Minimalistic Unsupervised Learning with the Sparse Manifold Transform

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 [21], 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 grayscale 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. Unsupervised representation learning (aka self-supervised representation learning) aims to build models that automatically find patterns in data and reveal these patterns explicitly with a representation. There has been tremendous progress over the past few years in the unsupervised representation learning community, and this trend promises unparalleled scalability for future data-driven machine learning. However, questions remain about what exactly a representation is and how it is formed in an unsupervised fashion. Furthermore, it is unclear whether there exists a set of common principles underlying all these unsupervised representations. The hope is that such understanding will lead to a theory that enables us to build simple, fully explainable "white-box" models [14; 13; 71] from data based on first principles. Such a computational theory could guide us in achieving two intertwined fundamental goals: modeling natural signal statistics, and modeling biological sensory systems [83; 31; 32; 65]. Here, we take a small step toward this goal by building a minimalistic white-box unsupervised learning model without deep networks, projection heads, augmentation, or other similar engineering designs. By leveraging the classical unsupervised learning principles of sparsity [81; 82] and low-rank spectral embedding [89; 105], we build a two-layer model that achieves non-trivial benchmark results on several standard datasets. With simple grayscale augmentation, it achieves 83.2% KNN top-1 accuracy on CIFAR-10 and 57% KNN top-1 accuracy on CIFAR-100.