apply_rope: xk out

Read the equation

In apply_rope, this statement defines or updates xk_out. The displayed multiplication combines the source factors. For tensors this is elementwise unless the called operation explicitly performs a matrix contraction.

Terms & definitions

The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.

How it works

1. Read xk_out as the quantity being defined or updated by this relation.

2. Substitute the source-defined variables or recorded values and follow the displayed arithmetic and indexing exactly.

3. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

Assumptions & limits

Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.

Original context

xk_ = torch.view_as_complex(xk.float().view(*xq.shape[:-1], -1, 2))
    xq_out = torch.view_as_real(xq_ * freqs_cis).flatten(
        -2)  # ..., num_heads, head_dim
    xk_out = torch.view_as_real(xk_ * freqs_cis).flatten(
        -2)  # ..., num_heads, head_dim
    return xq_out.type_as(xq), xk_out.type_as(xk)

xk_out = torch.view_as_real(xk_ * freqs_cis).flatten(
        -2)

Related builds