Training deep neural networks in biological systems is faced with major challenges such as scarce labeled data and obstacles for propagating error signals in the absence of symmetric connections. We introduce Tourbillon, a new architecture that uses circular autoencoders trained with various recirculation algorithms in a self-supervised mode, with an optional top layer for classification or regression. Tourbillon is designed to address biological learning constraints rather than enhance existing engineering applications. Preliminary experiments on small benchmark datasets show that Tourbillon performs comparably to models trained with backpropagation and may outperform other biologically plausible approaches. The code and models are available at https://anonymous.4open.science/r/Circular-Learning-4E1F.