Minimalistic Unsupervised Representation Learning with the Sparse Manifold Transform

Yubei Chen, Zeyu Yun, Yi Ma, Bruno Olshausen, Yann LeCun

Keywords: Unsupervised Learning, Sparsity, Low-rank, Manifold learning, Spectral Embedding

TL;DR: We build a "white-box" unsupervised learning model with two parsimonious principles: sparsity and low-rankness, the model can be viewed as the simplest form of VICReg.

Abstract: We describe a minimalistic and interpretable method for unsupervised representation learning that does not require data augmentation, hyperparameter tuning, or other engineering designs, but nonetheless achieves performance close to the state-of-the-art (SOTA) SSL methods. Our approach leverages the sparse manifold transform, which unifies sparse coding, manifold learning, and slow feature analysis. With a one-layer deterministic (one training epoch) sparse manifold transform, it is possible to achieve $99.3\%$ KNN top-1 accuracy on MNIST, $81.1\%$ KNN top-1 accuracy on CIFAR-10, and $53.2\%$ on CIFAR-100. With simple gray-scale augmentation, the model achieves $83.2\%$ KNN top-1 accuracy on CIFAR-10 and $57\%$ on CIFAR-100. These results significantly close the gap between simplistic ``white-box'' methods and SOTA methods. We also provide visualization to illustrate how an unsupervised representation transform is formed. The proposed method is closely connected to latent-embedding self-supervised methods and can be treated as the simplest form of VICReg. Though a small performance gap remains between our simple constructive model and SOTA methods, the evidence points to this as a promising direction for achieving a principled and white-box approach to unsupervised representation learning, which has potential to significantly improve learning efficiency.

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