PX1Xn

px1xn is a term used to describe a three-dimensional array or tensor with dimensions p by 1 by n. In this shape, the first dimension p often indexes samples or blocks, the middle dimension of length 1 is a singleton axis, and the final dimension n indexes features or positions. As a result, px1xn can be viewed as p copies of a 1 by n row vector arranged along the middle axis.

In practice, a px1xn tensor is frequently equivalent to a p by n matrix once the singleton middle dimension is removed, by applying a squeeze operation. The singleton axis can also be leveraged for broadcasting in computations, depending on the software library, to align with other shapes during elementwise operations. This shape is commonly encountered in fields such as machine learning and signal processing, where data are managed in batches and may include optional channel or spatial axes.

Common operations on px1xn include reshaping to p by n, permuting axes to move the singleton dimension, or expanding to p by 1 by n (or other extended shapes) to fit into higher-dimensional architectures like neural networks. For example, in a neural network input pipeline, a batch of p samples each with a 1 by n feature vector may be stored as shape (p, 1, n). Depending on the context, developers may squeeze or expand dimensions to obtain the most convenient representation for subsequent processing.

Notes: px1xn describes a shape rather than a fixed mathematical object, and its interpretation can vary with context and software library.