This paper presents an investigation of the challenges of training Deep Neural Networks (DNNs) via self-supervised objectives, using local learning as a parallelizable alternative to traditional backpropagation. In our approach, DNN are segmented into distinct blocks, each updated independently via gradients provided by small local auxiliary Neural Networks (NNs). Despite the evident computational benefits, extensive splits often result in performance degradation. Through analysis of a synthetic example, we identify a layer-wise dimensional collapse as a major factor behind such performance losses. To counter this, we propose a novel and straightforward sampling strategy based on blockwise feature-similarity, explicitly designed to evade such dimensional collapse.