1x11x2

The term "1x11x2" is a shorthand notation commonly used in mathematics, particularly in the context of linear algebra and tensor operations. It refers to the dimensions of a tensor or matrix multiplication involving three matrices or tensors with specific shapes. The notation indicates a multiplication sequence where the first matrix has dimensions 1 by 11, the second has dimensions 11 by 1, and the third has dimensions 1 by 2. The result of this operation is a tensor with dimensions 1 by 2.

This notation is often encountered in deep learning and neural network architectures, particularly when describing fully connected (dense) layers or operations involving reshaping tensors. For example, in a neural network, a layer might transform an input tensor of shape (batch_size, 11) into an output tensor of shape (batch_size, 2) through a sequence of weight matrices that align with the 1x11x2 structure.

The operation can be broken down as follows:

1. Multiply the input tensor (shape: batch_size × 11) by a weight matrix of shape 11 × 1, resulting in an intermediate tensor of shape batch_size × 1.

2. Multiply the intermediate tensor by another weight matrix of shape 1 × 2, yielding the final output tensor of shape batch_size × 2.

This type of operation is useful for dimensionality reduction or transformation in neural networks, where the goal is to map high-dimensional inputs to lower-dimensional outputs. The 1x11x2 notation helps clarify the structure of these transformations without explicitly writing out the matrix multiplications. It is also sometimes used in contexts like matrix factorization or dimensionality reduction techniques such as Principal Component Analysis (PCA).