# Simplicial Embeddings in Self-Supervised Learning and Downstream Classification Source: [Simplicial Embeddings in Self-Supervised Learning and Downstream Classification]() Collection index: [llms.txt]() Data updated: 2025-10-26T00:38:22.399Z Authors: Samuel Lavoie, Christos Tsirigotis, Max Schwarzer, Ankit Vani, Michael Noukhovitch, Kenji Kawaguchi, Aaron Courville Published: 2022-04-01T17:59:40.000Z ## 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 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()