstream Classification
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We introduce Simplicial Embeddings (SEMs) as a way to constrain the encoded representations of a self-supervised model to L simplices of V dimensions each using a Softmax operation. This procedure imposes a structure on the representations that reduce their expressivity for training downstream classifiers, which helps them generalize better. Specifically, we show that the temperature τ of the Softmax operation controls for the SEM representation's expressivity, allowing us to derive a tighter downstream classifier generalization bound than that for classifiers using unnormalized representations. We empirically demonstrate that SEMs considerably improve generalization on natural image datasets such as CIFAR-100 and ImageNet. Finally, we also present evidence of the emergence of semantically relevant features in SEMs, a pattern that is absent from baseline self-supervised models.
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