Where You Place the Norm Matters: From Prejudiced to Neutral Initializations

Abstract: Normalization layers, such as Batch Normalization and Layer Normalization, are central components in modern neural networks, widely adopted to improve training stability and generalization. While their practical effectiveness is well documented, a detailed theoretical understanding of how normalization affects model behavior, starting from initialization, remains an important open question. In this work, we investigate how both the presence and placement of normalization within hidden layers influence the statistical properties of network predictions before training begins. In particular, we study how these choices shape the distribution of class predictions at initialization, which can range from unbiased (Neutral) to highly concentrated (Prejudiced) toward a subset of classes. Our analysis shows that normalization placement induces systematic differences in the initial prediction behavior of neural networks, which in turn shape the dynamics of learning. By linking architectural choices to prediction statistics at initialization, our work provides a principled understanding of how normalization can influence early training behavior and offers guidance for more controlled and interpretable network design.