DimW1

DimW1 is a notation used in discussions of neural network weight tensors to denote the first dimension of a weight array W. In many architectures, weights are organized as multi-dimensional tensors; dimW1 provides a concise label for either the size of the first axis or the sub-tensor spanning that axis. For a tensor W with shape (d1, d2, ..., dn), dimW1 commonly refers to the dimension size d1, and in other contexts to the slice W[i0, :, ..., :] across the first axis.

In practice, dimW1 is used when describing parameter counts, memory usage, and dimension-specific operations, such as pruning along the first dimension, or when applying decompositions that separate contributions along that axis. In tensor factorization methods, dimW1 guides how the tensor is factorized into components a1 ⊗ b1 ⊗ ..., and how remaining dimensions interact.

DimW1 can appear in literature on structured sparsity, fast weight sharing, or tensorized neural networks, where attention to axis-specific dimensions helps optimize performance and resource use. It is often paired with related terms such as dimW2, dimW3 for other axes, and with general concepts like weight tensor, tensor shape, and parameter efficiency.

See also: weight tensor, tensor shape, structured pruning, tensor factorization, neural network parameters.