Title: Dominant Datapoints and the Block Structure Phenomenon in Neural Network Hidden Representations. Abstract: Recent work has uncovered a striking phenomenon in large-capacity neural networks: they contain blocks of contiguous hidden layers with highly similar representations. This block structure has two seemingly contradictory properties: on the one hand, its constituent layers have highly similar dominant first principal components (PCs), but on the other hand, their representations, and their common first PC, are highly dissimilar across different random seeds. Our work seeks to reconcile these discrepant properties by investigating the origin of the block structure in relation to the data and training methods. By analyzing properties of the dominant PCs, we find that the block structure arises from dominant datapoints — a small group of examples that share similar image statistics (e.g. background color). However, the set of dominant datapoints, and the precise shared image statistic, can vary across random seeds. Thus, the block structure reflects meaningful dataset statistics, but is simultaneously unique to each model. Through studying hidden layer activations and creating synthetic datapoints, we demonstrate that these simple image statistics dominate the representational geometry of the layers inside the block structure. We also explore how the phenomenon evolves through training, finding that the block structure takes shape early in training, but the underlying representations and the corresponding dominant datapoints continue to change substantially. Finally, we study the interplay between the block structure and different training mechanisms, introducing a targeted intervention to eliminate the block structure, as well as examining the effects of pretraining and Shake-Shake regularization.     