Symbol d
d is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
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Split each query or key vector of dimension d into d/2 two-dimensional pairs. Pair i is assigned a fixed rotation frequency
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Published contexts (2)
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Equation 2 · Open Models
How Llama's Architecture Actually Works, Generation by Generation
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
Split each query or key vector of dimension d into d/2 two-dimensional pairs. Pair i is assigned a fixed rotation frequency
Equation guide → · Article →Equation 12 · Open Models
How Llama's Architecture Actually Works, Generation by Generation
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
The one free parameter is base , the constant that sets how quickly the rotation angles grow across the d/2 frequency bands. A small base makes low-index pairs rotate almost a full turn per token, encoding fine-grained short-range position; a large base slows that rotation down, which is what lets high-index pairs still carry usable positional signal at sequence positions far beyond what the model saw in training. Llama 1 and Llama 2 shipped with the RoPE default of base = 10,000, matching the value in Su and colleagues’ original formulation. Llama 3 raised it to 500,000 specifically as part of extending context to 128,000 tokens [ 5 , 2 ] . Nothing about the rotation mechanism changed…
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